MAGNETIC STORMS AND SYSTEMS OF ELECTRIC CURRENTS

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• Collection: FOIA Collection
• Document Number (FOIA) /ESDN (CREST): 06028201
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• Document Page Count: 269
• Document Creation Date: December 28, 2022
• Document Release Date: September 25, 2017
• Case Number: F-2015-01649
• Publication Date: January 1, 1953

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AIR TECHNICAL INTELLIGENCE
TRANSLATION
MAGNETIC STORMS AND SYSTEMS OF BLECTRIC CURRENTS
(MAGNITN/YE BURI I SISTEMY ELEKTRICHESKIKH TOKOV)
BY
N. P. BENMOVA
/ FROM ZE
:TRUDY NAUCHNO-ISSLEDOVATELISKOGO 1NSTITUTA MNOGO MAGNETIZMA
NO. 10(20), 1953
LENINGRAD
159 Pp.
AIR TECHNICAL INTELLIGENCE CENTER
ATIC -262920
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WRIGHT:PATTERSON AIR FORCE BASE
OHIO
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066:I
10 .�
Ministry .of Agriculture .and State Deliveries USSR
Central Administration .of tha Hydrometeorological Service
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18_
.20_
TRANSACTIONS OF THE PF5EAlidi INSTITUTE FOR TERRESTRIAL MAGNETISM
Number 10(20)
N.P.Ben:tkova.
i MAGNETIC STORMS AND SYSTEMS OF ELECTRIC CURRENTS
Edited by
T.S.KerblAY
Candidate in Physical and Mathematical Sciences
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2.6
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1F,TS4974/V
GiMis
State Publishing House for Hydrology and Meteorology
Leningrad 1953
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Ministry of Agriculture and Stitt Deliveriei USSR''
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Central Administration of the Hydrcieteorological Service
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TRANSACTIONS OF THE RESEARCH IN
F-Ts-89 74/V
Number 10(20)
�
Gilds
GIDROMETEOIZDAT
(State Publishing House for Hydrology and Meteorology)
Leningrad .1953
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NOTE
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This work by N.P.Ben/kov ii devoted to a study of magnetic
storms and the electromagnetic processes responsible for thou's.
It contains a survey of the literature on this topic, a classi-
fication of storms, a descriptitin of the morphology of the phe-
nomenon, and a calculation of th:e extra-ionosphere, responsible
for the regular parts of the magnetic disturbances. It also
contains a description of individual storms and of related e-
lectric currents. One of the Chapters is devoted to the elec-
tric currents induced by the fitild of magnetic storms in the
conducting layers of the earth. This work is of interest for
specialists in geophysics, scientific workers, postgraduate
students, students taking advanced courses, and specialists in
the field of ionospheric physics.
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2--
12-- INTRODUCTION
14 __
Magnetic storms, i.e., rapid random oscillations of the intensity vector of the
16--
_geomagnetic field which from time to time disturb the normal march of the magnetic
18
_elements, constitute one of the most interesting geophysical phenomena. -They were
).
_first discovered at the very dawn of the development of geomagnetic research, when -
--the only magnetic instrument available was the magnetic needle, and have long attraci
I
- -
_ited the attention of both navigators and scientists. The Arkhangeltsk seafarers,
�
_.:sailing on voyages in the basins of the White Sea and the North Arctic Ocean, noted
J
_unexpected and random fluctuations of the needle, frequently coinciding itith auroral
'
1
�displays in the sky. "Our little mother deceives us when the North glows" * is a 1
1
well-known maritime proverb which runs back to the middle of the Eighteenth Century.1
At present, when not only magnetic, gyro tind astro-compasses but also complex radio-.
1
navigation and radio control systems are used for marine and aerial navigation, when'
shortwave radio is the principal means of communication in times of peace and war,
the study of magnetic storms has become of still greater practical interest, being a
necessary element of the theory and application of ionospheric propagation of radio
waves.
The theoretical significance of the study of magnetic storms is likewise very
great and not primarily, for geomagnetism itself, in which the problem of the irregu-
* The discovery of magnetic storms is usually attributed to Hiorter who, in 1741,
discovered the irregular fluctions of the magnetic needle. There is, however, reason
(Bib1.30) to assume that they were known to Russian sailors in Northern waters.
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1
-ircetto prodesses of the -earthris�atmbeipliere ;are-primarily-due- td- solar -radiations
I j
8-1 i
all forms, there is an intimate relation between the departments of geophysics and of
I
..... lar variations occupies a particularly important place, but also for other divisions!
1
of geophysics, such as the physics of the iupper layers of the atmosphere, the study- i
4 of the aurora polaris, the cosmic rays awl the earth currents. Since the electramag--1
1 . ;
J j
heliophysics. Magnetic storms, in particular, were the first geophysical phenomena
-for which a correlation with solar activity was discovered and which yielded abundant-
! 1
,material from the solution of a number oflproblems related to solar radiation and I
behavior of the active regions of the solar envelopes.
1
' The study of magnetic storms, the regularities in their course, and the e1ectro4
1
magnetic processes causing them, constpl4e the subject matter of the present work. !
Section 1. General Discussion of the Thedries of 14Agnetic Storms
Despite the great efforts made by geOphysicists of several generations in study-
ing the morphology and nature of magnetic storms, many essential questions still
remain controversial. This is explained, 'both by the complexity of the phenomenon
which requires the attentive study of a large amount of empirical material for the
clarification of any regularities at all, and its intimate connection with ionospher-
ic physics and heliophysics. A quantitative theory of magnetic storms is given its .
necessary empirical base only when we know reliably the composition of the upper
layers of the atmosphere, the velocity and laws of motion of air masses, the laws of
radiation by the undisturbed solar surface, and by the active formations of the sun.
The exceptionally rapid development of ionospheric aria solar physics, which awes
much to the work of Soviet scientists, allows us to expect that the combined efforts
of geophysicists and astronomers will lead in the near future to a solution of these
problems.
But even today, the basic stages of the theory of magnetic storms have already
been marked out. As far back as 200 years agop.the hypothesis was postulated that
magnetic storms are caused by minute particles of matter flying from the suit. The
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data subsequently accumulated on the geographical distribution of magnetic activity,
on its fluctuations with time, and on its correlation with solar activity, confirm
this view, and the works of a number of geophysicists (Arrhenius, Angenheister, and
mainly Stoermer, Birkeland, Chapman, and Alfven) laid the scientific foundation for
the corpuscular theories of magnetic storms. The existence of a corpuscular radiation
from the sun, proposed to explain magnetic storms and the aurora polaris and succes-
sfully used to solve a number of other problems, still remained a hypothesis until
recent years. It was only in 1950-51 that measurements of the Doppler shift of the
hydrogen lines in the spectra of the aurora confirmed the penetration of a stream of
particles into the upper layers of the earth's atmosphere.
The modern corpuscular theories of storms are based on a chain of independent
�
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problems, beginning with the .emission of the sun's geoeffective corpuscular radiation
the dynamics and electrodynamics of the corpuscular stream en route between the sun
and the earth, and ending with the electromagnetic processes taking place on the
earth's surface as a result of the interaction of the corpuscular stream with the
permanent magnetic field of the earth and the earth's atmosphere. The construction
of the system of electric currents, which constitutes the immediate cause of the
fluctuation of the magnetic field during the time of a storm, occupies a position of
considerable importance among the links of this chain. The mechanism of excitation
of these currents is in many respects still obscure, and the very existence of the
currents has not yet been confirmed by direct observations, as has been done for the
currents responsible for the regular diurnal variations of the magnetic field *. In
its present phase, however, geophysics offers no other hypothesis of equal value to
* Measurements of the magnetic field at great altitudes, by means of remote-reading
magnetometers installed in rockets, have shown the existence of a discontinuity in
the variation of the field at the height of the E layer of the ionosphere. This dis-
continuity confirmed the existence of electric currents at the level of 90-105 km,
which might, judging by their intensity and diurnal variation, explain the quiet
diurnal variations (So -variations) of the magnetic field. The hypothesis of currents
flawing in the uper lgyers of the atmosphere was postulated by B.Stewart long before
the experimental detection of the conducting properties of the ionosphere by radio
methods.
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explain the field of geomagnetic variations, without assuming electric currents ex-
ternal to the earth's surface. According to the Chapman-Ferraro and Alfven corpuscu-
lar theories of magnetic storms, which are widely recognized today, the excitation
of these currents in the upper layers of the earth's atmosphere, and beyond it, as
a result of the action of a stream of solar corpuscles is a physical reality. Other
authors consider the field of magnetic disturbance to be the direct field of flying,
charged corpuscles of solar origin. This view evokes two remarks. First, motion of
electric charges at high velocity is identical with an electric conduction current,
and thus, this view cannot be opposed to the current theory of magnetic storms;
second, considerably more theoretical and empirical arguments can be opposed to it
than can be cited in its favor. The ultraviolet theory of magnetic storms*, ac-
cording to
radiation,
atmosphere
which the prime causes of magnetic disturbances are outbursts of wave
likewise reduces the effect of the disturbance of the upper layers of the
to the formation of certain additional current systems.
For an explanation of the S -variations, a diamagnetic theory had been advanced
previously. According to this theory, the upper conducting layers of the atmosphere,
due to the rotation of charged particles about the lines of force of the permanent
magnetic field are, as it were, magnetized. The magnetic field of these layers,
superimposed on the permanent field, forms the diurnal fluctuations of the magnetic
elements. As a result of the work by Tam (Bib1.31) and others, this hypothesis has
been recognized as unfounded. However, even if the possible existence of a diamag-
netic effect were not open to funaamental objections, it would be quite impossible
to use the hypothesis for explaining such
ing magnetic storms. For any view of the
solar stream on the magnetic field of the
of the fluctuations of the magnetic field
complex fluctuations as are observed dur-
mechanism of action of a geoeffective
earth, it seems that the immediate causes
during a disturbance are electric
* This theory developed by Meyers and Hulbert, is at present time the object of
violent criticism.
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currents* excited in some manner outside the earth's surface itself, and by induction
in its depths. Thus an explanation of the morphology and nature of these currents is
of fundamental significance for the development of the theories of magnetic storms.
The calculation and discussion of the electric currents responsible for magnetic
storms is the primary purpose of the present work.
Section 2. The Electric Current Systems of Magnetic Storms
The problem of finding the density and configuration of the currents from the
magnetic field observed on the earth's surface is, in the general case, a many-valued
one. However, by calling on supplementary information from other fields of geo-
physics, the number of possible solutions is narrowed, leaving only one or two par-
ameters indeterminate. For example, the very plausible hypothesis was formulated
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ycx
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12
16
18 20 22 24 2 4 ,
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Fig.1 - Storm of 17 July 1947
Magnetograns of Krasnaya Pakhra Observatory
that the currents, responsible for the quiet diurnal variations, flaw in a spherical
layer concentric with the earth's surface. This allowed calculation of the system
of currents of the S variations by means of spherical analysis and served as a basis
for the formulation of the physical theories of the S . Only one parameter, the
height of the current layer, still remained indeterminate in the calculations of the
Sq -layer. Its value WAS found by consideration of experimental data on the ioniz-
* Not necessarily conduction currents. It is possible that the disturbances in the
polar region are connected with a peculiar type of discharge currents.
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ation of the D and E layers of the ionosphere.
_ The situation with respect to questions of the construction of the current_
4._ i
_ systems responsible for the field of perturbation is considerably less favorable.
410.: In spite of the large number of papers devoted to this subject, it has not yet been
- definitively solved. The main reason for this is the above-mentioned complexity of
10--
the fluctuations of the magnetic elemental during a storm. If the calm (quiet) di � al
12_
variations are so regular (cf. left part lof Fig.1) that a simple averaging of the
14_
16 --,
18
2 0_
22_
24_
.,b
--I follow each other without apparent regularity). The distribution of the vectors of
2U_
data for a few days in a month is suffic4int to determine the law of variation of t
magnetic elements, magnetic storms (as wiil be seen from the right side of the same
figure) belong to those very capricious and at first glance completely random phen-
omena which are so abundant in geophysics'. Magnetic storms are characterized not
only by complexity in the fluctuations of the vector of the magnetic field with t
(rapid fluctuations of various amplitudes and frequently of utterly irregular form,
� the disturbing force in space is also ex*emely complex. The form and amplitude of
- the oscillations at different stations, particularly those located in different la
itudes, often bear little similarity to each other (Fig.2). The rough valltative
14 _
characteristics of the field of magnetic storms (the disturbance is greater in high
36_
than in low latitudes, greater in the evening than in the morning, etc.) have long
�
been known. However, in order to study with more rigor the morphology of the fieldj
lo _1
-- by its spatial and time variations, the accumulation of a large amount of empirical
material was necessary, with long series of observatory data at a large number of
geographical points. While Schuster disposed of the annual data of seven observe-
I tories in his calculation of the potential of the quiet diurnal variations, which
allowed him to get an idea of the system of currents that well represents the mean
features of the field, the workup of materials rrom 22 observatories to a few years
permitted Chapman to find only the general outlines of the morphology of the storm
field.
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The second difficulty produced by the complex structure of the storm field in
studying the causative electric currents, is the need for a special mathematical ap-
paratus suitable for an analytical representation of the field and for the calcu-
lation of the current function. Spherical analysis, which is successfully used to
represent the permanent field and the quiet diurnal variations, has permitted so-
lutions of a number of fundamental problems of the structure of these fields, but it
is practically useless for the investigation of fields with a complex geographical
distribution.
All attempts made until now to construct a system of electric currents with
fields equivalent to the fields of magnetic storms, were based on modest empirical
material and were calculated by an approximate method (Chapman), or else were based
on data relating to only a limited part of the earth's surface (for instance, a few
polar stations) and were calculated under very narrow a priori assumptions (for in-
stance, the postulate advanced by Birkeland, Gnevyshev, and others as to linearity of
the current). As a result, these systems of electric currents do not represent (with
the accuracy that is desirable for theoretical and practical problems) the geographic
distribution and time regularities of the field of magnetic storms. Moreover, they
have been constructed without proper division of the field observed on the earth's
surface into the parts of external and internal origin, without investigating the
question of potential, and without considering a number of other questions whose so-
lution could be obtained only by means of the analytic representation of the field.
Most of the known current systems, and in particular the system of Chapman,
which is cited in all manuals and textbooks on terrestrial magnetism, are average
systems, equivalent to an average magnetic storm. The literature contains only few
works devoted to the study of elect:ric currents of individual magnetic storms and to
the relations between the average and individual pictures. It follows from this
that there is very great need for a new construction of the current systems of mag-
netic storms, based on the most complete possible empirical material and performed
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by analytic methods.
The publication of observations of magnetic observatories during the Second
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.1-3�' International Polar Year (1932/33), was
200 completed in the 19401s. During this year,
Do' over 60 observatories were in action. The
publication of the observations of a number
30 �
of Arctic observatories for later years,
i+ 100 3
500
places a rather broad empirical material at
ma our disposition today. The use of this ma-
terial, particularly abundant for the high
latitudes of the Northern Hemisphere, and
the application of new analytic methods,
0
40 /--------- rife
1-!r,' has enabled me to construct systems of e-
lectric currents that are more reliable
0
30 z
than those heretofore known. The discus-
*30.
sion of the electric currents so obtained,
_100 from the viewpoint of modern ideas on the
morphology of the ionosphere on a disturbed
,ina day, helped to explain the parameters of
1.-u0 these currents and to formulate certain
*301 conclusions on the mechanism of their ex-
1
h 1,
24 12h bh 20
citation. A consideration of the magnetic
Fig.2 - Storm of 8 April 1947
field on individual days made it possible
Magnetograms of Observatories:
to follow the development of the electric
Sitka (60�), Tucson (50�),
current systems of individual storms, and
Cheltenham (40�), San Juan (30�),
it was found that the current systems of
and Honolulu (210)
individual storms may be regarded the re-
sult of fluctuations of an average system. The use of analytic methods made it pos-
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�!sible to divide the field of disturbance into parts of external and internal origin,
and, on the basis of these parts, to judge the electromagnetic parameters of the in-
terior of the earth.
Section 3. Content of this Report
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It follows from the objects of this report, given in Section 2, that it includeS
two parts, a geophysical part comprising a study of the morphology of magnetic storms
and of the disturbed ionosphere, and a mathematical part giving the development of
practical methods of calculating the electric currents from the observed distribution_
of the magnetic field, to satisfy the specific requirements of our problem.. The geo-
physical part covers the following points:
1. Classification of magnetic disturbances and separation of the perturbation
field into individual parts. I consider that two groups of storms must be disting-
uished: world (A) and polar (P). The field of a worldwide storm, as stated by
Chapman, is made up of three parts: an aperiodic part or, as it has been customarily
called in all the earlier literature on geomagnetism, lithe stormtime variations"
(Dst), the disturbed diurnal variations (SD), and the irregular part (Di). However,
the worldwide storms are always accompanied by a series of superimposed polar dis-
turbances. The subdivision of the field of a worldwide storm must therefore be made
by means of a four-term equation
D.st+SD+Di+P �
The methods of calculating the various parts of the field are described while
Chapter II is devoted to the exposition of these questions.
2. Chapter III is devoted to a description of the geographical distribution of
the field of Dst* The same Chapter gives the calculation results for the potential
and currents of the field of Dst. The comparative simplicity of the field allowed
us to use the method of spherical analysis. Two alternate systems of currents were
calculated: the ionospheric layer of current, and an equatorial extra-ionospheric
current ring. The ratio between the external and internal parts of the field was
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obtained in good agreement with analogous data of other investigators.
3. The regularities of the SD-variations has been considered: the dependence .
on geomagnetic coordinates, the role of Universal Time, the features of the distri-
bution of SD on the polar cap, and the longitudinal members. The external system of
currents of the SD variation was calculated by the method of surface integrals and
compared with the Chapman system. The ratio of the external (Ve) to the internal
(Vi) parts of the potential is discussed. We find that the ratio Ve depends on the
latitude and that its mean value is 0.89.
The above-enumerated questions are discussed in Chapter V.
4. A current system of an idealized polar storm (Chapter VI) is discussed, con-
structed from data of Silsbee and Vestine by expansion of the storm field into a
series of Bessel functions. A resemblance of this system to the system of currents
of the SD variations was found.
5. The seasonal and 11-year fluctuations of the currents of the Dst- and %-
variations are described (Chapter VII).
The current systems for individual selasons and years were calculated by approx-
imate methods. It was found that the intensity of the Dst-current has cyclic fluctu
ations resembling the fluctuations of solar activity. The seasonal march of the Dst
current has two waves (one annual and the other semiannual) and is completely exp-
lained from the viewpoint of the corpuscular theory of storms. The seasonal and 11-
ear fluctuations of the current systems of S are much more complex. The material
1
Ipresented by a number of observatories has shown that, during the course of the 11-
1
year cycle and during the course of the year, both the intensities of the current
eddies and the position of the auroral zore vary. The intensities of the currents in
the middle and high latitudes obeys different regularities.
6. The Dst- and SD-variation of the density of ionization of the F2 layer of
the ionosphere are discussed. It was found that the Dst-variations in the ionization
of the F2 layer cannot, either from their geographical distribution or from their
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7. The electric systems of currents of individual magnetic currents are calcu,
18_1
' lated in Chapter IX. It is found that in all cases the currents, at a given instant
20:j
of time, may be represented as the result of the superimposition of typical systems
t1
of Dst-, Sio-, and P-currents. However, the intensities and configurations of the
Dst-' SD-' and P-currents vary within wide limits from case to case.
8. The external (principal) part of. the field of magnetic disturbances induces,
: secondary currents in the inner conducting parts of the earth, which in turn influ-
ence the magnetic field observed on the earth's surface. The separation of the po-
tential of the field of Dst and the potential of the P-storms into an external and
an internal part made it possible to calculate the conductivity of the deep parts of
the earth and the thickness of the upper nonconducting layer. The calculations were
absolute value, be responsible for the ionospheric system of electric currents
j
rquired for explaining the Dst -variations of the magnetic field. On this basis, the
4_1
- conclusion is drawn that the most probable cause of Dst -variations is an equatorial
I
- iring with a radius of 3-4 earth radii. A comparison of the SD-currents may be ex-
plained, both in intensity and in form, under the assumption of a drift of the charged
10-H
__I particles of the F2 layer under the action of the earthls permanent magnetic field
' and of its gravitational field. Chapter VIII is devoted to an exposition of these
14_
questions.
16 -1
A
I
made under three assumptions: 1) the conductivity of the deep parts of the earth is
constant; 2) the conductivity increases with depth; and 3) the currents induced in
the oceans and wet soil are allowed for. For the estimate of conductivity we use
not only the data on the P.-storms and the first harmonic of the Dst-field, but also
the data on the S -variations. The results so obtained on the variation of conduc
tivity with depth differ somewhat from those of previous authors and are in good
,agreement with modern ideas on the internal structure of the earth, based on seismic
data. The division of the field for the harmonic P3 of the Dst -variations cannot be
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explained within the scope of the Chapman-Price induction theory. Chapter X is de-
voted to these questions.
The mathematical part of the work includes the following factors:
1. The method of surface integrals proposed by Vestine in 1941 was used for
calculating the external and internal potentials of the SD-field. This 'method, which
is used for the first time in geomagnetism, required the development of practical
methods of processing the material and of a technique of computation.
2. The author of the present work has proposed a method of calculating the
current function on a sphere with a radius of a, if the potential observed on the
surface of a sphere R(R < a) is assigned in numerical or graphical form. The method
is based on finding the current function for regions internal with respect to the
sphere R, and on its extrapolation to outer space. The finding of the current
function from the known potential on the sphere leads to the solution of the inner
Dirichlet problem by the aid of a Fredholm equation of the second order. Practical
calculation methods were worked out. The method is applied to a calculation of the
currents of SD. The questions connected with the integral method of analysis are
discussed in Chapter IV.
The principal conclusions from the work are collected in the Conclusion.
Chapter I is devoted to a survey of the literature. Since this work is prim-
arily devoted to questions of the morphology of the perturbation field and of the
construction of the electric currents equivalent to it, out of the wide and varied
literature on magnetic disturbances only studies devoted to the solution of these
)'
very questions are mentioned in the survey. Works devoted to other divisions of the
theory of magnetic storms, to descriptions of individual phenomena, or to statistics
of magnetic activity are not considered in the survey.
The equations are separately numbered in each Chapter. In referring to an e-
quation given in the same Chapter, only its number is stated. In referring to an e-
quation from a different Chapter, its number and the Chapter number are given.
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CHAPTER I
SURVEY OF THE LITERATURE
Section 1. Basic Properties of Magnetic Storms. The Works of Birkeland
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The magnetic field of the earth is rarely completely quiet. Very often, the
smooth march of the magnetic elements, due to the quiet periodic variations (solar-
diurnal, Sq; lunar-diurnal, L; annual, A) is disturbed by irregular fluctuations of
varied form and amplitude. Any deviations of the magnetic field from the normal
march are called disturbances. Some of them are so small (tenths and hundredths of
a gamma) as to be detected only by special high-precision instruments (Bib1.16). The
strongest disturbances, expressed in large and sharp fluctuations of the magnetic
elements and lasting from several hours to several days, are called magnetic storms.
Storms are observed simultaneously either over the entire earth or, at least, in the
high latitudes. The amplitudes of fluctuation of the elements during extremely
strong storms exceeds 1,000y in the middle latitudes and 2,000-3,000 y in the high
latitudes. During the time of a medium (moderate) storm, the fluctuations are of the
order of 200-400-to 500-1,000y depending on the latitude. The rate of variation of
the elements likewise fluctuates over a wide range, sometimes exceeding a few tens of
gammas a second. Occasionally, very slaw and smooth variations of the elements are
observed (especially in the law -intitudes, in the Z-component). The fluctuations of
the magnetic elements during a storm are so diverse that, during the entire period
over which the observatories have been recording the magnetic elements, i.e., for
over 100 years, no two identical storms can be found.
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Despite such randomness of fluctuations, statistical regularities obeyed by
magnetic storms have long been known. These regularities are as follows: The in-
tensity of storms (characterized by the frequency and amplitude of the fluctuations, ,
the mobility of the curves, and the magnitude of the deviation from the normal values)
depends on the latitude. It reaches its maximum values in the high latitudes, in the
zone of maximum visibility of the aurora; as the pole is approached, the degree of i
disturbance again decreases. The number and intensity of the storms has a seasonal !
march with maxima at the epoch of the equinoxes, and also has an 11-year cycle. Thel
maxima of the magnetic cycle lag 1-2 years behind the maxima of the solar cycles. I
There is a correlation between individual magnetic storms and the manifestations of
solar activity: sunspots, flares, eruptions. This correlation is of a statistical ,
nature for the weak and moderate storms. The strong storms, as a rule, are uniquely
related to solar phenomena. Tendencies to a repetition of storms after a synodical_
revolution of the sun and to a lag of storms behind the passage of an active region
across the central meridian, have been noted. Finally, the distribution of the in-
tensity of a storm during the course of the day, the �diurnal march of magnetic act-
ivity", has been found.
An extensive section of the literature has been devoted to these regularities,
and served, as already stated, as the basis for the development of the corpuscular
theories of magnetic storms. Considerably fewer papers have been devoted to the
study of the structure of the field of the storm field itself. A.Schmidt and van
Bemmelen (Bib1.40) were among the first investigators who attempted to find the reg-
ularities obeyed by the storm field, According to them, the vector of the disturbance
systematically varies its direction during the course of the storm, and the 'teddies!'
into which the storm is divided are displaced along the earth's surface. Without
taking up this idea of the storm in detail, based as it was on the erroneous as-
sumption that storms are local and of terrestrial origin, let us turn to an exposition
of the memoirs of Birkeland (Bib1.38), which have not lost their significance even -
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today. Having set himself the problem of studying the distribution of the vector of
disturbance over the earth's surface and of explaining the origin of the storms,
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Birkeland commenced his investigations by accumulating observational data. He under-
stood the particular importance of high-latitude observations and organized two
special expeditions, in 1899/1900 and in 1902/03, during which a special system of
temporary stations, provided with apparatus of the same type and operating under a
common program, was used. In working up this material subsequently, Birkeland com-
piled, for several storms, maps of the geographical distribution of the vector of
disturbance for successive most characteristic instants of time. Birkeland defines
the vector of disturbance as follows: Fd = F - Fn, where F denotes the observed value
of the magnetic field and Fn the normal undisturbed value. The construction of these
�synoptic" maps showed Birkeland that, despite the apparent randomness of the fluctu-
ations of the magnetic elements, a certain systematic character is manifest in the
distribution of Fd. The vectors at closely adjacent stations are almost parallel;
a definite relation exists between the vectors and the longitude of the station and,
in particular, the latitude. Birkeland divided the listed magnetic storms, about 30
cases in all, into five types. Type 1, the most frequent, is characterized by the
almost everywhere negative horizontal component of the vector Fd. The maximum mag-
nitude of the vector is reached in the polar zone, declines sharply in the middle
latitudes, and again increases somewhat in the equatorial belt. Storms of this type
were called negative equatorial storms by Birkeland. Type 2, positive equatorial
storms, are storms with a positive horizontal component of Fd; the least disturbance
embraces all latitudes, but its value is usually much weaker than the disturbance of
negative storms. This type was rarely observed. Type 3 and 4 are positive and neg-
ative polar storms and are characterized by the fact that the vector of disturbance
reaches high values only in the high latitudes, while the magnetic field of middle
and law latitudes remains in fact almost undisturbed. Type 5, the cyclo-median
storms, of small value, reach their greatest development on the daylight side of the
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earth in law latitudes. As Chapman later pointed out, the cases of disturbances
classified by Birkeland as Type 5 would be more correctly included among the bay
disturbances accompanying sudden ionospheric disturbances and due to outbursts of
ultraviolet radiation. These bay disturbances are anomalous intensifications of
these S -variations, but not ordinary disturbances of corpuscular origin.
With respect to the equatorial storms Birkeland confined himself to the hypo-
thesis that they were presumably due to certain systems of electric currents flawing
not far from the equatorial region, and devoted all of his attention to a study of
the polar storms. The most characteristic feature of the polar storms'is a sharp
increase of the H-component of the vector of disturbance and the passage of the Z-
component through zero in the auroral zone. From this, Birkeland concluded that the
polar storms were caused by a powerful linear current flowing at a certain height
along the zone. Elementary counts, based on the use of the Biot-Sawara law, allowed
Birkeland to make an approximate estimate of the height (100-300 km) and the intensi-
ty (4 x 105 to 9 x 105 amp) of the current. The short duration of these storms (last-
ing from one to several hours) forced the assumption that the extension of the current
along the zone is short: 100, or a few tens of degrees. Birkeland postulated that
his horizontal current was a part of a U-shaped current system, whose vertical
branches extend beyond the limits of the atmosphere. The diagram of a typical field
of a polar storm (Fig.3) shows the distribution of horizontal projections of the
lines of force of the magnetic field (the solid curves), a graph of the variations of
the vertical component (the lower part of the figure), 'and the system of isopotential
lines (the broken lines). The hypothetical linear current flaws in the direction of
the principal axis of the disturbance, marked by the arrow. The maximum value of the
vector Hd, as will be seen from the diagram, should be observed at the point 0, the
center of the disturbance.
The question of the closure of the Birkeland current system remained open, as-
suming the possibility of the existence, at a great distance from the earth, of a
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very diffuse branch closing the current system, and also assuming the possibility of
an unclosed system.
This current system is in agreement with the views of Birkeland and Stoermer on
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the origin of magnetic
storms. According to the well-known Stoermer-Birkeland theory,
Fig.3 - Diagram of Magnetic Field
of an Elementary Polar Storm (ac-
cording to Birkeland).
The arrow shows the direction of
the principal axis of the disturb-
ance (C = Center of Disturbance;
Lines of Force; - - - - Equi -
potential lines; Z = Vertical com-
ponent of the storm field)
which is frequently set forth in the literature,
the storm field is the field of a solar stream
of charged particles of a single sign, deflected
by the earth's magnetic field toward the polar
zones. Solving the equation of motion of a
charged particle, Stoermer calculated the pos-
sible forms of the paths and, in particular, ob-
tained paths explaining the above descrived U-
shaped current: the particles, moving along
these paths, approach the earth from space,
penetrate the atmosphere in the high-latitude
region down to a height of 100-300 km, take a
horizontal segement of their path in the atmos-
phere, as a rule along the auroral zone, and
then once more leave the neighborhood of the
earth. Experimental studies by Brueche(ir-
radiation of a magnetized sphere by a narrow
beam of cathode rays), which allowed him to fol-
low the paths of individual particles, confirmed
the possibility of such paths and thereby gave
still greater significance to the Stoermer-
Birkeland theory. This theory is thus an attempt to systematize the data on mag-
netic disturbances, to establish an idea of the typical picture of a disturbance, to
calculate the electric current equivalent to it, and to explain its origin. The
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criticism of the physical bases of this theory is commonly known. Serious objectionE
to the theory (a stream of particles with only a single sign could not reach the
earth, due to the electrostatic repulsion of the particles; the invasion of the
earth's atmosphere by particles of a single sign must lead to great fluctuations of
electric potential during a storm, etc.) forced the various investigators subsequent-
ly to abandon the hypothesis of a singly-charged stream. Let us discuss the remarks_
provoked by the morphological part of the study. Since Birkelandls system of station
was located in a narrow longitudinal sector of the Arctic (Iceland, Spitzbergen,
Norway, Novaya Zemlya), he did not discover the fact that positive and negative polar
disturbances are always observed simultaneously, but in different hemispheres. In
reality, however, a polar disturbance usually covers all the longitudes of the polar
region, the direction and magnitude of the vector of disturbance being different at
different longitudes. It would thus seem more expedient to construct the system of
electric currents determining the distribution of the magnetic field at all longi-
tudes. Further, Birkeland had too small an observational material on the course of
disturbances in moderate latitudes. The morphology of the equatorial storms there-
fore remained actually unstudied by him, and he did not get a clear idea on the
currents responsible for them. The classification of storms introduced by Birkeland,
as shown below, likewise does not seem usable.
Section 2. Chapnants Investigations and their Revisions
A completely different approach to the study of the morphology of magnetic
storms is contained in the works of Chapman (Bib1.40). As far back as the beginning
of the Twentieth Century, the works of Moos, Director of the Bombay Magnetic Observa-
tory, contained indications that, during the storms, the horizontal component first
increases (first phase of the storm), then decreases below the normal (second or
chief phase, during which the fluctuations of the magnetic elements are greatest)
and then slowly return to the normal state. The return to the normal state [in the
literature, various terms are used - restoration phase, aftereffect, Nachstoerung,
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postperturbation, and noncyclic variation noncyclic change] takes several days, even
when the field is no longer disturbed by irregular fluctuations. The work of Mbos
gave Chapman ground for postulating that the storm field contains regular parts, for
which certain stable systems of electric currents influencing the distribution of
the vector of disturbance of the entire earth are responsible. The varied fluctu-
ations of these currents result in the individual features of each storm, the random
fluctuations superimposed on the average picture of the magnetic variations. Chapman
worked up the variations of the magnetic elements H, D, and Z for 22 observatories
located between 22� and 600 North Latitude. His calculations consisted in averaging.
of the values of the magnetic elements by hours, counting from the beginning of the
storm. As a result of averaging a rather large number of cases (Chapman used the
data of 40 moderate storms), the influence of the irregular fluctuations and of the
regular part of the disturbance connected with the local time was to a large extent
eliminated. He succeeded in finding the regular part of the storm field taking place
at the same World Time at all longitudes of the same latitude. He termed this part
of the field of a magnetic storm, the stormtime variations, i.e., the variations
taking place according to a time reckoned from the beginning of the storm. Daring
the 1930's and 19401s, the English term ustormtime variations?! was still used in the
Russian literature on terrestrial magnetism to designate this part of the storm field.
It seems to us preferable to use the term Maperiodic disturbed variations� as we will
do in future, while retaining nevertheless the symbol Dst-variations or Dst-field
which is generally used today in the world literature. The Dst-variations of the H-
(or X) component at all latitudes (or at least at the middle latitudes) were de-
scribed similarly by Moos for Bombay. The Dst_variations of the Z-component, on the
other hand, reduced to the decrease of the element in the first phase of the storm
and to its increase in the second stage. The amplitude of the Dst-variations of the
Z-component is smaller than the amplitude of the H-component. No regular aperiodic
part could be found in the element D. During the entire storm, the fluctuations of
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D, no matter how large they were, usually take place about the normal value of the
element. This is evidence that the horizontal component of the vector of disturbance
on the average is most often directed along the magnetic meridian. The Dst-variations
during the course of moderate and great magnetic storms are the same in form and
differ only in intensity. This made it possible for Chapman to conclude that the
average picture of the Dst-variations was constant (or, more accurately, stable).
In analyzing the classification of storms proposed by Birkeland, Chapman con-
cluded that the positive equatorial storms of Birkeland correspond to the first
phase of the ordinary storm, and the negative ones to the second phase. The insuf-
ficiency of the material, in Chapman's opinion, prevented Birkeland from noting that
the two types of storms are in reality only two successive phases of a single phe-
nomenon. The averaging of the value of the magnetic elements (after eliminating
the Dst-part for each storm) in accordance with the hours of the local days allowed
discovery of the relation of the field of the magnetic storm on the time of day.
This second regular part of the field of a magnetic storm is customarily termed the
disturbed diurnal variation (abbreviated SD) The existence of regular diurnal var-
iations on days of magnetic storms, differing from the diurnal variations on quiet
days, was noted, independently of Chapman, by a number of investigators. Chapman's
calculation showed the existence of the Sp-variations in all the elements, and their
regular change with latitudes. A characteristic feature of the SD-variations in the
H and Z components in the temperate latitudes is the minimum value of the elements
in the morning hours and the maximum values in the evening.
The third part of the storm field, in Chapman's opinion, is the irregular fluc-
tuations (Di) superimposed on the regular parts and giving a random appearance to
the variation of the magnetic field on disturbed days. Considering the regular
parts of Dst- and SD- to be the principal and most interesting parts, Chapman dir-
ected his efforts toward their further investigation, leaving the irregular part
aside. Considering that the Dst- and SD-variations we have described to be due to
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electric currents flawing near the earth's surface (in the atmosphere itself or be-
yond it), Chapman formed an idea, from the pbserved magnetic variations, of the con-
figurations and intensities of these currents. His systems of electric currents of
magnetic storms entered the geophysical literature as the most probable representa-
tion of the electric currents, and served as a starting point for the development of
the modern theoretical views on the nature of the phenomenon. His systems were con-
structed by an approximate method, without calculating the potential of the observed
fields of variations. He started out from the following postulates:
1. By analogy with the Sq-variations it may be assumed that the field of Dst
or SD observed on the earth's surface is the result of the composition of an extern-
al main field and an internal field due to induction in the conducting part of the
earth. The ratio of the external field E to the internal field I, i.e., E/I = 3/2.
2. The external system of electric currents is a spherical nonuniform current
layer concentric with the earth's surface. The height of the current above the
earth's surface h = 200 km.
3. The direction and density of the current may be calculated from the observ-
ed magnetic field by the Biot-Sawara law, by replacing at each point the action of
the nonuniform spherical layer by the action of a uniform, plane current sheet of
infinite extension. The current systems of the Dst- and SD- variation so obtained
are presented in Figs. 4a and 41). It will be seen that the Dst currents flaw every-
where westward in the direction of the parallels of latitude. The intensity of the
current increases somewhat in the equatorial region, and increases strongly in the
polar cap. The current along the auroral zone is represented in the form of a
linear current of high density. The total intensity of the current flawing in each
hemisphere is 200,000 amp; the current lines on the figures are drawn in such a way
that a current of 10,000 amp flows between adjacent lines. During the first phase
of magnetic storms (increasing H) the current should flaw in the eastern direction.
The current system of the SD-variations is much more complex. An analysis of
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the material as shown that on the whole the field of SD -depends on the latitude-and
local times. For this reason, without taking into account the possible slight longi-
tudinal asymmetry in the distribution of the field, Chapman constructed the current
system in the same way as the system of the S -currents, i.e., fixed, if viewed from
the sun. In order to explain the variation of the magnetic elements during the
course of the day, the earth must be imagined to rotate inside this fixed system.
The system SD consists of four current loops in the moderate latitudes and a layer
of almost parallel currents flawing about the polar cap. As in the case of Dst, an
increased intensity of the current is observed in the auroral region. The currents
presented in Figs.4a and 4b correspond to a moderate magnetic storm with decrease of
H in the principal phase equal to about 40y. During very strong storms, the
currents can be expected to increase by a factor of 10-15.
The systems of currents of Dst and SD, according to Chapman, call forth the
following remarks:
1. The empirical material that served for their construction is, absolutely
without question, insufficient. If the workup of the data of 22 observatories gave
a sufficient idea of the distribution of the Dst- and SD-variations in the moderate
latitudes, then the regular part of the storms in the high latitudes would still re-
main in fact, unknown. Chapman judged the intensification of the D5-variations in
the auroral zone by the geographic distribution of the value of Dm. The symbol Dm
denotes the difference between the mean diurnal values of the horizontal component
on disturbed and quiet days, that is, D = Tiq - lid. Since the principal effect of
the aperiodic storm variations reduces dawn to the decrease in the horizontal com-
ponent, it follows that the difference of the mean diurnal values of H on quiet and
disturbed days may serve as a certain characteristic of the value of the Dst -varia-
tions. Chapman judged the SD-variations inside the zone by the diurnal march for
all days, at the Antarctic Station of Cape Evans. The data from observatories lying
in the auroral zone itself were not fully available to Chapman. As shown by the
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materials collected by us for a number of high-latitude stations (cf.Chapter V), the
distribution of variations is in reality somewhat different.
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100000
>00000
271000 2TS. 000
Fig.4 - Currents of the Regular Parts
of the Storm Field (after Chapman).
Current strength in amperes (a - Dst
Variations; b - SD-Variations)
Birkeland system does not withstand the
2. The systems constructed by Chapman
actually corresponds to worldwide storms
(those observed over the entire earth). The
absence of a distinct boundary line between
world wide and polar storms (Chapman did
not pay proper attention to the question of
the classification of storms) lead to a
� certain distortion in the current systems
in high latitudes (cf.Chapter II and III).
3. My own calculations of the poLen-
,tial of the external and internal parts of
the SD-variations have shown that the ratio
I/E is not the same at all latitudes, and
that in any case, the value I/E = 0.6
adopted by Chapman is exaggerated.
4. The height of the currents h =
'200 km seems too low, which in turn would
affect the numerical values of the current
intensities found.
On comparing the Chapman and Birkeland
systems, Vestine, in his paper written in
collaboration with Chapman (Dib1.60) states
that the Chapman system better reflects the
actual course of a storm, and that the
test of comparison with empirical data. It
seems to me that in comparing the Chapman and Birkeland systems it must above all be
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borne in mind that these systems are responsible for different types of disturbances
and have been constructed from material that is not entirely of full value: Chapman
had almost no data on the high latitudes available to him, while Birkeland made
little use of information on the course of disturbance in the middle and low lati-
tudes.
The question of the necessity of verifying and elaborating the Chapman system
from more complete magnetic data and applying more accurate methods to the calcu-
lation of the currents has repeatedly been raised in the literature. The most ex-
haustive revision made in the above mentioned work by Chapman and Vestine. Up to
1937, (the work was published in 1938) certain worked-up materials of magnetic ob-
servations made during the Second International Polar Year (II MPG 1932/1933) were
available to the authors. In particular, there were observations within the auroral
zone (the Thule and Godhavn Observatories) and immediately in the region of that zone
(Bear Island, Matochkin Sharp etc). The values of the Dm- and SD-variations had been
calculated for all observatories, the SD-variations being taken as the difference
between the diurnal marches for international disturbed and quiet days*. This method
of calculating SD involves very little work and was subsequently used by a number of
investigators.
The mathematical difficulties connected with the calculation of the electric
currents corresponding to magnetic fields as complex in geographical distribution as
SD and D5t2 forced the authors to abandon the solution of the direct problem (calcu-
lation of the currents from the observed field) and to ,take up instead the inverse
problem (calculation of the magnetic field of the Chapman system of currents and its
comparison with the observed field). For this purpose, the current systems of Figs.
4a and 4h were broken down into several principal forms: S1, surface current in the
* The International Association for Terrestrial Magnetism and Electricity, since
1905, has been selecting, from the magnetic characteristics of a worldwide system of
observatories, the five quietest and the five most disturbed days in each month.
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polar cap in the'Dsi.-systald 1,1;linear current in the aUtbrarsone-in-the
S2, current layer between two tones; etc. The magnetic field of each component part
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of So I., etc. was separately calculated by applying the kat-Sewer* law to the el-
ements of the current and-porforming"the-corresponding-integration-over-the-surface'
or outline. This method led to rather complicated computational work and made majori
P � lation of integrals of the type f a cos Tdp , which are reduced to tabulated el-
liptic integrals; the surface currents over the polar cap in the middle latitudes
were assumed to be plane, and the evaluation of the surface currents 84 (the middle-1
latitude eddies in the Sd system) was not performed at all. As a result of graphic !
simplifications necessary. As an example we may say that the evaluation of the mag-
netic field of the L-current, assuming it to be of circular form, led to the calu-
2g
"integration, curves of the latitude dependence of the components of the SD and Dst
fields were obtained. Their comparison with the observational data showed that the
Chapman systems do not contradict them, but still did not remove the question of the'
desirability of a new construction of the systems, using all available material.
An attempt to elaborate the Chapman system was made in the paper by Vestine
(Bib1.58), based on the same starting material as the above-discussed work. It was
found that the Chapman systems had been constructed without allowing for the lati-
tudinal asymmetry in the distribution of the field. In the law and medium latitudes,
this asymmetry is actually small, but it is impossible to ignore it in the high lati-
tudes. Vestine expressed the very interesting thought that the asymmetry in the high
latitudes is due primarily to the noncoincidence between the magnetic and geographic
axes of the earth due to which fact the auroral zone is of an elliptical shape in-
stead of circular and is elongated in the direction of a line joining the magnetic
and geographic poles. For this reason, if we allow for the distance of a given point
of observation from the auroral zone, instead of simply taking into account the geo-
magnetic latitude of the point, then the longitudinal asymmetry is considerably dim-
inished. Vestine, on the basis of the magnetic data, determined the location of the
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'zone of linear polar current, which he found to be rather close to the position of
the maximum isochasm obtained as early as 3.867 by Fritz (for more details see Chapter
V, Section 7). Thus Vestinets work not only solved certair questions as to the mor-i
phology of the SD- and D3-variations, but also disclosed the possibility of uSihr-i
- I
magnetic data for pinpointing the position of the auroral zone. The magnetic data, I
being the result of continuous recording independent of the meteorological condition5
can provide more reliable conclusions than those based on auroral statistics.
Among the worth that followed the investigations by Chapman, the paper by Chynk
(Bib1.41) is worbh mentioning. It points out the existence of a seasonal asymmetri
in the distribution of the field of Dst-variatiorp. According to Chynri, the seas-
onal march of Dm has a maxima in spring and autumn, like various measures of magnetic
activity. However, in addition, it also has another maxim= in the winter.
Section 3. Analytical Representation of the Dot-Variations
Attempts at an analytical representation of the potential field of disturbance.
are also contained in the geomagnetic literature. These attempts related only to the
simplest part of the storm field, the aperiodic disturbed and noncyclic variations
or, more exactly, only to the middle-latitude parts of these fields. All known
papers on this subject (cf.Bib1.40 and 15) followed a definite object, namely separ-
ation of the observed field into an external and internal part, explanation of the
internal part on the basis of the induction hypothesis, and definition of the con-
ductivity in the depths of the earth required for such an explanation. Chapman and
Whitehead calculated the external and internal potentials of the Dst-variations by
expanding the spherical functions of the H and Z components of the field into series ,
from the same data that had been used by Chapman for his approximate calculation of
the Dst-currents. Since it was assumed that the field of Dst depends only on uni-
versal time and geomagnetic latitude, it followed that the values of the potential
for a definite instant of time were represented by series of Legendre polynomials,- :
and, since the potential was supposed to be symmetric with respect to the equator,
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only the odd harmonics were retained in the series of polynomials. Thanks to the
fact that the distribution of the D5-field in the high latitudes was not taken into
account, it was possible to represent the middle-latitude part of the field rather
well by the three first harmonics P1' P3' and P5. The division of the field into an
external and internal part (see Chapter III for more details) gave the following
ratio: I/E is 0.39. It turned out that this ratio requires, for the explanation of
the I-part within the framework of Lamb's induction theory, somewhat different elec-
tromagnetic parameters of the earth than those that follow from an analysis of the
S -variations. A more detailed analysis of the results obtained by Chapman and
Whitehead and other authors, and a comparison of those results with our awn calcu-
lations, will be given in Chapter X.
McNish and Slautsitays, who performed the spherical analysis of the values of
Dm, calculated the intensity of the external currents corresponding to those values
and obtained interesting conclusions as to the ratio between the internal and ex-
ternal part.
No attempt has been made to date at an analytical representation of the distri-
bution of the potential of the SD-variations or of the irregular part of the dis-
turbance.
Section 4. Position of the Points of Magnetic Storms. The Equatorial Ring
The papers enumerated in the preceding Sections exhaust all the studies of the
morphology of the regular parts of the perturbation field and the calculation of the
surface currents responsible for them. It goes without saying, however, that the
construction of these systems is not a proof for their existence. If we make no
supplementary postulates, then the problem of finding the currents from the magnetic
field is an indeterminate, many-valued problem, and an infinite number of such
systems can be calculated, each of a different configuration or at a different dis-
tance from the earth, whose field will likewise well represent the observed field
of magnetic storms. The postulate made by Chapman, however, that the layer carrying
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the currents is spherical appears entirely reasonable in the light of our knowledge
of the structure of the ionosphere. In fact, if we assume for example that the
height of the layer varies with the latitude or with the local time, by 100 km, then
this would mean a variation of only 1.5% in the radius of the spherical surface.
Under the assumption that the current layer is spherical, its radius (or the height
of the current above the earthts surface) can be theoretically determined from the
magnetic data just like the configuration of the lines of current or the intensity
of current. If we assume that the field potential is represented by a series of
spherical harmonics, then the cofactors of the expression (1-)r1 enter into each term,
where a is the radius of the spherical current layer and R the radius of the earth.
Then, by comparing the weight of the nith n2th etc.terms in the expansion, the
value of 'A' can be estimated. In practice, however, in view of the law accuracy in
determining the coefficients with spherical functions, it is imposiible to determine
a
- with an error of less than a few percent. Thus, to define the layer of the iono-
sphere in which the Dst-currents flaw, using a spherical analysis of the type pro-
posed by McNish and Slautsitays as basis, would hardly be possible. For any con-
elusion as to the height of the current layer, data on the structure of the ionosphere
would have to be used, together with an attentive study of the structure, ionization
density, number of collisions, and other parameters of the ionosphere, which would
help to answer the question as to haw far a certain layer meets the requirements that
a current-carrying layer must meet. While it seems almost unquestionable today that
the currents of the S -variations must be related to the lower part of the E layer
and the D layer, there are still doubts as to the perturbation currents. The hypo-
thesis that the disturbance currents are concentrated in the F2 layer seems the most
probable, since this layer shows the closest correlation with the magnetic dis-
turbances. Nevertheless, in discussing the possible position of the SD-currents,
Chapman pointed out that their most characteristic feature was the evening maximum
of intensity, while a maximum of ionization density in the evening is not observed
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���
12
1 4-
..",
tha_Sp7o1.47,:its_rfiain_unexplained in the papers of Chapman and his colleagues._ _Ai_
for the currents causing the D.-variations, the thought is developed in the papers
of Chapman and a number of aher authors lhat these currents flow tar beyond the
limits of the earth's atmosphere, encircling the earth with a ring located in the
equatorial plane. The idea of an(equatori.a3. ring current was first expressed by
Stammer to explain the great polar die
co of the auroral sone (00 = 22 - 230).
The calculation of the paths of the particles under reasonable assumptions as to
16 -
_their velocities, and allowing may for the permanent magnetic field of the earth,
- 1
__ileads to much lower values of e, equal, for example, to -2 to -40 for cathode rays,
2 0 _1 _
0
and to -16� to 19� for alpha particles. The magnetic field of the ring current in a
22.1
__iwesterly direction, reducing the horizontal component of the geomagnetic fields,
__leads to an increase of eo to the necessaTy values. There are also other geophysical
arguments in favor of the existence, in storm time, of an.extra-ionospheric current ,
_ring. But it is precisely the great regularity in the course of the magnetic storms
411 in the low latitudes (Where the irregular fluctuations distort the quiet march of tho
elements only slightly and where the return of H to the normal state, is slaw) that
- mike both these phenomena difficult to explain under the assumption of an ionospheric-
location of the sources of the field. Forbush (Bib1.43), in studying the correlation
- :between the magnetic storms and the cosmic rays, discovered such variations in the
_Antensity of the cosmic rays as confirm the generation, at a certain distance from
-4
the earth, of a magnetic field diminishing the H component of the earth's magnetic _-
4
__field. A detailed theoretical consideration of the possible influence of the equa-
_Jtorial ring is also presented in the papers by Vallarta and Hess (Bib1.35). In
--1,recent years, a number of papers devoted to the effect of magnetic storm on the
- * We will show later that the disturbed diurnal variations of ionization density
lisi-lof-the F2 layer satisfy this requirement, and thus eliminate the objection against
-7!
placing the SD currents in the F2 layer.
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cosmisireys have been published, most of-them likewise & i
thesis.'
According to Stoermer's calculations the ring should be of a very great radius,
of Oiaer of th. distance from the h-tn-the moon, and should be formed as a
.8�
result of the curvature of the paths of charged solar particles by the earth's maifr.
10
dnetic field; the ring is not necessarily a closed one. The energy of such a ring
-
must be great (current strength, 107 amp1. As an argument in favor of Stammer's
'calculated parameters, the "universe echo'', i.e., the great delay of a radio signal
!returning to the earth, has sometimes been advanced. It has been supposed that, in
�
e
_ passing through the ionosphere, a radio signal is reflected from the Stoermer elec-
tronic current*.
'
All later papers, however, express a different idea on the equatorial ring.
Thus, according to the Chapman-Ferraro theory of magnetic storms, the solar stream,
encountering the earth's magnetic field, forms a ring of much smaller radius, of the
order of two to four earth radii. Since the corpuscular stream is assumed by these 1
authors to be neutral, it follows that thei formation of a ring current is explained
by the difference in the velocity of motion of the positive and negative particles.
The papers by Chapman and Ferraro contain no rigorous mathematical treatment of the
question as to the formation of a ring out of the bodies of the corpuscular stream.
They give only a system for the physical explanation of the process based on the re-1
tardation of the stream by the magnetic field of the earth**. The question as to the
stability of a ring, if such a ring is actually formed, is treated with considerable
rigor, explaining the conditions of dynamic equilibrium of the ring (i.e., determ-
ining the allowable fluctuations of radius and current density) and demonstrating the
* Special observations made in 1947-1949 with high-power transmitters (Bib1.65),
failed to detect greatly lagging echoes.
** The USSR literature contains expositions of the Chan-Ferraro theory [cf. for
example, gygenson (Bib1.34)J.
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impossibility of a prolonged existence of a ring with Stoermerts parameters. In 1951,
Martin (Bib1.48) considered the process of formation of the ring on the basis of the
analogy between the electrodynamic processes connected with the motion of plasma in
�
�
�
the magnetic field and hydrodynamic phenomena. The ionized stream flowing around a
magnetic dipole is compared to a stream of incompressible fluid flowing around a
body submerged in the fluid; in this case, the pressure due to the interaction be-
tween the electric currents induced in the body of the stream, with the magnetic
field is identified with the hydrodynamic pressure. The parameters of the rings so
obtained (a = 5.5 R and I = 106 amp) proved to be of the same order as those calcu-
lated by Chapman and Ferraro. The literature also contains an attempt at determining
the radius of the ring directly from empirical data, independent of any theoretical
views on its formation. As is generally known, one of the most widely used character-
istics of magnetic activity is the u-measure, equal to the difference between the
diurnal values of the horizontal component on successive days. Considering that the
descent of H during a storm, and, consequently, the value of the u-measure, is due
to the magnetic field of the equatorial ring, the day-to-day variability of H may be
equated to the increase in the horizontal component of the field of the current MI,
thus permitting an evaluation of the ring parameters a and I, YU.D.Kalinin (Bib1.19),
who made these calculations under the assumption that the incrementAH was due either
to the variation in a from day to day (with the constant I), or to the variation in
I (with the constant a), found that the radius of the ring must be of the order of
two to four earth radii. As shown below in Chapter III, the spherical analysis of
the field of Dst permits determining the quantities a and I independently, without
'assuming invariability of one or the other.
The above-mentioned investigations by Forbush also confirm the small radius of
the ring (amounting a few earth radii). Indications pointing to other results have
appeared in the literature. The studies of Hayikawa, Negate, et al (Bib1.46) have
shown that the observable effect of magnetic storms in the distribution of the
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�
�
currents of cosmic rays cannot be explained under the assumption of a ring 'radius Of
1.1 R Dm which may be explained most easily by the fact
that H - Rd was calculated for a few of the strongest storms, while Dm is the result
of averaging the international disturbed days, most of which coincided with moderate
and even small storms. The excess of H - Hd over Dm in the high latitudes is to be
explained, in all probability, by the fact that in these latitudes, there is another
factor besides Dst, which likewise systematically lowers H during the time of a dis-
turbance. This factor, in my opinion consists of the irregular fluctuations suner-
imposed on the regular part of the field of worldwide disturbance.
* The values of Hq - Hc4 for Tikhaya 13ay are taken from the paper by A.P.Nikoliskiy,
and since the data for the Second International Polar Year and 1947 were unavailable,
the data for 1934 and 1946 were used instead. During the entire 12-year period of
1934-1946 for which Nikollskiy gives data, however, the value of H - is at all
q q
times of the order of 2Y.
** rhe graph of the latitude dependence of Dm for 1933, 1936, and 1938, constructed
from data collected by me, is presented in Fig.32 (Chapter VII).
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A consideration of magnetograms with polar storms on quiet days, magnetograms
�
of moderately
a)
Zo,c)
�
70
�
disturbed days, and of great magnetic storms will convince the investi-
gator that the polar storms of a quiet day
19320
and the great irregular fluctuations dur-
e) ing a worldwide storm are one and the same
� f)
� nhenomenon; during a worldwide storm, a
0 20
410
0
60
8
WO
(f'
90�-orkr
1947z
70
50
d)
�
d,
c ".
�
�
Se)
30
1
"H d large number of polar storms of various
120 -
4 H-
q
1)
�
0 20 40 60 80 100 1201filg-H
0)
0.7s.
g)
� 70 �
h) ed)
0 � 68)
e)
�
�
30
f)
amplitude and forms follow each other or
are sunerimposed on each other, and, being
accompanied by other forms of disturbances,
give the impression of complex random
fluctuations. This proposition has served
as the basis for the conclusion drawn by
Nikol'skiy that a magnetic storm is the
sum of individual pulsations piled one on
the other, a conclusion which in my opin-
ion is erroneous. It is correct to assert
that, during worldwide storms, a multi-
tude of polar storms is always superim-
posed on the regular parts of the disturb-
20 40 69 BO &V UV Z d
4 ance. A worldwide storm without polar
Fig.10 - Latitude Denendence: a) of
storms is impossible; they are an insep-
H - 0; and b) of Z - Zd; c) Tikhaya
q q q q arable part of it. But the worldwide
Bay; d) Sitka; e) Thule; f) Honolulu;
storm is not a result of the simple sum-
g) Bear Islands; h) Cheltenham
mation of the fields of the individual
pulsations of polar storms. It has a fundamentally new property, the regular parts
of the Dst and SD field, which do not belong to the individual nolar storms. This
idea of the classification of storms into polar and worldwide, and of their inter-
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'relation, may well solve the contradictione between individual investigators on the 1
t 1
;
'questions of the morphology and classification of magnetic storms. For instance,
�
1
NikollskiyIs conclusion that the regular lowering of H is absent during storms, due .
ito the presence of Dst-currents, can apparently be explained as follows: In calcu-
lating the mean values of Hd Nikollskiy need the tabular material on the hourly am-
plitudes of r11 and the mean hourly values of the H component. He selected the values;
of H in those quiet hours (at small values of rid, which immediately followed strong=,
ly disturbed hours (at large values of rH). In most cases, such sequences of a dis-
turbed hour followed by a quiet hour take place on days of polar storms since_in the
days of worldwide storms, the number of quiet intervals in general is very small. It
is therefore natural enough that the statietical treatment should have disclosed a
regularity inherent in the P-storms but not in the M-storms*, i.e., an absence of any
decrease in H. In the selection of quiet intervals for the calculation of Hd for
Sitka, Bear Islands, and elsewhere, we used magnetograms of worldwide storms and, as
shown by Fig.101 we obtained values of Hq Hd different from zero.
q
Chapman, as already stated, used the values of Dm to construct the polar part of
the Dst-currents. In the high latitude, however, the value of the horizontal compon-
ent of the field of P-storms, superimposed on the regular parts of the field of a
worldwide storm, is considerably greater than this same component of the Dst part.
It is, therefore, only natural that the calculation of Dm by simply taking the aver-
age should reveal the properties of P-storms, i.e., the sharp increase of Hq - Hd in
q
the polar zone.
We may also attempt to explain, from this point of view, M.N.Onevyshevls views
on the latitudinal distribution of the vector of disturbance. From Fig.1 and Table 1
of the Gnevyshev paper (Bib1.13) it would appear that, by the vector of disturbance
F, he means the deviation from the normal values at the instant of some distinct
maximum (for example, 2000Y at the Matochkin Shar Observatory), due to a great
* We will designate worldwide storms in this way to save space.
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..12-storm, consider- ably exceeding the Ds- t-part of the worldwide storm In value. It is 1
,
1
understandable from this that the,relation!between A F and the distance from the
-auroral zone, which is depicted in Fig.4 of the paper cited, characterizes the geo-
graphic distribution of the field of a P-storm rather than that of an 14-storm. This
I
and analogous graphs served as grounds foriGnevyshev to dispute the current systems
I
of the regular parts of the storm (the equatorial ring or the ionospheric systems of
1
surface currents). 1
�
�
As for the storms in which the vector of disturbance increases toward the pole
(upolaru storms, according to Gnevyshevis terminology), I am unfortunately unable to i
confirm or refute the existence of such storms, in view of the lack of empirical ma-
terial that would be necessary for this. It goes without saying that the discovery
of such storms, if indeed they exist, would be of great interest for the morphology
and theory of magnetic disturbances.
The examples given above show very plainly the extent to which the ideas of an
investigator about the morphology of a disturbance determine his theoretical views on
the physical explanation of the phenomenon.
Section 3. SD-Variations
Let us now discuss another regular part of the disturbed field, the SD-varia-
tions, whose existence was doubted by Nikollskiy. To study SD I used the same method
applied to Dst, namely, calculation of the variations for quiet intervals of disturbed
days. Here I obtained about the same results for middle-latitude and high-latitude
observatories as in calculating SD by conventional methods, i.e., SD = Sd - Sq. The
diurnal marches for the Sitka observatory presented in F1g.11 show that there is a
great resemblance between Sd - Sq and SI - Sq, except that the amplitudes of Sd - Sq
are greater than the amplitudes of SI. - Sq. The calculation of Sd - Sq for the low-
latitude station of Honolulu did not yield the expected results. In the low lati-
tudes, the Dst-variations are so great that statistical treatment of a very large
amount of material would be necessary in order to eliminate them, in spite of the
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�
�
fact that the number of quiet intervals on stormy days there is very great. The
quantity Sd - Sd was not calculated for the polar observatories, due to the lack of
the necessary number of magnetograms; however, a simple examination of the individual-
disturbed days is enough to show, as could hardly have been expected, that the ampli-
tude of the Sd - Sq -variations will decrease north of 600. On the other hand, it -
q
would appear that these variations will behave in the high latitudes in the same way
as SD, i.e., their intensity will sharply increase in the auroral zone. Figure 11
allowed me to conclude that the second regular part of the field of worldwide storms,
the disturbed diurnal variations, likewise has an existence quite as real a4 that of _
12001
Fig.11 - SD Variations of the Z-Component for Sitka Observatory
(Local Time)
Sd - S - - - Sd - Sq/
q
p(t)
the Oat-variations, being found in all cases where the field is free from polar dis-
turbances.
A second argument in favor of the existence of regular SD-variations, evidently
connected with the formation of a stable current system during worldwide storms, is
the repetition of the active periods of a storm on successive days, which is well
known to magnetologists. This repetition is manifected not only in the fact that the
disturbance increases at one and the same hour of the day, but also in the fact that
the main features and form of the fluctuations are sometimes repeated for several
days in succession. This phenomenon is easily explained under the assumption of a
current system encompassing the entire earth and fixed, if viewed from the sun. The�
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�
system exists for several days, at first developing and then weakening, repeating
the fluctuations at the very same hours of each day. The SD-current are apparently
weaker in the low latitudes and considerably more intense in the high ones.
Returning to Fig.11, we may say that the SD-variations of worldwide storms are
very similar to the time-dependence of the field of polar storms. For comparison, we
present in Fig.11 the diurnal variations of the Z component of the field of a typical
polar storm (taken from the vector chart of Fig.31) for the latitude (I) = 600. it will
be found that both curves, while differing somewhat in amplitude, have the same shape
and the same times of the extremes. Thus the currents of the SD-variations of world-
wide storms and the currents of the P-storms, when superimposed, intensify each other
without distorting each other.
Section 4. Division of the Field of Magnetic Storms
It follows from the above that the field of a worldwide magnetic storm may, in
my opinion, be separated into four component parts:
M. D.0 (0+ SDAf P (0+ Di.
The value of the different parts in high and low latitudes is not the same. The
part P(t) has a great weight (greater than the first terms) in the high latitudes,
while in the moderate and low latitude it is so small that here, without great error,
we may adopt the Chapman three-term equation.
SD+ Di
and calculate the regular parts of Dst and SD with conventional methods, by appropri-
ately averaging the available data for the mean hourly values of the magnetic ele-
ments. The value of Dm can serve as a good estimate of the order of Dst in these lat-
itudes; the SD-variations can be calculated as the difference Sd - Sq. Approaching
the auroral zone, all the weight of the terms P(t), SD (t), and Di increases so much
that it becomes difficult to separate the part of Dt by simple averaging, the more so
since the value of Dst in the H component decreases; although it does increase in the
Z component i1sti1l remains, in all probability, of the same order as in the temper-
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�
ate latitudes*. As will be seen later (cf.Chapter III), an attempt to calculate the:
1D5t of a polar observatory by the ordinary method is unsuccessful. The value of
Dm aHq - Hd in the polar latitude ceases to characterize the value of D8t; the pre-
dominance of negative polar storms has a strong influence on it. The Sd-variations '
. in the polar latitudes, as in the low latitudes, may be taken as to Sd - Sq, bearing!
in mind the fact that in this way wa are estimating both the regular part of the
worldwide storm and the part due to the superimposition of the polar disturbances.
The properties and features of the polar storms are more easily studied by con-
sidering the isolated polar storms encountered on days free of worldwide storms, as
has been done repeatedly by a number of authors.
The proposed division of the field of magnetic storms can be justified not only
from the morphological point of view, but from the genetic as well. The Dst-varia-
tions can be considered as the field of the equatorial current ring, the SD-varia-
tions as the field of the ionospheric currents encompassing the entire earth, and
the P-storms as the result of the invasion of the ionosphere in high latitudes by
corpuscles. For a worldwide storm, the presence of all three phenomena is charact-
eristic: the formation of a ring current, the formation of ionospheric currents,
and the deflection of the corpuscles toward the high latitudes. Penetration of the
corpuscles in the high latitudes always accompanies the formation of great iono-
spheric and extra-ionospheric current systems, but such penetration can also take
place without the formation of such systems. In such cases, only polar storms will
be observed.
* If we assume that the Dst-variations are really caused by the equatorial current
ring, whose field close to the earth's surface is almost uniform, then the value
of Z at the pole should be about equal to H at the equator. While the graph of
Zq - Zd (cf.Fig.10b) does not confirm this hypothesis, it still does not, in any
q
case, contradict it.
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1)
�
�
The above point of view on the classification and division of the field of mag- 7
natio storms was used by us as a foundatiOn for the workup and analysis of the mat-
erial on magnetic disturbances. The Dst-land SD-variations were isolated by statis-
tical methods from the data on worldwide Storms, and the three independent systems
of electric currents, those of the Dst- and SD-variations, and those of the P-storms,
were calculated. The electric currents of several individual polar and worldwide
storms were also studied, and their connection with the mean systems was shown.
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CHAPTER III
THE Dst -VARIATIONS
Section 1. The Starting Materials
�
�
To assure uniformity of the starting material, the observations at all observa-
tories were taken for one and the same interval of time, namely for 1931-1933.
There were two reasons for selecting these years: first, the largest number of data
have been published for 1931-1933; second, these years are years of minimum solar
activity. In years of high activity, the superimposition of one storm on another
makes it difficult to separate the storms and complicates any statistical investi-
gations.
For 1931-1933, I succeeded in collecting data of the hourly values of the mag-
netic elements for 66 observatories, whose names and coordinates are given in
Table 1. The Table shows that there are a sufficient number of stations located at
various latitudes in the eastern hemisphere. The number of stations in the western
hemisphere is definitely inadequate.
For 1931-1933 I selected 65 moderate and violent storms with amplitudes at
Slutsk ranging from 180 to 450 Y . It would have been desirable to determine the
time of the beginning of the storm separately for each observatory. However, the
lack of magnetograms from all observatories, that would be necessary for this,
forced me to assume that the storms begin simultaneously over the entire earth, and
to take the incipient moment according to the data of the Slutsk Observatory. A
comparison of the beginnings of the storms for several observatories showed that the
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e 1
�
�
No.
Observatory
�- -
(1,
.A.
IP
-
cp
X
,
-
1
Mule (Tn.)
880.0
00.0
00.0
76�.5
291�.1
- 19�.9
86�.9
2
Godhavn (God.)
79.0
32.5
- 17.5
69.2
306.5
- 11.2
78.2
3
Scoresby Sound (S.Z.)
75.8
81.8
-36.2
70.5
338.0
- 6.8
73.8
4
Angmassalik (Ang.)
74.2
52.7
- 22.5
65.6
322.4
-6.8
73.8
5
Sveagruvan (Sv.)
73 9
130.7
- 46.2
77.9
16.8
- 8.4
75.4
6
Chesterfield (Ch.)
73 5
324.0
1 14 9
63 3
269.3
-8.5
75.5
7
Tikhaya Bay (B.T.) Calm Hay
71.5
153.3
- 32.2
80.3
52.8
- 8.8
75.3
0
Bear Islands (M.O.)
71 l
124.5
- 37.9
74.5
19.2
-5.1
72.1
9
Juliaoenhaah (Yul.)
70.8
35.6
- 13.8
60 7
314.0
- 2.4
69.4
10
Fort Hoe (F.11.)
69.0
290 9
+ 24.1
62.8
243.9
-2.7
69.7
11
Point Barrow (P.B.)
60 6
241 2
+ 33.0
71.3
203.3
- 2.6
69.5
12
Tromso (Tr.)
67 1
116.7
- 30.8
69.7
18.9
+ 0.3
66.7
13
Chelyuskin (Chel.)
66.3
176.5
- 3 2
77.7
104.3
- 6 3
-73.3
14
Petsamo (Pet.)
64.9
125 8
- 27.6
63.5
31.2
0.0
67.0
15
Matochkin Shur (M,1.)
64 0
146.5
- 22.4
73.3
56.4
- 1.2
68.2
16
College, Fairbanks (K.F.)
64 5
255.4
+ 27.0
64 9
212.2
+ 2.0
65 0
17
Sodankyla (Sod.)
63 11
120 0
- 26.7
67.4
26 6
+ 2.4.
64.6
18
Dickson Island (Dik.)
63 0
161.5
- 12 8
73.5
80.4
- 1.0
- 68.0
19
Lerwick (Ler.)
62.5
88.6
- 23.6
60.1
358.8
+ 6.2
60.8
20
Kandalaksha (Kan.)
62.5
124.2
- 25.0
67.1
32 4
-
-
21
Domhas (Dom)
62 4
100.2
- 23.6
62.1
350.9
+ 6.5
61.5
22
Minuk (Min.)
61 8
301.0
+ 17.2
54.6
246.7
+ 3.8
63.2
23
Ucllen (Uel.)
61.8
235.9
+ 24.5
66.2
190.2
+ 4.4
62.6
24
Sitka (Si.)
60 0
275.4
+ 21.4
57.0
224.7
+ 5.5
61.5
25
Eskdalemuir (Esk.)
58 5
82.9
- 20 4
55.3
356.8
+10.5
56.5
26
Lovo (Lov.)
58 1
105 8
-22.1
59.4
17.8
+ 9.7
57.3
27
Slutsk (Si.)
56 0
116.3
- 20.6
59.9
30.5
10.2
56.8
28
Mule Skou (n.s.)
55 8
98.5
- 20 6
55.8
12.4
12.7
54.7
20
Agincourt (Azh.)
55.0
347.0
+ 3.8
43.8
280 7
11.5
55.5
30
Abinger (Al).)
55 0
83.3
- 18.4
51.2
359.6
14.8
52.2
31
de Iii! (D.B.)
53 8
89.6
- 18 9
52.1
5.2
15.4
51.6
32
Srednikan (Sred.)
53.2
210.5
+ 12 7
62.6
152.3
9.5
57.5
33
Moscow (Mos.)
52 2
120.3
- 17 0
55.5
37.3
14.3
52.7
34
Paris - Vol Joyeux (V.Zh.)
51 3
84.5
- 17 5
48.8
2.0
19.7
47.3
35
Yakutsk (Yak.)
51 0
193.8
+ 5.8
62.0
129.7
10.8
56.2
36
Svider (Sv.)
50 6
104.6
- 18.3
50.1
21.2
17.8
49.2
37
Cheltenham (Chelt.)
SO 1
350.5
4- 2 4
38 7
283.2
16.5
50.5
38
Kazan' (Kaz.)
49 3
130 4
- 19.7
55 8
48.8
15.9
51.1
39
Sverdlovsk (Sver.)
48 8
140.7
- 13.3
56 7
61 1
15.9
51.1
40
Zuy (Irkutsk) (Ir.)
41 0
174 4
- 1.8
52.5
104.0
18.6
48.4
41
San Fernando (S.Fer.)
41 0
71 3
- 13.6
36 S
353.8
24.8
42 2
42
Tucson (ruk.)
40 4
312 2
+ 10.1
32.2
249 2
24.6
42.4
43
South Sakhalin (royohara) (Toy.)
36 9
203.5
+ 6.7
47 0
142.8
22 4
44 6
44
Tbilisi (Th.)
36 7
122 1
- 13.2
42.1
44.7
29.7
37.3
45
Maytun (Mt.)
32 4
198 3
+ 4.9
43 2
132.3
27 2
39.8
46
Tashkent (rash.)
32 4
143.7
-9.0
41 3
69.3
31.6
35 4
47
San Juan (S.Zh.)
29 9
3.2
- 0 7
18.4
293.9
37.3
29.7
48
Tnoloyucan (Teo.)
29 6
327 0
+ 6 6
19 8
260.8
35.6
31.4
49
Helwan (Khel.)
27 2
106.4
- 12 7
29 9
31.3
40.0
27.0
50
Kakioka (Kak.)
26 0
206 0
+ 6.2
36.2
140.2
35.4
31 6
51
Honolulu (Con.)
21 1
266 5
+ 12 3
21 3
201.9
45.4
21.6
52
Zo-se (Z.Z.)
20 0
189.1
+ 2.1
31 3
121 0
42 7
21.1
53
Hong Kong (O.K.)
11.0
182.9
+ 0.6
22 4
114.0
49.7
17.3
54
Alibag (Bombay) (Born.)
9.5
143.6
- 7 2
18 6
72.9
54.8
12.2
55
Manilo (Aultipolo) (An.)
3 3
189 8
+ 2 0
14 6
121.2
57 8
9.2
56
Huancayo (Khuan.)
- 0 6
353.8
4 1 3
- 12.0
284 7
-
-
57
Elizabethville (Yel.)
- 12.7
94.0
+ 11.7
- 11.7
27 5
-
-
58
Apia (Ap,)
- 16 0
260 2
+ 11.7
- 13.8
188 2
-
-
59
Batavia (Bat.)
- 18 0
175.6
-0.9
-6 6
106 8
-
-
60
Pik'. (Pit.)
- 20.2
4.6
- 1 1
-31.7
296 1
-
-
61
Mauritius (May.)
- 26.6
122.4
- 10 3
--20 1
57 6
-
-
62
Cape Town (K.T.)
- 32 7
79.9
- 13 7
- 33.9
18.5
-
-
63
Wntheroo (Clot.)
- 41 8
185 6
+ 1.3
- 30 3
115 9
-
-
64
Toolangi (Tul.)
46 7
220.8
+ 9 5
- 37 5
145 5
-
-
65
Amberley (Amb.)
47 7
252 5
+ 15.1
43 5
172 7
_
66
South Orkney Islands (01-k.)
SO 0
10 0
- 7.2
-60 8
315 1
-
-
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0 _
error involved in this assumption is not greater than t2 hours, since in the major-
ity of cases..the.storms_begin_simultaneously..with .an.sac curacy. of 1,hour.._,The
�
�
-Illation of Dst was performed by the method proposed in his day by Moos. The hourly
-Ivalues of the magnetic elements were enteled for each storm on a separate line, and
-ithe resultant Table was averaged by columns corresponding to the hours of the time,
10 i
11 reckoned from the beginning of the storm. This averaging eliminates the irregular
12_1
-: fluctuations and the systematic SD-variations, provided only that the beginnings of
r
the storms are distributed with sufficien1 regularity among the hours of the, day.
i
, I
The distribution of the 65 storms selected by me revealed a marked predominance of.
storms beginning in the morning hours. Ii view of this fact, I excluded 11 storms
Ell
beginning a 4-7h Universal Time from thos selected by me. The final list of the
-154 storms, used as the basis for the calculations, is given in Table 2.
The Dst-variations of the three elements were calculated for 34 hours: from the
4th hour before the onset of the storm to the 30th hour after the onset. The calcu-
lation of the Dst of the declination, or 4f the Y-component, showed that neither in
the high nor in the low latitudes was it possible to discern any regularity in the
variations of these elements during the course of the storm. Since the previous lit-
erature also contained references to the absence of distinct Dst-variations of the
declination, the data on the accumulation were not included in the consideration,
and I assumed that the horizontal component of the field strength of Dst lies rough-
ly. (at least in the low and middle latitudes) in the plane of the magnetic meridian.
The Dst-variations of the H and Z components for the individual observatories
are shown in Figs.12 and 13. The time indicated on the diagram is the time reckoned
from the onset of the storm; the observatories are located in the order of decreas-
ing geographic latitudes. Our attention is struck by the mobility and irregularity
of many curves, which is particularly marked on comparison of Figs. 12 and 13 with
the well-known Dst graphs of Chapman (Bib1.40). An explanation of the presence of
random fluctuations on the graphs of Figs.12 and 13 might in all probability be
�
�
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-
!
�
�
2 �
* Table
.__
LietTof ii:cidei,aie and Grt Magnetic
2
Sri for 101:1034 - -
..,
No.
No.
No.
-iiit--0iiriiii
_
No,
_ _

of
Date
Onset
of
bate
Onset
of
of
Date
Onset
Storm
Storm
Storm
Storm
1931 r
43
5/VIII
4 h
16/I
3 h
14
3/II
2 h
29
15/X
4 h
44
8/IX
14
24/11
0
15
3/111
12
30
20/X
6
45
7/X1
11
3
1/VI
11
16
10/III
6
31
15/11
13
46
9/X11
9
4
20/VILE
1
17
28/111
5
32
14/X11
7
5
30/1X
18
18
I/IV
10
6
2/X
5
19
13/IV
8
7
12/X
9
20
22/IV
7
1933 r
1934
8
5/XI
13
21
23/IV
2
;33
19/1
10
47
I/I
4 h
9
8/11
1
22
25/IV
10
34
19/11
7
48
8/11
13
10
26/X1
7
23
27/IV
10
35
20/11
4
49
4/111
10
U
2/XII
5 h
24
2/V
16
36
21/II
8
50
30/III
15
25
4/V
13
37
19/111
11
51
29/VII
23
26
29/V
7
38
22/111
21
52
24/IX
2
1932 r
27
26/VIII
8
39
24/111
0
53
7/11
11
28
5/IX
22
40
17/IV
6
54
7/XII
16
12
25/I
5h
41
12/VI
16
13
27/I
4
42
23/VII J
6
explained by the insufficient experimental material and the absence of any smoothing
,process. A consideration of Dst at the polar observatories ( ' 650) shows that
the averaging of the data for 54 storms eliminated neither the irregular part of the
field nor the SD-variations. The influence of the SD-variations is manifested in
the marked diurnal periodicity of the curves presented, which is particularly strong
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for the observatories at Dickson Island, Matochkin Shar, Tromso, Petsamo, and Sodan-
kYla. Thus, the curves presented confirm the assertion made in the preceding Chap-
ter to the effect that the Dst-variations in the polar regions cannot be calculated
Ii **** sliztoinie **14i
I I II II I s SI
�
�
�
'FLO 11111111/
Fig.12 - Dst-Variations (Polar Ob-
servatories) *
SL
Sver.
Kaz..
Mos.
Min.
V 1.
D. B.
D. B.
Toy.
Azh.
Esk.
Chet.
S. Fer.
KA.
Ca .1( �
44 .4
II
th tok i4b2ah 4 it oh
I
1 X.
o----\VArNpr.
�
0-
N..
I}-
�
(ion u-
Ths
Born U
Bat. 0--
Ye).
May. 0�
vot.
KT. �-
Tut.
\
-
th 1111 tie .17
����������
--------------
Fig.13 - Dst.Sariations (Middle-Lati-
tude Observatories)
* Translator's note: For meaning of abbreviations in diagram, see Table 1.
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by the Moos-Chapman method. In the polar regions, the irregular fluctuations(Di), '
the Polar storms (P), and the SD-variations are so great that a simple averaging of
the material does not eliminate them. In view of this fact it appeared to be inad-
visable to use the date of the polar observatories given in F1g.12 in calculating
the potential function of the Dst field, characterizing the course of the disturb-
ance over the entire earth.
A consideration of the Dst-variations of the H and Z components of the middle-
�
latitude observatories ( 4 62�) allows
I I $
st:
I
.P6
lI
....-"C\�""*"'"."�"Iv--"Pa-V-"*"
-46:6 f\i""
Fig.14 - The Dst-Variations
(After Vestine)
us to draw the following conclusions:
1. The principal feature of Dst is
the lowering of the H component which is
well perceptible at all latitudes, and is
less in value than the increase in the Z
component.
2. The Dst-variations of the H compon-
ent are so similar in the northern and
southern hemispheres, both in form and in
sign, that it may be assumed that the dis-
tribution of H is symmetric with respect
to the geomagnetic equator. The distribu-
tion of the Z component, on the other hand,
is asymmetric with respect to the equator.
3. The Dst-variations of observatories 14ring at the same geomagnetic latitudes,
on the whole, resemble one another. Thus, it may be assumed that, in first approx-
imation, the Dst field depends on two arguments: the geomagnetic latitude 0 andli
.the time elapsed from the beginning of the storm.
4. A more detailed consideration of Fig.13 shows that the Dst-variations of the
observatories of the western hemisphere differ from those of the eastern hemisphere.
A difference is also noted between the observatories of the same hemisphere (for
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r.r�Zt�Pa���......,,�������..... � *�*..
exOtpler:Irkutsk-de Hilt, OapOown400latigi, etc.). It follows from the examples,
--given:that:the_fielCof_Dst_likewise-..cont' neLlongitudinal_terms_whichs_at_one_time
_, were found in the S -variations (Hib1.9).
6
,
vA�������...4110...0.P.M
The first phase,of the.storm (increa es Of the H component), noted by many in-
vestigators, was found to be vague on ma4 curves of Fig.13. The possibility is not
/
excluded that the absence of the first ph se is connected with a certain inaccuracy
in the determination of the time of onset
of the storm, which might occur in cases
when the storms begin gradually. To verify this assumption, I considered the data
on the storms with sudden onsets (So). The Dst-yariations obtained by averaging
- 13 So storms during the same interval of ime, are given in Fig.14, constructed from
materials furnished by Vestine (Hib1.62). Each curve of Fig.14 represents the mean
2'
for several observatories located at the orresponding latitude. A comparison of
--1Figs.13 and 14 shows the great regularity in the distribution of the curves of Fig.1
't
I
and the presence of a distinct initial ph se in them. The remaining conclusions enu.;
--merated by us with respect to the form ald distribution of the Dst-variations are
confirmed by Fig.14.
4 Section 2. Spherical Analysis of the Del 'Variations
1
In all possible types of calculation,of a theoretical nature it is more conven-
ient to operate not with the observed elements of the magnetic field H, DI Z, but
�
-with rectangular components. The geomagnetic components of the field of variations,
, XII V, v are connected with the variatiOns of D, H, Z by the following relations: 1
� X' H cos (DI � tp) 111 sin (D. � sin 1' D' , (1)
Y' = H sin (D0 � + H. cos (De � sin l' D'
Z' Z, (2)
1
-1where Do and Ho are the mean annual value of these elements, and y is the angle
'between the geographical meridian of a gi*en place.
In our case (absence of substantial and regular fluctuations in D), the second ,
,terms of eqs.(1) and (2) were rejected and it was shown that the variations of Y1
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18_
2, )
�
�
_
--
0
1:7�� noftwobsea..4
are ema n comparison-with Xl. Thus th reotilarcponeflt5rofithe.Det fie
-
were reduced to a calculation of k by th H cos 00 T the'varia-
v
�
�tiond of,X, so obtained Proving to be very similar to those of the,H component.
b
���
$1;
Ie.
4.�
� 71
4*
� �
� �
0
I.
oth
0
2o0
0
I II� I
O^ I 10
Fig.15 - Latitudinal Distribution of H
x � Northern hemisphere; o � Southe
�
1-�������1
10'
.--.........................r ...
SO- ' ... �� 444 �
I;
48
411
.10
and Z Components of the DA-Variations
n hemisphere; not taken into account
in calculating the mean.
11 Figure 15 gives graphs of the depend nce of XI and Z on if. for a few stormtimes
The data of the southern and northern hemispheres are presented together, allowing
,for the symmetry of the H component and ti e asymmetry of the Z component. The Dst-
,
variations of the individual observatoriegi (Fig.13) were first averaged by groups in
accordance with the value of 4, I and the clean data were then entered in Fig.15. The
dispersion of the points on both graphs ig relatively low, and, in particular, there
.is absolutely no detectable systematic di;ference between the data of the northern
I i
4and southern hemispheres, i
Since we abandoned the use of the Ds -variations calculated from the observa-
tions for the polar observatories, the culives of Xt and Z were extrapolated to the
I
.high latitudes, and, in accordance with tile considerations made in Chapter II, it
was assumed that, at the pole, XI � 0 and 'Z = XI equiv. The comparatively simple
form of the dependence of XI and Z on 4) allowed U8 to use the method of spherical
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�
analysis for the analytic representation of the field.
Neglecting the longitude-dependence of Dst, the potential of the field may be
represented, for a fixed instant of time 1, by a series of Legendre polynomials:
V� RE1 n(Rr )11 "
(3)
where, as usual, the terms En are responsible for that part of the field due to
sources external to the earth's surface, while the terms In are responsible for the
internal part of the field.
On the earth's surface, r = RI and
V= i? ICA (cos (i),
where
gn = En+ In.
(4)
(5)
Hence it follows that the rectangular components of the field in geomagnetic
coordinates, for r = R, will be as follows:
where
, 1 ()V dPn(cos 0)
X = =-- gndO
,
d V xi
Z (Tr- j (cos 0),
j n nE n � (n+ I) In.
( 6 )
(7)
(8)
The identity Y 0 completely corresponds to the absence of systematic Dst-
variations noted by us in the D and Y elements. The calculation of the potential of
the Dst field was performed independently for 56 moderate storms (analysis I) and for
13 storms with sudden onset (analysis II). The method of calculation in both cases
was one and the same. To find the coefficients of gn on the basis of the graphs of
the dependence XI ) (the heavy curve in Fig.15), I calculated the curves F (0) =
=X' sin e which, in turn, were represented by Fourier series in 0
F (6) sin O.
(9)
On the basis of the coefficients Olt ) I used the Schuster-Schmidt formulas
(Bib1.61 9) for calculating the constants gn, whose values are given in Tables 3
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and 4. The constants in (also see Tables 3 and 4) were found by the Schuster form-
ula by direct expansion of Z into a Fourier series in 0
o
�
*
Z . Ipzk sin kU.
k
Table 3
Analysis I
(10)
_
T
a
0
4
Ji
1
4 h
24.93
�1.23
3.19
6.70
�5.11
0.23
12
21.74
�3.56
0.79
1.36
�6.21
1.79
20
23.14
-0.61
-0.14
0.84
-4.65
2.38
28
27.80
-3.16
0.16
6.44
-4.49
0.63
,
The coefficients of the expansion of the potential into series of spherical
harmonics were repeatedly calculated by the Schuster method (Bib1.6, 9, 15), but
nevertheless the application of this method requires certain explanations. The
Schuster method is based on the replacement in the expression
of the series
by the series
i
or
'Si 'S.1(g", cos m). + h: sin mX) =
"
.6:ar d�wi
n m
..1 9
. N I cos mk zd gh"PE: + sin mX 1 hin"Pd
�...i
fft n==m
a ,.. in
km (6)=1 g:F07.4 m 1m (6). N h: Ph"
A
?I
km (0) = Icc, cos el; 10 (8). Ia, cos s8
s s
km (0) -= 'SIP, sin se; /". (0) = I b. sin se
s - �
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and on the calculation of g and h in terms of a ' a8 or 0 bs� For m = 2t,
. 8
Schuster recommends using eq.(13), and for m = 2t + 1, eq.(12). In these cases, the
equations connecting g, h, c, a or 0, b, are rather simple and convenient for cal-
culation.
Table 4
�
�
�
Analysis II
T
Y
gl
gic
_
1 h
-33.3
-0.54
1.15
-0.98
-6.19
-
lo
44.1
-2.05
-0.63
3.20
-15.5
-6.6
20
81.8
-0.90
-1.55
-1.20
-35.80
6.6
30
69.3
-0.66
-1.32
15.8
-12.84
-0.7
40
47.8
-0.54
-2.01
10.7
-11.41
2.46
60
32.8
-1.63
-1.24
9.36
- 9.92
1.10
However, the representation of the function km(0 ) (m being odd) known in the
interval from 0 to It, by the series 11s sin sO imposes on it the conditions of
asymmetry with respect to 0 = it and of its vanishing at the points 0 = 0 and 0 = it.
If the empirical function being studied satisfies these conditions, then the appli-
cation of the Schuster method is theoretically irreproachable, and in practice
assures high accuracy in the computation of the coefficients g, h. if, however,
km( 0) differs substantially from 0 at the poles, then the use of the Schuster method
distorts the distribution of the function in the polar caps and may introduce sub-
stantial errors. It follows that an application of this method to the calculation
of the coefficients of an expansion in spherical harmonics of the Z component of the
earth's permanent magnetic field, of the Dst field, or of the noncyclic variations
(i.e., of functions in the representation of which the terms P11 p3, etc., play the
principal role) is not completely successful, and, in any case, should be accompanied
by an estimate of the error to be expected. Accordingly, the calculation of the co-
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efficien'ts jn in eq.(7) for one instant of time (T = 12 hours) were calculated both
by the Schuster method and the method of least squares. The good agreement between
the results of the two methods (discrepancy of the order of 1%) and also a comparisor
of the initial curves of Z(0) with those calculated by eq.(7) (cf.Table 5) showed
that we could calculate jn by the Schuster method without great danger. Table 5
shows that the deviation of the calculated curve of Z(0) from the empirical curve is
significant only in the polar regions, where, all the some, we do not know the true
distribution of the field.
It follows from the symmetry of XI and the asymmetry of Z with respect to the
equator (0 = it /2) that, in the expression for the potential, eq.(4) must contain
only odd polynomials.
The numerical values of the constants g and j in analyses I and II (Tables 3, 4)
differ somewhat but are still in good agreement. In both cases, the first harmonic
has the greatest weight, having a coefficient gl of the order of 20-30 Y in the first
case and 50-80 y in the second. The larger values of the coefficients in analysis 1I
may possibly explained by the fact that almost all the storms making up the 13 Sc-
storms selected were great storms, while most of the storms among the 54 storms of
analysis I belong to the category of moderate storms. The coefficients gl calculated
for Dm by lqcNish and for Dst by Chapman and Whitehead (Bib1.40), lie within these
same limits (30-50 Y). The sign of gl is everywhere positive, except for the first
hour in analysis II, corresponding to the first phase of a magnetic storm, the sign
of the coefficient of the third harmonic g3 is negative, while the values of E5 in-
clude both positive and negative quantities. Of the coefficients representing the
expansion of L, the greatest is j31 characterizing the stable negative values.
It will be seen from a comparison of the coefficients g and j at different in-
stants of time that the storm reaches jts maximum development at the end of the
first day or the beginning of the second. The calculation by eqs.(5) and(8) of the
coefficients of the internal and external fields of E and I separately gave the re-
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suits shown in Table 6. In all cases, except for one, the absolute value of the ex-
ternal field is greater than that of the internal field.
Table 5
�
�
�
Dst-Variations of the Z Components, in
I = 4 h
1 = 20 h
Observed
Calculated
Observed
CalcuLated
700
3
4
-2
-2
50
7
8
-2 �
-3 .
30
5
4
5
7
10
3
3
2
3
The ratio I/E (Table 7) is very stable fur the first harmonic (mean value 0.40�
� 0.07 and 0.39 � 0.10). dithin wide limits, the ratiu fluctuates for the third
harmonic (- 0.17 � 0.12 and - 0.61 � 0.18) and is not very regular fur the fifth
Table 6
T
fY
1
LY
3
0
5
1Y
1
1Y
3
1Y
5
4 h
18.8
-1.4
1.8
6.1
0.2
1.4
12
14.9
-1.8
0.6
6.8
0.2
0.2
20
15.7
-1.0
0.2
7.4
0.4
-0.3
28
20.7
-1.6
0.2
7.1
0.0
0.0
1
-22.2
-1.2
-
-11.1
0.7
_
10
30.5
-3.4
-
13.6
1.3
-
20
54.1
-5.6
-
27.7
4.8
-
30
51.4
-2.2
-
17.8
1.7
-
40
35.4
-1.9
-
12.4
1.4
_
60
25.0
-2.3
-
4.5
0.7
-
_
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harmonic. The value of I5/E5 for I = 20 hours in absolute magnitude is > 1 and dif-
�
�
�
fers in sign from the corresponding ratio for other instants of time. this increa6e
of the scatter of 1/E for P3, and especially for P5, finds its natural explanation
in the fact that the absolute magnitude of these harmonics is considerably smaller,
and consequently, the relative errors are larger, than with the first harmonic.
The systematic change of sign of the ratio is a point of interest
1, I 15
->0; '0,
and the very good agreement of the results obtained in analyses I and II will be
noted. Table 7 also gives other data known in the literature
the perturbation field into an external and an internal part,
good agreement with our results. Phe mean values of 0.39 and
on the separation of
which are likewise in
0.40 obtained by us
for gp 1.)3t, agree exactly with the radio calculated by I,.cNish for Dm If, further-
more, we bear in atind that 11/E1 for Dst (according to the data by Chapman and White-
heLd) varies within the range of 0.36-0.42 and, for the nancyclic variations, is
equal to 0.30 (Ncilish) or 0.28 (Dolginov), then it may be considered as proved that
the external part of the first harmonic is equal, on the average, to 0.30-0.40 of
the value of the external part. Phe negative value of I3/E3 is confirmed by the
data of Mellish for Dm, and in part by the data of Chapman and .Thitehead for Dst.
rile numerical values of I/E will be discussed in greater detail below, in Chapter X,
devoted to the discussion of the inductive origin of the internal part of the fields
of variations.
Section 3. Ionospheric System of Currents of the D,t-Variations
It was stated above (Chapter II.) that two versions of the explanation for the
external part of the list-variations were proposed: one based on an ionospheric sys-
tem of currents, the other on an extra-ionospheric ring current. .ie used the data
of our anaLysis to calculate both these proposed current systems.
Assume that the magnetic field whose potential on the earth's surface is repro-
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sented by the series of spherical functions
11== P (g: cos m),-1-- it: sin m),) P,
n Ns
is caused by a current layer located on a, sphere having a radius of a(a R). Then
Table 7
�
�
Mean
Men
Dst
finabisi3
Dst
Anatysis 11
Dst acc. to Chapman
and Whitehead
D acc to Mc Ni5h . .
m �
nch acc..-to %Ai:141ov �
nth J 1923
Ace. to Mc Nishl 1926
Hots. nch a Non cyclic.
S
/1
13
I 3
17
Ei
E3
Es
E7
�
4 .
0,32
-Ci,16
0,78
12
0,46
-0,11
0,33
20
0,47
-0,40
-1,50
28
0,34
0,00
0,00
0,40
-0,17
1
0,50
-0,58
10
0,45
-0,38
20
0,51
-0,86
30
0,35
-0,77
40
0,35
-0,75
60
0,18
-0,34
0,39
-0,61
1
-5/-11
-0,5/-0,5
-1/0
3
-2/-6
-1/1
-2,5/-1,5
6
3/11
-2/2
-3,0/-1,0
12
10/26
1/1
-1/0
18
10/28
0/0
-1/0
24
11/26
-2/-1
0/-0,5
so
9/24
0/1
-1/-1
36
9/23
1/-1
0/-1
42
7/21
0/1
-1/-1
48
7/20
1/-1
-0,5/-0,5
0,39
-1,12
0,27
-0,80
0,28
0,20
0,86
1,46
0,23
0,37
JAY;ations
the distribution of the current function in the layer can be calculated by the
Bidlingmayer formula
1 10 IC;' \--1 2 n 1 (ay: A
n ) cos MX + X;111 sin mX) P;,"i.
n m
In our case
10 Nyi+Inn E. p A
4r. Ailmi R n cA42
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Since the most probable region of concentration of the currents responsible for
the magnetic disturbances is the F2 layer of the ionosphere, we assumed h = 300 km
and calculated, from the coefficients En Of analysis I, the current density for T
�
�
�
equal to 4, 12, 20, 28 hours.
As an example, Fig.16 represents the current systems for T equal to 12 and 28
hours. Since the potential of the Dst field is represented only by zonal harmonics,
-----
2S'
I- - - - - - -
Fig.16 - Electric Currents of the Dst-Variations; a Current of 20,000 amp
Flows Between Two Adjacent Lines
Positive values of current function; - - - Negative values
it is natural that the lines of current shown in the diagram should be parallel
circles. Since only the odd polynomials (P1, P3, P5) entered the expression for the
potential, it follows that the configuration and intensity of the currents in the
northern and southern hemispheres are identical, but that the sign of the current
function is different. In the northern hemisphere, V > 0 and I < 0 ( the lines of
current are given by broken lines) while in the southern hemisphere V < 0 and I > 0
(solid current lines). The Chapman current system (Fi41;.4a) does not allow for the
change in sign of the current function on crossing the equator, in view of which
fact, the current systems in Figs.4a and Fig.16 differ in their outward
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�
�
forms*.
The lines of currents in Fig.16 are so drawn that a current of 20,000 amp flows
between two adjacent lines. The intensity of the currents in the two systems is
about the same. The total value of the current flowing from east to west between
the pole and the equator is equal to 180,000 (for the system constructed by us). The
DI
current density p =7;-= 0.0002 amp/cm. The direction of the current in Fig.16 is
determined according to the rule that current flows around Imin clockwise and around
Imax counterclockwise. Thus in both hemispheres the current flows westerly (luring
the main phase of a storm.
A comparison of the current systems (Fips.4a and 16) will show the increased
density of the current lines in the polar regions in the Chapman current system, cor-
responding to the intensification postulated by him for the Dst field in the high
latitudes. This densification of the current lines is absent from the systems con-
structed by us. Conversely, a certain densification of the lines in the equatorial
regions can be noted, which expresses the well-known fact that the amplitude of Dst
increases in the low latitudes. The current density varies from P= 0.0001 amp/cm
at latitudes (I, from 50 to 600, to p = 0.0003 amp/cm near the equator. A comparison
of the current calculated for 12 and 28 hours shows that during a storm the config-
uration of the current system hardly changes and that only its intensity varies.
Only in the prolonpation of the first phase of the storm (T = 1 hour in analysis II)
is the direction of the currents opposite (from west to east). rhe systems of Dst
curves in Fig.16 correspond to a mean decrease of H in the temperate latitudes, by
40-50 Y. During certain storms, this decrease reaches 1000 Y, so that the intensity
of the currents equivalent to these storms should increase tJ 3-4 x 106 amp, and the-
density of the current should be p = 0.0004 amp/cm.
* The figure of the Dst-currents given in Nitre's monograph (Hib1.50), also shows
that the current function is of opposite sign in different hemispheres.
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3ection 4. The Equatorial Current Ring
�
�
�
Leaving the discussion of the question as to the actual existence of the re-
sultant system for later (cf.Chapter 1/111), let us now turn to a calculation of the
equatorial current ring, which presents an alternate explanation for the Dst-varia-
tions of the magnetic elements. As is generally known, the potential of the magnet-
ic field of a linear ring current whose center lies on the axis 0 = 0, may be repre-
sented by the following series of spherical functions:
VP - 2Tri I 1 � cos bo -H1 � cos290) ..4.\-1 In P� (cos 0) pn' (cos Bo) (11.
there i denotes the current s trencth in the ring, 00and a are the polar distance.
and radius of the ring, respectively, while it and 0 are spherical coordinates of the
point P. If the ring lies in the plane U = 900 (the plane of the equator), then cos
= u and
Vp Pfl(cosO)P�(0)(4!-)ni.
It
(15)
confining our3elves to the first three terms of the sum and substituting numer-
ical values of P11' (0) in e.(15), lie have
V 1,- Pi� 3- (21)8 3 P15
o \ (�:y P, I �
2 / a
(151)
Let us likewise confine ourselves to three terms in the expression for the ex-
Lerna I. part u C the De L po Len Li al. For the earth's surface (r ,Z), we have
V1, R 1E E1'3 +
(16)
Equating the potential Ve, calculated fivm the observations, to the potential
of the magnetic field of the ring, an equation will be obtained by which the param-
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eters of the ring can be evaluated. Equating eqs.(151) and (16), we have *
�
�
�
RE' =-- 2111--aR--
RE3 =- � 2Tri (If
RE, 21d )5
Combining eqs.(17) pairwise, we obtain the following three equations:
Ei . (�}' _5E5 (IV
\RI 4 E5 \R ) 8 E5
(17)
(18)
which lead to the numerical values of a/R given in Table 8. As will be seen from
the Table, the values of a/R fluctuate within
lations of a/R on the basis of E3/E5 in E1/E5
the radius of the ring during the development
relatively narrow limits. The calcu-
indicate the systematic increase of
of a storm. But the data for E1/E3,
which should be most trustworthy of all, do not display this increase.
ue a = 3.8R � 0.8R is in good agreement
Kalinin that have been discussed above.
ical data from the field of terrestrial
The mean val-
with the views of Chapman,-Forbush, and
Thus both theoretical arguments and empir-
magnetism and cosmic rays lead to a magnitude
--
of the ring of the order of 3-5 earth radii. It goes without saying that the ring
may be considerably larger than this during individual storms, but all the same
Stoermerls hypothesis of a rind with a radius of several hundred earth-radii must
be rejected. The current strength in the ring corresponding to the Dst-variation
of 56 moderate storms is equal to
aE,
1-=--- =----7 X 106A,
27r
* The term 2 rt i in eq.(151) denotes
entire surface of the earth. There
determines the field potential with
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is no analogous term in eq.(16), since eq.(16)
accuracy to a constant.
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and that corresponding to 13 Sc storms, equal to i = 20 x 105 amp. This estimate,
too, is in good agreement with the ideas of Chapman and Ferraro on the current ring.:
Table 8
�
�
-L-
E,
--,4-
Es
1.13
_LE
Mean
,
-1"-- 5
E5
4 Hours
4.5
-
2.1
3.3
12
3.6
2.0
2.7
2.8
Analysis I
20
5.0
2.5
3.6
3.7
28
4.5
3.3
3.8
3.9
Mean
4.4
2.6
3.1
3.4 � 0.8
1 Ifour
-
-
_
,
-
10
3.8
-
-
-
20
3.8
_
_
_
Analysis II
30
5.9
-
-
-
40
5.2
-
-
-
60
4.0
-
-
-
Mean
4.6 � 1.0
_
_
_
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CHAPTER IV
CALCULATIOU OF ELECTRIC CHRRENT.3 OY ['HE bdimiou oF SURFACE :INTEGRALS
Section 1. The Vestine Lethod of Jeparating the Observed Field into
an External and an Internal Part
�
�
Spherical analysis, applied by us in the preceding Chapter to the study of the
field of the Dst-variations, was long the only method for calculating the potential
from the magnetic elements observed at a number of points of the earth's surface.
It has been repeatedly used with great success in the representation of the perman-
ent field and the S variation, and has allowed the solution of a number of major
problems of the nature and structure of these fields. It has also been used in con-
sidering the secular and annual variations, and, as we have seen above, of certain
parts of the field of variations: Dst' Dm, and nch. Uut the use of spherical anal-
ysis is limited by the requirement that the field studied must possess spherical sym-
metry and that it can be successfully represented by the first few terms of the
series. If, however, the field has a rather complex structure and requires a large
number of terms for its representation, then the labor needed in calculating the co-
efficients is immeasurably increased, and the series so obtained ceases to be con-
venient for various practical or theoretical applications. Accordingly, the spher-
ical analysis of the SD-variations, which characterize a complex geographical distri-
bution, would seem a 212211 to be doomed to fail, and Chapman, Vestine, and other
authors who have studied SD, have abstained from any analytic representation of the
field at all. In 1941, Vestine (81b1.57a, b) proposed a new method of mathematical
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�
�
�
analysis which, according to the author's idea, was to replace spherical analysis in
the case of rather complex fields. This method, based on the representation of the
potential of the field by the aid of surface integrals, allows a separation of the
potential into a part of internal origin and one of external origin, from the com-
ponents of the field as observed on the surface of the sphere. Since it imposes no
restrictions whatever on the configuration of the field, I decided to apply this
method to the calculation of the potential of the SD-variations. For the purpose of
our work, however, as for many questions of geomagnetism, it is necessary not only
to separate the field into an external and an internal part, but also to calculate
the electric currents whose field is eluivalent to the observed field. The calcula-
tions performed by us showed that this problem, too, is successfully solved by the
aid of surface integrals.
Since the method of surface integrals is here used in geomagnetic practice for
the first time*, its mathematical foundations and practical methods will be discussed
in the present Chapter, while the description of thu calculations of the currents of
the 3D-variat10n5 will be reserved for the next Chapter.
The theory of the method is very simple. Let the volume v he surrounded by a
closed surface 3, and let there be, both within and without the surface 3, sources
exciting the magnetic field. If U and V are functions with continuous first deriva-
tives in the region v and on the surface 3, and continuous second derivatives in the
volume v, then Green's fundamental theorem indicates that
f (UAW � VAU)dv. f (ug_1/._ v ands
On , (1)
* in Vestine's note (Bib1.57b) the calculation of the potential of the geomagnetic
field at one instant of time is riven as Ln example, anti the work by VesLine and
Davies (bibl.61) on the interpretation of magnetic anomalies contains several form-
ulas based on the solution of two-dimensional problems by the aid of surface integrals.
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_!wilere n denotes the direction of the external normal. Let us assume that U = hr .4-
s (r = distance from a fixed point P outside S to the variable point Mo in v or on S)
and
f�
�
�
V= Ve4 VI,
(2)
,where Ve is the potential of the field ofthe sources external with respect to So and
:Vi is the potential of the field of sour* internal with respect to S; we then have
a!
( 1
� r
� V r ds.
-cirt
For any point of the volume v
( R i = density of the internal magnetic masses). Consequently, the left side of
eq. (11 ) gives
r I
7 e V dv = � dv � 47r V i;
and the potential at the external point Pe of the field of internal sources yields
a �)
t f ("all v r ds
V 4n r an an
(3)
By similar reasoning we get the result that the potential at the internal point
Pi of the field of external sources reads as follows:
a)
f V
r(ava h v_ = _ ds.
dn
(4)
Let the points Pe and Pi be located on the external and internal normals to S
passing through the point of the surface 13, where both and
Pi
. 1 . 1 '3N,
Then, taking ds as the potential of a single layer of the density
411 r 'an
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�
�
Z I
. Z1/ 1 r r --
- 1/4 TI: ) and----J V� de as the potential of a double layer of the den=-_.
4n 'an
1 _ _---
sity p . v, and allowing for the known properties of the potentials of single and;
4n -
double layers, we get the result that
V,, 1p_
2r-ds+Vipiids+27tpd=
a--
av I al
Tw 7 Ft ds+I V ds Ve ,
a �1
f -a-- ds �[f ds �
/. al
tf 1 d V d 1
4-1-c- 7 -an �
4 , V -,T;L: ds+ Vp
(5)
(6)
where pi. and P_ denotes that the approach to the point was from the side of the ex-
ternal and internal normals. Hence,
ilf(tav a
-177)71�V-ir ds.
(7)
Knowing the distribution of the surface S of the total potential V and its nor-
mal derivative 'a n, Ve - Vi may be calculated for any point of the surface; then,
by combining eqs. (2) and (7), the value of Ve and Vi can be separately determined.
It must be noted, however, that the potential Vo of any uniform double layer of
a density of Po, located on the closed surface S, equals zero outside the surface
and -4 + 0 inside it. For this reason, if, to the postulated double layer with a
density of 1/4 it V, we add a layer of uniform density po = -V0/4n , then ,eq. (3) will
remain without change, while eq. (4) will take the form
a-1
/ [1 d V
V 7 (V � ds+ V.,
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whence I
�
il
[1 av a-.
Velp_-= ;Ft 7 Tr �(V� Vo) ds Vo.
Instead of eq. (5) we will now have
1 la I 1 aV a1 7
VIIP+= 47t 7 an ( V� Vo) ds+
and, consequently,
�
1 )(11 [1 aV a1 r
� � (V � Vo)� ds Vo.
2n . r an an
(9)
(10)
It follows from eqs. (9) � (11) that, if the potential V on the surface 3 is
known only with an "curacy to an additive constant" then the values of Ve
1/1 and
lie may be l'ourici only with an "curacy to constant) while the values of Vi will be
calculated exactly. Besides the above general formulas, Vestine also gave formulas
applicable to cases when the surface 3 is a sphere or a plane. In spherical coordin�
ates with the pole coinciding with the point P (cf.Pig.170), the distance between the
points P end M (rOm ) is equal to
or
r 2R sin �e = 2R sin fp,
2
01
sin 4, 1
� � C = �
ri 4RI sin 4, �
Denoting V/ n by Z, let us now transform eq. (7) in to
2s 2
I (V -F2RZ)cos t dt
8' 8'
2s r
1
g-t f f (V � Vo+ 2RZ) COS tio cl+
6 o
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if the value of V on the sphere is known only with an accuracy to the constant Vo.
It was eq. (12) that I used to separate the potential of the So-variations into
an external and an internal part.
�
�
�
Fig.17
The solution of the two-dimensional problem leads to still simpler formulas.
In cylindrical coordinates r, z, whose origin is place at the point PI PM = r, and
i.e.,
co 2n , co 2n
a�
1
V -a r dr di) _ Z dr dtp, (10
0 ;
to find the difference of the external and internal potentials, it is suffic-
ient to know the values on the plane of the L-component of the field.
section 2. Practical Methods of Calculating the External and Internal Potentials
The fundamental difficulty in performing practical calculations of the differ-
ence Ile V1 by eq. (13) is that it is given in coordinates connected with the posi-
tion of the point 13, for which we seek the value of Ve - V. The transformation of
the equation to any fixed coordinate at all (for instance, geographic or geomagnetic)
by means of the usual formulas for the transformation of coordinates, leads to a
complex expression Inconvenient for mass calculations. In view of this fact I adop-
ted the following technique:
If we denote by V and 2- the mean values of V and G on the circle 0C latitude
T = const, then eq, (12) is transformed into
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�
�
17
In order to calculate the integral of eq.(15), we must find, for each point P
on the surface of the sphere, the mean values 2 and V along the circles of latitude
'(P being taken as the pole of the coordinate system). For this purpose, the formu-
las of transition from one system of spherical coordinates (fixed pole) to another
(with the pole at P) were used for preparing overlays
on which the lines W = const were plotted. The formu-
las for calculating the overlays were obtained from
the solution of the spherical triangles NDQ and PDQ
Wes
Fig.18
(15)
(Fig.18). The figure uses the following notation:
N, pole of the fixed system of coordinates. In this
system, P( 00 IA 0). In coordinates with the pole P,
the point Q is determined by the polar distance 0 and
the longitude X . On dropping from Q a perpendicular to the prolongation of the arc
NP and denoting the arc ND by k, we have
whence
From PQD it follows that
tg k= tg cos (A � A0),
tg QD
tg shi�PD
tg QD = sin k tg (A � A0),
tg X=
tg (A � .A0)
stn (k �130)
ctg = ctg (k � 60) cos X.
By combining eqs.(17) and (18), we get
cos2 (k � 90)
ctg2 e = tg2 (A A0) MO k sin2 (k �) �
(16)
(17)
(18)
(19)
8quations (17) and (19) give an expression for the coordinates of an arbitrary
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�
�
�
,point Q in the system with the pole PI in terms of the coordinates of the points P
and Q in the system with the pole N. By eq.(19) we calculated the curves of T = 0/2
= const for various values of 0 andA ,and plotted them on the coordinate net
_
(So m. 20�
Fig.19 - The Overlay
0, A . By the aid of the overlays so obtained, the process of calculating Ve and
Vi at the point P( 00 ,.A0) reduces to the following:
1. From the components observed on the earth's surface, we must calculate (for
instance, by integration of the X component) the potential V for a number of points
covering the entire earth with a uniform net.
2. Plot the value of the potential and the 2 component on the coordinate net
0,X. For brevity we will, in the following, call a coordinate net with plotted
values of any element a cartoLram.
3. Placing on the carto.-rams of L and V the overlay traced on transparent paper
on the same scale and calculated for 00,A0, take off the values of V and 2 along
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each line of 41, equal to WI, 1112, etc. and average those values of V and Z.
4. Calculate for each value of Iv the binomial (2ItZ + 17), and, by means of num-
�
�
Table 9
8 D VAtiti0113, 2 -4ornponeat
1$
20
22
go 0
0 24 24 1.2
i 0
1 ... 2.8 -26 ..46 .- 1,2 -. 7 IA 16
log
70
Go
00
40
20
10
0
to
0 '
39
4o
eo
70
__
80 3 9 4.9-2,1
60 66 65(3
34
---..--..2$ -.49 ,... 8 .1......-ur 31
-27 -61 4 4 ..
I �1 �110
F1
le-'----3
4,8
M 4 6P � 20----"=20-------m16--...--m-6�w24. �.4 _J$} -.4 8
5I%
3 -55 2,3 36 2,3 1,0
*1------r1;1 ! I 47 1 ~4
60 -4 __:o 10---12
12 -.. 16 .16 -15 ... 1
4
30.------1
7 115
2,7 1p 3 -1'
7 /
0 - i -
_i 7
-;
I? ip____..4
- 1
405
0
1
..1
�n�
-1
t -
�
? ..-=
i
1
30
0
( 0 $
i
:
1
9 -130
I -
0
.
9
-
9
10 (1,--�
0
0
p_______.. 1)---
0
4
0
i 0
0
i
0......-........-1
6 - 9
;o
0
P o
1
I Or_
,
6

o o o
0 I-6-41i -
t _
_____.;
% 1-----..-1
0 0 0 .
o---1 � i /
1
4 ,0
�3 �/
o
0 1
4
_ 1 ?___.....1
- - f 0
�1 �1,0----- t
7 7 t
12 It le 115
I I
40-4 115"---28
-------0 -1. f p
/I? - 7 - 15 -27 "' 18 - 12
I 1
- -
1,4 �
3 -- g5;
,0 84---111 CO 3P v 4
-----Ap----,11? 30 ---"Iip 4i 1 --..--.4
I I
'-' 213 - lo - 51 -2? -JO
go
4,30---10 g_____116._____ 6 _______2:1 ---196 .4p 1,....____.
50 - sp - . 27 ds 105 11!16 6,0 ��� to �- 4 ...
1-7
-in-4.3--,'--2 . .., 2,1
78 451--0111
216 3' 49 -11-31 3,8 INg3
'' 24 -1 ,_
0 0 112 7 ''. 1'3
3
1

4
6 10 :2
Local' GeorriAq net cc 'rime
14
16
If
21
14
erical or graphical integra Lion, obtain the difference Ve - V1 front eq. (15).
5. Knowing VP= Ve + Vi and lie - V., find Ve and Vi separately. As an example,
Fig .19 and Tables 9 and 10 give cartograms of the Z and V of the 30-varia Lions and
an overlay for P( 0) with 6) = 200. The geo1na'neLic coordinates have been taken
as the fixed ciordi nate system; the overlay and carLogram are given in cyindrical
projection, while the isolines of Iv are drdwn at intervals or 50. For one and the
same values of El but different values of A 0, one overlay can be used, by shift-
ing it in proper manner on the carLogram. With preliminarly prepared carLograms and
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overlays, the calculation of Ve - Vi for each point is not so laborious.
Section 3. Calculation of the Electric Currents by the Integral Nethod
For calculating the currents whose field correspond to the external and inter-
nal parts of the observed magnetic field, the method of integral equations was se-
lected. As is conunonly known, the solution of potential problems is one of the
Table 10
SD-Variations V X 10-3 CGS
7 4 6 8 10 12 14 16 IS ao 22 21
0 0 t 10 1 10 i o
r---r�i--7-7-127�r .--7---r-717 -20 �1---7: �1-1---"---w�r-13 se 40
28 32 23 1
80 11 6.4 49 0 1.4---t1.4 4.1 78 12 35 1 32 134 90
76 9.0 76 4 2.4 -IS - 57
I -95
I -64 -52 -22 is
I 76
70 72 810 1.8 IS 24 26 30----".50 24--4 37 13 72i0
23 1 - 14 - 37 - 2,6 - Ill
1 i
I 213 1p 14
603 ! 23
3.0-- 411 13 3.2 1? 1,1 19-4,5 47 3:7 60
..----....3
7 34 -52 -17, -32 -
I 12 I? 11 4,8 1.0 313 11:_____277 so
6 - 3,1 - 4p - 4p - 2.7 -ii)
12� V p---4.5
18 40 1.9-37
114 1111 .- 6
50 .7 3,4 3:0 41 3P
4065.-- 2,1 to 36 _ 2? Ilp 15 ,..............r." 4�
40------V
30 5�,2,11 3P 2:7 iii f; If 213
24 --49
31 2?
23 ii2 - s
Y s 30
..5 - 24 - 31 IP - ,
.1 - 1.8 - 2P -23 -$0
1 -2 2p 24 .1,11 ? ... 4
-2 - 1.1 -17 - 14 - I A 1,3 15 11,3 - 2 .
n A i 1,6 2p 15 t 2 2111
20-2�
---Ip I
0 -o
- 2 1 - i - 9i4.0
f � !
i ___9
- ? - s
I
�
1 1
I � ;
2
tO � 2--..... f----.- I? - iso et 2 10
2
to 2 -; 210
1 2-
- ?--------1 lIp 11 $
-13
Ii6 -115 - ip
2 1.1 117 1:1 6
20 2
4 lh
15 t2 118 1 443 15_____71_-----i
t _
20
2P 2,3 1,0 - 4 - -3 -24 -II
30 5 21 3o A7 y i 1.4 2h 43 11 $1 30
5 24 3p 31
1 Ip i_____-.1
-1-1
r - 29 - :i4 - r - I? 6
6 ii 1 16 10 27 1f3. - 1 -$8 - 1p -41 -34, .- 1p s
I 3:3 4p---- 3.1 1.4
40 .5-- 28 4p 36 5.40
3 212 1 1
50 7 31 3IP 1:1 ao 12 ip 20 46 1? 37 16 7 50
7 3.4 5,2 41 32 11 -1,2 - 2,1 - .i8 - 30 - as
1 - iss 7
49 43 3.2 1? 4? v A A 00
-23 -3 gi 317 26 11
i - III
-
i 9 --.- 45
- 1.9 - Ill - 14 .
70 .72- 80
9034 .- i4
.78 - 1i0. - 2,6
1,3
18 --...15
-14_7
V ?I :'
41 5P
$3
is 1.1
42
2.4
I 5?
4.1
3,5 2.2
37
III__ 3.2 -13
I
- 3s - 14,
IIS----..._ �7270
- t 11 14
-25 -32 -25 - 2 11 14 1,12 20 II -3 -If ( - a
0 1 0 t 9._ t 0 0 , - 0 , II I) i 0 t , 0 1
go . go
0 2 4 -6 0 10 12 14 . II II 70 � 27 74
Lo cad Qeornegriettc Time
classical field3 of application of' integral equations. The internal Dirichlet prob-
lem for the sphere is reduced to the Fredholm equation o the secund kind:
�
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27cvp ' ds,
91
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�
�
L_ where v denotes the density of the double
of the potentialjtspigned for the surface,
and the values of r and a are the same as
tiOnii-Of-our roblm do not lead directly
layer located on the sphere, Wi are values
of_the sphere_(_AWi !!_0 inside the sphere&
in Section 1. Unfortunately, the conch-
to .this easily studied equation. The spec-
ific peculiarity .of our problem resides 11 the fact that we ktiow the function Ve on
the surface Sl of a sphere of the radius R (on the earth's surface), satisfying the
Laplace equation inside the sphere Sl, while we desire to obtain distributions of
ithe current function on the surface S of a sphere of a radius a, if a 'R(cf.F1g.17b).
._.
Since the magnetic potential of a current layer with a current density of V is equiv7
alent to the potential of an inhomogeneous magnetic layer of a density of V, it fol-
lows that we can replace derivation of the current function by derivation of the
density of the double layer.
Let M( 0, T) be a variable point of the sphere S; and let M1(191, T) on Si and
,P( 00)0 ro) be a certain point inside the sphere S1 or on its surface. Then,
/ .1 1
vh f u 7
VP = dn ds '
(21)
where r = PM. Since the values on the surface S1 are assigned, it follows that the
expression V for n0 - R may be found by the aid of the Poisson integral
V �
R2 vf V ,
� as,
4TcR r3
s, I
(22)
where r1 = PR By equating the right sides of eqs.(21) and (22), we get the Fred-
1'
holm integral equation of the first kind:
for r0 = R
el
f V 1
R2 � r2 ' V(.45 M r dS
0
417R r3
n
J. al
Vhf, == y 0, 0 -af, ds.
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t)
�
�
It is generally known that the solution of Fredholm equations of the first kind!
4
i
Hin the general form is very complex and rtiquires.the core of.the equation and the
1
I i
t t
I ,
Ifree term to satisfy certain conditions. 'This compels us to dispense with its solu-i
:tion.' In order to reduce the determinaticin of the density to the solution of eq.(20),
I ,
the function Ve, which is harmonic within the sphere, must be extrapolated, by some :
method, to the external space. But this is extremely difficult, since Ve in the ex-
ternal space is an irregular function. Iltherefore decided to take another path.
Namely, knowing the function Ve at any point within the sphere Si, the fictitious
density v is calculated for certain surfaOes P RI and then the values of v are
extrapolated to p =. a. This procedure is legitimate in principle, since v-is a func-
tion regular throughout the entire space. In order to show that this method assures
the accuracy necessary for many geophysical problems, we present two examples.
I. Let, on the sphere R, the potential of the external sources be assigned as
Rgll (cos e) cos 12 (k)2'
Everywhere, for p < R, we have AV = 0, and therefore V may be analytically con-
tinued on any p < R. For
V gRlicos cp(-1.k)
V ---- g RIlcos (121)1 ,
V = gRI:lcos .
Assume that we are on the sphere R3.
Then: 1) we know the field of V on the sphere R3; 2) we know that it is of ex-
ternal origin; and 3) we do not know at what P (P > R3) its sources are located. It
may therefore be assumed that the field is located on the sphere R2, R1, R, etc, so
that the current density can be calculated by the usual formulas. If the potential
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V
on the sphere R3 is represented by the function
cosrny
sin my
then the current density on the surface of P (P > R3) will be
�
�
�
10R1 2n-1-1 (F)0,COSnVfim.
4re n+1 " sin my n
In our case n+ 1 - 5 and R3 Y = gR()2, whence
n + 1 3
25 11 "
2gi=� COS y.
67t R
25 1
Denoting - 6n P2 cos T g by B, we have
R2
for
P
=2
i = B 2
;
at R2 = 0.96R
i = 0.92B;
for
p
= R1
i = B Ri
;
at Ill = -.98R
i = 0.9613;
for
p
=R
i = BR;
at R = 1.00R
i = 1.00B.
But in reality the current flows along the sphere p > R, where we do not know
the value of Ve. Let us find i for P > R by simple graphic extrapolation (Fig.20).
Then, for a = 1.02R, we have i = 1.04B. Check: from the value of V on the sphere R
we have, for a = 1.02R:
25
� PI cos y (1,02) �-=. 1,04B.
II. On a sphere of a radius of RI the potential
)4110 cos T.
Is known.
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On the sphere
�
�
�
p =-- V gRIloc os (11.)11,
P RI V gRPlocost
P=R, V= gRP10 COS 0i)11 .
,t
WO
422
�104t t t
qm eem (448 vie 2 4 VS 4"
= B (-)2
Fig. 20 - Calculation of Current Density by Extrapolation
(. Calculated Values; x,Extrapolated Values)
Starting out from the values of V on the sphere R3, we have
10R121t p --
P cos qv' R ) = -9 B P10
%1
47 11 \Rs/ 10
where B = -
210 1
g RP10 cos T.
44
For p= 0.96R
For p = 0.98R
For p = 1.001t
oil
B (-01�
R I
i = 0.67B,
i = 0.82B,
i = 1.0013.
1,IU
Extrapolating on the graph of Fig.20 for a = 1.02R will give i = 1.2013. Accord:-
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ing to the fonuulai of spherical analysis, i = 1.2281 i.e., the error is 2%.
Section 4. Finding the Current Density from an Assigned Potential on the Sphere.
Extrapolation of the Potential
After having .thus reduced the solution of our problem to the classical problem
of finding the density of a double spherical sheet from values of the potential as-
signed on the sphere, we must select a practically convenient method of solving
eq.(20). Equation (20) is a special case of the equation
�
�
27tvp -I-- X f CoS a ds
(25)
for X = + 1.
The usual method of solving an integral equation of the second kind by the aid
of resolvents is inapplicable in this case, since the series expressing the resolvent
becomes divergent at X = + 1. Two methods of solving eq.(25) are known in the liter-
ature. The first was given by Neumann in 1875, and the second by Bogolyubov and
Krylov in 1926. Neumannts method (Jibl.14) reduces to the following: Since
then
and
cos .3
a An
� (4,
r
vp cos a
27:vp
r2
cos a
Vp -= (Vm � vp) 7i ds 4Tcvp
cos a
This transformation is necessary in order to replace the integral PlicTi-ds,
which has a sincularity at the point M, coinciding with P, by a convergent integral
that has no singularities as P.
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The equation
�
�
�
x f f VP
COS a
v 4-,-, (v p � v m) d s
is solved by the aid of the series
vP [UoP XUIP ?N./2p + � � � + XnUnpi,
(26)
(27)
which is convergent for X = + 1.
The functions Un are determined successively through the recurrence formulas:
Uop = VP
�
I COS a �.� s
id 1P k OP id OM r2 44
. faj _1, m, COS a
LI
n n� 1 P r3 ds
(28)
This method is convenient since the value of the nth term depends on the first
(n � 1) terms and does not depend on the (n + 1)th and subsequent terms. Thus, in
order to pass from the nth approximations to the (n + 1)th approximation, it is nec�
essary to add, to the sum of n terms, an (n + 1)th term without changing the first
n terms.
On transforming eq. (28) into a form convenient for our calculations, we have
have
u = f Ads2r-sia
1 Al sin Ode dk.
P 47:
(29)
Denoting the angle between the radius vector of the points 11 and P by 6, we
r 2R sin --
2 ' =-----,
aIt
where cos 6 = cos 0 cos 0 + sin 0 sin 0 0 cos (X � 0), if the coordinates of P are
n N 0 and the coordinates of 1.; are 0, X.
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Whence
�
�
21%
Up= Fg-ti f I (VP �VM ) cosec �8 sin 0 de dk.
2
(30)
We remark that, for M P, cosec 6 /2 � w, but since Vp UM � 0, it is easy
to show that (Vp � Vm) cosec 6-- remains finite.
2
If, in calculating Up we take for each point P its JIM system f coordina Les
with the pole P, then 6 fl and
0
2 rt
I P 8n
U
0
(Vp � VA!) cos
o de di..
2
31)
()it
Iritroducing 0 /2 = ii nd VP = V = I (V � V1.) LIN ( the iilean v1iie of V1, �V11
2 P
from the parallel circle), we have
and in general
U p f tip M) COS d+
0
1 f Unp = 2 j Lin _ m) cos ip
0
Un _1, p 21 .1. Al cos 4) 0.
(37)
(-33)
Thus in zero approximation, the function of current density isvP = � 1//i ii V
and, in first a pproxim,, Lion,
1[3
VP= LITE P-- -21
0
etc.
r.
I
V,
COS (I) dq)
( )
These formulas very clearly oirJW that, i n e ro pproxima Lion, the current den�
sity is equal to the po Len Li al with an accuracy to a cons taut cue Cr] C I cut. The ri.fo re,
for a rough estimate of the configuration of' a current system, it is suffi ci en t, to
construct the isolines of potential. In first approxima Lion, as will he clear from -
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eq. (34), the value of the current density is detelmined bi the inequality:
I 47C 1 VPI 500),
Ve/V = 0.89. The figures so obtained differ considerably from the value Ve/V = 0.60,
adopted by Chapman, by analogy with the S -variations. It is not possible at the
present time to give a trustworthy explanation of the latitudinal dependence found
for Ve/V. Two hypotheses may, however, be advanced: 1) The variation in Ve/V with
the latitude indicates the unequal conductivity of the earth at different latitudes;
2) it is possible that the height of the current layer is different at different lat-
itudes, which would seem to be entirely plausible in view o r our present knowledge
as to the heights of the ionospheric layers.
Section 5. Discussion of the Accuracy of the Lethod
Let us now dwell on the question of the accuracy of the integral method of rep-
resenting the field. First of all let us evaluate the error in the caLculLtion of
V. On replacing integration by 311:lunation, we have V = RAO Y, X, where the X, for
simplicity, are denoted by XI .
rhe error in V is evaluated as follows:
8v=_ReeEsx,
where 5 X is the error in X.
For AO = 50, ft = &.4 103 and 6X = 1, 5, Pnci 10 y , we rind tha t the 1110XilalUil
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error accumulated up to the pole 6V1ax is 12 x 103, 12 x 104, and 60 x 104 CGS, re- -
spec tively. The mean error 6V = 1/n 6V1ax is 0.5 x 103, 3 x 103, and 6 x 103 CGS.
At latitude 55�, the maximum error for 6X = 2 y will be 6 Vmax =14 x 103 and the
mean error 6V = 1 x 103 CGS. If the accuracy of X is lower in the polar cap
(4) 550), for instance 6X = 10 y then the errors 6 Vmax = 6 x 104 and 6V = 3 r.
103 will accumulate up to the pole. Judging from the graphs of Fig. 25, the accuracy
of the observed data of X in the middle latitudes is actually of the order of 2 Y,
while in the polar latitudes it is of the order of 10 Y ; thus the accuracy of V ob-
served can be evaluated as 1 x 103 CGS in the middle latitudes and 3 x 103 CGS at
the pole. 31nce the observed value of the potential reaches 100 x 103, the error
would appear to be allowable.
The error accumulated in the calculation of Ve - Vi may be evaluated AS follows:
On replacing the integral expression eq.(12, IV) by the summation expression, we
have
�
�
V, � AO EE (2RZ + V) cos
For Alf = AO = 50, cos q = 0. 5, we have
10-2
;We � i) - o ' (2ROZ � V).
6,3
Phe accuracy of observation of Z is lower than that of X; the calculations have
been made under the assumption of a 6Z equal to 2, 5, 10, :nd 20y (fable 11).
in this calculation we assumed a mean error 6 / for the entire earth, since in
calculating' Ve - Vi the values of V for the entire earth enter the integrand expres-
sion. Che number of terms in the expression 6 (Ve - Vi) is 6i0. The small Cable
presentedshowsthatl)theerrorA(Ve-V.)L, due more to the inaccuracy of Z
than to the inaccuracy of X; 2) the ine&n error 6 (Ve - Vi s one or two orders
smaller than the error of the observed V, even under the least favorable Lssumptions
as to 6Z. Thus the practicL1 ,ccuracj of Ve is the same as the accuracy of V.
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In the calculations presented we did not take into considerPtion ,,he errors of
the mathematical operations themselves (integration, etc.), since these my be per-
formed with a very high accuracy, much higher than the z:ccurac,y of tie initial data.
�
Table 11 if
ZZ
2X104
5X10-5
10X104
20X10-5
2R6Z
a v
2,5X104
o,3>004
0.5X104
cox 1 oi
13X104
c1,3x ico
26X104
o,3x 104
7, ( vr -- vd max � . .
3X104
7X104
13X104
26X104
7, ( Le � VI) cp . . .
24
56
104
208
rhese evPluations of the error; indic Ite thPt, the integral methyl e Li
pr)viite tide luP te accurtcy. in practice its ccur-ic,r L., completely leteri .ine I by the
accuracy of the observed experi1ient:..1 nccuracy of the
)h3erved
ckta, of lc )urse, we mean not Only the . ccurncy ()f the observations themselves, but
also the stability and representatIve nature of the mean data and the distribution
of observation points over the earth ;urf.,ce.
Seation 6. l'he Current .3,ysteni of 6 -Variations
From the values of Ve calculated by the integral ae thod, distribution of the
current density in spherical .1aier of radius a = 1.05 ft (0.05 1t = 31.3 km) was con-
structed, correspondinL to the heiLlit of the F7 .1.E.yer of' the ionosphere, to which it
is most probable that the currents of the magnetic disturbances c.oi be referred.
The current system so obtained (:'ip.29) like the above-oescribed Chapman s,stem, con-
sists of four current eddies, of which the two more intense are loc- Lei on the morn-
ing and evening sides of the polo.r cap, and the other two in the middle latitudes.
Me signs of the current functions are different: the polar evening z nd
latitude corning edlies have a positive sio: for the current function, the polar
If All values given in Table 11 are in the CGSivi system.
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morning bnu idale-latitude evening eduies a no -ative cent-i's of the polar
current eddaes ,,ru located Jn the 2 %nu 15 hour meriJibns, those uC the middle-lati-
tude eddies on the 4 z. no lu hour morilians. Che evenine ond morning eduies are un-
�
�
�
equal in intensity: the morning rolar eddy is more intense thcn the eveninc eddy,
while ;Ale evening pdddle-latitude eddy is more intense than the morning eddy. In the
zone q = u7 - 700 (the E uroral zs'ne) the current lines E:,re closely spaced, giving us
tn.. right to liken this pert of the current ystem to the linear current flowing
eastward on the evening side of the earth Eild westward on the morninE .Ade. It is
this crowding_ of the lines of force that is responsible Cor the specific pecu-liarity
of the cour:,e of magnetic and ion.)1..pheric phenomena in the zone.
picture 30 cum,truleted for the currents bllows U3 to interpret in the fol-
lowing manner the pattern of geographic distribution of :it) described by us in )ection
3 in each hemisphere, there 1 re fur characteristic t pes of D-variz,tions:
I.
eircwapolar type, chin rb c to ri zini the daily minimum in the XI nd compon-
ents; the 1,1p1itude of is very :mall. Chi:, type cJrres..onds to the center of the
polr cap, over which the currents flow in '.he unifono layer in the direction of the
20 - 3 hour meridiz-n.
li. Polar t:ipe, observed netweet1 the zone of close ,pE cing of the cur..nt lines
at the latitude 67 - 7u�, ad the lc titude or the c'nter of the polbr eddies (+ =
750).
II is characterized by the afternoon ma_ximuk in
t -
41. � mid
the .1E�ti;ne
in L. Uhi e mpli Lude of both COliponeut,3 is hirh.
111. hiddle-latitude type, observed between the auroral zone nd t he latiLuue
over unich the centers of the midule latitude eddies bre located (+ = )5(3). IL is
characterized by an evening maximum' in XI and
L'A�
IV. pow-latitude type (between the lbLitude 0C the centers of the middle-
latitude eddies and the equator) with an evening minimum of X' nd c.n evening maxi-
mum of 4.. fhic amplitudes of both components, especially of nmall.
Jirectly over the latitudes or the centers of Limo eddies 0 = 750 and + = 550)
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and under the zone of crowding of the current lines, transitional forms are observed,
characterized by the change in sign of the XI variations and the maximum increase in
the amplitude of Z in the former cases and by the change in Jign of and an increase
�
�
la
Fig .29 - Current 3ystem of.SD-Varitions.
current riven
in thousands of amperes. A current if 10,Cou ,:mp flows hettecn two
Successive lines of current. file coordin-LJ net is the coollthgnetic
latitude and feom.LneLic time
intensity of
, positive VIALULIJ Jr current func-
Lions; - - - - netotive values)
in the amplitude of AI 1U una latter Ca3U.
file location of the centers of the ihialle-lititude ,nd polar edileo at the var-
ious iheridians is in full uLreemont �,ith tht. :ell-knowo fact Lic't Lie time of occur-
rence of extreme values of Su is different in the ,nd polLr Lluitudes.
The unequal intenoity of the dornint -nd eveninc extreme vLlues is likeui-e under-
standable if we bear in �ind LlizIt the height of the evehinl. mLximum of 3D in the
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�
middle latitudes is greater than the depth or the morning maximm. In reality, as
pointed out above, the auroral zone (or the zone of linear current) is not a true
parallel circle. For this reason, the boundaries or the regions c0rre3fonling to
the various types of SD will likewise deviate from the parallel.
A comparison of the oysLem of currents of Su calculated us, which we shall
hereafter term the IIIIZM* system) with the Chalimn system (cf.Yig.hb) discloses a
limber of substantial differences. First, in the Chapman SUR of SD-currents, as in
his Ust-system, the signs of the current function are not indicated. Obviously, the
difference in sign of the current eddies discovered by us must be of signific;nce in
the construction of a quantitive theory of tha SD-variations.
The second difference of the IIIIZM system is the shift of the centers of the
polar eddies, that of the morning eddy to 2h of t eomagnetic time, that of the even-
ing eddy to 12 - 10, while in the Chapman system both eddies are centered symmetri-
cally at 6 tnd 131. Because of this disp1:-.cement of the eid7 centers, the currents
in the polar cap have a direction r erpendicular to the :-. - 14 hour meridian, which
well explains the j-variations of the hurizozit L components ( L Thule .:n1 oodhavn,
with the minim= of X, at 10. Accordint to the Chapman system, a itinimum if X' at
18h and a zero value at 12h might be exp(cted t thee observatories.
The position of the L.orninL riddle-latitude eddy likewi.ie does not Pcree in the
two system;, tem nd tho r,1):.J lute vP1 ues of the i lten7,it of tl.c poi: r ed I -s is ii Mr-
era.. In tAle Chapman sys t,em, the Lot:] in tens i Li .if 'hi e current flow in{ thr )14 n e
poldr cap L 45u,u0u Lmp, in the nI1ZI., si2te., it i2 7(.(i,606 7.1lip. In th.
man syste-I, ru r.3uver, the inten ;iv of !Jle r.ornilr rid eveni4 el hies the j.. e.
However, it does see', Ln-;t it the lifftreces kexc .rt ;,1 the lifference in
the signs of the current function) r re iue r)t Inch t, the different h.ethol if
calculation as t,J f,Le difference in t!:e tarLir d,LT ew.lur-
tion of thE: ihte-isity if the currents fr)m iur I- gave the followinr results:
* ferrestril 1 ,,z-trietism Aesearch In:,titute
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As is coimmonly known, the density of a uniform current layer of sufficiently great,
extent is I = ,-571 where Fe is the field induced by this layer on the surface of the
�
�
earth, perpendicular to .irection of 1. Assumin: 1,1ir L the ratio of the external_
field to the observed field (F) 13 elual to k, we have i. = . If the width of the
2 it
.
belt of current is 1 then the total current, is I = where Is the me:�ei value
cm,
of the flux density which, ti thout ereat errpr, can be taken a.; elual to 2/3 1m'
if parabolic distribution of the density in the flux is assumed. IL follows frm)
this that,
I -kF 2 / CGS.
2rc 3
(1)
Applying this approximate formula to the observed variation:3 at Thule (Xlmax
= 600, setting the width of the flux at 32�, Lnd replacing the value of tie coerfici-
ent k = 0.t, adopted by Chapman, by the value k = U.y found by us for the polar cap,
we have
0,9X(0/ 10-5 2
6,3 X -7:3- X 32 X 1,11 'X 107 CGS ---22X 104 A.
Phus i r)uu h es Lima to of the current likewise leads Le odd:, in ten-Ili es half as
great, as th)se Liven by Chapck:n. As for the Jirections of the r.rallel currents
flowing throug,11 the t.olar cap, ,'1.3 Vie nave llrerd,y noted, it follow,-; lirectl froL, the
observa Lions a I, ;..nd (-iodic) vn that, the curren t$ 13113L he to the - 20
hour meridian instead of to t) - 1 )_ hour meridian, as is the c.I.se in the Ulla an sys-
tem. thus the absence of a loud agreement between the polar va Lue of the 3D-currents
in the Gha;Jrian s/stew rid the observed v-ri.itions is explained .3.L..ply b the intic-
uacy of the ibery tiuni ii Lerials that were available to him. The calculations
presented above .31.ow that the -pproximrite method of estim,!ting the int,�,,n.;ity *.nd
directiJn of the currents gives very good results. Of course, the approximate meth-
od does not make it possible to .separ; he the interna 1 r nd externr1 parts from the
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�
�
11:��������+
' ..10.111M
observed field, to obtain the numerical v'filues of the poten Liza, to determine the
:dens if the current functi in, nor to elucidate the letai 13 )f the configuration of
the currents, etc. but it i 3 Inply suffici en t to obtain ; miugh picture o f the cur- -
_
rents neces ;ary for ; iuli ta Live li �;cuss ion of w rious problems.
oec Lion 7. rh... Polr h rt., of the 3D-Currents
Cite distribut ion or ,�,10: -c i rrenL' iii t heriirorn 1 z iiie shown in �if. 79 was al -
comp. red L tu i th t. .e "r et. ; f' the current obt,��ined under the 1..3S1.11..,tion
of I in Zi rity U the curren L. s t� Led in Gaz. pter 1, the czij Cu L., Lion of the in Len-
si heij nt, posit 1,ui t. the line ,r curr2tit iii Lho r uror: 1 �z,, mile 1-i: 3 been cr,rried
out by n number of outmors fr in, boery it jolts p ir o f ,tz Li iris )r .' 1' ,everal
pai rs, different re ;lilts, (ependint 'it the ..teri; I, used. hccordingly, we
repea Led Jur c. Leulations usin! the oPI,lt; dr L 1..,e used in construe ting the s� stern )1'
surface current3.
fhe listribution ut the vector's o Lite n ,t.ic field f the linez,r e1ectric
current 10 SC.:1101H Li repre ,eted in ii .30. in c.insiderinl this fif ure we ::,uot
iniaL Inc the current to flow perpen Ii cular
S tot he plane of the �-,z per in the ii rec Lion
.1\
,
the pr per tJw; ri the oboervor, � nd
,ts 1. to 1),3 I he t ht �f' the current
0 ive the earth' s lie
ore t.v..0 points which the v-c to i's of the
vim netic field .1 re I. no..n. un the Irrwin,
they rre c L .1 :A.. ii IC 'rent sid,ls of 0,
the projection f the current onto the earth' ., ourf cc. .11 fr). irawing
that:
r.'11; . 30 - Pa ttern of kagneti c Field of
hod?. nit:, I. r Current
AO h ctg a
ijT) h ctg ri
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observed field, to obtain the nuineric.1 values of the potential, to 'detem.ine the
1
sicns of the current function, nor to elucidate the letails of the conficuration of
the current:43, etc., but, it i unply sufficient to obtain a rough picture of the cur-
rents ;�:i necessary for a iurlitativc liacussion of v nuns lq.oblems.
�
�
�
zwcLion 7. Vhc Polar Pz rt of the 613-Currents
The distribution of' the :3D-currents in the ruroral z me shown in was al--
so cow; ro�i by us let ":1' r the current obtlined Inter the assui.,pLion
of iinarity of the current. As st�,ted in Chapter 1, the caicul: Lions of the inten- _
sity, hiei h t, position ur the linear current in the ruror.1 has been carried
out, by a number of outhors frthi observ.,tions J f � or ir ofst,z ti nis or of ieveral:
pai Ts, ielding different results, dependinE on the !,a Lori; 13 used. Accordingly, we
repeated .)ur c,ilculations usint the 3P111U &Li we used in constructing the system of
surface currents.
_listribution of the vectors of the ntacn.:!tic field of the linear electric
current is schematic:Ill:, repre.,ented in ,�ig.30. in considering this; figure we must
144
A,
Ni
S
,1`
, �
, fh. � *" -
,
1 \ ,
\I
I P
ithaeine the current to flow perpendicular
to the plane of the -,aper in the lirection
fro!" the paper towvn.1 the observer, and
as !Mile it to be the heirht of the current
ab )ve the earth' s surface, w .ile : rid 13
a_
vo.
ore two points a L which the vectors of' the
ma tie tic field arc known. On the drawinc, -
they are toc:-L,L1 at, different sides of 0,
the projection of the current onto the earth' c, surface. it. follows fror, the drawing-
- Pattern of' I�iagnetic Field of
I orizontal ,,ine,tr Current
in i .30 that:
AOz/ictgoz
BO It ctg p
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�
�
-
h
AB
ctg a ctg p
"CA
tg 7- -
'A
X
ZB
(I) 0 = (1) B h ctgp - h ctg a,
if (1) is the latitude of point 0 (in our case of the auroral zone) and and (I)
0 A B
are the latitudes of points A and B.
The vector of the magnetic field created by the infinite linear current 1 at the
distance r is equal to
or
Consequently, if H is expressed in grams, I in amperes and r in kilometers, then �
h X A h XB
I 5rH ,--- 5
sin a sin a sin fi sin 13
I 5h X A (1 � ctg2 a) 5hX8 (1 + ctg2P).
(7)
For the case where both points A and 13 are located on the same side of the pro-
jection of 0, we have
AB
h ctg - ctg a '
430.-- (13B+ h ctg (PA � ctg a.
(3')
(61)
Equations (3), (31), (6), (61), and (7) allow us to calculate all the parameters
of the current if we know the distance between two observatories whose observations
are available to us.
A' consideration of Fig.23 shows that the most convenient pairs loct-ted near the
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auroral zone are as follows: I) Petsamo-Bear Islands; II) Fort Hae-Minuk;
III) Point Barrow-Uellen; and IV) Tikhaya Bay-Dickson and MaWchkin Shar. This
selection of pairs was made so that the two stations should be on about the same
geomagnetic meridian, i.e., that the direction of the hypothetical linear current
should be perpendicular to the line connecting the stations.
Table 12
�
�
I I
II
III
,
, IV 1
Hours
h kill
+0
Ix io4
h km
4,0
Lx104A
h km
fo
Ix104A
h km
4,0
lx104A
A,
,
0
314
64�.4
-17
74
62�.3
- 2
469
63�.8
-18
2
401
64.5
-37
232
63.7
-15
254
62.9
-11
4
483
65.9
-24
364
64.6
-20
265
64.2
- 8
466
610.7
-44
6
342
67.9
-12
442
65.8
-16
348
66.8
-17
528
62.0
-13
8
271
69.8
7
1082
68.2
- 9
350
67.0
- 5
10
1078
66.3
15
421
64.6
5
360
67.2
4
12
1270
70.1
32
580
67.5
18
645
67.6
14
293
66.0
8
14
767
69.0
29
593
67.0
24
624
66.6
19
118
64.2
4
16
561
67.0
35
442
66.6
21
585
64.9
24
18
189
65.0
13
283
65.7
14
320
63.7
16
,
20
165
62.6
5
235
63.0
10
22
331
65.1
3
-
-
-
The results of the calculations of h, 4)0, and I for corresponding pairs of
stations given in Table 12 allow us to draw the following conclusions: The height
of the current layer varies within 1,ide limits, from 200-250 km in the night hours
to 1000 km and more in the daylight hours. Since all four pairs used agree in indi-
catinE an increase in height during the daytime, and since this is confirmed by the
sthtistics of the heights of the F2 layer in the polar regions, the diurnal march of
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the height of the current may be considered to exist in reality. file most reliable
height detenuinations appear to be those in the night and early morning hours (0-6) '
and in the afternoon hours (14-20) when the replacement of the surface current by
the linear current is most logical. In these hours, all stations five results in
agreement with each other (increase from 250 to 500 km in Lie period 4 toh and de-
crease from b00 to 250 km in the period from 16 to 2011), which are very close to
those of ionospheric measurements. At the end of the &:/- (20-)4h) tiLL at noontime,
�
the values of the heiLhts are very diverse. The calculated values ften appezr ab-
surd; h > 1000 km or h < U km (cf.omissions in the heiflit column or Table 12). The
poor results during this period are entirely understandable if we bear in mind that
in these hours there is no crowding of the current lines (cf.Fig.:!9) which might be
compared to the linear current.
Owing to the relatively great dispersion of the values of h, no systemic differ-
ence in the values calculated for different pairs of stations is found, it can only
be noted that the calculation of h for the pair IV gave the worst results, which
most probably can e explained by the fact that the fikhaya day Observatory is lo-
cated far from the one of linear current r.nd is in the region or cti)n of the sur-
face current flowing in meridional lirecti)n through IThe polar cap.
Thus the determination of the height of the current in the polar zone by the
above-presented formulas, as rough as it may ho, :Ain does indicate that in the
high latitudes the current ,ystem of SD can likewise be referred to the level of the
F2 layer, and that we did not commit a great error in adoptinE the height of the
system h = 0.05 k for the entire earth as an Pverate. in more detailed calculations-,
which would be outside the scope of the present work, the diurnal fluctuations and
the latitudinal variations of the height of the current layer should also be taken
into account.
The variaLiins in the geomagnetic latitude of the linear current zone ( l ()
give a still more regular picture; All stations agree in indicating an increase in
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the northward shift of the linear current during the daytime hours and a southward
shift in the night hours, uhich is full agreement with the position of the zero cur
�
�
�
rent Jine on eig.29. Che unexpected drop in the value of (1) 0 at 10h and the great
scatter ..tt 2u-241 is explained, s in the case of the calculation of heights, by tlie
absence of civwdinL of the current line:, in these periods of the day. "here is a
notabLe systematic difference in the values f
(I) II' (1) 0 III' anq 4) 0
pairs of stations, i.inuk-Fort Azle nd Point Barrow-liellen give about the same value
fluctuaLinL in the morning ni -lid eveni. hours about (Po = 660, which is in complete
agreement with the position of the Lo te )n which we have trawn along the
isoa..fiplitudes of 11SD. As should have been expected on the bi.sis of Fig.23, the pair--
rikhaya y-I:a Wchkin .jh,',r and oickson be the s Juthernmos t position of the
zone ( (1)c) = 63 - 6/1.0). there is a certain lack of correspondence between eig.23 and
the values of Fable 1 only for the pair Pe tsi.i .o-deL r islands ( (I) 0 = 650) z, long the
isoamplitudes and (Po = 67� for the :turning Laid evening hours of Table 12. Thus the
calculation of the latitude of the zone of linear current on the averat.e is in very
good agreement with the position of the zero current line in the system of surface
currents and allows the position of the zone to be ma,le more precise at various long-
itudes.
A comparison of the intensity of the linear current with that of the surface
current flowing in the belt 60-700, indicates good agreement, both in order of mag-
nitude and in diurnal distribution. file systematic difference in l ... 1111 again
indicates the existence uC the longitudinal asymmetry in the distribution of SD, re-
peated1.} noted by us. For obvious reasons, there is no special point in aLtrching
any
siLnifici nee to the scattered values of IIV�
Ile above-described parameters of the linear current, calculated by us from the
SD-variations for the Second International Polar Year, :-Tree in part with the para-
meters from the calculations of Sucksdorff and (1311)1.55) and ha rang (4ibl./il1). In
part-Lenin'', the diurnal variations of altitude nd density are about the sa.:,e for
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all three studies. We did not, however, discover the existence of two branches of
the current on one and the same meridian, which would follow from Ilarangis work. We
likewise fail to find even indications of the existence of the "almost vertical"
linear current calculated by Sucksderff. On the contrary, the idea obtained by us -
as to the parameters of the linear current is in full agreement with the system of
surface currents, which is more objective, and has been calculated without a priori
assumptions as to the configuration of the current.
�
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CHAPTER VI
POLAR STORM
jection 1. Expansion of the Field Potential and Electric Currents into 3eries
of Cylindrical Functions
�
�
As has been stated above, during the time of a polar storm (P), the fluctuations
in the magnetic elements in the hiLh latitudes reach great amplitudes, often exceed-
ing 1000 y, while in the low latitudes a polar storm manifests itJelf in the form of
small bay-shaped disturbances. It follows from Figs.7a and 6b that the field of a
P storm for (I, < 550 is so small by comparison the field in the polar cap that,
without great ermr, a field that vanishes at n = 50� may be adopted, and the distri-
bution of vectors considered only on the spherical -iegment (I) < 40�. In this case,
taking the spherical segment as a portion of a plane, the potential of a P stint inE.y
be represented by a series of riessel functipn6. The appruxirha Lion will of course be
very rouLh prid will jive particularly Frea t distortions alonL the edLes of the re-
gions considered, but it will still enable us Li separa be from the field observed on
the earth's surface that part due to ion ispheric sources, and to form an idea on the
cunfigurtion and inten'A_ty of the currents flowing in the ionosphere. In the cent-
ral part of the polar oegb,ent, we h,ve < 5o,anti it is here that the must incense
fluctuations if the 1�agnetic field are c.incentr; ted, v,hile the distortions Intro-
duced of the repli cement of the spheric, 1 urfL. ce Lj a plane surface are rel; tively
small.
In view if the fact that the expansion if Bessel functions is here used for the_
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first time in investigations if Lho variable t:.z.toLotic field if the eLrl.1., we will in
this 3ect,i(lin derive the necessarT foi..u1 tid will uv tu iu ex', to a des-
cription of the current system obtained for the P stonns.
After selectinE a system of cetlindrical coordinates r� 11) z suc that, its
�
�
�
Lin coincides with .he JuaEnetic OYiU role, th: t, the plane
= c)rre..-;!�,n t
earth' s surface, Lnd that the posi Live axi:, z i. lirec Lei f /' let U. r O'T'C )pri
the potential of the storir at, some fixed inst., int if time T by the Fourier-les >el
series:
zIn
V (ittl;an cos /1? p semi Sill in?) e j (kirm r)
n in
zk"s
VI +EI(2�inicos.�+,,,,,�, sin imp) e J (Ain
a IJ
P
n m
(1)
^
The first ii if of the series c )nverres in the half- ;1... cc > 0, bel )w ti.e ur fa re
of the earn, ; lid represents tne telt, tz 1 Inc to ex Lern; L sources (Ve). ilie second
half ..f the series c)nverEes fur z () �-:n I r-)prese,,It., the potent i 1 )f the field due-
tu external 3 )urcoG I ere X denotes the rout, of the 1:;(1..,',e1. fancLiin of
the n order, rid e),.(1) v7-..nist,e3 on the surface of ti-e C,, Under of r,diu. r = P .
iince we hivees:.3umed thLt V = U for 0-, 40�, the numeric. ] vz lee .if p Ui Jur
equ&.1.3 the 1.enctli of the seEment of the Heriiiiin t.elAreen 0 := 00 and
= 40�, i.e.., 111 x /IU len, or L4. 5 x 10 cm. Cho field inten-i Ly is
V v
F - ---grad V ti R , 7
(2)
where .t lenotes the component of the horizontal vector directed slow_ the teomacnetic
meridian. iince the direction toward the pole is use:: con:;idered posi Live in
Leomagnetic measurements, while r increases with incre:.sitir, dist/glee from tile pole,
OV
we have, from eq.(1), X R -or �
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From eq.(1) we also have
�
where
)."1
n
(2� cos np
nrn nm
v,� m
sin 'up) e
r
p � �' 111 -
,
COS nl� SIII n
P
R n 11
un the earth's surface, /, U and
v (a cos np b�,,, sin np)J (km _
fim n n p) $
n in
Z= (c cos rtep d�,� sin niz) \,
.41 n p
n
in
anm= C n (cie
nin rim nm nmf
Am
dnm= --n (Pe �� Pi ) �
nm �nm
bnm Pe
nm
If awn ... ptun are known, then
e ( a
nm 2 nm
p
(3)
run run may be cciculated by the formulas
�
Hh-P
),ffl CHM) ;
m � ).1nn nm
= (an + d
al
n
nin
1
-
(ann,
(brim
� �),m dnm '
The values of cnin and dnin are easily obtained by expandinc into series Jn
m (A n r ) the properly work-up datc of the variati.ms of the 2: component of the Eeo-
macnetic field. For Lite calculation of anrand bnin it is more convenient., to riz-ke use
of the data of the variations of Lite _;.1 component. From eq.(.21) IL follo.ls, for
r(.) > r, that
r� ru
V , � V ---= f X dr It V � Xdr+ r V.
. r . if li 0
r r
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Taking 1'0 = e, we have
�
� J X dr,
(8)
since, by hypothesis, V = b.
On finding, by numerical integration of the X1 component, the value of V for all
the region r < pj we may find the coefficients anm and bnm of the expansion of eq.(4).
0
From the distribution of the potential Ve found on the surface z = 0 it is not
difficult to pass to the distribution of the currents responsible for it. Let the
potential Ve known on z = 0 be due to a plane layer of currents lying at the level
z = -zo. Denoting the value of the potential for the lamer surface of the layer by
V_, and that on the upper layer by V+, we have, under the condition that the normal
derivative is continuous,
dV av_
Oz = di �
(9)
Since the current layer is equivalent to a double magnetic sheet, the second
411 equation
V+ � V .47c/
'
(10)
where I(r, T ) is the density of the current layer, will also hold for the level
z = - zo. On expanding V+, V_ and I into a series of Bessel functions, we have
V
(cL n-m cos n? P k
n .1.
n(?) e P 41/ ' m r
n p
n
Am
zn)
Iv+ == (Mt. COS ncp + pt. sin it?) e P / 1 fflt r
n n p a 5
1==VIS-11(S
nm
it ft
z I < zo,
z I > zo,
cos /up Tnnt sin ni)),/,,(XT-r-p ) as z I zo.
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Substituting eqs.(11) � (13) in eqs.(9) and (10), and equating the coefficients
of the same cos nfp
Jn, we have
sin nip
�
�
whence
m+ ==--a� a4 --a� --=4ITSnon'
nm nml nm FIR1
fi+ ==--p� p+ --p� ==4.7TT
Inm nm, nm nm nmit
sant 2afTm ;
nm 27s nnt
For z = 0, we have the two identical expressions:
n_nt
V (a dos It? p
nm - sin np) e n7J )."3
n' n p f
n in
1/, 1Si
n m
(ae dos nv. P e sin
, non IIflI
Lori
On equating them, we have
, m.7� s�
n ' n
P .
e Pnm
e e
nm nm nm
ae k m
nm n �
S n m � � P � 2 'Cam -
n
Pen,
2T:
zn
e P
where z is the modulus of the height of the currents postulated by us.
0
Section 2. Starting Material. Results of the Analysis
(16)
(17)
(19)
As our starting material for calculating the currents respunsible for polar
storms, we used the data collected and worked up by Silsbee and Vestine (131b1.54).
Polar storms are so diverse in form and in intensity that the formal averacing of
series of observations cannot give such good results as it jives with th: So or SID�
variations. Nevertheless, the statistics of a lar-e number of storms for certain
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'
���'
mamma, lir .4r �ftliguin
observatories given by these authors do show that there is a definite regularity in
the distrIbution of storms by hours of the day. The relation between the number of
storms and the time of day given in Table 13 shows that the positive stoms
deviation in H, All > 0) and the negative storms ( A11 < 0) are usually encountered at
different tines of the day, the diurnal march of the bays !unending on tht latitude
of the point of observation, rite list of observatories used in the work of 311sbee
and Ves tine, and the number of bays registered, Pre Liven in fable 14.
Table 13
Jiurnal Ilarch or Frequency of 3a7-.3hc ped Di:Aurbotice:3
(1;umlier of liays in ,;)
cr
from - to
Alf
Hours
1
2
3
4
5
6
7
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
38
+
4
4
3
5
6
5
3
3
7
8
5
3
2
4
3
4
7
5
3
5
5
4
4
70
- 63
+
0
o
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
3
2
1
1
1
0
0
-
14
11
10
9
8
6
4
3
2
1
1
1
0
0
0
0
0
0
1
3
4
6
8
10
43
- 40
+
8
6
4
3
2
10000000000011
3
6
6
910
-
0
0
0
0
0
0
1
1
2
3
3
3
3
4
5
5
4
3
2
2
2
1
U
0
3 - lb
+
9
6
5
3
2
2
1
0
0
0
0
0
0
0
0
0
0
0
1
3
6
8
8
9
-
0
0
0
0
0
0
1
1
1
2
3
2
2
2
2
3
4
4
3
3
2
2
1
0
A consideration of the form and intensity of the bay-shaped fluctuations for all
three elements enabled hie to cpristruc t for each observatory a picture of the mean
(or more exactly, idealized) bays by averacinL, the didturbatices encountered at. one
and the same hours or local time.
ehese men bays were ilifferent for different hours
of the day of the local day, but resembled each other for observatories located at
the same latitude. In other vnrds, I found that the storm field depends on the local
time and the latitude. As in Chapter V, allowance was made, in averaring, for the
local reoma.gneLic time and the geomagnetic latitude. Figure 31 friVCS the distribu-
tion of the field of an idealized hay for Oh Universal Time. The coordinate net on
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�
�
�
����1��"..mmommimin.....
Table 14
- ,
Group
Observatory
(13
..
A
Number of Bays
-
1
Thule
8�3�.0
(P.O
204
2
Julianahoab
70.8
35.6
227
Fort Rae
69.0
290.9
243
fromso
67.1
116.7
99
Collet e, Al..sk;�
64.5
255.h
146
Dickson
63.0
161.5
103
3
Tucson
40.4
312.2
191
Ebro
43.9
79.1
147
Wa theroo
-41.8
1A5.6
,173
4
Antipolo
3.3
189.1
117
Iluancayo
-0.6
353.8
98
MoL3disci0
-2.7
114.3
124
Apia
-16.0
260.0
72
_
the map is formed by the reomagneLic paraliels and meridians. On the edge or the
diarram, the local l'eumarnetic time of the meridians correspondinc tou Universal
Time is shown. In preparing the diat ram, I used not only the values of the vectors
for the 13 enumerated observatories ['or Oh, but also for 21 and 3h, the latter values
being placed on the meridians corresponding to 21h
+ A � 690 and 3h + A � (-90 reoinhg�
netic time. The horizontal component o the :Aunt' Cield is repre.;ented by the vector,
the vertical component by the digit at the origin or the vector. It will be clear
from the Cigure that the vectors of H are directed primarily along the ceomarnetic
meridians, that the vectors reach their maximum values in the zone 4) = 60 - 650, and
thin t, at latitudes lower than 50� they are necligibly small. The representation of
the field of a polar storm shown in Fig.31 by a series of Bessel functions was accom-
plished in the following, manner: The data of the Z components were interpolated for
�
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:various latitudes ( 4) equal to 901 701 67, 64 and 50�). For each latitude I calculat-
'ed the coefficients of the expansion of Z into the Fourier series:
Z = (p, cos ny q,1 sin ny),
�
where the argument T corresponds to the geomagnetic longitude A. For a satisfactory
representation of Z it proved to be sufficient to confine myself to n = 0.1 and 2.
�
�
7'
Fig.31 - Field of Polar Storm (According to Vestine). The horiz3ntal
component of the field is shown by an arrow, the vertical by numerals
(in gammas). The corrdinate net is the geomagnetic latitude and the
geomagnetic time
Then pn and qn were represented by a series of Bessel functions of the nth
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order
nm4 n Vsn 711
r
qn.21idnsei
�
�
�
fT
while cnm and dnm were found by the well-known formulas
Cnm=--
dnm
2 Iv rpn(r)Ja(): Le)
21 rqn(r) in (A7 -r-)
[ _ 1(A')12 �
The values of the H component, as indicated above, were first integrated to ob-
tain the value of the potential V, and then anm and bnm were calculated by means of
eq.(4).
Table 15 gives a summary o-f-Che coefficients anm
Table 15 *
� � �
d so obtained.
run
m
1 1 2
3
4
5
co
�32 �39
53
46
�50
�51 �77
�6
60
�30
21
27'-81
�84
73
�34
�26
�64
�18
25
1
22
�31
�7
8
�2
�12
ao
347
1.66
�0.60
0.02
� 0,09
at
�
b1
3 28
3.66
�1.48
�0.25
1,04
a,
103
1.36
0.18
0.09
0,11
b2
_
_.
Equations (4) and (5) satisfactorily represent the initial observed data, as in-
dicated in Table 16 which gives the calculated and observed values of V (in CGSM) and
* In Table 15 the values of the coefficients are given in units of 10-5 CGS. The
values of al and b2 do not exceed a few units of the fifth decimal place.
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of Z (in' y ) for four points.
The separation of the potential into portions of external and internal origin
by means of eqs.(6) and (7) showed (Table 17) that the external potential Tis consid-
�
�
Table 16
A
Zobs
zcalc
Vobs
Vcalc
i
30�
00
-170
-140
5 x 10-5
5 x 10-s
80 1
90
- 60
-90
5
6
� 66
66
0
90
120
180
100
200
2
2.5
'' ..
2.5
erably exceeds the interrial potential V. For a quantitative estimate of the ratio
of the external to the internal fields it is more convenient to represent V in the
form
where
II(�A � 1 (nO + es) m V -- Ee
1, g 4-e
n
711 V (a` s m)2 7 (Peam)1; tg
an m
RI
nm ((tin)'� (pin ; tg cnst rn M
I
Table 17 gives the value of e '�. and also of f = I/E and 6 = y
n 'n
(20)
(21)
This fable shows that in two cases f> 1 and in one case f could not be calcul-
ated, because of the smallness of the initial coefficients. In Chapter X, we will
show that the values obtained for f and 6 are in agreement with the hypothesis that
the internal part of the field is of inductive origin. The mean value f = 0.86 is
the same as that obtained for the polar cap from the data of the SD-variations
(Vi/Ve = 0.89), which indicates the plausibility of these values. The value f = 0.86
- 0.89 considerably exceeds the corresponding values for the Scr and Dst-variations
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�
CHAPTER VII
SEASONAL AND 11�YEAR VARIATIONS OF THE Dst AND SD CURRENTS
Section 1. The 11�Year and Seasonal Variations of the Dst Currents
�
�
The present Chapter is devoted to a discussion of the variations that the mean
pictures of the electric currents described by us undergo with the seasons of the
year, and with the 11�year cycle. It is not possible to collect the observational
data for a series of years from the wide net of observatories that is necessary for
the mathematical calculation of the currents. I therefore confined myself to the
study of the 11�year and annual variations of the Dst and SD variations from indivd�
ual base stations, on the basis of which I then drew my conclusions as to the varia�
tions of the current system as a whole. As my basis I selected observatories with
long series of observations whose variations are characteristic for the correspond�
ing regions.
Let us first turn to the 11�year fluctuations of the Dst currents. The depend�
ence of the degree of magnetic disturbance on the level of solar activity is widely
known: the coefficient of correlation between the annual numbers of the u�measure
of magnetic activity and the relative sunspot number may go as high as 0.9. Since
with increasing solar activity, the number and mean intensity of the disturbances
also increases, it may be expected that in the 11�year cycle the mean characteristic
of the Dst variations will vary and, consequently, the intensity of the system of
currents equivalent to it will also vary. Instead of the very laborious calculation
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in whose analysis the data from the entire earth were used. The possibility is not
�
excluded that this discrepancy is not fortuitous, and that it indicates the aniso-
tropy of the deep parts of the earth (for more uetails, see Chapter X).
�
�
�
ao
2,313
0,30
pi
a,
1A8
0,63
5
z
�
�
�
0,14
1,51
Table 17 *
E x terna 1 Veld
2 3
00 -044
025 001
2,09 -055
0.85 0,12
0,02 0,00
1A6 0,56
4
5
-0,10
0,03
-410
0,04
-025
0,56
000
01016
0,00
0,02
032
057
71
264
277
89
92
E,. . .
065
085
0,10
OtO
72
348
359 ,
0
90
Internal Held
1
2
3
4
cro
1,02
072
-.016
^r1107
-0,25
-0,01
0,10
P1
1,80
1,57
-492
OA
a2
0,40
0,51
006
0,011
P2
-414
-0,02
0,00
0,00
1,82
1,59
0,92
0,10
vi
260
261
91
0
0,42
0,51
0,06
008
�2
20
3
0
0
fi
12
0
62
274
0,06
342
5
-4,12
-0,04
0,48
0,06
-0,02
0,50
265
0,06
18
Ratio 01 Internal and External 'Fields
1 2 3 4 5
1,21 0,81 1,67 0,31 0,68
0,65 0,60 0,60 - 1,00
9
-36
24
16
-2
92
--32
-4
0
90
The ionospheric currents whose field is identical with the field of the ideal-
ized polar storm were calculated by eqs.(13) and (19). The disturbances of the polar
ionosphere, as a rule, extend to heights of 100-3U km. Down to these same heights
the lower boundaries of tha aurora usually descend. This forces us to consider that
the most probable height of the currents of polar storms is the region of the E layer.
of the ionosphere, i.e., 90-120 km. The highly local character of the course of these
storms, when the form and intensity of the disturbance varies considerably over a dis-
tance of a few hundred kilometers, likewise prevents us from referring these currents
to great heights. These assumptions forced us to use zo = 100 km in eq. (19) . Phe
* In fable 17, the values of a,
and in degi-ees.
E, and I are Liven in gammas and those of
6
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*of the Dst variations for different years, I limited myself to the consideration of
�
�
�
the quantity Dm = Hd - Hq. A consideration of Dm is entirely adequate for judging
the geographic distribution or time fluctuations of the field of Dst, since, as noted
above, Dm is approximately equal to the mean value of DstH on the two first days of
a storm.
From Fig.33, showing the relation of Dm and (I, it will be seen that the geo-
graphic distribution of Dm in the middle latitudes (t 500) varies little during the..
course of the 11-year cycle: the curves of Dm(t) in the years of high activity
(1938) and low activity (1933) almost parallel each other. In the high latitudes
(t > 500) there is a considerable change in the form of the curve of Dm(t). However,
as repeatedly pointed out, the hm of high latitudes are due mainly to polar storms
and do not characterize the Dst field. In view of this it can be considered that,
from year to year, there is little change in the configuration of the Dst current
system, but that there is considerable change only in its intensity.
In the preceding Chapters we have pointed out that the approximate method of
evaluating the intensity of currents gives good results, close to those of the exact
mathematical methods. Thus, for example, the intensity of the Dst current flowing
west along the parallels of latitude in each hemisphere, according to the data of
spherical analysis, is I = 180,000 amp, while the approximate estimate, based on the
value of Dm at Huancayo, gives I = 176,000 amp. Starting out from this good corre-
spondence, the current strength of Dst Was calculated from the Huancayo observations
for 1922 - 1944. As will be seen from Fig.34* the current strength undergoes great
fluctuations, from 12 x 104 amp in years of low solar activity to 40 x 104 and 50 x
x 104 amp in years of high activity. Corresponding to this, the mean current den-
sity varied from 1.2 x 105 to 5.0 x 10-5 CGSM. Just as in the consideration of the
* The values of I for 1919 - 1922 are calculated from the values of Dm at Watheroo,
and for 1945 to 1950 from Dm at Zuy. The values of Dm at Watheroo and Zuy were mul-
tiplied by the factor 1.2 to reduce them to the values at Huancayo.
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coefficients s and T (in amperes) calculated under this hypothesis are given in
Table 18, and th3 resultant system of currents is given in Fig.32. A comparison of
sks
�
�
�
.1
S.
1.3
11.3
11,5
Fig.32 - Current System of Polar Storms; Intensity of Current in 10,000
Amperes. The current flowing between two adjacent lines of current is
10,000 amp. The coordinate net is the geomagnetic latitude and geomagnet-
ic time. ( positive values of current function; - - -negative values)
the current system of Fig.32 with the Silsbee - Vestine system, constructed on the
basis of these same data, but by an approximate method, indicates their gre&t resen-
blance. This is still another confirmation of the conclusion drawn by us in Chapter
V to the effect that the approximate method gives a good idea of the configuration
and intensity of the current lines, and can be successfully used in cases where a
qualitative idea of the current system must be obtained without great expenditure of
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.11-year cycle of other magnetic characteristics, a lag of the magnetic maxima behind
the solar maxima is noted in good agreement with the corpuscular nature of magnetic
disturbances.
80�
0 In the work of Chynk (Bib1.41), cited in
�
60 �
106z. Chapter I, it has been established that Dm has
40
systematic seasonal fluctuations. Besides the
20 �
double wave with maxima at the epoch of the equi-
noxes and minima at the epoch of the solstices,
�
60- . which is inherent in all measures of magnetic
033a. S.
40 �
, activity, a simple sinusoidal wave with a maxi -
20 mum in the winter for each hemisphere and a
80' minimum in the summer may also be separated
�
�
60-
1.938e. from the annual march of Dm. At Huancayo, lo-
40 � � .
� cated close to the geomagnetic equator
20
(4) mi -0.6�; T = 12�S), the value of Dm is about
equal at the December and June solstices (cf.
Fig.33 - Dependence of
Fig.35, which gives the values of Dm for the
Dm = Hq - Hd (in y) on the
years 1922 - 1944). This compels the assump-
Geomagnetic Latitude
tion that in the epoch of the solstices the
lines of zero value of the current function are not deflected far from the geomagnet-
ic equator, in contrast to what happens in the case of the S variations. The inten-
sity of the current (in 104 amperes) in the northern hemisphere, (calculated from
the DmH of Zuy Observatory) and the southern hemisphere (calculated from the DmH of
Watheroo Observatory) is shown in Table 19. The mean values for 1938 - 1944 of the
intensity of the Dst current are given separately in Table 20 for the northern and
southern hemispheres.
Thus the seasonal fluctuations of Dst actually do have a maximum at the epoch
of the equinox and a minimum at the epoch of the solstice. The summer minimum is
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labor.
The system of currents represented in Fig.32 consists of two eddies in which the
current flows in opposite directions. This explains the fact, illustrated by Figs.9
and 31, that at polar stations located in different hemispheres the storms are usual-
ly observed simultaneously but have different signs for the H component. The current-
eddy located on the morning side of the polar cap is considerably weaker than the
evening eddy: The total current in it reaches 16,000 amp, while on the evening side
it is 55,000 amp.
The system so described is completely different from the currents postulated to
explain the polar storm by Birkeland, but, conversely, it does resemble the polar
�
�
part of the currents of the SD-variations.
fhis resemblance is entirely understand-
able if we bear in mind the fact that the polar disturbances, which everywhere accom-
pany worldwide storms, make the greatest contributions to tha SD-variations.
Table 18
m
1 2 3 4 5
so
�32X103A �17X103A 8X103A 23X103A 1 X108A
si�
� � _ _
Ti
�26 �40 11 5 13
s2
�11 �16 �2 0 �1
T2�
� � � ---�
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""ollism,`���P�wmaiRiamimamm...
'deeper in both hemispheres than the winter minimum.
Table 19
�
�
�
year
d)
1
c) 1 e)
c)
d)
e)
year
c)
d)
I e)
1919
12
18
26
1935
12
16
22
1920
10
15
31
1936
17
19
28
1921
10
39
16
1937
15
25
38
1922
9
13
21
1938
35
34
49
46
26
51
1923
5
8
21
1939
26
45
48
29
39
44
1924
5
19
11
1940
18
25
64
1925
15
17
16
1941
25
40
42
27
31
43
1926
18
23
41
1942
21
15
28
23
10
29
1927
4
20
28
1943
18
29
28
23
20
27
1928
13
28
22
1944
21
14
22
22
11
20
1929
30
19
22
1945
17
11
20
1930
26
29
28
1946
24
25
63
1931
13
16
14
1947
42
30
56
1932
13
17
19
1948
25
25
34
1933
16
16
19
1949
38
35
44
1934
9
16
15
a) Watheroo; b) Zuy; c) Summer; d) Winter; e) Equinox
Section 2. 11-Year Variation of the Middle-Latitude Part of the SD Currents
The 11-year and seasonal fluctuation of the SD variations are considerably more
complex. The mean annual SD variations were calculated for a number of observatories
for all years for which the data was available to us. As an example, the SD varia-
tions for three observatories (Dombas, Slutsk and Huancayo) are given in Tables 21 -
23. A consideration of the materials collected by us has shown a very systematic
variation of the SD variations from year to year. In many cases these changes are
expressed in the increase of the amplitudes with the increase of solar activity.
But in a number of cases, changes of form and a shift in the time of the extreme val-
ues is observed (thus, for example the SDH of Slutsk, the SDZ of Uellen and Matoch-
kin Shar, etc). At different latitudes, the cyclic variations of SD proceed dif-
ferently. The peculiarities noted in the variations of SD force us to assume that
the intensity, location and dimensions of the four current eddies making up the cur-
rent system of SD vary during the course of the cycle, the variations in the polar
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and middle-latitude eddies being unequal. In this Section we shall discuss the fluc-
tuations of the middle-latitude eddies responsible for the course of the SD varia-
tions in the belt oft 60� geomagnetic latitude.
�
�
�
70
25
40 Sit.
65
: 60
Fig.34 - Cyclical Fluctuation of Electric Currents of Dst and SD Variations
(W - relative sunspot number; Ist - intensity of Dst current;D - inten-
sity of middle-latitude eddy of SID current). The dots indicate the inten-
sity of the additional eddies. Jsp - intensity of polar eddy. Units of
intensity -104 amp.'! o - geomagnetic latitude of auroral zone (from 1922 to
1936, from data of the SD variations at Sitka observatory, from 1934 to
1943, from data of the SD variations at Uellen Observatory)
Table 20
�
Hemisphere
Equinox
Winter
Summer
Northern
36 x 104
28 x 104
23 x 104
Southern
40
28
23
Middle
38
28
23
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The variation of the SD variations at the low latitude observatories during the
11-year cycle are small (for example, the SD variations at Huancayo, Watheroo and
Paris), and manifest themselves mainly in variations of amplitudes. In the equatori-
al zone, the SDZ components differ little from zerb, while the H components of the
contrary are rather distinct. At the latitudes of the centers of the current eddies
= 1.400 _ 509, the SD variations of the X components are faint while those of the
Z components are distinct. In view of this
a)
50
0
0
40
�
o
�
30
�
so
4,
�
o
20
10
1111
fact, it is more convenient to select the am-
plitude of SDH (or X) at the equatorial sta-
tions (Re) and the amplitude Z at the middle-
�
latitude stations, as our index of intensity
of the SD variations. The values of RH and
Rz given in Table 24 for Huancayo, Watheroo,
Paris, and other observatories show that there
is.no exact parallelism between the march of
the amplitude and the annual relative sunspot
numbers; but still the periods of elevated
activity (1925 - 1931, 1936 - 1942) are like-
wise marked by an increase of amplitude at
0 � 20 40 60 80 100 120 W
Fig.35 - Values of Dm = Hq - Hd
from Huancayo Data for 1922 - 1935
(o - I, II, XI, XII months; o
- V,
VI, VII, VIII months; W - Relative
Sunspot Numbers)
all observatories. A certain shift-of the maxima is noted (a lag of the maxima of
the SD amplitudes behind W), which is entirely absent in the Sq amplitudes (for com-
parison we also give in the Table the R(Scl H) for Watheroo and the u-measure of activ-
ity). Particularly characteristic in this respect is the maximum of the cycle 1923
- 1933 which occurred in solar activity and Sq variations in 1928, and in SD, in
1930 (see the very sharp increase of RSD at Watheroo). The march of the RSD numbers
is less smooth than the march of RSq, the u-measure and W. The cyclical variations
depends on the latitude: at Paris, the RSD are greater than at Watheroo and Huan-
cayo.
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�
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The observatories located in the zone of the center of the middle-latitude eddy
32 40 - 50�), display not only considerable fluctuations in the amplitudes of SD, .
but also a variation in the form. This indicates that the position of the center of
the middle-latitude eddy varies in latitude from year to year.* Thus, according to
the data of the Sd at Slutsk (cf.Table 22) it is very clear that in 1924, 1931, 1933,
and 1935 the center of the eddy was at the latitude of Slutsk, in 1932 and 1934 some-
what north of Slutsk, and in the remaining years south of Slutsk. In the first
years of those enumerated, the SDH hardly deviates from the zero line, in the follow-
ing group of years the form of SDH approaches the low-latitude type (with a minimum
in the afternoon hours), and in the years of the last group, the form of SDH is typ-
ically middle-latitude, with a clear maximum in the evening hours. The same varia-
tions in the phase of SDH takes place at Sverdlovsk, Kazan!, de Bilt, and Zuy. To
give a more impressive idea of the fluctuations of the center of the middle-latitude,
eddy, Fig.36 shows the position of the center of this eddy in 1932 - 1933, 1938 -
1939, 1941, 1944, and 1948. The position of the center in the II International Po-
lar Year is plotted from the most complete data of all. It will be seen from the
figure that it represents, like the zone of magnetic activity, an ellipse which, in
very coarse approximation, is confocal with the zone of magnetic activity. This is
evidence for the view that the asymmetry of SD, which was mentioned in Chapter V,
also exists in the middle latitudes, but to a lesser degree. On the territory of
the USSR the line of the center of the eddy passes through Slutsk, north of Sverd-
lovsk and Kazan!, somewhat north of Zuy, and considerably to the north of Toyohara,
South Sakhalin. In another year of minimum (1944), in which the value of W was al-
most identical with its 1933 value, the SDH at Zuy is close to that of 1933, but at
* There is also a small shift of the center of the eddy during the hours of the day,
which is manifested, for example, in the shift of the maximum of SDZ at Slutsk from
19 hours in 1932 to 1730 hours in 1939. But this shift is very small by comparison
with the variation of the latitude of the center of the eddy.
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'Sverdlovsk and Kazan' SDH is almost of transitional type, which compels us to plot'
the line of centers in 1944 somewhat to the north of these observatories. In the
years of high activity, the line of centers plainly descends to low latitudes, but
�
�
�
t.
Fig.36 - Position of Line of Centers of Middle-Latitude Eddies in
Different Years of the Solar Cycle. The Coordinate Net is Geomagnetic
this movement is not parallel in the entire sector we are discussing. The fact that
in a year of exceptionally high activity (1948), the position of the lines according
to the data of Kazan', Sverdlovsk, and Zuy was almost the same as in 1944, appears
to be somewhat surprising. Thus the conclusion may be drawn that the fluctuations
of the line of the center of the middle-latitude eddy are very complex, and that the
data of observatories located at different longitudes must be used for their study.
Considering however, that on the average, with increasing activity, the lines
of the centers descend by 5 - 6�, I calculated the intensity of the current of the
evening eddy (14) for 1922 - 1944, based on the value of the evening minimum of SD
at Huancayo and using the above described approximate formula. It was found that
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'the march lip is completely parallel to the march of RH at Huancayo. It follows tha
,SD depends almost completely on the value of X and depends little on the extension of
the eddy along the meridian. Consequently, the error of �4� which may possibly have
�
�
been made in estimating the position of the center of the eddy will distort the value
1
of 'SD only slightly.
Table 24
b)
c)
Rz
d)
Rz
e)
f)
q)
h)
i)
i)
w
-
S ft
q
Rz
Rz
Rz
Rz
Rz
RH
1916
- 066000
LO ����� .er c6 to to to co � cr) co kr o)
�-� C4 C4 �-� Cs4 c%4 c�I css
�
X) CO Ci') g co o es Mu" 0 0 In M 0 2) VI 0 0
CI CI 'V 'Tr cT7 C4 C4 CI � C4 CI
160,In0004���t1)N.LOV,00%0
ts on es oo co �
o o in cv
0 01 0 ",IT 0 CI)
56
1917
104
1918
80
1919
20
64
23,2
1920
18
38
15,8
1921
20
26
12,4
1922
18
14
14,2
1923
14 :
35
75
6
12,4
1924
12
30
72
26
15,0
1925
15
50
98
44
14,4
1926
22
100
125
64
19,6
1927
24
60
120
70
22,2
1928
19
65
125
78
23,0
1929
24
d 55
65
19,5
1930
32
240
36
14$
1931
16
120
21
14,0
1932
17
60
115
11
14,4
1933
18
57
110
6
13,2
1934
15
40
80
8
16,8
1935
21
58
110
36
15,0
1936
22
22
60
117
80
18,0
1937
23
24
114
25,4
1938
31
38
105
110
23,6
1939
32
40
110
89
24,2
1940
27
47
68
18,4
1941
30
49
46
20,0
1942
21
26
27
17,0
1943
26
28
15
18,4
1944
20
22
10
16,t
1945
20
35
1946
52
92
1947
152
1948
136
a) Year; b) Watheroo; c) Paris; d) Slutsk; e) Sitka; 0 Tromso; g) Lovo;
h) Dombas; i) Huancayo; j) u-Measure
The following features must be noted in the march of ID (cf.Fig.34):
1. The values of I1 vary by a factor of almost 3 from the year of maximum ac-
SD
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.tivity to the year of minimum activity (3.8 in 1925 and 11.0 in 1927 and 1943).
2. After 1938 the values of II continue to rise almost monotone, reaching very
SD
high values in the years of the minimum (1943 and 1944). Since material for only two
�
�
cycles is available to us, it is difficult to give an explanation for this phenomenon.
3. In some years (years of high solar activity: 1927, 1928, 1937) the center
of the eddy splits into two parts, that is two maxima are found in the SDH at Huan-
cayo. The secondary maxima are marked by dots on Fig.34.
1
4. The agreement between the cyclical variations of In and I% is small.
at
Thus, for example, the sharp drop in I1 in 1928 corresponds to a smooth march of
SD
1
In , and, on the other hand, the maximum of I1 in 1930 corresponds to a minimum
at at
1
in I, 1
The fluctuations lc are less regular than the fluctuations of I, ; the
SD. "D 'st
latter follow the cyclical variations of W considerably more closely. The march of
I1 displays no tendency to a lag in the time of the maxima with respect to W, and,
SD
on the other hand, a certain lag of the epochs of the minimum does appear. The 1re-
latively poor correspondence between In and IA becomes particularly interesting
'st
if we bear in mind the fact that the intensity in both systems of current is calcu-
lated from one and the same empirical data of the X component at Huancayo Observa-
tory. This poor correspondence, it seems to us, is one of the indications of the
different nature of these two current systems, the Dst currents being more directly
correlated with the intensity of solar activity, while the SD currents may possibly
be affected by other factors as well.
Section 3. The 11-Year Variation of the Polar Part of the SD Currents
For studying the fluctuations of the polar eddies, the SD variations of the ob-
servatories at Dombas, Lovo, Sitka, Godhavn, Sodankyla and other Arctic Observator-
ies were calculated by me. The fluctuations of SD at the polar observatories from
year to year are considerably greater than at the middle-latitude observatories.
The cyclical variations of the amplitude of SD reach their maximum value in the im-
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'mediate vicinity of the auroral zone (observatories at Tromso, Sitka, etc). At the
observatories with the circumpolar type of variations (Godhavn, and, in part, Tikhaya
Bay) the variation of the amplitude is again considerably smaller. Since all the
�
�
above enumerated observatories are far from the centers of the current eddies, the
SD variations of the horizontal component are of the same type as to form in all
years, and differ only in amplitude. A change in form is observed in the SD of the
observatories located beneath the zone of the hypothetical linear current: Sodankyla,
Matochkin Shar, Dickson. In the Second International Polar Year, a transitional
type of Z variations was observed at these observatories: at Sodankyla, it was close
to the midale-latitude type, while at Matochkin Shar and Dickson it was close to the
polar type. This indicates that the iohe of linear current, (or of strong concen-
tration of surface currents) must pass to the north of Sodankyla and to the south of
Matochkin Shar and Dickson. In years of high activity, the SD variations of Z at
all three observatories take on a distinctly polar form, which confirms the well
known fact of the descent of the zone to lower latitudes with the growth of activity.
To obtain the numerical data on the location of the zone and the intensity of
the current in different years of the 11-year cycle, I calculated the value of I and
(Po, using the formulas for the linear current (cf.Chapter V), from the data of few
observatories, assuming that the height of the current during the entire 11-year
cycle did not substantially vary from that of 1933. The replacement of the surface
system of currents by linear system as we have seen in Chapter V, allows a rather
good estimate to be made of the. position of the auroral zone. The assumption of the
invariability of h does not of course correspond to the actual behavior of the
heights of the ionospheric layers, and this produces a certain element of the arbi-
trary in my results. But whatever scanty information on the 11-year fluctuation of
the height of the F2 layer in the polar latitudes is today available indicates that
these fluctuations are not large. The calculations made separately for the morning
and evening hours (cf.Table 25) show that the latitude of the zone and the intensity
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Table 25
�
�
�
Year Time of Day
40; / 104 AC--1 41; /X 104A
5itka. Dorn bas
1920
1921
1922
1923
1g24
1925
1926
1927
1928
1929
1930
1931
1932
1933
1934
1935
1936
a)
a)
b)
a)
a)
a)
b)
a)
b)
b)
a)
b)
a)
b)
A)
b)
a)
b)
b)
a)
b)
a)
a)
b)
a)
b)
a)
b)
67,4
65,7
66,8
65,2
66,0
65,2
62,7
62,2
62,7
62,2
63,5
63,0
64.6
63,8
63,3
63,2
67,2
63,2
64,6
64,6
65,7
65,4
69,8
66,2
68,0
64,6
62,7
62,7
-18
16
-16
13
-19
18
-19
19
-19
17
-23
16
-28
24
-42
31
--32
24
-23
19
-23
20
-28
18
-65
17
-20
15
66,4
68,2
67,1
70,3
68,5
67,8
68,5
69,6
68,9
71,5
67,1
68,2
65,3
65,3
66,4
64,6
66,7'
66,0
65,6
66,4
65,3
65,7
69,7
68,9
67,8
68,9
68,2
68,6
69,3
68,9
69,0
66,4
b9,0
66,8
-9
5
-7
6
-10
6
-5
3
-5
-7-
4
-9
6
-43
7
-10
7
-9
5
-7
4
-8
4
-10
5
year
D
ITime or Chelyus kin ickson
01'111 X 1041
4)0� liX i0a A
tilatothkin Sher Wien
4).0 I/ X 104A 4).30 /X 104 A
1933 a)
b)
1934 a)
b)
1935 a) 45,5 -100
b) 59,5 44
1936 a) 51,4 -121
b) 59,1 55
1937 a)
b)
1938 a)
b)
1939 a) 56,7 -79
lo)
1940 a) 49,7 -123
b) 47,4 150
1941 a) 54,3 -106
b)
1942 4) 54.6 -76
b) 52.8 78
1943 a) 56,1 -96
b) 49,6 -148
1944 i) 56,7 -61
b) 1 46,4 124
a) morning b) evening
61,0
62,9
60,2
62,1
-60,8
61,9
60,4 �
61,8
60,1
60,9
59,1
59,3
59,7
59,3
60,7
60,6
59,3
59,9
60,3
60,9
59,0
60,5
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17
-27
17
-34
22
-32
22
-39
30
-55
48
-46
53
-43
34
-50
36
-37
26
-45
33
61,9 -33
64,1 18
61,8 -26
64,3 13
61,5 -42
62,7 31
59,6 -72
59,6 76
59,5 -39
59,8 50
60,3 -45
61,5 41
55,6 -65
61,4 29
64,6
64,0
65,0
63,4
62,6
62,7
62,3
62,1
62,6
62,0
63,0
62,9
62,3
62,6
64,6
63,6
64,2
63,0
-21
15
-19
15
-19
16
-27
23.
-31
19
-26
19
-17
17
-29
10
-22
25
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�:
of the current vary about equally in the two halves of the day during the course of
these years. No systematic difference whatever was found in the cyclical variations'
of I or 410 at various times of the day, as should have been the case if the morning
and evening disturbance were due to different solar agents (cf.Chapter I).
In view of th'e fact that the fluctuations of the parameters of the current, from
the data of observatories located south of the auroral zone, lead to similar results
for all those stations, Fig.34 gives the mean values for I and 410 of the morning and
evening hours at the Sitka Observatory for 1920 - 1926 and the Uellen Observatory
for 1933 - 1943.* The southward shift of the auroral zone was distinctly manifested
during the course of both maxima: this shift amounted to 4.5� in the 1923 - 1933
cycle, and to 3.5� in the 1933 - 1944 cycle. But the return to the high latitudes
after the 1938 maximum was not immediate. In 1943, already characterized by low val-
ues of the solar activity, the position of the zone was only slightly north of its
1937 position. There is a strikingly good correlation between the position of the
zone and the intensity of the zonal current, which is notable not merely in the gen-
eral tendency of the variations during the 11-year cycle, but also in the oscilla-
tions in individual years (for example, the increase of 0 and the decrease of I in
1940, in 1942, etc). The absence of parallelism between the 11-year fluctuations of,
the intensity of the current in the polar zone and the middle latitude current eddy
indicates that possibly the mechanisms exciting them may be somewhat different. The
curve of annual values of the intensity of the polar currents would appear to dis-
play two maxima each in the course of an 11-year cycle, of which one is located on
the branch of rising activity, and the other on the branch of falling activity (cf.
years 1930, 1935, 1938, 1939).
6
The variations, with the solar cycle, of the position and intensity of the po-
lar current, according to the data of observatories situated in the zone itself or
* The absolute values of I and (po, as already stated in Chapter V, differ somewhat
between the different observatories.
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�
north of it, are less regular. Thus, for example, according to the data of the Dick-
son Observatory, the southern position, of the zone connected with the maximum of 1938
was maintained until 1943 inclusive. The fluctuations of the position of the zone,
from the data of the Matochkin Shar and Chelyuskin Observatories, according to the
extremely fragmentary information represented by the data of Table 25, appear to be
entirely random. The intensity of the polar current, according to the Chelyuskin
data had maxima in 1940 and 1943, but according to the Matochkin Shar data, in 1937.
It is possible that the results obtained may be interpreted as follows: during the
11-year cycle the width of the auroral zone varies. Its southern boundary is regu-
larly shifted southward in the years of high magnetic activity and northward in the
years of low activity. The northern edge of the zone is either little shifted at
all during the 11-year cycle or is shifted according to certain peculiar and still
imperfectly elucidated laws of its own. These facts are in good agreement with the
view of auroral investigators to the effect that the cyclical fluctuations of the
auroral frequency in the zone and in the polar cap are different from those at lower
latitudes. Thus Vegard denies any existence whatever of a regular cyclical behavior
in the auroral frequency. Tromhold indicates a cyclical march inverse to the march
- of solar activity. On the polar cap, the 11-year oscillations have 2 maxima each
(on the branches of falling and rising activity), and in the zone itself'the 11-year
march has a transitional form. Pushkov and Brunkovskaya (Bib1.28) have found that
the southward displacement of the auroral zone on days with elevated magnetic activ-
ity does not involve the weakening of the auroral displays to the north of the zone,
which once again indicates the possible expansion of the zone with increasing ac-
tivity.
The question as to the position of the zone of linear current and of its fluc-
tuations in the 11-year cycle is of great importance in calculating the working fre-
quencies of radio waves over routes passing through high latitudes, since this zone
is at the same time the zone of maximum absorption. In view of this fact it appears
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�
�
�
b) c)
12 240 12 GLT
I S I I I --
H
Sakti.
11
Y.T.
M.Sh
K
it:
1St
Fig.37 - The SD Variation of the H and
Z Components of the Magnetic Field in
1932 - 1933 from USSR Observatories
a) Winter; b) Equinox; c) Summer
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to be necessary to continue the accumula-
tion of material on magnetic disturbances
and their auroral displays, which will
help to pinpoint the position of the zone.
The material on the SD variations
considered by us allow us to draw two con-
clusions: first, that the study of the
SD variations can yield useful informa-
tion on the diurnal march, on the 11-year--
fluctuations, and on other peculiarities
of the zone, and second, that the present-
ly available data from observatories sit-
uated inside the zone are insufficient
for the formulation of any reliable pic-
ture of the displacement of the northern
edge of the zone.
Section 4. Seasonal Variations of the SD
Currents
Let us now consider the seasonal va---
riations of the current systems of the SD
variations. The literature summaries of
the SD variations (Bib1.4, 6, 61) show
that the seasonal variations of the SD of
all three elements are small, especially
in the middle and low latitudes. As in
the case of the 11-year fluctuations, the
character of the variation of the compo-
nents with the seasons is completely de-
162
�
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termined by the position of the observatory with respect to the current eddies. At
�
�
�
observatories far from both the centers of the eddies and the zone of linear current,
the seasonal variations reduce, on the whole, to an increase or decrease of the am,
plitudes. Observatories near the centers of the eddies often note an inversion of
the the phase of X, while observatories located in the neighborhood of the polar cur-
rent note an inversion of the phase of Z. Figure 37 gives the SD variations of a
few observatories for the Second International Polar Year, which give a clear idea
of the seasonal variations characteristic for different types of SD. The amplitude
of the variations is greatest at all latitudes in the epochs of the equinox and is
smallest in the winter period. Their position of the centers of the middle-latitude
eddies does not remain constant throughout the year, descending southward in the sum-
mer months and ascending northward in the winter. From the SD variations of the hor-
izontal component at Zuy Observatory, at the latitude of which the centers of the
eddies were located during the Second International Polar Year, it is clear that in
summer the middle-latitude type of SD is observed, while in winter the type observed
is low-latitude. In the equinox, when the lines of centers occupy an intermediate
position, the SD at Zuy are of transitional type with very small and irregular oscil-
lations during the course of the day.
At observatories close to the auroral zone (Dickson, Natochkin Shar) the middle-
latitude type of SD variations is observed in summer and the high latitude type in
the equinox (cf. the SDZ components) while in the winter the SDZ components have a
characteristically transitional form. This indicates that the fluctuations of the
auroral zone are similar to the fluctuations of the line of centers, more specifical-
ly, that zone occupies an intermediate position in winter, descending to the south
in the equinox and ascending to the north in the summer months. The position of the,
line of centers of the middle-latitude eddies and of the auroral zone, calculated
from the data of the whole net of observatories, is shown in Fig.38a. The broken
lines in the sector 180 to 2700 denote the absence of data for these longitudes.
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'The intensity of the middle-latitude eddies (I) and of the high-latitude eddies (II
.(in amperes), calculated by approximate formulas for the surface current, are given
in Table 26.
1
b)
3
c.)
5
d)
4
e)
4
Table 26
12
18
16
,15
1938-1939
I
IL
4
16
7
26
5
21
5
21
Note. The values in Table 26 are given in 104 amp.
a) Second International Polar Year; b) Winter; c) Equinox;
d) Summer; e) Year
The seasonal fluctuations differ in years of different solar activity: in the
years of high activity they are considerably sharper. Figure 38b gives the position
of the line of centers and of the polar zone for 1938 - 1939. The character of the
displacement of the line of centers and of the zone remains the same as in the years
of the minimum, but the value of the shift is considerably greater. It will be seen
from Table 26 that in the year of the maximum the seasonal fluctuations of the in-
tensity of the currents likewise increased.
Summarizing all that has been said in the present Chapter, the following con-
clusions may be drawn: the seasonal and 11-year fluctuations of the Dst and SD vari-
ations, which differ in character and amplitude at different observatories and for
different elements, find their explanation in the changes undergone by the systems
of electric currents responsible for these variations. The 11-year fluctuations of
the Dst currents follow the 11-year cycle of solar activity most closely of all,
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A
�
ease. 201 /09/11 C0602F2ni
AM69-SI-d
�
NMI
�
Fig.38 � Position of Auroral Zone and Lines of Centers of Middle�Latitude Eddies
(a � 1932 � 1933; b � 1938 � 1939; - - - Equinox, ------ Summer; �.�.�. Winter.
The Points Mark the Position of the Magnetic Observatories. The Coordinate Net
Used is Geomagnetic)
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with the lag that is characteristic for geophysical phenomena due to corpuscular ra-
diation. The seasonal march of Dst has the pronounced equinoctial maxima which like- -
wise confirm the corpuscular nature of the phenomenon, amplitude and also have an
annual march of small amplitude with extreme values at the epoch of the solstices.
This second annual wave likewise may be explained within the frame of the corpuscular
theory, if we bear in mind that it is not only the heliographic latitude of the earth
that varies during the course of the year (Corti effect) but also the angle between
the magnetic axis of the earth and the line sun-earth. As stated by Bartels, the
variation of this angle during the course of the year changes the direction and mag-
nitude of the field on which the charged particles coming from the sun impinge and,
Consequently, also modifies the conditions of the course of the disturbances. The
11-year and seasonal variations of the currents of the SD variations are much more
complex. The correlation between the 11-year fluctuations of solar activity and the
intensity of the SD currents is not so close, and is different for the middle-
latitude and polar currents. It would seem that the fluctuations of the SD currents
are not due only to fluctuations in the intensity of the corpuscular radiation, but
also to the condition of the upper layers of the atmosphere. This latter differs in
different latitudes, depends on the solar radiation of both types (photon and cor-
puscular), and obeys its own more complex regularities.
�
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CHAPTER VIII
MORPHOLOGY OF THE DISTURBED IONOSPHERE AND THE CURRENT SYSTEMS
OF MAGNETIC STORMS
Section 1. Ionospheric Disturbances
�
�
In the preceding Chapters we have described the calculation of the, electric
currents corresponding to the external part of the field of magnetic storms, and we
have discussed the properties and peculiarities of these currents. But since we
used only geomagnetic data in studying thaes currents, many questions still remained
obscure: the distance of these currents from the surface of the earth, the actual
physical conditions in the medium in which, as we postulate, the currents are locat-
ed; whether the current layer can be identified with one ionospheric layer or anoth-
er; and so on. We have seen in Chapter I that the discussion of these questions in
the literature is only beginning. In order to give answers, though only provisional
ones, to these questions, it is necessary to formulate an idea as to the variations
that take place in the ionosphere during the time of magnetic disturbances. In the
present Section we shall briefly set forth certain information of the morphology of
ionospheric disturbances, taken from literature sources, and other data obtained as
a result of the work up of the data from a number of ionospheric stations.
The first investigators of ionospheric disturbances were Bulatov, Berkner and
Wells and Seaton (Bib1.3, 40) whose works give a detailed description of magnetic
storms from observations at Tomsk, and in South America and Great Britain. The.au-
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�
�
�
'thors noted the basic features of the behavior of the disturbed ionosphere: the
ering of the critical frequencies of the F2 layer and the increase in its heights,
the appearance of a sporadic layer at the level of the E layer, the fused and scat-
tered reflections, indicating the inhomogeneous, cloudlike structure of the'iono-
'sphere, and the increase of absorption. These features were further confirmed by a
number of works of Soviet and foreigh authors, and a description of them may be found _
in modern surveys of ionospheric physics (Bib1.1, 2). One of the latest works devo-
ted to the description of the individual disturbances is the paper by Burkhard (Bibl.
39) on the magnetic ionospheric storm of 15 March 1948. The data of about 30 iono-
spheric observatories were available to Burkhard, who calculated the value for each
observatory of A .
foz _ foz
'n
rz
where 1'0 = critical frequency of F2 layer on day of
0
storm and fn = corresponding value for a normal day. The latitudinal distribution
of A discloses obviously decreased values of f�F2 in the high latitudes and increas-
ed values in latitudes near the equator. The dispersion of values is relatively
small, which forces us to accept, without doubt, the relation found. A work by Yu.
D.Kalinin (Bib1.22) is also devoted to the morphology of an ionospheric disturbance.
To elucidate the regularities of the behavior of the ionospheric layers, he used
statistical methods common to the methods used in geomagnetism. He studied the Dst
and SD variations of the critical frequencies and the heights of the ionospheric lay-
ers for two ionospheric observatories, Leningrad and Tomsk. An analysis of the ma-
terial showed that the parameters of the E layer remained in fact normal during the
time of magnetic disturbances. This conclusion is in full agreement with the well
known fact that usually, in the middle latitudes, the disturbance affects only the
F region and only in the strongest storms does the disturbance penetrate down to the
underlying layers and disturb their structure. In the variations of height of the
F2 layer and particularly of the critical frequencies of that layer, a regular part
could be detected. The Dst variations of f�F2 are characterized by an increased in-
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�
'dex of f�F2 in the first hours of a storm, followed by a decrease in the subsequent
hours of the storm. The SD variations of f�F2 differ for the winter and sumner
months and are not the same at Tomsk and Leningrad. A consideration of the materials
for two years for two stations is, under all circumstances, inadequate for any judg-
h) ment as to the geographic incidence
0 tO 20 30
fn of the disturbed variations, or even
as to how much the variations change
a)
WWI from year to year. Nevertheless the
b)
work has shown that statistical meth-
(5rm)
ods are fully applicable to the study
c)
(4r5)
10.5mc of the ionosphere of ionospheric
disturbance.
d)
(3ws)
Analogous results have been pub-
e)
(2E s) lished by Appleton and Piggott (Bibl.
. 36) in 1950 on the question of the
,ors)
dma.
Fig.39 - Dst Variations of the Critical
Frequencies of the F2 Layer
a) Alaska; b) Slough; c) Hobart;
d) Watheroo; e) Brisbane; f) 'Juan-
cayo; g) 0.5 mc; h) Hours
correlation between magnetic and
ionospheric disturbances. After
working up the data on the F2 layer
of a number of observatories located
at different latitudes, the authors
concluded that in the middle latitud-
es ionospheric disturbance usually
take the following course: during a few first hours of the magnetic storm an in-
crease in the critical frequencies of the F2 layer is observed. This is the posi-
tive phase, which is replaced afterwards by the negative phase, in which the de-
crease of f�F2 in absolute value considerably exceeds its increase during the first
phase. The negative phase lasts considerably longer than the positive phase. The
return to the normal state of the F2 layer is slow, dragging out to a few days, as
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�
occurs with the phase of restoration of the Dst variations of the magnetic field.
The negative values of f�F2 are observed during the entire magnetic storm. In the
high latitudes, on the contrary, the ionospheric disturbances as a rule have only a
negative phase, commencing immediately together with the magnetic disturbance. The
negative disturbances of the OF2 of the high latitudes differ substantially from the
negative phase of the middle-latitude disturbances. But it is precisely the restora-
tion of the normal state of the F2 layer after the polar disturbance that occurs very
rapidly, without a long drawn-out period of after-effect. This fact, it seems to us,
is responsible for the negative disturbances in the F2 layer that accompany polar
geomagnetic storms. There are indications in the literature that by now the Dst and _
SD variations of f�F2 have been calculated for many ionospheric observatories, but
more detailed data on the results of such calculations are not available to us.*
The papers devoted to the variation of the critical frequencies and the heights of
the regular layers during the time of a disturbance have been enumerated above. In
addition to works of this kind, there have also been a large number of other inves-
tigations with respect to special types of disturbances (for example sudden iono-
spheric distvrbances due to outbursts of ultraviolet radiation), formation of addi-
tional layers at various heights during storms, the correlation of E sporadic with
the degree of magnetic disturbance, the nonuniformity of the ionosphere, etc. In
view of our basic object, to elucidate the ionospheric conditions of a typical mag-
netic storm, these studies are of less interest for us. Indeed, the existence of an
Es layer of corpuscular origin, related to and correlated with the degree of magnet-
ic disturbance, is very probable. However, in the middle latitudes, in a large num-
ber of cases, Es is observed with a completely quiet field, and Es is often absent
during a storm. There is therefore no reason to consider that its formation leads
* This question is also considered in the papers by Martin, Louis Waldo, and Apple-
ton and Martin, published before the completion of the present work (cf.Proc. Roy.
Soc. and Journ. Atm. Terr. Phys., 1952 and 1953).
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to the formation of the electric currents responsible for the regular parts of the_
field of magnetic storms.
This applies to an even greater extent to the appearance of additional high lay-
�
f* F2
a)
(65.A)
b)
(52w)
c)
(43's)
d)
(30�5)
e)
(2rs)
frs)
12 24 hours
IA
1 0,5 mc
Fig.40 - SD Variations of the Crit-
ical Frequencies of the F2 Layer
these questions.
a) Alaska; b) Slough; c) Hobart;
The additional statistical treatment of
d) Watheroo; e) Brisbane;
the ionospheric data performed by us leads
Huancayo; g) Hours; h) 0.5 mc
to the following results (Figs.39 and 40):
1. The Dst variations of f0F2 have a two-phase character at all latitudes: in
the high and middle latitudes, the first phase is positive and the second negative.
In the low and equatorial latitudes, on the contrary, the first phase is negative
and the second positive. Thus the geographic distribution of the Dst variations of
ers during the time of a disturbance. Addi-
tional and sporadic layers at the .level of
the F2 layer and above it are not invariably
observed during the time of magnetic distur-
bances, and it is not probable that they are
connected with the regularly originating cur-
rents.
On analyzing similarly the other mani-
festations of an ionospheric disturbance, it
may be concluded that the reguiar parts of
the field of a magnetic storm are most like-
ly to be related to such processes in the
ionosphere as variations of density or circu-
lations of large scale. Starting out from
these considerations, in the present survey
we have touched only on a few investigations
devoted to the consideration of precisely
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�
�
'the magnetic field and f0F2 do not resemble each other.
2. The SD variations of f�F2 vary strongly, depending on the season and on the
level of solar activity. Nevertheless certain regularities in the geographic distri-
bution of SD can be established: the amplitude of SDP1F2 is smallest in the equato-
rial regions and greatest in the polar latitudes; the time of the extreme values
likewise varies with the latitude: in the low latitudes the minimum is observed in
the forenoon hours, and the maximum in the afternoon hours, while in the high lati-
tudes, on the contrary, the minimum occurs in the second half of the day and the max-
imum in the first half. It follows from this that the geographic distribution of
Spf�F2 is analogous to that of the SD variations of the magnetic elements.
3. The Dst and SD variations of f�F2 are considerably less regular than the
corresponding variations of the magnetic elements.
No regUlar disturbed variations of the E layer are detected, either at low lati-
tudes or in the polar regions.
Section 2. Conductivity of the Ionospheric E and F Layers, and the Dynamo Effects
in the F2. Layer
As we have seen in the preceding paragraph, the density of ionization of the F2
layer underigoes variations during the time of a disturbance, depending on the storm-
time (Dst variations) and on the time of day (SD variations). Our task is to eluci-
date the question whether these variations can cause the rise of the electric cur-
rents responsible for the Dst and SD variations of the geomagnetic field. In order
to compare the quantitative characteristics of the ionosphere (for example the den-
sity of ionization or the velocity of motion) with the intensity and configuration
of the electric currents, it is necessary to have some working hypothesis about the
mechanism of excitation of these currents. The hypotheses in the literature as to
the causes for the origin of the currents of magnetic disturbances may be divided in-
to two main groups. The first of these groups includes the hypotheses related to
the aasumpiion of the deep penetration of solar corpuscles into the earth atmosphere
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f)
�
�
.(to the level of the F region and lower). As we have already shown, this hypothesis
has recently been confirmed by auroral spectroscopy, and thus there should be no
doubt of the penetration of corpuscles down to the very lowest layers of the iono-
sphere in the polar latitudes. But the question as to the penetration of corpuscles
into the ionosphere of the middle latitudes still remains unsolved. Eckersley (Bibl.
42), Burkhard (Bib1.39)� and a number of other authors consider it possible that the
penetrate in all latitudes, and explain, by the direct
puscles, those variations that are observed in the ionosphere and
of the earth during the time of a disturbance.
According to Eckersley, the positive ions penetrate somewhat deeper into the at-
mosphere than the electrons, and the vertical electrostatic field thereby formed is
the prime cause of the drift of charged particles and of the excitation of the eled2;-
tric currents responsible for magnetic storms. Without making it my task here to
action of the cor=
the magnetic field
give a complete critical discussion of Eckersleyis work, I may say that
vertical field should in my opinion prevent the further invasion of the
into the atmosphere, and thus, the process of a disturbance, as soon as
an electric
corpuscles
it began,
should at once thereafter die out, without leading to the formation of stable cur-
rent systems.
According to Burkhard, the entrance of corpuscles into the ionosphere leads, in
some manner (the author does not specify precisely in what manner) not to the in-
crease of ionization but to its decrease. The corpuscles emitted by the sun during
quiet periods penetrate the earth atmosphere at all latitudes and reduce the ioniza-
tion of the F2 layer due to ultraviolet radiation. During the time of disturbances,
the parameters of the particles vary in such a way that the particles are collected
toward the polar regions of the earth, without reaching the low latitudes. Accord-
ingly, there is a particularly strong decrease in the density of ionization in the
high latitudes, while in the low latitude there is an increase, connected with the
disappearance of the negative corpuscular effect. We have cited Burkhardls reason-
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ing in order to show to what absurd conclusions the speculative idea of the deioniz-
ing action of the corpuscular stream, developed without any connection with experi-
mental data, can lead. Not only is the course of the arguments of Eckersley and
Burkhard erroneous, in our opinion, but the very penetration of particles into the
�
�
�
lower latitudes would appear to be contradicted by a number of facts. First, the geo-
graphic distribution of the aurora is such that, at relatively low latitudes, (ci) =
= 30 - 40�), it is observed only during exceptionally strong magnetic storms, while
the ordinary moderate and great magnetic storms are accompanied by a shift of the
isochasms by only 5 - 60 toward lower latitudes, from their mean position (1-0 = 670)..'. -
The calculation of the paths of the particles in the magnetic field and the determin-
ation of the zone of their penetration into the ionosphere that have been made by a
number of authors, with various objects in view (Stormer, Bugoslayskiy, Vallarta,
Alfven, Martin, and others) are likewise all in agreement that the approach of par-
ticles to the earth in the low latitudes is impossible if the velocity of the parti-
cles is less than the velocity of light (for instance about 1000 km/sec). It goes
without saying that particularly great active formations on the solar surface emit
corpuscles at high velocities (about 3000 km/sec and perhaps even higher) which are
little deflected by the magnetic field, and produce the aurora in the middle lati-
tudes, while the intensifying the ionization in the high layers of the ionosphere or
the (more energetic) lower layers of the ionosphere (cf. work of N.V.Mednikova
(Bib1.24)). But such powerful processes are relatively rare, and consequently, we
should not take them as a basis for discussing the possible mechanism of excitation
of the electric currents of the regular variations, flowing around the earth during
moderate and small magnetic storms.
The following argument against the approach of the corpuscles to the earth sur-
face is provided by the morphology of the magnetic disturbances. The great but
smooth deviations from the normal values in the march of the magnetic elements, and
the absence of a local character in the course of storms in the equatorial latitudes,
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�
�
�
all speak for the view that the fluctuations of the magnetic field are due to stable
current systems encompassing the earth as a whole, which are not disturbed by the in--
vasion of streams of charged particles.
It follows from this that it is more advisable to assume that the middle-
latitude parts of the currents of the magnetic variations are excited in the iono-
sphere, if they can be referred to the height of the ionosphere at all, without di-
rect entrance of additional charges into the ionospheric layers.* The authors of the
works placed by us in the second group share this viewpoint. In Chapter I we have
already mentioned the investigators (Yu.D.Kalinin, S.h.Matsushita,Khiroyama) who have
attempted to explain the currents of magnetic storms by a dynamo effect in the iono-
sphere. In addition, the thought has been expressed that with the existence of an
external extra-ionospheric primary field varying with time, the currents in the iono-
sphere would be excited owing to electromagnetic induction, and would make their con-
tribution to the observed disturbance field. These thoughts have been developed in
the paper by Ashour and Price (Bib1.37), and in certain papers by Sugiura (Bib1.55).
But the dynamo and induction effects are not the only methods for the excitation of
currents. It is well known that the excitation of currents in an ionized gas by the
combined action of two fields of force on the particles (magnetic and gravitational
fields, or magnetic and electric fields) is also possible. The current so excited
(drift current) has been used to explain the S variations and the regular field of
the sun. A number of considerations, which we shall present below, compels us to
consider the drift also as a possible cause of the formation of the currents of mag-
netic disturbances. It is to the discussion of the dynamo, drift and induction me-
* The literature sometimes gives as an argument for the penetration of corpuscles
into the ionosphere the so-called "geomagnetic effects" in the F2 layer (the depend-
ence of ionization density on the geomagnetic latitude, etc). But it would appear
to be more plausible to explain these effects by the redistribution of the charges
already in the layer under the action of the earth magnetic field.
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.chanisms of excitation of ionospheric currents that this and the following Sections
of the present will be devoted.
The question of the excitation of electric currents in plasma and of the evalua-
tion of its conductivity has been discussed with great vigor in the literature of re-
cent years. The works of Pedersen, Tamm, Cowling et al (Bib1.23) show that the
value of the conductivity of an ionized gas depends substantially on the magnitude
and direction of the magnetic and electric fields acting on the particles, on the
length of the free path, and on the parameters of the particles; the motion of the
particles in the plasma will be completely different from that in the case of a rare-
fied gas, the interaction between whose particles may be neglected, and which has
been considered in their time by Stormer and Chapman. In the works of Tamm and Cow-
ling, the conductivity of an ionized gas is considered specially in its application
to the earth atmosphere. Tamm assumes the ionosphere to be completely ionized and
gives approximate expressions for the conductivity, one of which expressions is true
for regions of short free paths and the other for regions of long paths. Cowling
considers the ionosphere as a ternary gas composed of electrons, positive ions, and
neutral molecules, and obtains more general expressions for its conductivity. It is
not hard however, to show that the gonclusions of Tamm and Cowling do not contradict
each other. If the charged particles of the plasma are under the action of a mag-
netic field (1), an electric field CO and a gravitational field (acceleration of
gravity g) and, is also undergoing motion of translation under the action of certain
other forces, at the velocity -a, then according to Tam, the density of the current
formed by the translation of particles of one kind will be:
�
eN "Y ;11 - 1ft riv1.1 1)- �V
kr N kT.771,
3 Onit T N 2rn v
(Nmi -I- We (E �grad (kTN)) i1 r X.
Here the density of the given gas (N) and the temperature (T) are not assumed
to be uniform, r is the radius of vortex motion of the particles about the lines of
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0
'force of the magnetic field, and X = free path of the particles. The component of
density of the current parallel to gin the field of the long free paths (r 4=X) is
likewise described by eq.(1). If we have a binary gas (N.", n_ = N), then, from
eq.(1), neglecting the temperature gradient and density gradient, we get
�
�
�
where
(P [Zia r ,
Nell Nen Ne2 Ne
co== 2e2N 4- � �
3 VNTet j/m�+ ) 1, in_ m+v+ rn_v_ st+v+ m_v_
(3)
(4)
is the conductivity of the gas in the absence of a magnetic field. Here v = kinetic
velocity of molecules, and V= numbei of collisions per second (Xv = v). The cur-
rent described by eqs.(3) and (4) is the dynamo current used by Schuster and Chapman
to explain the Sq variations.
According to Cowling, in an ionized gas under the action of the crossed, mutual-
ly perpendicular electric and magnetic fields Eland -HI an electric current of den-
sity
(5)
is excited, where .gt must be understood as meaning not only the proper electrostatic
field -E* of some external origin, but also the electric field arising as a result of
the motion of the mass of gas in the field H at velocity w, that is
and, consequently,
7141.1)-F ([11if +hi;
(6)
(7)
The first term in the expression for j denotes the Schuster-Chapman dynamo ef-
fect, while the second indicates the formation of a current in the direction of the
velocity of motion of the gas or in a direction perpendicular to the crossed mag-
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'netic and electric fields. The expression 01, according to Cowling, is equal to
�
a
� t,
� 1 + '
(8)
where T =; time of free path (T = v-1), and w = angular velocity of procession of the
eH
particle (w =-7r vi.= rw). It is identical with the expression for the conductiv-
ity of a gas in a direction perpendicular to the magnetic field, introduced into the
literature by Pedersen:
ae2 (81)
a I � vi+ .2 �
r _ v 1
For a region of short free paths (-T - -(7-'4 I) neglecting the value of co2,
we have 01 ..='0' ) as is put in the Tam equations. The conductivity ollis determin-
- o _
ed by the expression
CuurC
c11 =_-_-
_f_w2:2 �
In the field of short free paths,
oil � and all al.
v
(9)
(10)
Consequently, Tamm did not make a large error by neglecting the current in the
direction of w (or perpendicular to and i) for this region. In the region of long
free paths ( v I )
V11 V
01 ,11 �-�,.
01 .cic cil < co
(n)
and, consequently, the current in the direction of 11 is considerably greater than
the current in the direction of -E!. It is therefore entirely natural that in the ap-
proximate equation of Tamm, out of the terms describing the dependence of the cur-
-.
rent on H and El only the term [W, + Fz4], ro should be retained.
112
Ne 011
The scaler Coefficient __ is the same as the coefficient in eq.(5).
H2 11
411 In fact,
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Thus eqs.(1) and (2) of Tamm and eq.(5) of Cowling do not contradict each other: --
Let us see now to what extent the identification of this or that ionospheric
layer with the region of long or short free paths is correct. The angular velocity -
of motion of a particle (co = IT) depends only on the parameters of this particle and
the magnitude of the magnetic field. Neglecting the variation of the earth magnetic
field with height for the region of the ionosphere, we find that for all ionospheric
layers the velocity of an electron ke.= 5 x 106 and the velocity of an ionized oxygen
molecule (A. = 102. The number of collisions in the ionosphere has been repeatedly
determined from the experimental data on the absorption (Bib1.1), and has also been
calculated by the formulas (Bib1.11):
�
�
ne4 �hi vI-- (kl)2 Niv In (0,37 e2N)
V/ �
= 167t V 17" a2N�,v
3
kr
(lar
v; � 11 Ni 'In (0,37 ,
e2N)1.3
(12)
Here �11 denotes the frequency of collision of electrons with neutral molecules,
v.7 with positive ions, vi the number of collisions of ions with molecules, and vi
of ions with ions; a = effective diameter of a particle (for air the value na2 = 7x
x 10-16 is usually taken); -NT = kinetic velocity of the particles. The collisions of
electron with electron and ion with ion with the same sign may be neglected in eval-
uatingithe total number of collisions, and therefore the term vt will have a sub-
stantial value only in those regions where there is a sufficient number of both posi-
tive and negative ions. Radio methods enable us to determine directly only the ef-
fective ionization density Nef, while the actual number of charged particles
m.
N = Ni 1 remains 'unknown. But a number of supplementary considerations (the
me
magneto-ionic splitting of a deflected radio signal,etc) allow us to judge the ratio
between electrons and negative ions in the layer 1 =III. There is no doubt today
lie
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�
that the conductivity of the F2 and F1 layers is due primarily to electrons (n_ < ne).
It is also probable that, in the E layer as well, the conductivity is determined
mainly by the electrons, since in the D layer the number of free electrons is in all
probability small. The first columns of Table 27 give the values of Nef adopted in
'the modern literature for all layers, together with the possible values of 1; the
following columns give the values of ne, n_, and the most probable values of nm,
all calculated on the basis of Nef
and 1. Columns 7 � 12 give the values of ye
HI
vf calculated by eq.(12), as well as the total number of collisions for particles
of a given kind, ve or vi. Column 13 gives the value of v determined from experi-
mental data. It will be seen from the tables that in the D layer, the total number
of collisions is determined by the collision of charged particles with neutral par-
ticles, and none of the three assumptions as to the value of 1 contradicts the order
of the observed vef. For the E and F1 layers, as will be seen from the table, the
data on vef agree only with the assumption 1 = 0, that is, with absence of any sub-
stantial number of negative ions. The value of rim for the F2 layer is determined
only indirectly, namely on the basis of the number of collisions. For an ionization
density of the order of 106 ions/cm3 and the assumption that ionization in the layer
is due to electrons and positive ions (1 = 0), this number of collisions corresponds
to the effective number of collisions between electrons and ions (cf.Table 4, p.971
. of the Ginzburg monograph Bib1.11). About the same number of collisions takes place
for electrons and neutral molecules, if the molecular density nm 1011. From this
it is concluded that the number of neutral molecules in the F2 layer does not exceed
1011 molecules/cm3. It is true that the literature also contains hypotheses of the
complete ionization of the F2 layer,, particularly in the daytime.
The data of Table 27 show that the D layer is a region of short paths of both
ions and electrons, that the E layer is a region of short paths for the ions and
0 long ones for the electrons, and that the F1 and F2 layers are a region of long free
paths for particles of both kinds. The conductivity 01 which determines the dynamo
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'effect has the smallest value in the D layer and rises for the higher layers just-ds:
�
�
�
the conductivity olI does. In the D layer 011 *"I while in the overlying layers
al and au are of comparable value, and all is even somewhat greater than al. Evalu-
ating the integral conductivity of the R region, Cowling shows that it is possible
that the conductivity of this region is considerably less, since the presence of cui--
rent in the magnetic field leads to the excitation of ponderomotive forces [wH] which-
retard the further motion of the charged particles, that is, it is as though they de-
creased the value of the conductivity. Thus the current that arises should be damped
after the time-- (where P is the density of the mass), which amounts to 45 days
Gill
for the E layer, 3i hours for the F1 layer and 20 min for the F2 layer. The damping
of the currents does not occur if the particles are under the constant action of a
force, that is, if the motion of the particles is accelerated, or if under the ac-
tion of the magnetic field a polarization of the gas occurs, neutralizing the retard-
ing force [wH], or if currents screening the internal parts of the volume from the
action of the magnetic field are induced on the surface of the moving mass of gas.
In accordance with the above, Cowling considers that the conductivity* of the
F2 layer in reality does not exceed al = e x 10-9, and that the conductivity of the
E layer is practically constant (for instance, al = 10-7 for 1 = 25). Cowling con-
cludes from this that the total conductivity of the entire ionosphere must be within
the range from 10-7 to 1041 and must be due primarily to the charged particles of
the E layer.
The values of ;al dh given in Table 27 force us to apply the following correc-
tions. Since the more probable value of the conductivity for the E layer would seem
to be j al dh = 10-9, then the integral conductivity of the entire ionosphere, caus-
ing the dynamo effect, is probably not more than le, while both layers of E and F
* Under the condition that the motion takes place under the action of tidal forces.
From what has been said it follows that the conductivity differs for different kinds
of motion of the gas.
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possibly yield equal contributions to the value of the conductivity. The conclusions
drawn as to the conductivity of the E and F layers are based on the values of the --
ionization density for a normal day. On a disturbed day, however, (cf.Chapter II),
the order of magnitude of the ionization density remains the same and, consequently,
the order, of magnitude of the conductivity should likewise not differ markedly from
that of a normal day.*
It follows from Chapter III and VII of the present work that the Dst variations
of the geomagnetic field may cause ionospheric currents flowing westward along the
parallels of latitude and having a density of about 3 x 10-9 CGS in a year of moder�
ate solar activity. If these currents are attributed to the action of the dynamo
effect, then it would be necessary to assume the presence in the ionosphere of a sta�
ble wind of meridional direction with a speed of the order of
�
�
W =--
3 X 10-5
0,3X 10-9
----- 105 cm/sec.. 1 Krrisec.
* After the present work had been completed, I learned of the paper by J.K.Csada,
Acta Phys. Acad. Sc.Hungaricae I (3) 235 � 246, 1952, which considers the variation
of the electromagnetic parameters of a gas under the influence of turbulent proces�
ses. It is shown that the local magnetic field formed in presence of turbulence
lead to an increase of magnetic permeability and to a decrease of the electric con�
ductivity of the gas. The turbulent processes occurring in stellar atmospheres may,
according to Csadafs calculations, reduce the conductivity of the atmospheric gas
by several orders of magnitude. During magneto�ionospheric disturbances, it is gen�
erally known that turbulent processes also develop in the ionosphere. However, as
shown by rough preliminary calculations, owing to the low temperature and the low
degree of ionization of the ionosphere of the earth, the turbulent processes in it
cannot lead to such great changes of the electromagnetic parameters as occur in stel�
lar atmospheres.
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�
�
�
A number of experiments in recent years (cf.Bib1.21 3, and 27) indicate the ex-
istence of horizontal movements of the clouds in the ionosphere in both its lower
layers and the F2 layers. In most cases, however, the authors give lower values for
the velocities. Thus, according to the data of Australian stations, a systematic dis-
placement of clouds in the F2 layer, having a meridional direction and a velocity of
80 - 400 m/sec, has been found. Observations at Slough have shown displacement from
time to time, of the F2 layer as a whole (or of parts of it) at velocities of 120
m/sec in east-west direction. Velocities of the order of one kilometer a second are
noted considerably less often. Thus, for example, from the observations in Austral-
ia the usual rates of motion of the clouds of the F2 layer (of the order of 400 -
500 m/sec) increase, sometimes to 1800 m/sec, during magnetic storms. It would thus-
appear that the dynamo-excitation of the Dst currents requires somewhat higher rates
of motion in the ionosphere than those usually observed. A still more weighty argu-
ment against the dynamo hypothesis of the Dst variations is the configuration of the
current system, which is a latitudinal distribution of the current lines from east-
ward during the first phase of the storm and westward during the second stage. To
explain such a form it would be necessary for the Dst variations of conductivity
(and, consequently, of the critical frequency of the F2 layer) to be of a very regu-
lar character, which would be the same over the entire earth, with an increase of
f�F2 in the first phase of a storm and a decrease in the second phase. However, as
will be seen from Chapter II of the present work the Dst variations of f�F2 only
have such a form in the middle latitudes, while in the low latitudes, their form, on
the contrary, is negative in the first phase of the storm and positive in the second
phase. The irregularity and instability of the Dst variations of f�F2, which is
particularly striking on a comparison with the Dst variations of the magnetic field,
compels the definitive recognition of the impossibility of explaining the latter by
the dynamo currents flowing in the F2 layer of the ionosphere. These same consider-
ations as to the dissimilarity of the Dst variations of f�F2 and of the magnetic
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�MINWIMIYMI0
�
Table 27
11.
ze 0
Laytt!e) it , 141.r.v1 :.-Ne
,
_ 4,;.;,:6,:,-.4'.:0 it.1,,:s.t.:,i;.1'.1w .urtkiirqi
_:,..i.:11:,-., : ,,
.1. ,...-41.�;....1, ;..-11.41, ��1
_I .,-,,,,q..-:, ., ..21 ,."..1:- �..fi.5 1 � 1.."44.4;i1 .i54.w"
1 ):..�1:11A-T,t ),--.,. ..: , a , . _x kik
-1
1
It'
� �
1 L _
2
'4
.1
�
maw*
0
20
r� �
��;
�jt!i j
.11+ � �
h � ���
II X. IV 5 X 10,
Ix"
5X 101
�
������
',ix loll
. � �
� e.
va
11188-1081 1Q108 -1
108-108
3 X 105 I - 1 3 X IV - 2 X 101
105.
1
1,5 X.105 7,5 X 108 I 7,5 X 108
10,15
2 X 107 I 10
00=���
50 I 6 X Ks 1,6 X 10181 1,6x 101�1
105
P2
. 5 X 101
0
X 105
5 x 10 I 1011
2,5X 105
1,2 X 10801 1,2 X 1011
2 x 108 108
4 X 107 I 108
� 2 'X :105
0 I 2 X 108
2 x 108 I 1010 -1011 - 101-101
layer
sod
el
e
all
s
1 11
at at
3
T ym
D
10-17
1,2 X 10-3
6 x 10-2�
10-17
10-22
2 X 105
2,5 x 10-16
5 X 10-2�
2,5 x 10-21
2,5 x 10-16
2,5 X 10-21
2 x 105
2,5 X 10-14
_
-
2,5 x 10-16
2,5 x 10-21
2 X 105
E-
2,5 X 10-16
3 X 10-12
1,5 x 10-14
2,5 x 10-16
2,5 x 10-16
2 X 108
-
-
-
-
-
Fl
F2
4 x 10-14
10-17
24 X 10-14
1,5 X 10-14
2 X. 10-14
7,5 x 105
_
_
-
I _
-
7,5 x 108
3 X 10-13
2 X 10-16
1 x 10-16
3 x 10-14
10-"
1,5 x 101
Note. In this Table the values of Nef ' n' and v are given in 3./an3, 6 in the CGS-
system, and y in cm, while 1 and 6) are dimensionless quantities.
�
'a
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Table, 27 (cont.)
,�1
rIm
���1
riv
�
1
108
2 X 106
6X 104
101
-
$x10-$
101
10,
6 x 1011
10f
1i'.�1
5 x 10-1
104
5 X 10s
6 x 101
107
5 X 10-2
HP
_
6 X 102
104
_
ao
107
5 X 101
6 X 102
104
,111
5 X 107
1 X 102
6 X 104
�
�
2 X 103
60
60
106
4 X 10i
4 x 107
7 X 104
60
l X 104
6-60
30
102-104
5X 102
�
�
�
lo-4
tim=1.
10-1
7,5 X*Icr"
I 1,7
5,2 X 10-11
1 3,3 5X 10-11
f 44dh
f .41 dh
falidh
f dh
5 ell A
2,4 X 10-12
1,2X 10-13
2,0 X 10-11
2 X 10-16 2 X 10-11 1 X 10-18
1,0 x lo-43
5 X i-' I 5 X 10-12 5 X 10-15 5 X 10-10 8 x 10-3
5 X 10-12
5 X 10-m 5 X 10-1�
5 X 10-15
6,0x 10-9
3 X 10 f 5 X 10-1� 5 X 10-12 6 X 10-6 3 X 10-8
1���=.1.
MIMEO
Mb=
7,5 X 10-11 1 2 X 10-7
1 X 10-7 1,5 X 10-7 10-7 10-7
������
3 X 10-9 1,5 X 10-6
4,5 X 10-7 1,5 X 10-6
4 X 10-7 10-6
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'field also force 115 to abandon other possible mechanisms of excitation of the iono-
:spheric currents, although these, too, may not lead to any quantitative contradic-
tions with respect to conductivity or motion in the ionosphere.
Let Us consider in greater detail the possibility of current originating in the
'ionosphere in the direction of motion of the gaseous masses. It follows from Table
27 that the conductivity fon dh of the F2 layer in the direction of motion is one
order of magnitude greater than the conductivity fa dh. Moreover, in the case of
the formation of a current in the direction of motion of the retarding mechanical
force a11H2w, which arises as a result of the motion of charged particles in a direc-
_ tion transverse to the magnetic field, would cause not a decrease in conductivity as
_ with Cowling's examination of the dynem.o effect, but the excitation of a Hall cur-
rent of perpendicular direction. Thus the value of the conductivity foil dh in the
- F2 layer would hardly be much less than 10-9, and, cOnsequentIy, if there are any
- displacements of ionized masses or winds in the layer, they would lead to the exci -
--tation of currents of relatively high intensity in the direction of these motions.
411 _ It follows from eq.(7) that to explain the Dst variations, very low velocities would
-be sufficient:
3> 100.
9 9
The latter value was rejected owing to the unreliable value j',/ - E- = - 15�
2
and for convenience of calculations, s = 32 was taken. A recalculation of eq.(64)
with the new values of the constants:
v-=0,17, 0,62 � 106q 1/70 , 0,42,
v = 0,23, = 0,89 � 105q1/170., f.=0,40
gave the following relations:
for PI lg xo - - 13,31 � 31,41 lg q
� 31g x0-= - 13,61 � 32,44 lg q �
(78)
Allowance was made for the influence of the surface currents on the Dst varia-
tions in the following manner. The internal part of the first harmonic was repre-
sented by the approximate formula
(time in hours).
For n = 1,
F -TS -8974/V
25e-0.04(i-20)
aff, di,
di
D =-- InE (n +1) �0 di =
dt
4 - 3,1 10 e�o.o2 � 20)
-I- 5,6 � 10 - 4 e� 0,04
� - (t-20)
Cg ":-� 1,34 � 105,
231
(79)
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�
�
CoL) - 4 ,2e-u2 (( -2U) � 7,5e- 0,04 (t-20) .
Tor t 20 firs CoD -I- 3,3 Ei==. 55 � 3,3 = 52,
t = 30 hrs CoD +1,6 El = 45 � 1,6 . 43,
60 hrs CoD --.0,4 El. 25 + 0,4 = 25.
Whence Ei may be approximated by the expression
Ei 52e-0,018(1- 20).
(80)
The revised value of q) (0 for t = 30 hours in completely identical with the pre-
vious value. Indeed, for t = 30 hours I. = 18 - 0.8 = 17, and (p(30 hours)17-=
52
0.33.
For the new values of the constants (v = 0.1, a = 0.018, T = 2.3
the numerical quantities entering into eq.(69) are somewhat modified,
are connected with each other by the following equation:
0,67 = 10,8x00,1 q3,2 � 1,04 � 1013 X01,1 q5,2 + 9,14 � 1013)(01,2,75,4.
x 10-16x02),
and q and xo
(81)
On solving eq.(81) in turn by the first and second equation of eqs.(78), we get
the following results:
0,949
2,5 � 10-13
Sinde the mean value of xrD for the upper layers of the earth is obviously less
than theivalue 5 x 10=6 CGS taken by us, the most probable values of the parameters
q and x may be expected to lie between the above values and those calculated in the
0
preceding Section.
Section 6. External and Internal Parts of the Harmonic P3 of the Dst Field
In the present Section we shall discuss the application of the Lamb-Price in-
duction theory to the third order harmonic of the Dst field. From eq.(42), which
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holds for the case IL = 1, it follows thaty(t) > 0, since all terms of the series
co
1
z_ 1
�
�
�
are always < 0.
Indeed: for s <
13J
1Cs`� � <
K2 and a
9

> o.
Imh(t) will be of the same sign as
corresponding to it, and the ratio
limits*
-a t.
0, and
-a L t.
a consequently e � c P > 0, and
From this it follows that each term of the potential of the induced fields
-amt.
(1 _ e n )
13
E3
sis of the noncyclical variations. Thus the four spherical analyses of the aperiod-
the term of the inducing field El"
for any instant t must lie within the
Fmk
.11
/nth
1.
Einnh
Accordingly, the negative ratio -E- for the harmonic P3 (cf.Table 8) is very
surprising. The data obtained earlier by other authors (cf.Table 8), however, do not
contradict our results. It will be seen from the Table that the negative values of
-- for the harmonics P3 and P7 are also obtained by Mc.Nish in the spherical analysis
of Dm. The values of the coefficients E and I for the third and fifth harmonics in
the Chapman-Whitehead analysis are at the limit of accuracy of the analysis. But all
13
the same it does seem possible to assume that with these authors ---< 0, while 15
E3 Es
>0. A positive sign for was obtained only once by S.Sh.Dolginov, in the analy-
ic part of the storm field, made by different authors and from different starting ma-
* The erroneous assertion of Chapman and Whitehead that can vary within any lim-
its from - c= to + co is connected, as was shown later by Chapman and Lahiri, with
the failure to allow for the free damping currents, which has already been mentioned
in Section 1 of the present Chapter.
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1
terials, all speak in agreement in favor of the alternating sign of the ratio L:
w>0 for PiohdA; E 1500 km, obtained from short-period variations, must be con-
sidered unreliable. According to Chapman's calculations, in a sphere of uniform con-
ductivity, 70% of the induced currents corresponding to the harmonic Pi and 77% of
2
the currents corresponding to P3 are concentrated in the peripheral shell of the
sphere, 0.911q< r < Rq, that is, with our values of q, at depths of 400 - 1100 km.
The increase of x with depth, of course, also increases the downward propagation of
the currents, but still, a substantial part of the currents would hardly be induced
at levels deeper than 1300 - 1500 km.
The allowance for the currents induced in the upper layers of the earth crust,
as would be expected from simple physical reasoning, increased the values of x (see
curves 7 and 8). Thus, for example, at depth 1100 km, the value of x increased from
50 - 65 x 10-13 to 70 - 110 x 10-13. In the upper layers of the conducting core
(d < 700 - 800 km), however, the corrected values of x are somewhat smaller than the
uncorrected values.
From the series of curves of 1((d), calculated by Lahiri, Fig.46 gives the two
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that he considers the most probable. Curve 9 is calculated on the assumption Ko =
= 4 x 10-14 CGS, q = 1, 5 = 37, and x2 = 2 x 10-6 CGS. Curve 10 assumes xo = 2.3 x
x 10-13, q = 0.903, 3 = co and x a = 5 x 10-6. Both curves indicate the shallow
1
�
�
X.10 13
sat!
NW-
100
I I
� I
. I
:;
depth of the level at which x increases
(d 600 - 700 km). The discrepancy between
the curves 7, 8, and 9, 10 can be explained
not only by the different starting materials,
but also by the different method of calcula-
tion. One of the Lahiri curves (not given
on the figure) is calculated under the as-
sumption xo = 4 x 10-11, q = 1, and s = 30
(without allowing for the conductivity of the
oceans) coincides almost completely with our
own curve 7. Thus a consideration of Fig.46
4 shows that the following distribution with
-=�C_
.:-r 2
depth is the most probable. The surface lay-
. 1 .1
L4
1500 Mm
ers (mainly on account of the oceans, which
Fig.46 - Conductivity of the Earth
occupy 0.7 of the earth surface with a mean
(x) from the Data of Geomagnetic
depth of 4.2 km) have a very high conductiv-
Variations
ity. The action of the ocean may be taken as
equivalent to a spherical layer of conductivity lc, -a =.2 - 5 x 10-6. The conductiv-
ity of the first 200 km is roughly the same as that of the dry rocks on the earth
surface, that is, it does not exceed 10-14 CGS. The induction of currents at these
depths may be practically disregarded. A substantial increase of conductivity be-
gins at depths 200 - 3C0 km, while a sharp rise is located at d =900 - 1000 km, and
a still steeper ascent of the curves is found at depths 1100 - 1200 km. The calcu-
lation of a model with a sharp surface of separation gives a moderate value of the
conductivity. It is naturally greater than the actual value in the upper layers of
00 500
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the conducting core, and smaller than the actual value in the deep parts.
The distribution of conductivity so obtained does not contradict the modern idea
on the structure of the earth. As will be seen from a comparison of Figs.47 and 46,
the region of the earth crust (to a depth of 60 - 80 km), is characterized by very
low values of the conductivity which, in all probability, is connected with the anis-
otropic state of matter, and with the predominance of rocks with low iron content.
A slight increase of conductivity begins from the upper layers of the outer shell
downward, and a more substantial increase occurs in the lower layers of the shell,
which are characterized by a change of chemical composition, an increase in the metal-
lic content, and an increase in density and temperature.
�
�
A certain analogy is noted between the curves of x (d) and the dependence of the
velocity of longitudinal waves p on the depth. The second-order disoontinuities of
Repetti (d = 950 km) and Gutenberg (d = 1200 km) find their reflection in the curve
ofx (d) as well: at these depths, as already remarked, x (d) appreciably changes its
direction. Thus the modification of the physical properties of matter at a depth of
900 - 1200 km, on the transition from the lithosphere to the barysphere, may be con-
sidered a confirmation of the change in the electric characteristics of the earth.
It is true that the analogy between the curves ofx(d) and p(d) noted by us does not
by any means indicate any parallelism of the curves. On the contrary, the increase
of the gradient of the functionx(d) at depths of 900 - 1200 km is 'related to the de-
crease in the gradient of p(d). The curve of temperature distribution given in Fig.
47 for comparison (TG for Gutenberg and TD for Jeffreys) and of density (Pi according
to Gutenberg, and P2 according to Bullen) also confirm the changes in the physical
properties of matter with depth.
This conclusion as to the variation of conductivity with depth may be consider-
ed a first approximation. The .olution of the question of the negative sign of the
third harmonic, and the more detailed study of the polar storms and other forms of
local disturbances may possibly introduce substantial corrections in the conclusions
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so obtained. In order to judge of the nonuniformity of the deep layers it would seem
advisable to apply the formulas of the plane problem to disturbances of local type
30001
I I
11
�
1000
4-
500
1000 1500 2002 km
Fig.47 - Internal Structure of the Earth
(bays, pulsations). In this way it will be possible to obtain an extensive material
on the conductivity of various depths 'and various areas of the earth.
Conclusion
Section 1. It follows from all the above that the primary object of the present
work, the construction of the electric currents causing the magnetic disturbances,
has been accomplished. The calculations we have made are based on a sufficiently ex-
tensive empirical material (65 observatories) which allows us to expect that the
field of calculated currents will be a good approximation to the field of observed
variations. A consideration of the morphology of the disturbances, which preceded
the calculation of the currents, shed light on certain questions of the structure and
geographic distribution of the field. The most substantial of them are as follows:
1. The classification of magnetic storms and the separation of the storm field
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into its component parts. It appears to be most correct to divide storms into two
main categories, worldwide and polar. Polar storms reach their maximum intensity in
the auroral zone, and manifest themselves in the middle latitudes in the form of
small bay-shaped disturbances. The field of polar storms depends on the local time
and has no aperiodic part symmetric with respect to the earth axis, just as it has no
prolonged after-effect.
The data on worldwide storms collected by us have confirmed the advisability of
the separation of the regular parts, the Dst and the SD variations, from the disturb-
ance field, as proposed by Chapman. Worldwide storms, in our opinion, are always ac-
companied by polar storms superimposed on each other, and therefore the field of a
worldwide storm should be divided by the means of the four-term formula
Dst+SD+P�DI.
�
2. The worked-up data on the Dst variations of a worldwide net of observatories
have confirmed the fundamental features of the structure of the field described earli-
er by other investigators (position of the vector of the disturbance in the plane of
the magnetic equator, low dependence of the field on the longitude, form of the Dst
fluctuations of H and Z in the temperate latitudes). A more detailed examination of
the question, however, by means of an evaluation of an estimate of the values of H
and Z for the quiet intervals on days of worldwide storms, has shown that the Dst
field does not have a sharp increase in the auroral zone, and varies smoothly from
equator to the poles.
3. The SD variations, on the other hand, do have a sharp increase in the auror-
al zone, and the form of SD is determined primarily by the distance from that zone
and by the local time. The SD variations of the magnetic elements have been used to
pinpoint the position of the zone. The data used by me have compelled me to place
the position of the zone considerably further south than the Vestine zone. No de-
pendence of the SD variations on Universal Time was detected. The form and amplitude
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of the variations in the region near the pole have been elucidated.
4. It has been established that if the Dst field is considered as a function of
(Ia and T and SD as a function of V and tMP then there are no substantial anomalies
�
�
�
in the geographic distribution of Dst and SD. In particular, the complete normality
of the disturbed variations at Huancayo has been specially noted.
5. Alconsideration of the geographical distribution of the SD variations has
shown that the linear current flowing in the auroral zone cannot explain the middle-
latitude part of the field. For this reason it has been shown to be more correct to
take the SD system of currents as a system of surface spherical currents.
The currents of the polar disturbances have likewise been taken as surface cur-
rents, but extending only over the polar cap down to latitudes (I = 500
.
Section 2.! The extensive starting materials used made it advisable to calculate the
currents of the disturbances by analytical methods.
The Dst currents were calculated on the basis of a spherical analysis of the Dst
variations. For calculating the currents I used an expansion of the storm potential
into a series of Bessel functions. The complexity of the geographic distribution of
the SD variations preventing me from using spherical analysis, and forced me to turn
to the method of surface integrals. The method of calculating the external and in-
ternal parts of the potential from values of the potential and Z component, assigned
on the surface of a sphere, proposed in 1941 by Vestine,.has been further developed
in the present work. A method has been given for calculating the density of the sur-
face currents from the potential assigned on the surface of the sphere. The method
is based on the extrapolation of the values of the external potential for points in-
side the sphere, the calculation from it of the current density from it (by solving
a Fredholm equation of the second kind, to which the external Dirichlet problem
leads), and extrapolation of the function of current density for external points at
the distance of the hypothetical current layer. An analogous method of solution may
be applied to the calculation of the internal current systems. All the laborious
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S
�
�
operations in the course of the calculations of the currents by the integral method
are now reduced to a single type and allow use of the very same overlays to facili�
tate the calculations. A consideration of the accuracy of the method has shown that
the errors of the mathematical operations themselves are considerably less than the
accuracy of the initial geomagnetic data. The accuracy obtained as a result of the
calculations performed is sufficient for the construction of a general picture of the
currents.
The method can yield good results only in the case where the radius of the
current�carrying layer differs little from the earth radius. But since in most geo�
magnetic problems, both for the main and irregular fields, this condition isrsatis�
fied, it follows that the method may he recommended for the investigation of a number
of questions, as for example the construction of the currents responsible for the sec�
ular variations, the study of magnetic anomalies, and the like. The possibility is
not excluded that the integral method may also find application in other branches of
geophysics, replacing spherical analysis in the case of fields of rather complex
structure.
Section 3. The current system of the Dst variations consists of current lines paral�
lel to the circles of latitude. It differs substantially from the well known system
of Chapman by the fact that there is no crowding of lines in the polar zones, and by
the different signs of the current functions in the northern and southern hemispheres.
On the basis of spherical analysis of the *List variation, I also made a calculation
of the equatorial ring current, which yielded the following results: radius of ring
a = 3.8R � 0.8R; current strength I = 7 x 105 amp. These values were calculated on
the basis of the ratio between the harmonic coefficients of terms of different or�
ders and is in good agreement with the ideas of other authors on the ring current.
The current systems of SD variations, like the corresponding Chapman systems,
consistS of four current eddies. The intensity and location of the polar currents
proved to be different from what would follow from the Chapman data. The signs of
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�
�
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the current functions, which are different in each pair of eddies, also constitute a
substantial difference.
The current system of the P-storms resembles the polar part of the SD currents.
A calculation of the linear current flowing along the zone from the data of the SD
variations is in good correspondence with the crowding of the current lines on the
map of surface SD currents. A calculation of the linear current, based on four pairs
of Arctic stations, allowed me to establish the fluctuations of the height of the
linear current, of its intensity, and of its position throughout the course of the
day. The results proved somewhat different from the analogous results of other in-
vestigators.
In this work the seasonal and 11-year fluctuations of the SD and Dst currents
have been considered. It has been found that the intensity of the Dst currents var-
ies rather regularly throughout the 11-year cycle, displaying the lag in the epochs
of the maxima by 1 to 2 years with respect to the solar maxima, which is character-
istic of all phenomena due to corpuscular radiation. The seasonal fluctuations of
the Dst current can likewise be explained from the point of view of the corpuscular
origin of the ring current: the maxima in the equinoctial epoch may be explained by
H
the Corti effect, the additional maximum in summer by the Bartels effect.
The fluctuations of the SD currents are much more complex, and are different at
different latitudes: the 11-year fluctuations in the intensity of the middle-lati-
tude eddies do not display a good correspondence with the march of the solar indexes.
Small displacements of the lines of the centers of the middle-latitude eddies have
been found. The 11-year fluctuations of the polar eddies are considerably greater
with respect to their intensity and to the position of the auroral zone in years Of
high activity, there is a marked increase in the intensity of the currents, and there
is also a shift in the position of the zone toward lower latitudes. The seasonal
fluctuation l of the middle latitude eddies are small, while those of the polar eddies
are considerable. An intensification of the current in the equinoctial months and
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summer has been found, together with a shift of the zone from higher latitudes in the
summer to lower latitudes in the equinox.
Section 4. The current systems calculated for individual instants of individual �
storms are in good correspondence with the average pictures depicting the regular
part of the disturbance field. The 26 individual cases considered showed that in all
cases the position and signs of the current eddies are the same as in the average sys-
tems. It is true that the form of the current lines and the intensity of the cur-
rents varies not only from storm to storm, but also from hour to hour within wide lim-
its. But all the same the consideration of the individual storms confirmed the phys-
ical reality of the concept of a stable current system embracing the entire earth,
and causing the magnetic disturbances.
Section 5. Data on the disturbed-day structure of the ionosphere have been adduced
�
�
to judge the location of the currents of magnetic storms. A calculation of the Dst
and SD variations of the ionospheric parameters has shown that the greatest and most
regular variations take place in the F2 layer.
The Dst variations of ionization den-
sity of the F2 layers display a two-phase character at all latitudes; in the high and
middle latitudes, the first phase is characterized by an increase in ionization den-
sity, the second by a decrease. In the equatorial latitudes, on the contrary, the
first phase is negative, the second positive. This lack of correspondence between
the Dst variations of the magnetic field and f�F2, and also the great regularity of
the Dst of the magnetic elements - which is absent in the Dst of the ionospheric para-
meters, forces complete abandonment of any possibility of explaining the Dst varia-
tion by ionospheric processes, and, on the contrary, supports the hypotheses of an
extra-ionospheric ring current.
The SD variations of f�F2 are similar in their geographical distribution to the
SD variation of the magnetic elements: at latitudes higher than = 400, SD repre-
sents a simple wave with a maximum in the evening and a minimum in the morning,
while in the law latitudes, this relative position of the extreme values is reversed.
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�
11�11.
This resemblance makes it possible to explain the SD variations by currents in the
F2 layer. The possible mechanisms of formation of these currents have been investi-
gated. The values of the conductivity of individually layers of the ionosphere in
the direction of the magnetic field (Go) and in two directions perpendicular to it
(o./ and al') have been reviewed, and' it has been found that for the F2 layer, the
conductivity along the velocity of the mechanical displacement of the gaseous masses
(all) is greater than the conductivity of the dynamo effect (al). Thus it would ap-
pear that the dynamo effects can hardly have the decisive role in the formation of
the SD currents. The currents induced in the ionosphere by the alternating magnetic
field of the equatorial ring current are likewise very small. In all probability the
greatest part in formation of the current is played by the currents of latitudinal
direction which either arise owing to the drift effect or owing to the motion of the
earth in the field of the ring. The experimental data known from the literature as
to the vertical motions or the vertical gradients of the ionization density in the F2
layer, which are particularly increased during the time of a disturbance, allow us to
consider that the drift of charges under the action of the magnetic and gravitational
fields is not eliminated, owing to the equilibrium between the force of gravity and
the partial pressure in the gas, and consequently, may be adduced for the explanation
of the magnetic variations. I have schematically shown here that, owing to the SD
variations of the ionization density of the F2 layer, currents of latitudinal direc-
tion may lead to the formation of current systems resembling the middle-latitude part
of the SD currents.
Section 6. The separation of the observed potential of the Dst, SD - variations, and
P-storms into an external and an internal part led to the following results.
The ratio � for the first harmonic of the Dst field is about 0.40. Consider-
ing the internal field to arise by induction from the external field, I calculated
0 by the Lamb-Price formula that the conductivity of the earth core (corresponding to
II _
0e40) = 4.4 x 10-12 CGS, ad that its radius is 0.94R. If the influence of
El
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the superficial conducting layers is taken into account, however, and the conductiv-
ity is assumed to increase with depth by the exponential law:
x=xw -5
p
40 then
�
�
S=26, p--= 0,91RAmixo � 10-13.
1
The curve relating K to the depth, calculated by this formula, discloses the
sharp rise of x at the depth 900 - 1200 km at which Gutenberg and Repetti found dis-
continuities in the variation of the velocity of longitudinal seismic waves. Thus
the information on x obtained from magnetic data does not contradict the modern idea
of the structure of the Earth.
The mean ratio
E + 1
for P-storms was found to be 0.86. To use these data to
judge the structure of the Earth, I solved the Lamb problem in cylindrical coordi-
nates. The numerical values of x according to the data of the of various terms
of the P-storm potential ranges between 10-12 and 10-14. In spite of the great scat-
ter of the values of it these values do not contradict the conclusions drawn from the �
first harmonic of the Dst variations.
The ratio JL for the third harmonic of the Dst variations was found to be nega-
tive. Comparison of this conclusion with the data of other authors compels belief
in its authenticity, but it does not appear to be possible to verify it from the
viewpoint of the induction theory (under the assumption of the spherical symmetry of
x). The possibility is not excluded that this result may indicate the existence of
great nonuniformities of conductivity in the depths of the Earth. At the present
time, however, this question still remains open. The ratio for the SD vari---
1 + E
ations ranges from 0.79 for the middle latitudes to 0.89 for the high latitudes.
A This value differs appreciably from that adopted by Chapman for the entire Earth,
- 0.6. The latitudinal dependence of for the SD current may similar-
I + E 1 + E
ly be considered as an indication of the absence of spherical symmetry in the dis-
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tribution of x.
Section 7. All the arguments of morphological and physical character advanced in the
present work compel us to accept the following mechanism of formation of magnetic
storms. A powerful corpuscular stream arriving from the Sun acts in several ways on
the geomagnetic .field. First, interacting with the geomagnetic field, it leads to
the formation of an equatorial ring of currents, whose field produces the Dat varia-
tions of the magnetic elements. Second, as a result of the drift of charges, or of
some other mechanism, electric currents are generated in the upper part of the iono-
sphere at both high and low latitudes. Since the conditions in the ionosphere are
substantially related to the solar altitude, a characteristic property of these cur-
rents is their dependence on the local time (the Sp variations). And third, a cer-
tain part of the particles, becoming detached from the body of the ring (or from the
corpuscular stream itself), are directed under the action of the magnetic field to-
ward the polar regions, where they penetrate deep into the Earth atmosphere (to the
levels of the E and D layers of the ionosphere), causing auroral displays and intense
magneto-ionospheric disturbances there. The polar magnetic storms connected with the
immediate processes in the ionosphere are of very local nature, and their course is
governed by local time.
Thus the field of world-wide storms always contains three components:
the Dst
variations, the SD variations, and the P-storms. The fluctuations of the Dst and SD
systems, and the superimposition of P-storms differing in form and intensity, gives
the fluctuation of the magnetic elements a complex, random character during world-
wide storms. The storm field also has smaller irregular fluctuations (Di), which
may perhaps be connected with some ionospheric processes of more local type.
Less energetic solar streams do not lead to the formation of an equatorial ring
nor of ionospheric currents. The particles of such streams, detaching themselves
immediately from the body of the stream, proceed to the Polar regions and cause Po-
lar storms there. Thus the P-storms can be observed even in the absence of world�
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wide storms.
It goes without saying, of course, that this work does not answer all questions
connected with the construction of the current systems of magnetic storms. The pos-
sible investigations in the domain of the morphology of the disturbance field and of
the disturbed ionosphere have not been exhausted, and no physical explanation of the
origin of the currents has been worked out. In this work we have only considered
the macro-structures of the disturbances in the geomagnetic field and in the iono-
sphere, and we have merely marked out paths along which the solution of the questions
of the formation of the currents may be sought.
In studying the morphology of the field of magnetic storms in the future partic-
ular attention must be paid to the individual fluctuations, to the irregular part of
the field Di on which the present work has no bearing. It is necessary by eluci-
dating the statistical regularities, or by analyzing the individual phenomena to con-
firm, on a large amount of material, the proposition here enunciated to the effect
that the individual fluctuations during worldwide storms, noted on the magnetograms
in the middle latitudes, are the result of the superimposition of polar storms piled
one on top of the other.
In the present work we have collected a large amount of factual material on the
regular variations, and have given a representation of it in the form of current sys-
tems. This material, it seems to us, may be of great use in the solution of the fol-
lowing practical questions: reduction of the magnetic observations to the middle of
the year, and short-term magnetic forecasting. The methods of reduction existing at
the present time, for days that are not magnetically quiet, are very imperfect, and
are particularly unsuitable for high latitudes. The systematization of the regular
disturbed variations, and the calculation of the current systems, will help to eval-
uate the possible deviations, during a disturbance, of the values of the magnetic
elements from the normal, and to interpolate (or extrapolate) the observatory data
for the points of observation. It also seems to us that the representation of the
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...111111=1111111=1.11.....
average purrent system of a magnetic storm will help to increase the accuracy of the
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geographical distribution of the degree of disturbance by time of day, and to evalu-
ate the amplitude of the possible fluctuations, both of which accomplishments are
necessary for short-time forecasting. Thus it is desirable to continue the consider- -
ation of the morphology of disturbance presented in this work, and to give it a form
convenient for utilization in practical problems.
To a still greater extent it is necessary to continue the study of the morpholo-
gy of the disturbed ionosphere. The regulAr variations of Dst and SD of the disturb-
ed ionosphere that have been considered in this work should be calculated for the
largest possible number of years and points of observation. The study of the mor-
phology of the disturbed ionosphere is not only of theoretical value but is also of
great practical value for the maintenance of shortwave radio communication through
the ionosphere. In view of this fact it is inadequate to have merely a schematic re-
presentation of the geographical distribution or time fluctuations of SD and Dst, but
it is necessary to have a distinctly elucidated picture of each observatory separate-
ly. Of particularly great interest is the study of the polar ionosphere, the proces-
ses in which are the cause of the polar magnetic storms and of the high-latitude part
of the SD variations.
As for the method of calculating the current systems from the data of geomagnet-
ic variations, the integral method developed in this work has enabled us to obtain
the numerical values of the external and internal potential, and of the current func-
tion, with sufficient accuracy. In future, however, in cases where it may be suf-
ficient to obtain only a rough picture of the distribution of currents, or when the
sparsity of data makes it impossible fully to utilize all the advantages of the meth-
of, it will still be possible to use an approximate method employing the analytical
technique for solving the fundamental problems of geomagnetism on the basis of an
extensive empirical material.
The question of the mechanisms of excitation of electric currents in the iono-
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sphere may be considered as having merely been posed in the present work.
I shall consider my object achieved if the present work attracts attention to
the study of magnetic storms and thereby encourages the further development of the
theory of geomagnetic variations.
�
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TABLE OF CONTENTS
Page
Introduction 1
Section 1. General Discussion of the Theories of Magnetic Storms 2
Section 2. The Electric Current Systems of Magnetic Storms 5
Section 3. Content of This Report 9
Chapter I. Survey of the Literature 13
Section 1. Basic Properties of Magnetic Storms. The Works
of Birkeland 13
Section 2. Chapman's Investigations and Their Revisions 18
Section 3. Analytical Representation of the Dst-Variations 26
Section 4. Position of the Points of Magnetic Storms.
The Equatorial Ring 27
Section 5, Electric Currents of the Auroral Zone 33
Section 6. Penetration of Corpuscles Into the Earth's Atmosphere.
The Alfven Theory 36
Section 7. Dynamo Theory of Magnetic Storms 42
Section 8. Bay Disturbances hh
Section 9. Current Systems of Individual Bays h5
Section 10. Irregular Part of the Storm Field h6
Section 11. Conclusions
Chapter II. Division of the Field of Magnetic Storms 50
Section 1. Classification of Storms. Polar Storms 50
Section 2. Worldwide Storms, Dst-Variations 53
Section 3. SD-Variations 58
Section h. Division of the Field of Magnetic Storms 60
Chapter III. The Dst-Variations 63
Section 1. The Starting Materials 63
Section 2. Spherical Analysis of the Dst-Variations 1 68
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Section 3. Ionospheric 3y3tem or Curr.A.' of the Dst-Variations 75
Section 4. The Equatorial Current Ring 79
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Chapter IV. Calculation of Electric Currents by the Method of
Surface Integrals 82
Section 1. The Vestine Method of Separating the Observed Field
into an External and an Internal Part 82
Section 2. Practical Methods of Calculating the External and
Internal Potentials 87
Section 3. Calculation of the Electric Currents by the Integral
Method 91
Section h. Finding the Current Density from an Assigned Potential
on the Sphere. Extrapolation of the Potential 96
Section 5. Practical Methods. Conclusions as to the Suitability
of the Method 100
Chapter V. The SD-Variations 104
Section 1. Basic Data 10h
Section 2. Dependence of the SD-Variations on Local and Universal Time
The SD-Variations in the Polar Regions 107
Section 3. Selection of the Type of the Current System 114
Section h. Calculation of External and Internal Potential 116
Section 5. Discussion of the Accuracy of the Method 120
Section 6. The Current System of SD-Variations 122
Section 7. The Polar Part of the SD-Currents 127
Chapter VI. Polar Storms 133
Section 1. Expansion of the Field Potential and Electric Currents
into Series of Cylindrical Functions 133
Section 2. Starting Material. Results of the Analysis 137
Chapter VII. Seasonal and 11-Year Variations of the Dst and-SD Currents-.., 142
Section 1. The 11-Year and Seasonal Variations of the Dst Currents 142
Section 2. 11-Year Variation of the Middle-Latitude Part of
the SD Currents 145
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Section 3. The 11-Year Variation of the Polar Part of the SD Currents 157
Section 4. Seasonal Variations of the SD Currents 162
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Chapter VIII. Morphology of the Disturbed Ionosphere and tlie Current
Systems of Magnetic Storms 167
Section 1. Ionospheric Disturbances 167
Section 2. Conductivity of the Ionospheric E and F Layers, and the
Dynamo Effects in the F2 Layer 172
Section 3. Explanation of the SD Variations of the Magnetic Field
by Drift Currents 187
Section h. Currents in the Ionosphere Induced by the External Field 194
Chapter IX. Current Systems of Individual Storms 199
Section 1. Polar Storms 199
Section 2. Worldwide Storms 206
Chapter X. The Internal Part of the Disturbance Field 211
Section 1. The Inductive Origin of the Inner Part of the Field. Survey
of the Results Obtained 211
Section 2. Solution of the Induction Problem in Cylindrical
Coordinates 215
Section 3. Determination of the Earth Conductivity from the Data of
the First Harmonic of Dst (the Lamb Model) 221
Section h. Determination of the Constants (I, s, (Lahiri Model) 225
Section 5. Allowance for the .Upper Conducting Layer 229
Section 6. External and Internal Parts of the Harmonic P3 of
the.Dst Field 232
Section 7. Variation of Conductivity with Depth and the Internal
Structure of the Earth 236
Conclusion 240
Bibliography 251
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