TRAJECTORY OF RAYS IN A MAGNETICALLY ACTIVE IONIZED MEDIUM - IONOSPHERE

• Document Type: CREST
• Collection: General CIA Records
• Document Number (FOIA) /ESDN (CREST): CIA-RDP82-00039R000200120028-7
• Release Decision: RIPPUB
• Original Classification: R
• Document Page Count: 53
• Document Creation Date: December 22, 2016
• Document Release Date: April 25, 2012
• Sequence Number: 28
• Publication Date: September 18, 1952
• Content Type: REPORT

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Tra
ecto
of RaYs in a Ma netica Y
,~at~.ve'Ioni ed Medium ~ Ionosphere.
Ya, L. A:L'pert
Th
Ys
a Fi,zichesk$, Val XII,
zvest~.ya ~kade~.i Nauk SSSR, Ser~.y'
I
o 3, Moscow, May/June 198 F
N
a~
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STAT
STAT
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TRAJECTORY OF RAYS IN A MAGNETICALLY 'ACTIVE IONIZED
MEDI:JN__~., IONOSI'IrERE
Ya. L. Al 'p?z?t
(Report read at the conference o:F` t he AII.MUnion Scientific
Council on Radi.ophysics and Radiotechnology of the OB'MN AN USSR,
on 13 December, J.9L17, )
10 INTR01)UC T'l ON
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The question of the trajectory both of the monochromatic
wave and of the quasichromatic group of waves (signal) in a non-
homogeneous anisotropic medium, has not been fully analyzed up to
this time.
In this article we examine the study of radio wave propaga-
tion in the ionosphere. It presents an ionized nonhomogeneous
medium consisting of free electrons and it corresponds to the case
of artjfihl anisotropy provoked by the external magnetic field of
the earth.
The active magnetic properties of the ionosphere lead to the
fact that the monochromatic, linear polarized, electromagnetic
waves which are propagated in it are subject bo double refraction.
(In the case of longitudinal wave propagation/, when the direction
of the ray coincides with the direction ofthe external magnetic
field vector, we have essentially the Effect of Faraday, while in
the case of a transversal wave propagation, when the normal to the
wave front and the external magnetic field vector are perpendicular
to each other, we have the Effect of
STAT
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In the linearly polarized signals which constitute the group
of linearly polarized monochromatic waves, both groups o; waves acre
divided the signal splits into two elliptically polarized sig~
Weis each one of which is subject to a different refraction and
absorption in the medium. Because of this, these signals, called
common and uncommon, diverge and are propagated in the ionosphere
through different paths.
It is known that the ionosphere is nonhomogeneous according
to the height z, and the value of the square of the refraction
exponent n2' of each one of its layers diminishes with the increase
of the height over the surface of the earth from a value, equalling
one at the beginning of the layer, to values equalling less than
zero, The value n2 depends on the degree of ionization of the
layer, the wave frequencyand the orientation of the external mag-.
netic field in relation to the front of the wave. This leads to
the fact that with all frequencies which are lower or nearly
touching the value of the so-called critical frequency with which
the layer: become transparent, there occurs a complete reflection
from the layer (not considering the absorption in it). Therefore,
beginning from a certain height n2 < a for the given frequency,
the further penetration of waves of this frequency into the layer
ceases and all the energy of the wave falling on the layer is
returned by the layer, (One must note that upon passing the
critical frequency in the direction of higher frequencies, the
reflection coefficient from the ionosphere drops sharply.) It is
natura:L that each of the waves, common and uncommon, is subject to
k
a complete reflection in different parts of the layer since they.
have a different value of n2 and the condition for a complete
reflection n2 W Q (1) is satisfied at various degrees of ionization (2).
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The retardation of each one of the waves reflected by the layer
i$ also different in relation to the Lalling wave.
In view of the fact that the approximation of geometrical
optics es is applicable to the analysis of radio wave propagation in
the ionosphere almost up to the very point of reflection of the
wave (where n2 0), one may speak of the trajectory along which
the wave is propagated from the beginning of the layer to the
region of its refection and back. In other words, we may speak
of its path an the ionosphere, that is, the examination of the 4
question from th point of view of rays is fully justified. It is
obvious that the quetion of the actual, trajectory of the wave in
the ionosphere and about the shape and, type of the wave reflected
from it offers considerable interest. At the same time, up to the
present this problem has not received its due explanation in litera-
tures mainly because of the complexity and huge volume of the
theoretical calculations. Because of this a series of interesting
and important facts were overlooked and not examined to their
conclusion.
In the old work by Zhekulin [3] it was mentioned that the
complex correlation between n2 and the angle between the direction
of wave propagation and the direction of the magnetic field of the
earth must lead to a rather "peculiar" trajectory of the normal to
the wave front through the ionosphere (see below). However this
point refers to a physically unreal case since it characterizes
only the complex kinetics of the front normal of an infinite flat
monochromatic wave. In practice, on the other band, we :always
have to do with a limited sinusoid -- with a group of monochromatic
waves and also with a flat wave limi.ted in space, as we may put
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it with a "piece" of a flat wave, or with a spheric wave.
In a later work Booker U4] analyzed this question more
thoroughly and presented a correct physical picture of the
phenomenon (It should be noted that the author became acquainted
with Bookerts work only after he had already completed the basic
part of the present work.) Booker, however, in many respects
limited himself. to 'the general, theoretic side of the question.
Ire relation to the new phenomenon in to ionosphere, experi~
mentally discovered by the author, and named "Effect of Ionosphere
Anisotropy " 1), there arose the necessity to calculate the trajec-
tory of the rays in the ionosphere. During this calculation certain
theoretical difficulties were encountered. The basic difficulty
however was the huge volume of the calculations in view of 'the
necessity and desirability (and this presented an essential interest)
oi' carrying the calculation to a numerical result, to a graph.
This result could be achieved by the method of graph-anal'y'tical
calculation.
This present work contains the results of these calculations
and the analysis of the trajectory of the ray in the ionosphere
while also examining certain characteristic peculiarities of the
wave reflected from it.
tE
2. TENSOR OF THE DIELECT}?IC CONSTANT AND `r
COEFFICIENT OF IONOSPHERE REFRACTION
Let us examine the propagation of a flat monochromatic wave
C l c
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ti
in an ionized medium consisting of free electrons, Here
is the normal of the wave front (G. ,, 'y' are its angular coeffiw
cients, respectively the cosines of the angles o, o, 7 of the
normai with the axes x, Y, z), c&.is the angular frequency, t is the
time, r(x, y, z) is the space point vector, s is the speed of light
in a vacuum, and n is the refraction of the medium.
We began with the electron movement equation
E
(2.2)
from which the member symbolizing the medium absorption has been
removed and where m and a are respectively the mass and the charge
of the electron (the negative sign of the electron charge has been
taken into consideration); ro(xo, yo, zo) as the electron displace-
menu vector; E is the vector of the electric field of the wave (it
is assumed in (2.2) that the effective field acting on the electron
as Ee f f = E); and Ho is the constant magnetic field of the earth.
Since the vector of the polarization of the medium volume unit
is
P = Noero and ro C/7 e l t
J
where No is the number of electrons in one cubic centimeter, instead
of (2.2) we will have
where
1 (2.3)
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The equation (2.3) introduced into the expression of the
electric induction vector D E + Lvfl"Fa gives
Az E
,C yC
C JU v) ) 'j + 'v) ,
a 1 w 1 4
- (h:ii \i)
- b,
-
;:--'
and thus the tensor of thL dielectric constant appears as
+(LLL&
-~ /#4? .y
h~
, -
S _ha&
I ~r 1I 1
V y
/
Y1 1'
r1. -NM. I A.M (JI~I P
7
~
'__'???_M?_._w,__.q__'_?___ V /-_ I ,,
From (2.6) it can be seen that the tensor is a hermit [isolated
instance?L
In order to draw the basic formulas it is more convenient to
choose the system of coordinates so that the axis Z coincides with
the vector Ho. r2hereby (2.5) assumes a simpler form
where
sE7
1bj
z ?E1 + (
d(: s
V
2.6)
Henceforth we will proceed from the phenomenological equations
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F /
_MW~M+MMgMM,KMIMiMMYU1111r~ V
''I
/ W
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oV MaxWe11
and from the wave equation deriving from it
"
E
wil.
0+
which are transcribed for the hat monochromatic wave in the
vec aking (2.1) into Consideration)vector :Corm (t
_1 EfNJ fl 7L:AJ (2.9)
and
r
w ,
? 1 1.~ e v^ c E N h ( 2 10) E bstituting (2.7) into (2.10), we obtain the homogeneous
Su
system of equation relative to Ex, Eye Ens
( _ - ) E ~ + ( a E - & - Y )
C- - - / + ( - - 2) + ( ! ) E V ( 2 , ii)
( y) ff ',q1) F1 + (- o E
The cond?t~.on for the existenCe of a nontrivial solution for
~.
the algebraic system of equations (2.11) is that its determinant
should be equal to zero;
) " fi + f I
-.fly
1.i TI...
The determinant gives a bi-square equation with respect to n
.0
-? !!~I::I!:t -E~ (2.12)
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1&
from which we obtain, by utiiizing (2.8) a certain formula for n
the square of the exponent of ionosphere refraction;
- .t____4_u____.__.?__~ ..
2 I- v~ ~- A (/ - It) :i:
I
~Y
From the formula (2.13) follow the double refracting properties of
the medium The upper sign of the root corresponds, as is usually
said, to the refraction exponent n1 for the common wave, while the
lower sign corresponds to the refraction exponent n2 for the un-
common wave. An analysis of formula (2.13) shows that this termin-
ology is not satisfactory since both waves are essentially uncommon.
Figure
values
assume
1 shows the relation of 1/n1 and 1/n2
of v and for a fixed value h2 = 0.1.
that for each one of the curves shown
values of 1/n1 and 1/n2, when ) o = 0 (
to y for various
For clarity's sake we
in the figure the
1), are equal to similar
segments for all the values of v. Thus the curves in the figure
characterize the change of the shape of the wave front with the
increase of v (and consequently also of No (see (2.b)), i.e. with
the nearing of each wave to the place of its refraction where,
respectively, nl = 0 and n2 = 0. (See also Figures 2 and 3 where
we present the family of curves nl and n2 in relation to v for
various values of . )
From Figure 1 we see that the shape of the front of each
wave changes substantially upon penetrating into the. layer. In
the reflection sector a common wave assumes a saddlelike shape,
while the uncommon one assumes a strongly stretched elliptical
shape. In other words both waves cease to be spherical in the
medium. The so-called common wave, one may say, has more uncommon
W.S
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properties than the one that we are want to ca1i.unoom1on,
0
Relation of the quantities 1/nl and 1/n2, respectively,
Figure 1.
for a comrrtan and an uncommon wave, to 1 o for various values of V
and. for a fixed value h2 = 0.1.
wwnNWwMwuwwaww+YMIMUMwn?rrMnv*'^^"w^"'"w`~"'"r"'"~"~"~w~w.ww+..~++
Figure 2. Relation of the refraction exponent nl of a common wave
to V with various values of
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Figure 3. Relation of the refraction exponent n2 of an uncommon
wave to v with various values of
In order to fill out the picture let us mention a few general
properties of the expression (2.13)?
In the whole frequency diapason the refraction exponent n~
has but one zero which is not related to the quantity h, i.e., to
the external magnetic field, and is determined from the condition
(ih case o:f W 1 n1 = o with v - 1 + h)
vo = 1
(2.1L)
This same condition is observed when the external magnetic
field is absent, when n2 = n2 2 = 1 - v. The refraction exponent n2
1
has two zeros for h ( 1, with
h and v = l + h (2.1~)
For, h > 1, n2 has one zero, when v W 1 + h.
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 COMPONENTS OF THE FIELD VECTOR; POLARIZATION
PROP ERTThS OF THE WAVE
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The expression n2 has infinite values for n , in the .fequanoy
n a.n the frequency diapason h co s y