JPRS ID: 9034 USSR REPORT EARTH SCIENCES

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L~- OF RAD I 0
WR~JES I N THE I ONSPHERE

l8 JRNUARY 1~80 BY R. G. SH I ONSK I Y C FOUO 7 1 OF 2
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JPR~ L/8860
10 January 1980 ~
Transiation ~
_ Long-Distance Propagation of Radio
~Naves in the lonsphere
By -
A. G. Shionskiy
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;1
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- JPRS L/8860
10 January 1980
LONG-DISTANCE PROPAGATION OF RADIO WAVES IN THE IONOSPHERE
Moscow DAL'NEYE RASPkOSTRANENIYE RADIOVOLN V IONOSFERE in
Russian 1979 signed to press 24 Apr 79 pp 1-152
Book by A. G. Shlionskiy, "Nauka" Publish~rs, 850 copies
CONTENTS PAGE
~ Foreword 1
Chapter I. Propagation of Ultra Long-Range Radio Signals 3
1. Aruund-tt~e-World Radio Echo 3
2. Inverse Radio Echo 11
_ - _
3. Attenuation of Circumterrestrial,Inverse Echo Signals 14
4. Effect of Azimuthal Anisotropy of Ionosphere on
Propagation of Ultra Long-range Signals 18
5. Antipodal Propagation of Radio Waves 28
6. Ionospheric Radio Echo with Multisecond Delays 33
Chapter II. Long-Range Propagation of Radio Waves with Emitter
Located in the Ionosphere 37
1. Experimental Study of Long-Range Radio. Signals 38
2. Effect on Characteristics of Long-Range Signals of
~ Global Properties of the Ionosphere 42
- 3. "Antipode Effect" in Reception of Signals Transmitted
in the Ionosphere 48 -
3.1. Reception of Antipodal Signals at Mirnyy
from the First Sputnik 48
3.2. Reception of Antipodal Signals from Artifical
Earth Satell.ites at Middle-Latitude Points 51
3.3. Observations of Antipodal Signals from Arti-
ficial Earth Satellites in the Near-Equatorial 52
Region
~4. Experiment on Propagatio~ of Signals Between an
Emitter and Receiver Situated in the Ionosphere 53
-a- [I -USSR-FFOUO]
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CONTENTS (Continued) Page
Chapter III. Refraction of R.a~~~ Waves in Ionnspheric Ducts 55
1. Initial Assumptions of the Extremal-Parametric Method
of Analysis of Characteristics of Ionospheric Ducts 58
2. Combined Quadratic Model of Altitude Variation of
Eiectron Concentration 63
3. Combined Quadratic Model of Altitude Variation ~
of Modified Dielectric Permeance 68
4. Limiting Boundaries of Channels. Magnitudes of
Minimum of Modified Index of ftefraction 72
5. Axes of Ionospheric Ducts. Magnitudes of Ma.ximum
of Modified Index of Refraction 74
6. Upper Limit of Frequencies of fteflection
of Radio Waves in the Ionosphere 77
~ ~7. Limiting Frequencies of Degeneration of Ionospheric
Ducts g3
Chapter IV. Some Characteristics of Ionospheric Channels 8g
1. Refraction Characteristics of Capture and Re-entry
of Radio Waves by Ionospheric Ducts gg
2. Some Refraction Characteristics for Ionosphere-Based
Emittei s 95
3. Some Characteristics of Radio Wave Oscillation
in Ionosphere Channels 101
4. Cluster and Phase Paths 108
~ 5. Absorption of Radio Waves in Ionospheric Channels 112 ~
~ 6. Spatial Damping of Radio Waves in Ionospheric
Channels 117
References 121
. ~
-b-
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PUBLICATION DATA
English title . LONG-DISTANCE PROPAGATION OF
~ RADIO WAVES IN THE IONOSPHERE
- Russian title , DAL'NEYE RASPROSTRANENIYE
RADIOVOLN V IONOSFERE
Author (s) ,
A. G. Shlionskiy
Ed:itor (s) ,
r
Publi~hi.ng House , Nauka
Place of Publication , Moscow
Date of Publication , 1979
Signed to press , 24 Apr 79
Copies , 850
COPYRIGHT . Izdatel'stvo "Naiika", 1979
- c -
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LONG-DISTANCE PROPAGATION OF RADIO WAVES IN THE IONOSPHERE
Moscow DAL'NEYE RASPROSTRANENIYE RADIOVOLN V IONOSFERE in
Russian 1979 signed to press 24 Apr 79 pp
1-152
[Monograph by Aleksandr Grigor'yevich Shlionskiy, Nauka, 850 copies, 152 pages]
[Text) Annotation
Conditions and characteristics of ultra long-range (around-the-world, inverse, an-
tipodal) and long-range propagation of short radio waves in ionospherie channels
when the emitter is on the Earth's surface and in the ionosphere.
Results of analysis and interpretation of experimental data and a theoretical
consideration of the relationship of characteristics of ionospheric radio wave-
guides as a funetion of key-points of the ionosphere are presented.
The book is of interest to radiophysicists, radio engineers, graduate and other
- students specializing in the field of long-range ionospheric propagation of radio
- waves.
Table 2, illustrations 66, references: 118 titles. ~
Foreword !
Both experimental and theoretical research of long-range and ultra long-range
propagation of decameter radio waves have revealed the important role of
waveguide ionosphere modes possessing extremely favorable energy and other
characteristics. In a still greater measure, the role of these modes is increased
when the emitter is placed in the ionosphere and even more so if the receiver
is located in near space. Therefore the results of experimental, theoretical and
applied research of conditions of ionospheric waveguide propagation of radio
waves in long-range and ultra long-range routes for emitter placement on the
Earth's surface and in the ionosphere have not only a scientific but a~so a
tremendous practical significance.
Problems in this field were rather complex, and research begun in the 1920's and
especially actively conducted in recent decades are continuing in both the
1
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experimental and theoretical planes. Still, now the need has matured for a
certain systematization and generalization of the results obtained. In solving -
this problem, the author mainly relied on the results of those studies which were
carried out with his participation and set the goal of completely capturir.g
various existing theoretical approaches and experimental findings. Some review
information in different trends of research have been cited in the introductory
- portions of each chapter and the corresponding studies are included in the
bi bliography.
- Underlying the book is the extremal-parametric method (EPM) for determining
a complex of characteristics of ionospheric radio waves. This method is based
~n analytic relationships of waveguide characteristics as a funetion of extremes
of altitude variation of the modified index of refraction and of these extremes
as a function of extremes of the vertical gradient of eletron concentration.
Key ionospheric points (predicted critical frequencies, geometric pa-
rameters, etc.) can be used as initial data to determine certain properties of
waveguides.
- In Chapter 1 are presented the results of experimental research on propagation
of ultra Iong-range signals when an emitter is placed on the Earth's surface.
Different properties of ultra long-range signals are considered; observable
variations are interpreted, allowing for the effect of azimuth anisotropy of ~he
ionosphere and orientation of ultra long-range routes with respect to the
terminator line.
" In Chapter II are investigated the results of experimental research of pro- -
pagatio:~ of long-range signals when the emitter is located in the ionosphere.
Interpretation was done to allow for the global distribution of electron
concentration in the ionosphere of distinctive features affecting optimum
conditions and other properties of long-range signals.
In Chapter III are analyzed conditions of radio wave refraction in the ionospher~,
_ initial assumptions of EPM are presented and the bases of its mathematical
apparatus, models of altitude profiles of electron concentration and modified
dielectric: permeance are justified. Materials are adduced on calculating limiting
boundaries and channel axes, frequencies of degeneration, etc.
In Chapter N are considered the refraction properties of capture and escape of
radio waves from channels for varied emitter positi~n (on the Earth's surface,
~ in the ionosphere), several integral characteristies (intervals of oscillation of
beams in a duct, cluster, phase paths, absorption, etc.), spatial attenuation of
radio waves in a channel, etc.
Mathematical and graphical relationships adduced in the book can be used both
_ for analysis of experiments and for prediction of conditions and characteristics
of ultra long-range and long-range propagation c~f decameteter radio waves for
ground-based or ionosphere-based emitters.
The authors ara deeply grateful to the following persons for reading and
criticizing the book: Yu. N. Cherkashin and T. S. Kerblay, as well as V. V.
2
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Kuryatnikovaya and L. I. Shlionskaya for their aid in preparing the manuscript.
Chapter I
_ Propagation of Ultra Long-Range Radio Signals
In the initial period of use of short radio w~ves for tong-range radio com-
rnunication in the 1920s, radio signals were detected with large time lags
corresponding to the curvature of the Earth (world-wide radio echo) or
propagation through a long inverse route 20,000 to 40,000 kilometers in length
(ir~verse radio echo)[i-4]. Long-range radio echos detected in several operating
radio lines connecting different continents on the Earth were first cansidered
mainly as interference in radio station recept~on. But it soon became clear that
the emission of echo signals was very interesting. So, in the late 1920s the
effect of "inverse echo" began being used for long-range communication through
the reverse route between England and Australia.
In addition to world-wide and reverse signals, signals have been recorded from
s~nsors situated near the antipodes of a receiver at a distance of about 20,000
- kilometers (antipodal signals), as well as signals with delays ranging from units
to tens of seconds, whose origin is most difficult to explain [5-J.2). -
Because many distinetive features of long-range echos could not be explained as
skip modes, various hypotheses were then advanced on the possible mechanics
of propagation [13, 14] and special experiments were run (15-19].
Because several distinetive features of ultra long-range signals can appear in
shorter routes, on the order of 10,000 to 17,000 kilometers, the results obtaiy~ed
can be used to investigate long-range propagation as a whole for ground-based
and ionosphere-based emitters. �
�1. Around-the-World Radio ~cho
When circumterrestrial radio signals (KS) are received the largest amount of
experimental data is obtained at medium-latitude points (Western Europe, North
America, eastern and European parts Qf USSR). tiS receptiun w~s also done in
the Arctic, near-equatorial region and in Antaretica.�
From 1926 through 1934, world-wide signals were recorded in Ferlin from a
number of North American, South American and Asiatic com:mercial radio
broadcasters [1-3]. From 1927 through 1929, the USA recorded world-wide ~
- signals from European radio broadcasters [4].
From 1941-1944, in Denmark world-wide radio signals were received from
broadcasters situated on all continents of the globe [15-18]. In the ~ost-war
period, special experiments have been conducted using powerful transmitters and
highly directional transmitting and receiving antennas. In the winter of 1958-
1959, KS observations were made in Sweden on a transauroral radio line running
3
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between the geographic and geomagnetic poles [201. From 1960 to 1970,
intensive KS rese~rch was done in the USA [21-231. -
World-wide radio signals were detected in the USSR in the 1950s in receptior. of
signals of baekward sloping probing (VNZ)[24].
Since 1967, KS research has beer~ conducted in Antaretica at the Molodezhna~a
So~~iet station with reception of the Moscow transmitter in.. the transauroral
quasi-meridional direction [25, 26J. Tn 1970 to 1971, KS observations were made
in the eastern part of the USSR [27-32]. Some KS observation results have been
obtained in Cuba [31]. In 1974-1975, KS reception was also done in the middle
latitudes of the USSR [29, 30, 38J. -
The experiments which have been conducted permit us to judge the variations in
- diverse KS characteristics: time of curvature of the globe, attenuation, pulse
_ distortion, optimum periods of reception and direetions, etc.
When KS is received in middle latitudes of eastern USSR, :ne transmitting and
receiving points were almost superposed (distance between them was about 0.05
pereent of the world-wide path). The azimuth of the maximum of the narrow
directionality of the receiving antenna system rotated in a 360� sector.
_ Emission of signals was done into no~-directional antennas of type VGDSh-ZU and
directional antennas of type RGD 6~/4 I. Azimutha.l characteristics of KS,
seasonal and diurnal and frequency variations were investigated. ;
Est:mat~s of probability (in ~ercentages) were derived for passage of KS as a
function of time of day (LT) and season, characterized by the amount of eases
of KS reception in a period of observation (Fig., 1.1).
Working frequencies and KS reception time intervals arQ indicated in Fig. 1.2 by
- straight lines and in the 360� sector by little circles. The data adduced
correspond mainly to emission in~o a non-directional antenna of type VGDSh-2U.
KS have well expressed seasonal and diurnal variations. In the winter, KS
reception was only during the day, from 9:00 a.m. to 7:00 p.m. local time (LT)
and in the summer, only at night from 8:00 p.rri. to 4:00 a.m. The best KS
reception conditions occurred in the winter (2:00 p.m. to 4:00 p.m. with almost
100 percent probability). In summer, probability of reception reached 80 percent ~
(11:00 p.m. to midnight, LT). The worst KS reception was during the equinox.
So, KS in April and September, 1971 were not recarded. In October, 1971, KS
reception was noted only in directional emission.
Furthermore, diurnal vat�iation of KS in October is similar to winter.
Some seasonal and diurnal asymmetry of KS reception probability has been
noted. So, KS reception in winter is better than in summar, and in the second
half of the day it is better than in the first. We should indicate the possible
connection of this ~fS asymmetry in KS with the seasonal and diurnal asymmetry
of ionization oi the F-region of the ionosphere. In most cases, world-wide radio
routes were reversibly independent of azimuth, time of day and season and
- frequency [32]. ~
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~00~ � �
b0 _
60
40
20 -
0
0 y ~ ~6 20 2y
Fig. 1.1.
f,M('~ .
- 20 ..o~
+weao-~.ao...o- _
~17 . ,~p_
..woaaooooooo...
- ~ 4 � --a~~w~-oaaao --.aoau -
-raooa~ -~o
i{ 4 8 ~2 ~ ~6 - 20 ~ Zy t,v
Fig. 1.2.
Figure 1.3. shows the measured bearings of optimum directions of KS reception
for winter, summer and equinox (points, triangles and circles, respectively). The
. calculated diurnt~l variation of bearings A are also plotted; they form minimum _
angles with the terminator and values of these angles
n(min for the same seasons (winter-solid lines; summer-dashes; equinox-dots -
and dashes). Variation of OC m;n is shown by smooth curves with noon peak.
Other curves show variation of A. Straight lines indicate bearings 40 and 140�
(their inverses 220 and 320�), corresponding to boundaries of the sector of non-
polar rc~tes.
~
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A
~IbO~ 360' .
? /
%
, ~
.
ro
120 300 ~ 4 q.;.�'~
~ o0
, ti;f~ �oo
. ~ � _
_ ~ ~p . . , . o
� ~ r' .
. 's'' ~ '
so z4o
�
/ ~
/i ~
~ ' ' ~ ~ ~ i
0 ~80~ ~j'/ ~ ~t.~~1/~ _
0 ~ i ~g' ~ ~ ~ ` a t,V
-60
~ Mi~
Figure 1.3
t,4 �
9
- g r
~
~ ~
- 6 1 ~ 1_I ~ III
c'nonths
Figure 1.4
In all seasons, measured optimum bearings are close to eslculated A. Best KS
~ reception was in both summer and winter at O~ min = 10-20�. KS were not
observed in periods where Oc min reached 50-65�.
KS reception bearings deviated from calculated A usually in the direction of
pQlar routes. Only in rare cases did optimum bearings of KS reception drop
~ehind the auroral zones.
Improved KS receiving conditions usually involve broadening of a signal arrival
sector and range of working frequencies. -
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t,4 �
16 1 .
I -
14 i
~ i
I '
i
~ ~ ~
12 I I
i
1 ~ II ~ III
Figure 1.5 -
n~
100
i
i
80 ~
I
1
I
'j i
I ~
' 1
I
~ ~ ~
4~ i ~ ~ 1
- 1 ~ I ;
- I ; ~ ~
~ ~ ~ I I
~ ~ 1
~ I I
~ ~ I I -
~ ~ ~ ~ months
0 I .
, j ~_I ~ ~V V VI YU Yui IX x X! X~I
- Figure 1.6
The probability of KS reception greated increased in direct proportion to emitted
signal power, e.g, when highly directional transmitting antennas were Used or if
the sensitivity of the receiving equipment was increased. However the nature of
the seasonal-diurnal and other patterns does not depend on technical parameters.
In December 74-March 75, in middle latitudes of European Russia, KS ob-
servations were made in two f'rxed directions with transmitter and receiver
positions at one point. Emission and reception were done using highly directional
transmitting and receiving antennas. The power of the standard transmitter was
about 100 kW [28]. Observation results are shown in Figures 1.4 and 1.5. Figure
1.4 corresponds to bearing 220, Figure 1.5-to bearing 3090, Along the vertical
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. line is shown local time (LT) at the observation ~~~;i~t. Blackened ~rea is time
_ intervals when KS were received in different manths and days. In direction with
bearing 22�, KS at a frequency of 11 MHz were received mainly in the morning
at 6:30 a.rn. to 9:00 a.m.; with oearing of 309� at a frequency of 19 MHz--in
the latter half of the day at 12 noon to 5:00 p.m. Straight lines in Figures 1.4
and 1.5 indicate appro�cimate theoretical variation of moments of coincidence c~f
fixed direction with bearing A( a min) from winter solstice to equinox.
Reception of KS was mainly noted in periods + 1-2 hours from moment of
coincidence of the route bearing with theoretical bearing A(with slight
- asymmetry). In this context, pc min usually was more than 10�, reaching 19�
at equinox at bearing 22� and 35� at bearing 309�.
Thus despite the great discrepancy in longitude from other middle latitude -
points, the ma~n quantitative characteristics of optimum KS reception were
preserved. From Figure 1.4 and 1.5 it can be seen that daily variations in KS
in both directions are significant. In routes with bearing 309~, the probability -
and duration of time intervals of KS reception are much greater than in a route
with bearing 22�. For a whole series of days, KS reception in route 309� was
present and in route 22~ was absent. Differences can be ex~alained by the fact
that in a route with bearing 309�, because of great values of the coefficient of
antenna gain, the output of sounding pulses was several times greater than in the
route with bearing 22�. Furthermore, integral attenuation in the route with
bearing 309� not intersecting the auroral regions and with emission at higher
- frequeneies of 19 MHz were apparently lower.
_ In e~periment [29], study and reception of signals were done at a middle latitude
point ir~ the transauroral direction with a bearing of 30 and 210Q during a two-
yea?� period from August 1972 through September 1974 under conditions of
gradual (~on-monotonous) subsidence of solar activity (Zurich ~iumbers W of
sunspots changed from 80 to 20). Probability of KS reception (expressed in
percents of ratio of the number of days of KS reception to the total number of
days of observation in a given month) changed from 34 to 100 percent. In
periods close to solstices, KS were received almost daily. Probability of KS
_ reception on a winter day was about 83 percent, on a summer night about 70
percent. When W is greater than 50, KS were received two times with
attentuation averaging 10-13 dB in seven cases.
KS were received at frequencies of 12-21 MHz, mainly above the muf skip
modes. Experiments showed that with reduced W, KS can pass through the
transauroral world-wide route with high probability.
In experiment [30], measurements were made of the angular characteristics of
KS. The transmitter was located in Irkutsk and KS reception was done 100
kil~,~ieters from there using a broad-band phase direction finder. Pulses in the
18-20 MHz range were studied with pulse width of 1-20 ms and pulse repetition
rate of 5 MHz. In December, emission was done through a VGDSh antenna with
maximum in the N-S direction; on other days-using a rhombic antenna with
bearing 302�. Measured bearings of KS arrival were within 117.5-127.5�, and
angles of KS arrival in the vertical plane were 4-10�. Errors in measurement
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_ of bearing and angle of KS arrival were no more than 0.5 and 2.5�, respectively.
In the near-equatorial region, observatiens were made in Guam (13�30 N. Lat.,
145� E. Long.) with placement of transmitter on Okinawa, 2,250 to the NW of
Guam on 14-23 February, 1963 [22].
Studies were carried out on near and world-wide inverse routes 37,750 k;~~meters
long. Bearing of the inverse route from Guam was 132~. Power of the
transmitter was about 0.7 kW, with emission through a rhombic
antenna. Broadcasts were in the 14.5-21.8 MHz range. Greatest duration of
reception and field strength were at a frequency of 18 MHz. Optimum
conditions for reception (100 percent of days) were in the 10 a.m. to 4 p.m.
- period LT, wherein about 1 p.m., field strength was at a maximum. Theoretical
moment of coincidence of route bearing with the direction forming the minimum
angle o( min with the terminator corresponds to 1-2 p.m. LT at oc greater than
42�. KS reception at significant angles of the route with the terminator
indicates the existence in the equatorial region of factors which improve their
characteristics. In 1973 (June-October), in the Cuba-USSR route, KS were
observed using the VNZ method. Transmitter power in the pulsed mode was
, about 80 kW, rhombic antenna, width of radio pulses 1 ms with repetition rate
of 12.5 and 6.25 Hz. Sounding from Havana was done in a direction with bearing
39� at a frequency of 16.2; 14.9; 12.2; and 10.? MHz from 5:30 p.m. to 11:30
p.m. Havana time (60� West Longitude)[31].
KS reception occurred only in June and early July at frequencies of 16.2; 14.9;
and 12.2 MHz. Most favorable for reception was the evening period in the
summer, which corresponds to convergence of routes with the twilight zone.
Appearance of KS at these frequencies and those periods when there is a large
number of signals from back scattering, indicates the possible role of scattering
in ionospheric irregularities as a factor of channel capture of KS.
In Antaretica, at the Molodezhnaya station, KS received from tlie Moscow
- transmitter have been observed since 1967. The length of the direct quasi-
meridional route was 13,700 kilometers. A 20 kW transmitter operating in a
pulsed mode was used with a rhombic antenna aimed at the Molodezhnaya
station. Emission was done every three hours at 10 working frequencies in the
4.5-23 MHz range. At the Molodezhnaya station, reception was accomplished
using an omnidirectional antenr,a. At each frequency were measured field
strength and relative delay time of pulsed signals received.
KS were mainly observed in periods near the equinox. Seasonal variation of the
ratio of the number of days when KS were observed to the entire number of days
of reception in a given month (in percents) is shown in Fig. 1.6 by dashes. In
periods near the equinox (March, April, September, October), KS were received
almost daily only in the evening from 6 p.m. to 7:30 p.m., within + 20 days from
the moment of equinox. Two-time direct echoes were observed only in March
~t evening twilight. Therefore, KS appeared in periods when the route passed -
through the evening (twilight) and morning (post-sunrise) zones, i.e., when it
forms the smallest angle with the terminator. Direct KS p~ss b~tter when the _
direct route is found in the evening, twilight zone. KS were observed at
frequencies of 11-23 MHz. Optimum frequencies correspond to the least
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attenuation and lie in the range of 16-21 MHz. The upper limit of frequencies
can be riiuch higher than the , standard maximum usable frequencies ( ~nuf )
of the route.
KS observations in the transauroral directiQn were m~de from December, 195?
through February, 1958 at the high latitude Swedish point of Kirun (67.8� NLat,
20.4� ELong). A 4kW transmitter was located in Coolidge, Alaska (64.8� NLat,
147.8� WLong). Emission was done through a three-elemei~t Yagi antenna. The
length of the direct route was 5,200 kilometers. Reception bearing was 312� `
[20]. Of the three working frequencies used, 12.18 and 21 MHz, KS reception
only occurred at 18 MI3z. KS were received in a period 1-1.5 hours after
coincidence of the route with a bearing near the terminator, these moments
being extremely close to the moments of maximum probability of KS reception
(see Fig. 1.7).
14
1 ~
I ~ ~ ~
~0 ' ( ~ I
I~ ( ,
~i ~I
6 i~ ~ ~ i
�I ~ ~
z . . I I
o ~
4 4 ~6 ~ 2 t~V
Figure 1.7 -
Experiments showed that rounding-the-globe time ` is extremely stable. The
difference in various experiments is within 5 percent. According to [2], 2' _
136.05 to 137.60 ms. Averaged value of 137.788 ms corresponds to the
active path which is 1,300 kilometers larger than the Earfh's circumference, or
average altitude of the world-wide path equal to about 200 kilometers. Slight
greater values of were obtained in [25]: 0.1367 to 0.1393 sec, with 0.1382 sec
- most probable. In practice, the spread of values of Z lies within measurement
error which does not exceed + 1 ms. Variations of T as a funetion of time of
day, season and solar activity are not revealed. Frequency variations of ~ are
also small. A negligible increase in ~ is noted in direct proportion to frequency
(by 1-2 ms in the entire frequency range), and it is difficult to exclude the possi-
ble effect of various equipment factors and measurement errors.
With world-wide propagation of pulses, high stability of their shape is observed
in many cases regardless of the time of day, season and frequency when
transmitting and receiving points are separated by various distances. No
substantial distortions were noted in repeated KS. Distortions of KS shape were
often less than in direct signals running much shorter paths. In addition, cases
of substantial change in KS shape were observed, in all likelihood due to the
presence of multipath emission [23]. KS primarily propagate in the plane of the
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great circle. Deviations from it in 90 percent of the cases do not exceed + 30
[21]. Individual measurements of the angles of KS arrival in the vertical plane
yielded values of 15-25� to the horizon in some cases. For the e~isting corpus
of observations, the range of frequencies fo KS is constrained below about 10
MHz and above about 40 MHz, whereas 15-22 MHz was often optimum. KS
recept;on is noted in many cases at frequencies much .high than muf and with
substantially less attenuation per unit path length than in direct signals.
Reception of KS usually improves somewhat when solar activity is increased.
In all expeniments, attraction of favorable routes toward the twilight zone was
noted. Analysis of KS observations in middle latitude points of various
longitudes, at high latitude points and in transpolar routes and the near-equa-
- torial region yields close quantitative charaeteristics of optimalness associated
with the relative juxtaposition of the route and the terminator.
Bearing anisotropy of KS routes occurs. Optimum directions usually form a 10-
20� angle with the terminator. Some deterioration is noted in KS reception
conditions in transauroral direetions and during magnetic ionospheric dis-
turbance. In [27], for reception in middle latitude points was f:xed the deviation r
of optimum bearing of KS reception from the direction which forms a minimum
angle with the terminator toward a direction which does not intersect the
auroral regions.
In experiment [20] in the transpolar route, KS were received with low magnetic
activity. During disturbances with KS reception in middle latitude points in
routes of varying orientation, a decrease was noted in the probability of KS _
reception, duration of reception during the day, signal levels and range of
working frequencies (reduction of upper limit and rise of lower limit of
frequencies) with a rise in the planetary index of magnetic activity ~Kp. At
very high values of the index, KS completely vanished for several days.
Deterioration of KS reception with a rise in magnetic activity shows up more
clearly in the twilight zone,' because it passes near the geomagnetic poles [211.
Conclusions derived from analysis of experimental~data permit us to recommend
the use of quantitative characteristics of relative juxtaposition of the route and
terminator (see Chapter 1 �6.4)
as empirical prognosis of optimum conditions of KS reception. It is necessary,
however, to bear in mind that even with optimum conditions there can be no KS
r~ception if field strength level-which depends on emitted power, working
frequency and integral attentuation in the route--is below threshold.
KS reception will not occur (regardless of emitted power) if the working "
frequency exceeds the limiting frequency of reflection of radio waves on the
ionosphere (frequency of degeneration of the ionospheric ehannel). In this
connection, substantial differences in KS characteristics can oecur under
optimum conditions (signal level, frequency range) in different seasons, time of
day, solar activity, during ionospheric magnetic disturbances, etc.
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�2. Inverse Radio Echo
~ Propagation of radio waves through a large arc of the great circle 20,000
kilometers) was record~d in the 1920s during the initial period of assimilation of
the SW range. A large number of inverse signals (OS) were recorded, for
example, during reception in 1927-1934 (during half-cycle of solar activity W) in
Berlin from a number of North American (New York, Mexico), South American
(Venezuela, Rio de Janeiro, Buenos Aires, Santiago) and Far Eastern (Shanghai,
Bangkok, Java, Nagoya, Mukden, Manila) transmitters.
IS passed primarily ir, directions firming minimum angles with the terminator,
in some cases at working frequencies above the muf of the inverse route with
attenuation lower than in the direct route [1-3].
Use of the "inverse echo" effect to raise reliability of communication, i.e. for
practical ~urposes, was begun back in the late 1920s in the commercial rote
connecting England and Australia: Grimsby (55�33' NLat, 0�05' WLong) to
Melbourne (37~40' SLat, 145�08' WLong). Length of the direct route was 16,850
kilometers and the inverse route was 23,150 kilometers. The short route passed
through Europe, India, Indochina; the long one--through the Atlantic Ocean,
South America and the Pacific Ocean. Receiving and transmitting stations at
both points are identical. The antennas had high directionality in the horizontal
plane and could be reversed. Ghange of emitting direction was done in
Melbourne 1.5 hours after sunrise to the inverse route and about 3 hours after
sunset to the direct route. In the short path, audibility at Grimsby improved as
the terminator moved away from Melbourne towards Grimsby and re~ched its
hig:~est values when the path was in total darkness. After sunrise in Melbourne,
aud~bility in the direct route began to drop sharply and after a short interval of
time vanished comQletely. In the long path, the maximum audibility in Grimsby
corresponded to total illumination of the direct route. ~ Therefore, the darkened
part of the Earth was best. Fixed working frequencies about 11.6 MHz were
used. Audibility in the direct and inverse routes was comparable in the
corresponding periods. Because of reverse, assured communication was provided
about 70 percent of the day [33).
From 1941 to 1944, US (and KS) observations were intensively earried out for
reception of the world network of transmitters in Denmark in the frequency
range from 10 to 20 MHz [15-1?]. From 14 to 23 February, 1963 in the inverse
(almost world-wide) Okinawa-Guam route, a special experiment was run [22].
The Okinawa transmitter, which emitted in the direction of the inverse route
37,750 kilometers in length, was picked up in Guam and simultaneously at
intermediate points in Salonica and Malta. Reception of signals at the end point
observed at specific periods (when absent from the intermediate points on the
route nearer to the emitter) was interpreted as direct experim~ntal proof of
propagation without intermediate reflections from the Earth under conditions of
assured input and output of energy from ~ the ionospher?c channel with ground-
based emitter and receiver because of the horizcntal inclindes of the ionosphere.
In 1967, OS observations from the Moscow transmit~ar were begun at the
Molodezhnaya station [25, 26]. The large circle was oriented almost along the
helographic meridian and intersects, thereby, the polar regions. The length of
the direct route was 13,700 kilometers and the inverse route was 26,300
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kilometers. Reception was achieved in the 4.5-23 MHz range at 10 working
frequencies. ~
The seasonal variation of OS obtained in 1967 is shown in Figure 1.6 by solid
lines. In contrast to non-meridional routes, the most favorable season for OS
was during the day of equinox from 6:00 a.m. to 5:30 p.m. LT. During this period
(March, April, September, October), OS were picked up almost daily. Probability
of OS detection sharply dropped during solstices ( N 10-15 percent).
Optimum conditions of OS reception were when: a) the inverse route coincided
with the evening (twilight) and morning (post-sunrise) zones. In some cases
reception e~en of two-fold OS; b) the sun was located at the middle point of the
direct route. The bulk of inverse route passed in the darkened region and its
end points were identically removed from the boundaries of the darkened region.
In the first half of the day, including noon, OS were observed in the 10-23 MHz
range, after noon and in the evening twilight-primarily at frequencies of 11-15
MHz. Frequency relationships of OS attenuation were much less expressed than
in ordinary direct signals. In practice, the amplitude of OS was almost unchanged
with freque~cy �~nd time and day. Despite the doubly long length of the inverse
~ route (intersecting the northern and southern polar regions), and the emission one
order lower in the inverse direction, during daylight hours of equinox only OS
passed at 10-16 MHz and there were no direct signals, apparently because of
high attenuation. At 18-20 MHz, amplitudes of the basic signals and OS at that
time were identical. At higher frequencies, amplitude of the basic signal was
much higher and OS had decreased somewhat. OS passed at frequencies above
muf of skip modes of the inverse route by 5-8 MHz. So, at midnight during
the entire y.ear, muf in the direct route even on specific days did not exceed
18 MHz. However at noon in periods near the equinox, OS were often passed
through the midnight zone at frequencies up to 23 MHz.
The cited OS characteristics indicate the high probability of the non-skip
mechanism.
- In I969-1970, observations wer,e made in Leningrad of inverse echo-signals from
ham radio transmitters situated on various continents of the globe, at various
distances and in various directions [34, 351. OS reception was done at
frequencies of 7-7.1, 14-14.35, 21-21.45, 28-29.5 MHz. Experimental values of
_ bearings of OS arrival for September, January, May and July were derived as a
funetion of time of day and working frequency. Medians of experimental
bearings were compared with theoretical azimuths of directions forming a
- minimum angle with the terminator. As a result, good correspondence between -
them was attained. At the same time, there was some relationship between the
difference in said azimuths and the working frequency. As the latter increased,
at frequencies of 21-29.5 MHz was recorded a slight delay of the experimental
azimuth from the theoretical. For example, in January and July it deviated by
5-10�. For the lower frequencies, ?-14.35 MHz, both azimuths vanished
completely. ~S reception occurred when the theoretical azimuth was closest to
the terminator. So, in January, OS were picked up only during the day, while
in July it was primarily at night. However during the equinox, in the hours of
sunrise and sunset, the difference in azimuths was even noticeable at low
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frequencies 7 to 14.35 MHz (up to 45 and 20�, respectively). The direction of
OS arrival deviates toward the non-polar routes from the theoretical azimuth
which intersects the auroral zones. In May, there is a shift from the day
conditions of OS reception to nighttime conditions. The width of the OS
reception sector contains two peaks: morning and evening. The peak for low
frequ~ncies slightly outstrips the peak for high frequencies, similar to measured
azimuths.
- In September, at about 12:00 noon LT at a frequency of 7 to 14.35 MHz there
is a deep valley in sector width which is apparently due to the significant
influence of ionospheric absorption. In September at high frequencies in the
evening, the width of the sector is slightly greater than at low frequencies. In
January, on the other hand, sector width is greater at the low frequencies.
Sector width of OS is maximum in twilight periods for low frequencies. In
equinox, sector width at high frequencies is greater than at low frequencies and
vice versa during solstice days. Some possible deviation in direct proportion to
a rise in working frequencies of the optimum OS azimuth from the direction -
intersecting the terminator at a minimum angle is associated with the need to
assure reflection of radio waves on the ionosphere.
In 1971-1972 (from October 14 through February 29), OS observations were made
aboard the Borovichi scientific-research ship in the water landing area of the
Atlantic Ocean [36]. Reception of signals from the 20 kW Moscow transmitter
was done virtually around the clock. Pulses of 300 mes in width and frequency _
of 12.5 Hz were emitted to an anten:~a isotropic in the azimuthal plane at 10
fixed frequencies in the 5-23 MHz range. In the period from 9:20-10:30 am and
12:2,0-1:30 p.m. LT, in almost 60 sessions, OS were received mainly at high
fre~uencies of 16-23 MHz. Duration of OS was close to that of the emitted
pulse. Probability of receptionof OS grew in direct proportion to the length of
the direct route. OS intensity in some sessions was the same as in direct signals
or even 1-3 dB higher. There were cases where at frequencies 20-23 MHz only
OS were received, although the direct signal passed at the lower frequencies.
OS had low dispersion, possibly due to the low-mode structure and smaller
contribution of the scattered component. Optimum OS routes passed near the
twilight zone. In addition to the direct signals, OS were recorded at frequencies
near the muf of the inverse route. In the near-noon period LT, when the
inverse route was removed from the twilight zone and was more uniform and
working frequencies were much higher than muf, OS reception deteriorated. In
a direction perpendicular to the twilight zone, only weak isolated pulses were
received which were difficult to identify.
Results of experiments on OS reception indicate attraction of optimum inverse
routes toward the twilight zone. Many characteristics of OS indicate the
important role of non-skip modes in their propagation.
�3. Attenuation of Circumterrestrial and Inverse Echo Signals
Based on currEnt measurement:> of world-wide and inverse echo signal levels, we
- can assess their attenuation. Results of KS and OS measurements made at the
Molodezhnaya station in reception of the Moscow transmitter in a meridional
direction during years of high and average solar activity were used for that
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purpose; OC received in middle latitt~des of the northerr? hemisphere in routes
of diffPrent orientation, during a period near the minimurr, of solar activity,
were employed likewise [37].
Resulis of the first experiment are given in Figures 1.8, 1.9; thc second
experiment results are shown in Fig. 1.10.
In Figure 1.8 Are presented the amplitude-frequency characteristics of OS and
KS for one of the most probable periods of detection (equinox, March 1967) in
various intervals of local time. Tne solid curves are monthly medians of
_ measured field strength of E signals in decibels with respect to 1 microvolt per
meter. Vertical fragments characterize the spread of field strength values on
various days, if the reliability of OS detection at a given frequency is at least
30 percent.
Individual cases of detection are indicated by dots. The frequency with the -
greatest reliability of detection at a given time of day is noted by the figure
- whic}- indicates the percentage of detection. In cases where reliability of
detection is less than or equal to 50 percent, the monthly median was
determined in terms of the smallest measured value. The dotted curves
correspond to the theoretical field strength E for skip modes of radio wave
propagation allowing for additional absorption in polar regions. Th~ length of -
the inverse route was 26,300 kilometers. The length of the KS path in the direct
direction was 53,700 kilometers. Calculation of E for KS yields about -100 dB.
The measured KS attenuation with respect to the level of the unabsorbed field
EH comprises 20-30 dB. The measured OS attenuation averaged about 20 dB
with respect to Eg or 30-50 dB less than the value predicted for the skip mode
9F 2(dotted line). OS and KS passed at frequencies of 12-23 MHz (with a
measurement frequency ragne of 4.5 to 23 MHz). Maximally observable
frequency of OS and KS is almost double the theoretical muf. The relationship
of OS AND KS amplitude as a funetion of working frequency is weak. It has
a flat peak in intermediate optimum frequencies. Variations in OS amplitude
with time of day are also negligible.
In Figure 1.9 are shown the limits of amplitude measurements for OS and KS in
various equinox months (March and September) of 1967-1972 with a change in -
solar activity W= 110-60 at fixed frequencies: OS-12.8 MHz (at noon and
transitional hours LT), KS--18.2 MHz (evening hours The horizontal dashes are
the monthly medians of field strength.
The best conditions for OS and KS propagation relate to 1967, a period of
increased W. OS were regularly observed for six years, and periods of reception
showed no pronounced changes in amplitude, although reliability of detection was
changed.
After 1967, conditions of KS propagation deteriorated and only in 1972 did they
improve again. Measured KS attenuation ~'or the distance D= 53,700 kilometers
with respect to EH at working frequencies f W= 18-21 MHz comprised 20-30 dB
in 1967 and 30-35 dB in 1972. (see Figure 1.8). In other years (1968-1971),
integral attenuation of KS exceeded 40 dB (with this attenuation, the KS level
is below the threshold of equipment sensitivity).
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E~,6 6:30-i:30
. .
z0 EH ' ' OC
a . .
-20 ~ . z4
- 40 ~
-fi0 12:30-1:30 ~.;n.
~
20 EH .
OC
_ZO 5 ~ , 2 , � -
-40 ~ . _
-gp ;:,:3Q-7:3;1 a.m. _
i
i
z0 E H ~OC
o � -
-20 20
-40
-60 ~ ~;:3;~-7:30 ~.m.
40
20 - EH 67 67 KC (53700KM)
o ~ i, Mr~
-z0 1Q z0 -
Figure 1.8
Reiterated KS were recorded in March, 1967 from 7:10-7:40 p.m. LT at fW =
18-23 MHz with a reliability of detection of 35 percent. Their attenuation with
respect to the first KS was 8-20 dB.
According to published data, attenuation sometimes did not exceed 5-10 dB [18~.
- When the emitter is situated on an artificial earth satellite, KS attenuation
changed with respect to attenuation of the direct signal at a frequency of 34.3
- MHz within 3-18 dB. �
In Figure 1.10 are cited the results of OS observations in a period of low level
in routes having different orientation: north-east (N-E), south-east (S-E), west
(W) and south-west (S-W) extending 25,000-38,000 kilometers. Observations were ~
made at frequencies of 6.5 to 22 MHz. The most complete measurements in
various seasons were obtained at frequencies of 12.5 to 17 MHz, for which
Figure 1.10 is plotted. At other frequencies of the selected range, OS were only `
detected in a small number of ~ases in individual months. Routes with the
greatest volume of field strength measurements were selected for analysis
(average of 200-250 measurements per month). Averaging was done for the
month period within the sector of azimuthal angles no greater than 10� and 1000
kilometers in distance. In the observations made, OS were recorderl only under
optimum conditions of propagation along the evening (twilight) and morning
(post-sunrise) bands.
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Figure 1.10 shows the seasonal variations of OS attenuation with respect to EH
for routes of different orientation and extension. For most directions, seasonal
variations of attenuation were small. Only for the north-east direction in some
months was attenuation noticeably higher than average. The relationship of
attenuation as a funetion of route orientation was also extremely weak. The
fregUency dependence of attenuation is also very weak. When working frequency
was changed, maximum attenuation drop did not exceed 6 dB.
E, rq6
20
~ 6:40 a.m.
_2 oc
.2
p 12:40 p.m.
- -20 ~ ' � OC -
20
- 6:40 p. m.
, Q
. . ,
-20 �
- EO
0 � . 7:10 p.m.
' � KC
,~ZA
~t ~X ~I ~ ~ 'a_ ~ u ~1 LX !1 L~
~967 i965 1969 ~970 197~ ~97Z
Figure 1.9
Some rise in OS attenuation with a decrease in level W may be caused, in
particular, by the passage of radio waves of the lower frequencies. According
to [3], at middle latitudes during a high level of W there occurred OS reception
under both optimum conditions and with great deviations in the route from the
terminator and even normally to it. At low values of W, OS were received only
under optimum conditions. Propagations of ultra long-range signals at
frequencies exceeding standard muf, reduced attenuation with weakly ex-
, pressed frequency dependence, small variations and weak depend on route
orientation indicate the important role of non-skip modes.
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r~ux ur~r'1C1AL US~; UNLY :
N-E
60 27,500 km
_ - - - - - - -
ZO ,
N-E
s0
38,000 km
~ 20 "
~a
~
v S-E
a~
o s~ 30,000 km ~
- a ~^--L_. _ _ r-~-- -,_.`J-- -
C '
~
C
S-E
~
~
~ 60 _ 32,500 km
~ ~
a~
~ _ _I-L.r- -
~
ZO
W
60
_ 25,000 km
~0
S-W
60 ~ 32,500 km
no data _
20
ix 3C 1~r T v Y v_n vir Time of Year
Figure 1.10 .
�4. Effect of Azimuthal Anisotropy of Ionosphere on Propagation of Ultra Long-
Range Signals ;
Variations observed in optimum directions and periods of reception of ultra lAng-
range signals are a consequence of the space-time changes in the ionosphere and
its azimuthal anistropy. Variations in the structure of the ionosphere alter the
configuration and parameters of ionospheric waveguides and thereby the
conditions and characteristics of radio wave propagation.
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- However various aspects of this interrelationship and the relative role of various
parameters of the ionosphere in the formation of azimuthal-time characteristics
of signals have been insufficiently investigated. This kind of analysis is
necessary to reveal the relative role of various factors of radio wave
propagation (conditions of refraction, absorption, etc. in different sections of
routP;) and the physical interpretation of the observable interrelationship of
opti~num conditions with the terminator.
Underlying one of the possible variants of analysis used in this study is the
comparison of several characteristic ionospheric parameters for optimum and
unfavorable conditions of reception of ultra long-range signals [38, 39]. A
waveguide mechanism of propagation is possible in a significant portion of the
ultra long-range route. It is natural to consider that an important role should
be placed by ionospheric conditions in both the waveguide, i.e., mainly in the F-
region and in sections of the possible capture-release where beams intersect the
absorbing D/E-region and refract in the F-region.
Typical ionospheric parameters must be selected to allow for relationships
appearing in the extremally-parametric method of channel characteristics versus
- ionosphere parameters.
The channel closest to degeneration in a section where fmax is the upper limit
of frequencies of radio wave reflection has a minimum value (and also the
transverse cross section and volume). This section is mo~t ~ritical for refraction
of beams in the ultra long-range route
= f ~2 ~cro) r� ~(r)
f max o t z r
Because the quantities fmax and fpF2 are directly related and change of the
second multiplier is much less than fpF2, we can roughly consider that (fpF2)min
corresponds to (fmax~min. Let us take (fpF2)min in the route as one typical
ionospheric parameter. Necessary angles of rotation of
refracting beams for capture-release by the ehannel are funetionally associated
with faF2 in the appropriate sections. The channel can be either completely
world-wide or partially world-wide. In the first case, capture and release must
- be realized in a region of end points with a radius of 1,500-2,000 kilometers.
Integral absorption in the route and in capture-release sections when intersecting
the D/E regions can be characterized respectively by the parameters (fpE)ep
(assuming skip modes) and fpE (51J.
Let us take (fE)ep as a typical parameter of ultra long-range routes. It is
assumed that this choice is justified for channels passing in the lower part of the
F-region and F/E-valley, i.e., closer to the altitude of the maxmum layer E
~hmaxE), than to hmaxF2. According to observations, optimum world-wide
routes primarily corresponded to the smallest change along the route of zenith
angles of the sun, which should be tantamount to a minimum value of (fpE)cp.
Absorption in channels having an upper boundary along hmaxF2 we can roughly
characterize b,y the second parameter fpF2ep. All selected typical ionospheric
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~30 ~oo ?0 40 10 0~0 40 TO 100 130 ~60 170 ~40
90
4 90
70 _ To
S 6 ?
50 ~S 3 35' ~ 8 50
~
30 4 10 ~ 30
~ S 6 ~i 'i
ao i +z �
C b
p , ~ C
' 0
ro 40 I I ~ i' a' ~
- , ~0
1~ ~ ~ ~ I
30 t ~ , i g ' ~ g ~
30
4 i
/
50 50
~ 9 5 ?
70 b ' - ' ~ ?0
6
90~ 6 90
i3o 100 70 40 ~o o~0 40 70 ~oo ~30 160 ~70 d OP
- Figure 1.11
parameters can be rather easily determined using global ionospheric maps, which
can, for example, be found in weather forecasting publication. In view of the
appearance of the geomagnetic longitudinal effect in the F2 layer, global
distributions f~F2 and fpE differ substantially at the same physical instants of
time. Especially typical are differences in the position of the extremes of
distribution of fpE and fpF2. For the regular E-layer (f~E)max is located in the -
subsolar point, while (fpE)min is at its nadir. Both extremes are geographical
antip~des with respect to one another.
In the F2-layer, the region (fpF2~max located in the near-equatorial region is
displaced with respect to the nadir and is located primarily in the polar
latitudes. High latitude minimums in ionization of the F-layer occupy many
thousand kilometers in latitude and longitudie and are arranged above the low
latitutde boundaries of the auroral zones of the northern and southern
hemispheres. The deepest minimums of ionization of the F-layer are arranged
in the northern hemispher~ in winter (Fig. 1.11), and in summer are in the
souther, while in equinox there are ionization minimums close in magnitude in
both hemispheres at the same time.
An example of the global distribution of critical frequencies of the F2 layer in
Figure 1.11 corresponds to December, 1971 at 6:00 a.m. LT. The solid line
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denotes the large circle of direction nearest the terminator which is plotted with
a ~3otted line.
]~ines oi the ground-based terminator sink in the polar regions, reaching the
geographie poles during equinox, i.e., 90� latitude; in periods of the winter and
summer solstice, about 67� latitude; therefore, they intersect regions of
minimum ionization.
Mr~
,9 oF'z
z f ~
~ -
5 ~ .
.
- ~ ~ _winter
i
3 - ~ -summer
` equin~x
3 _ ~
f~E . , � .
, ,
. ~ ~
,
0
9 (1oFz)~P
. �
� ~ ? .
7 - ,i'
. _ -
. ;
.
S
- 3V1MA
nETo
PA6HOaEHCT6NE
5
(feFZ)~,~ ' ~ -
3 - ~~�j'~,
.
. ~
. ~ ~ . ~ . ~ ~ ~ ~ ~
~ ? t,4
0 4 b ~6 20 Z4
Figure 1.12
Both extremes fpF2 in the general case are not antipodes because of con-
siderable differer~.ces in absolute values, etc.
Directions from a prescribed point, corresponding to the minimum (fpE)ep (in a
route intersecting the terminator at a minimum angle) and the maximum
(f~F2)min, should occupy an intermediate position between directions to
_ extremes of the global distributions. In the general case, both typical directions
can change according to point coordinates and the period of observation. Let
us adduce the results of variation analysis of typical ionospheric parameters for
both optimum periods of time and direction and for unfavorable ones, for the
reception of KS in a combined receiving and transmitting point.
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J'o F~, -
~x
~o
- ~ ~ i05~ -
8 / ~ ` /~/1~r/
' i ~ ~~a
~ / i
6 . ~
~ ~~0' i'
~
4 . ~ ~35
.
D~,~~~ thousand
' ' ' ' ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ I u n)
V Ci+(1'n- sl~ ]I,~P -~lU'6 n' e)Zr" ,~-J~ (?^nur) ~4.28)
~
where ~
_ 3~ r~(r~-r,) (r~-r,)2 Ug-Y
. ~,:p--z uG_un + ~Ub-Un~ ~
e ~ arc Cos ~r^- r ue-v_
' u~f
~=u~ rs rb u6-u�
(r~- rb~ -(u;-V) .
(see ��3, 4, Chapter N).
In t:~e limiting case of a beam slipping along the channel axis (v = ug) -
Tcf
_ 3~ tr~-r (r2 -u.a) (4.29)
Z r~ Ll6-U~
and
c ~l _ ra - lle , (4.30)
9
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~ 1S,KM�HeneP
0,3
0,2
.
g1
- y?h j rMOx
0
qos qo4 qo~ o,oi5 qo2 o c~o qoos
2 a s a ~o ~x f~fKp
Figure 4.14
Let us consider the frequency dependence of radio wave absorption in ionos-
pheric channels in limiting cases of propagation near the upper boundary rA of
the channel (steepest beams retained by it) and along the axis rg of the channel
[102). Formulas of the frequency dependence of absorption can be derived on
the basis of the EPM using analytical expressions for rA(f) and rB(f) (��4, 5,
- Chapter III). Let us substitute them in the formula of the coefficient of
absorption ~ per unit length, whose frequency dependence is completely defined
by the right side of the expression
~`-1s(f)= fN (r(i))/fi
~ -f~ (r(i))Jf2 ~ -
As a result we find (2c/~ )~A as a function of f/fcr~ Ym~rmax and (2c)/ 1~ )~B
as a function of f/fM
4� PfM/fi =~r -1~~~1~'~~ .
Calculated frequency dependencies of absorption for several values of key point
parameters of the ionosphere are presented in Figures 4.14 and 4.15. The nature
of the frequency dependence of absorption at the boundary (rigure 4.14) and the
axis (Figure 4.15) of the channel are very different. Absorption on the channel
boundary monotonically decreases in inverse proportion to working frequency to
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RM�HEt1EP ~
6 ~
4
~
~
2 ~
~ ~ g,. g000~
p o0000 - - - - - - - - - - - - - - - - -
z s +o 'a f ~ fM
Figure 4.15
fonrn,
~ fM
~7
i
~
5
0.0 O~OOOi 0~0003 0~0005 0~0007 ~
Figure 4.16
its final minimum values corresponding to the limiting frequency of channel
degeneration. Absorption on the channel axis at first decreases in inverse
proportion to working frequency and, after passing through the minimum for real
C~ slowly increases, fluctuating within comparatively small limits. In terms of
absolute value, absorption along the axis is many times less than along the -
boundary of the channel. The substantive qualitative difference in the frequency
variation of absorption at both levels is the result of the opposing nature of
displacement with increase of f of the level rA, which drops to altitudes with
smaller f2N, and the level rg which rises to altitudes with greater f2N. In the
second case there is a compensating effect, wherein the ratio of f2~(rB(f))/f2
fluctuates slowly. In calculating the possible change of J with altitude, the
curves can change slightly because ~(f)N ~(r(f)). With more likely increase
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of V with altitude, A will be inversely proportion to f and con-;equently, the
drop in ~~A(f) will be somewhat accelerated. Because oi' the increase in
, g in proportion to frequency, '~B(f) will fall somewhat more slowly ~t low f
and rise more quickly at high frequencies. The qualitative distinetion of the
frequency dependence of absorption at the boundary and axis of the channel are
retained in this case as well.
Estimates of actual values of c~, can be made for existing N(r)-profiles. In Figure
4.? 5, the solid line roughly corresponds to the upper limit of oF
for middle latitudes (values of indicated above for dotted line are not
probable). For twilight conditions, the values are ~ are extremely low; this
involves a reduction in absorption along the channel axis. In a horizontal-
ly-heterogeneous route in different sectors, values of can differ, but the -
resultant frequency dependence of integral absorption must retain a qualitative
nature.
From the condition of the minimum of absorption at optimum frequencies fopt
, ~ ~'(?"e(f))=0
we find the formula
f on'r _ ~i
fM - ~ ~ ~4.31)
The calculated relationship of foPt/fM as a function of is shown in figure
4.16. As ~ increases there takes place a monotonic drop in fop t/fM. Optimum .
frequencies greatly depend on the quantity min N in the trougFi; they are also
affected by other parameters of the trough and maximum of N'r.
In a horizontally-heterogeneous route, the resulting optimum frequency can be
roughly represented by the expression
f onT - n, ~~fN+~" 4 ~+~Q ~4.32)
i n-t rn ~ -
i
whE~c�e n is the number of discrete points in the route.
The weakly expressed frequency dependence of absorption along the channel axis
and values of fopt for actual and fM correspond to observed aspects of
damping of iiltra long-range signals. They usually have weakly expressed
frequency dependence, reduced absolute values with minimum above standard
(�3, Chapter I). The observable characteristics differ considerably from
the usually well expressed frequency dependence of damping of skip modes with
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minimum below MPCh [37].
- Theoretical estimates confirm the assumptiot~ of largely super-refraction of ultrtt
long-range signals and indicate their tendency to pass near the channel axis over
mucr of the route.
�6. Spatial Damping of Radio Waves in Ionospheric Channels
The significant difference between spatial damping of energy flux density and
spherical divergence in free space becomes even clearer when there is more
heterogeneity of the medium and refraction and smaller altitude dimensions of
the region of radio wave propagation. This region, in the case of ionospheric
radio ducts, at very high working frequencies, is much less than in skip modes.
Based on radiation concepts of energy flux density of a refracted, reflected and
focused beam in conjunetion with the mathematical apparatus of EPM, we can
find analytical expressions to determine spatial damping of the electrical fields
of radio waves in channels.
In general form, the factor of longitudinal focusing of energy flux density in the
plane of propagation of radio waves
sin ~P,(r,l 4 ~
' cos ~f cr) ~ d 9(`Fol~d~Po ~ -
where ~~(r~) is the initial an~le of beam escape at level rp of the emitter, ~Q (r)
is the angle of the beam with the vertical at level r of the receiver; 9 is the
interval of oscillation.
In a spherically-symmetric medium
sin ~Qo (rl _ ~
cos ~p tr~ - cosecz ~p, o~-~ (4.33)
tl (r)
because u(r)sin2 ~(r) = u(rp)sin2 ~O~rO~� -
For any emitter and receiver height u(r~) and u(r) can be derived by using
analytical quadratic models of u(r) (Chapter III, �3-5). At levels below 100
kilometers, n= 1 and u(r) = r2. On the Earth's surface u(r) = d2, where d is
the Earth's radius. When an emitter and receiver are situated at the same level
rp = r, we find u(rp) = u(r) and sin ~p/cos tan ~p. In the general case, we
use models u(r) corresponding to intervals of altitudes in which the emitter and
receiver are found. These cases are possible: 1) emitter in interval [rB, r R],
receiver at [r rA); 2) emitter in interval [r n, rAl, receiver at [rg, r,.~]; 3)
emitter and receiver both in interval [rB, r 4) emitter and receiver in interval
[r~ , rA]; 5) emitter and receiver in interval of altitudes below 100 kilometers,
e.g. on Earth's surface.
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Using the appropriate models of u(r), we find analytical expressions for thc
multiplier sin -P~/cos ~P(r) for any ~osition of emitter and receiver.
Analytical expressions for d9( ~p)/d ~ can be found by differentiating with
respect to the expressions of A( ~ ~g from �3, Chapter IV.
For gently sloping beams reflected below r n, we find:
d~(~Po) _ s~viZ~'o (9-d~)cos~Q, cos~p.
d~o cus:~Pd (a,- cosz ~,)'~z arc cos
d, ] . (4.34)
Gentiy sloping beams oscillating near the channel axis are most important,
_ because as ~p decreases, the probability of beam retention by the channel over
most of its expanse also decreases.
_ Allowing for the factor of longitudinal focusing , electrical field strength is
represented in the general form
E(r~A) = 173 PN,~ S i n. ~ i
r sin9 cos~P~r~ de~~e~~d~Po ,
Here Pem is emitted output.
The multiplier 1/~ eonsiders the sphericity-induced divergence of beams
where 0< 8