# SCIENTIFIC ABSTRACT BASS, F.G. - BASS, F.G.

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CIA-RDP86-00513R000203910019-6

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RIF

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S

Document Page Count:

100

Document Creation Date:

November 2, 2016

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June 6, 2000

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19

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Publication Date:

December 31, 1967

Content Type:

SCIENCEAB

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I-M am.
69948
Roo sov/141-2-4-3/19
AUTHORS; Kaner, E*Ae and Bass F.G.
TITLE: 1propagatioll 9? 7 "ec roma&ag e Waves in a Medium With
Random Irregularities Placed Above a Perfectly Conducting
Plane
PERIODICAL: Izvestiya vysshikh uchabnykh zavedeniy,
Radiofizika,
1959, Vol 2t Nr 4, Pp 553 - 564 (USSR)
ABSTRACTi Formula* are dextred for the main statistical
character-
istics (average field, amplitude aud phase fluctuations)
ard- thair dependence on th's frequency and polariration
of radio wav'es'band the distance and height of the
receiving and transmitting aerials. In order to have a
complete statistical description of the radiation field,
it is necessary to know the distribution function
f(60 of the random deviations be of the dielectric
constant from the average value ; which for simplicity
was taken as unity. However, at present the theory does
not give an unambiguous answer to the problem of the
distribution of be . If one considers that this
Cardl/6 distribution is normal and takes only small
fluctuations,
69948
SOV/141-2-4-3/19
Propagation of Electromagnetic Ifives in a Medium With Random
Irregularitles Placed Above a Perfectly Conducting Plane
then in order to obtain a complete statistical description
it is sufficient to know only the second moment of
f(be) or the correlation function bt(r 1)bz(r2) . it
is assumed that the correla&"n function is of the form
given by Eq (1,I), where bea is independent of the
coordinates (statistically uniform medium) and the
coefficient W depends only on the moduli of the
differences between the components of the vectors r
and E2 The distribution function of each of the
components of the field E = E + ig (Z and E.
r i r 3.
are the real and imaginary parts of E ) is taken to be
of the form given by Sq (1.2), where the symbols involved
are defined by Zq (1-3). Using this formula, it is shoifn
that away from the minima of the mean field, i.e. when
the mean phase is given by Eq (1.4). The
Card2/6
69948
Propagation of Electromagnetic
Irregularities Placed Above a
SOV4141-2-413/19
Waves in a odium W th Random
Perfectly Conducting Plane
mean square phase fluctuation is given by Eq (1.5),
the mean amplitude by Eq (1*6), the mean square of
amplitude fluctuation by Zq (1.7) and the mutual
correlation between the amplitude and phase by Eq (1.8).
Thus, a complete description of the radiation field is
obtained if the mwm field and the corresponding mean
square values are known. In order to calculate these
quantities, use is made of Maxwell's equations which, 'vK
after the exclusion of the magnetic field, can be
.reduced to the form given by Eq (2*1). Assuming that
e = I + be, 9 = 9 +~4 , the final equations are of the
form given by-Eqs-(2,3) and (2.4). These equations must
be supplemented by the appropriate boundary condItIons
on the separation-boundary. If the latter is a perfectly
conducting plane, the tangential component's of the field
must be zero (Eq 2-5). The subscript 00011 indicates
that the quantities are evaluated at z = 0 , where the
x axis Is normal to the separation boundary and passes
Card3/6
69948
-2 1 3/19
propagation of Electromagnetic Waves in a Medium"42't4hl R;nUom
Irregularities Placed Above-a Perfectly Conducting Plane
through the point z0 at which the radiator is located.
The x axis passes along the projection of the line
connecting the point of observation r(L,O,z) with the
radiator r0 (0,0,Z) # The boundary condition for the
vertical component 9 is given by Sq, (2*6). it is
assumed that 176CJ~c k I6'el or kt,,> I , in which case
polarization corree ions can be neglected, Accordingly, the
vactor'equations (2,3) and (2,4) can be reduced to the
form g1ven by Eqs (2-7) and (2o8), subject to the boundary
condition given by Eq (2.9). The b function on the
right-hand side of Eq (2.7) is due to the presence of the
source at the point r. . These equations are solved
for the mean field in Section 3, and it is shown that in
order to find this field above the perfectly conducting
plane, it is sufficient to replace the propagation
constant k by the quantity x = k \(-r-7--
in which
Card 4/6
69948
SOV
ch~1-2-4-3/1&9
I n
MI
Propagatlon-of Electromagnetic Waves In a e um with dom
Irregularities Placed Above a Perfectly Conducting Plane
944~ is given by Eq (3*11) (Which is the same as the
value of eoi in an infinite medium - Ref 5). SectIon 4
is concerned with the statistical characteristics of the
field in the distant zone. In this section, formulae are
derived for the mean square fluctuations mentioned above.
It is shown that the fluctuations increase rapidly near
the minima of the mean field and this Is associatea with
the interference structure of the electromagnetic field In
space. The interference effecis are most sharply defined
when the amplitude of the direct and the reflected waves
is the same. If the modulus qf-the amplitude reflection
coefficient is different from unity,. the interference
phenomena do not lead to such a stron3increass in the
fluctuations* In the came of small reflection coefficients
one can use the formulae obtained for aninfinite medium.
If the correlation function can be approximated by a
formula of the form be2 exp [_ (X2 +_y2)/12 - Z2 /12
Card5/6 4 -L
699j
soV14i-2-4-3/ig
Propagation of Electromagnetic Waves in a Medium With Random
Irregularities Placed Above a Perfectly Conducting Plane
the amplitude and phase fluctuations are given by
Eq (4-17), The rap14 increase in the relative fluctuations
near interference minima and in the distant zone is not
associated with an increase in the absolute fluctuations
but a decrease in the regular component of the field.
There are 7 references, of which 6 are Soviet and
I Is English.
ASSOCIATION: InstItut radiofiziki I elektroniki AN USSR
(Institute of Radiophysics and-Electronics of the
A7c-.Sc.. Ukrainian SSR)
SUBMITTED: March 19, 1959
Card 6/6
69949
9, *00 sov/14l-2_4-4/i9
AUTHORS: Bass, F.G. and Kaner, Z*A*
0"
1, 01'
TITLE: C=alation f Electromagnetic FielAFluctuations in a
Medium Having Random Irregularit and Placed Above a
Perfectly Conducting Plane
PERIODICAL: Izvestiya vyashikh uchobnykh zavedeniy, Radiofizikat
1959, Vol 2, Nr 4, pp 565 - 572 (USSR)
ABSTRACT: The present paper is the continuation of the paper on
PP 553-564 of this issue. Using the results-obtained
in that paper, general formulae are derived for the
spatial correlation functions for amplitude-and phase
fluctuations, assuming that the relative fluctuations are
small. If the fluctuation part of the electromagnetic
field is much smaller than the regular component (at
points distant from the zeros of the latter) the phase
and amplitude fluctuationz are given by Eqs (1,I) and
(1.2). The correlation between the amplitude and phase
fluctuations at different points 1 and 2 is then
g1v6n by Zqs (1.3) and (1.4). Under certain s:Lmpllfy*ng-
assumptions, it can be shown that the phase and
Cardl/2 amplitude correlations are equal and we given by Eq (1-5).
699h9
sov/141-2-4-4/19
Correlation of Electromagnetic Field Fluctuations in a Medium.Having
Random IrregUlarities and Placed Above a Perfectly Conducting Plane
Thus, the phase and amplitude correlation functions are
completely defined by the quantity
using Eq (1.6) derived-in the previous paper,
it can-be shown that is given by Eq (1-7). This
equation is then used to calculate the correlation for two
special cases, namely, the case of transverse and longi-:
tudinal correlation. There are 3 Soviet references.
ASSOCIATION: InstItut. radiotiziki i elektroniki AN USSR
(Institute-of-Radiop ysics and Electronics of the
Ac.Sc. Ukrainian SSR)
SUBMITTED: March 19, 1959
Card 2/2
~k 2400
69959
AUTHOR:
Bass, F.G SOV/141-2-4-14/19
WMVFOW%W I
TITLE;
On the
heory of Artificially Anisotropic- Dielectrics
PERIODICAL; Izvestiya
vysshikh uehebnykh zavedeniy, Radiofizika,
1959, Vol 2, Nr 4, pp 656 -
658 WSW
ABSTRACT:
A number of recent works (Refs 1-4) consider the
problem
of the propagation of electromagnetic waveswix a medium
whose
permittivity and permeability are periodic .functions
of-one-of the
coordinates. In the following, an attempt
is made to determIne the
average (over a period) electro-
magnetic field under the assumption
that the deviations of
the permittivity v and permeability It from
their average
values 1 and j are small (the averaging being carried
out
over the space period). FtLrther',' it is assumed that
e and IL are
real functions but otherwise they can be
arbitrary, scalar or
tehsorial real periodic functions
.6f the coordinates. The period is
much smaller than the
wavelength in the medium. The electric and
magnetic
fields 9 and H are given by:
Card 1/3
69959
soy/141-2-4-14/19
On the Theory of Artificially Anisotropic Dielectrics
9 = z0 H Ho
W
= 90; H = Ho
By averaging the Maxwell equations for 9 and H , it
is possible to obtain'the averages E 01 Ho,~ t and
These are defined by:
:Lw iW
rot E0 (pH0 +on); rot H 0 (cE 0+ at) (2)
rot (ILiq. +- PH0 rot ag 0) (3)
c c
where =Ii--;; a e The quantity a and 0
can be represented by the Fourier series given :Ln.Eqa
Card 2/3 Consqquently, and. I can be expressed by Eqs (5);
69959
fBOY4,141-2-4-14/19
On the Theory of Artificially Anisotropic D e ctrics
The fields Z 0 and % are therefore given by Eqs (6)
where the parameters 10 and el are defined by,9cp Q;
The permittivity and permeability tensors are expressed ;y
Zqs (8). The author thanks P.V. Bliokh and B.A. Kaner
for valuable discussions. There are 6 Sovid references.
ASSOCIATION: Institut radiofiziki i elektroniki AN USSR
(Institute of Radiophysics and Electronics of thg Ac.Sg.-
Ukrainian SSR).
SUBMITTED: May 15, 1959
Card 3/3
80241
24, 2400 S/141/59/002/06/023/024
9032/E314-
ATJTHOR: gA583 F.G*
TITLE: iffeMiA7Meelectric-constant Tg a r i a Medium With
Random Irregularities
PERIODICAL: Izvestiya vysshikh uchobnykh zavedeniyj
Radiofizika,
1959, Vol 2, Nr 6. pp 10i5 - 1016 (USSR)
ABSTRACT: The equations for the mean electric field A and the
fluctuation part t were shown in Refs I a-nd 2 to be
of the form given by Eqs (1) and (2). If be is small
compared with the mean N~alue ;c , Eqs (1) and (2) can be
simplified to the form given by Eq (3), where W is the
correlation coefficient between' fluctuations In the
dielectric constant, which is considered to be an even
function. If the electric field varies much more slowly
than the correlation coefficients then Eq (3) can again
be simplified into the form given by Eq Mg where the
effective complex dielectric-constant tensor is given by
Eq M* The mean electric field in a medium with
anisotropic irregularities can be described by the sam
Cardl/4 equations as those used in the theory of crystals and,
80341
S/141/59/002/06/023/024
2012#
OaJ4
Effective DielectrIc-constant Tensor in um With Random
Irregularities
consequently, two-phase velocities are possible (Ref 3).
If the corresponding Integrals are convergent, then In
Eq (3) it Is possible to expand the exponent in the
expression under the integral -sign into a series of powers
of
kVT
The expression for cilk is then found to be given by
Eq (6). If 6z depoiLds only on a single coordinate,
say, x , then the correlation coefficient depends only
x r - r' It the integration, In Eq (5) is
on P
completed with respect to ey and Pz and the
resulting expression Is expanded In serles of powers of
k f;
then one obtains the relation given by Eq (7), where: Pf
Card2/4
8OU1
5/141/59/002/06/023/024
,10120
OaJ4
Effective DielectrIc-constant Tensor UM With Random
Irregularities 00
w (1P X)dpx i A x or k A x
0
The expression for the effective dielectric-constant
ten or, when the fluctuations Os depend on only One
coordinate, can also be obtained without assuming that
be Is small, provIdaj terms of the order of
-k 2; in Zq (2) can be neglected. If, further, one also
neglects Z y and Z. , then the second equation of the
system given by Zq (2) simplifies to the form given by
Eq If the averaging process Is carried out for
Eq then since 0 , one obtains Eq (9) and,
hencel Eq (10)e
Card3/4
S/141/59/002/o6/023/024
Effective Dielectric-constant Tensor in &EA194914ith Random
Irregularities
There are 4 Soviet references*
ASSOCIATION: InBtitut radiotimiki i elektroniki AN..USSR
(jna+j+ut^ nf R&dinin ics of i
SUBMITTEDt September 21, 1959
Card 4/4
~ (9)
AUTHORS: Kaner, E. A., Basel F. G. SOV/20-i27-4-17/60
TITLE: On the Statistic Theory of the Propagation of Radio Waves
Over
an Ideally Conducting Plane
PERIODICAL: Doklady Akadsmii nauk ME, 1959, Vol 127, Nr 4, pp 792
795
(USSR)
ABSTRACT: In the present paper# the statistic characteristic
elsotro-
magnetic field propagated in a medium with small random fluc-
tuations 69 of the dielectric constant -E . + 6E over an
ideally conducting plane is calculated. It is assumed that the
medium over the surface is statistically homogeneous,,and that-
and ~682> donot depend on time.and on the coordinates.
The problem is restricted to large-scale fluctuations, i.e.
the correlation radius is large as compared with the wave
length* For a complete statistic description of the field, the
mean value of the field and the mean square of the fluctuation
components must be found. In a limited medium, the fluctuations
grow near theinterference minimum of the field components.
The theoretical results obtained in the consideration of the
Card 1/3 problem described are further dealt with. On the basis
of the
On the Statistic Theory of the Propagation of Radio
SOV/20-127-4-17/50
Waves Over an Ideally Conducting Plane
Maxwell equation and neglecting polarization corrections,, the
Maxwell equation is transformed intoA~ + k 2
p6(1-?0), (2). This method of statistic description was
ev-eloped in the papers by Lifshits and collaborators (Ref 2).
:
A solution is found which shows that at a sufficiently large
distance from the source the distribution of the components
is normal at any diatributioh-law of 6L. In equation (2)" P
denotes the regular and � the fluctuation components, k-0/0,
f-4%0~t. At a distance L )kl 2 from the interference minimum#
the distribution of the phase and amplitude is a Gaussian
distribution, near the minimum it is a distribution according
to the law by Rayleigh. The conditions obtained mean that for
a complete statistic description of the electromagnetic field
it is sufficient to find the mean (regular) field and the mean
square value of the fluctuations (r)=k ers?
Card 2/3 Z~O
On the Statistic Theory of the Propagation of Radio
SOV/20-127-4-17/60
Waves Over an Ideally Conducting Plane
for each field component. There are-3 references, 2 of which
are Soviet.
ASSOCIATION: Institut radiotiziki i elektroniki Akademii nauk SSSR
(Institute
of Hadlophysics and Electronics of the Academy of Soiencesp
USSR)
PRESENTED: April 8, 1959, by M. A. Leontovich, Academician
SU13MITTED: April 4, 1959
Card 3/3
69415
s/141/60/003/01/007/020
d?, E032/Z414
AUTHORt Bass, FOG.
TITLEt Boundary Conditions for.the Average Electromagnetic
FielODn a Surface with Random Irregularities and
Impeaance Fluctuations
PERIODICALt Izvettlya vysshikh uchebnykh tavedeniy, Rad:iofizika,
196o, Vol 3, Nr 11 PP 72-78 (USSR)
ABSTRACTt The propagation of electromagnetic waves above a surface
with random irregularities has been discussed by
Feynberg (Ref 1) in the case of a vertical dipole placed
on a certain average plane surface relative to which the
random irregularities are assumed to take place. It
was shown in Ref 1, that the propagation of the average
electromagnetic wave above a surface with random
irregularities is equivalent to the propagation above a
plane surface having a certain effective complex
dielectric constant which depends on the statistical
characteristics of the random irregularities. The
present paper gives a derivation of the boundary
Card 1/5 conditions for the average electromagnetic field over a
69415
s/i4i/60/003/01/007/020
ZOWZ414
Boundary Conditions for the Average Electromagnetic Field on a
Surface with Random Irregularities and Impedance Fluctuations
surface (which is not necessarily plane) with random
irregularities both in geometrical form and electrical
properties. The discussion is limited to vell-conducting
surfaces which satisfy the Leontovich boundary conditions.
The discussion begins with a consideration of the
propagation of a sonic wave over a surface with a
random Impedance. The boundary condition for the field
(~ on the surface can be written in the form given by
Eq (1). The orthogonal system of coordinates employed
is as follows3 the Z axis directed along the normal
to the underlying surfaces and the X and Y axes
are chosen so that they are tangential to the principle
lines of curvature. In Eq (1), 1 Is the impedance of
the,separation boundary, k = w/c, and the dependence
on time is taken to be of the form e-iWt. The random
impedance way be looked upon an a sum of the average
impedance and the random component, and similarly for
Card 2/5 the field It Eq (1) is statistically averaged, on
69415
s/141/6o/003/ol/007/020
E032/E414
Boundary Conditions for the Average Electromagnetic Field on a
Surface with Random Irregularities and Impedance Fluctuations
Card 3/5
is led to Eq (2) where the horizontal bar indicates
average quantities. On subtracting Eq (2) from Eq (1),
and neglecting second order quantities, Eq (3) is
obtained. The boundary conditions for 4~ can be found
by expre ssing_ +1 (the random component of the field)
in terms(of. 41'using Eq (3) and then substituting
into Eq 2) The resulting boundary condition is given
by Eq (4) and it is clear from this equation that the
boundary condition is non-localg ie the derivative on
the left depends on the value of (P on a certain area
having a centre r and whose effective linear
dimensions are oCthe order of the correlation radius
between a(r) and a(r'). If the correlation radius is
much smalle; then the radius of curvatureo V is the
Green function for the plane. If one assumes that the
correlation function depends only on the distance between
the points r and r, , the boundary conditions given
by Eq (4) caR be rewritten in the form given by Eq M-
The case is then discussed where the integral boundary
69415
s/141/60/003/01/007/020
E032/E4i4
Boundary Conditions for the Average Electromagnetic Field on a
Surface with Random Irregularities and Impedance Fluctuations
condition goes over into a local one. The discussion
is concluded with a consideration of the Leontovich
boundary conditions. On a random surface z =1 (X'Y)'
these conditions are of the form given by Eq (9) where
E and H are the total electric and magnetic fields
and E =L E + as H = H + h. If the boundary conditions
(9) ire';ppilled t7o th-e suTface z =-O, and the
appropriate averaging process is carried out, the
average and fluctuating components of the electric
field are given by Eq (10). It is assumed that
impedance fluctuations are not correlated to geometrical
fluctuations. In order to find ez and the
z derivative of ex,y use is made of Eq (11) which gives
the field at an arbitrary point in the upper half-space
in terms of the tangential components,Tf)the electric
field on the surface (Ref 2), where - I is the magnetic
field due to a dipole whose moment is in the direction of
Card 4/5 the i-th axis, the tangential components of the electric
69415
s/141/60/003/01/007/020
E032/E414
Boundary Conditions for the Average Electromagnetic Field on a
Surface with Random Irregularities and Impedance Fluctuations
field on the average surface being zero. If the
integration surface is approximately plane, the
expressions given by Eq (12) are obtained. If on the
other hand impedance fluctuations can be neglected, and
geometrical fluctuations are uniforms the expressions
given by Eq (13) are obtained. The theory is then
applied to the case of the propagation of electromagnetic
waves due to a point source,over a spherical earth. In
conclusion the author thanks Ye.L.Feynberg for discussing
the results and E.A.Kaner for helpful suggestions.
There are 5 Soviet references.
ASSOCIATIONtInstitut radiofiziki i elektroniki AN USSR
(Institute of Radiophysics and Electronics, AS UkrSSR)
SUBMITTED: July 23, 1959
Card 5/5
S/l4i/6o/oO3/O2/Oo6/o25
AUTHORS: Bass, F,G.-and.-,Kh-nkin,- A.1 E192/E382
TITLE: on the Theory of the Propagation%of Electromagnetic
Wave?'
in a Nonhomogeneous Medium with a Fluctuating Permittivity
PERIODICAL: Izvestiya vysshikh uchebnykh zavedeniy,
Radiofizika,
1960, Vol 3, Nr 2, pp 216 - 225 (USSR)
ABSTRACT: The electric field E in a medium with random non-
homogeneities satisfies the following equation:
rot rot E - k 2CE = 0 (1.1)
where k 2 = 02 te2 (w is the frequency and C is the
velocity of light) and s is the permittivity which can
be represented as e = ;(r) + be(r) , where i(r) is
the average permittivity and be(r) is the random.
permittivity component. The problem is solved under the
assumption that the following inequalities are fulfilled:
- I
2
Cardl/5 I L--,/C
S/141/60/003/02/006/025
On the Theory of the Propagation of ElectigUagR86fic Waves in a
Nonhomogeneous Medium with a Fluctuating Permittivity
where is the wavelength,
is the correlation radius of the random
permittivity component,
a is an interval of which i(r) changes
significantly,
L is the optical length of the route.
Eq (1.1) can be solved-by the method of successive
approximations, so that the field can be represented by
Eq (1.2), where the principal and the first approximations
can be determined from Eqs (1.3) and (1.4), respectively.
In many cases,. i can be regarded as the function of z
only. In this case, if the electric field of the first
ipproximation is perpendicular to the axis z -9 it is given
by Eq (2.1); If the field is inclined to the axis z it
is expressed by Eqs (2.2). Eq (1.4) can be written as
Eqs (2-3). The solution of the second of these equations
takes the form of Eq (2.4). This satisfies Eq (2-5). The
solutioii of Eq (2.5) Is In the form of Eq (2.6). The
CardZ/5 VC,
S/141/60/003/02/006/025
ElA2/E ftc
On the Theory of the Propagation of Electro agni Waves in a
Nonhomogeneous Medium with a Fluctuating Permittivity
following statistical characteristics of the random
components of the electric field, as given by Eq (2.6), are
of interest: the reflection coefficients V 1,2 and
depolarisation coefficients D 1,2 which describe the
rotation of the polwisation plane. These coefficients
are defined by Eqs (2-7). Further parameters of interest
are: the average square value of the phase fluctuation
pi and the relative amplitude fluctuati ons a i and their
correlatidh functionso These are defined by Eqs (2.8).
The expressions for the reflection and depolarisation
coefficients are in the form of Eqs (2.9), where K
represents the correlation function for the permittivity
fluctuations, while F 1 and F 2 are defined by
Eqs (2.10). The correlation functions for the case of
L/k V - 0
Eq.(2) holds for (q fo)-1 < I (where R. In a characteristic
dimension of the sea tering volume and q represents the change
In the wave vector due to scattering). This is true for the
present situation. As the transmitter-receiver distance is
increased, the fluctuating component falls off much less rapidly
than the regular component. Hence at great distances the latter
can be ignored in comparison with the former. At such distances
the mean square fluctuations of phase and amplitude are given by:
Card 2/
Phase and amplitude fluctuations in... s/i4l/61/004/002/017/017
E133/E135
< b(P 2 >- -n2/3, (In A In A > )2 2/24,
< > - Jr/2. 33t (6)
- M2 < < 2
If the fluctuating component is small in comparison with the
regular component, the fluctuations in phase and relative
amplitude are equal and given by:
X: / 2- JF.21 - I(k2R sin X/43TIV19192) 2 ~ (ror)-l
2
... dv W(q) (3)
This relation does not give explicitly the dependence on
distance,
frequency, etc. which can be derived, however, from:
a ~e2(rx*l) (9192 )-2 %If (ho) f (h) 1 -1 exp (2t ix) (8)
where: x = (ka/2)1/3e; ti C~4 2.03; and the remaining factors are
shown In Fig.l.
Card 3/0'
Phase and amplitude fluctuations ... s/llil/61/004/002/017/017
E133/E135
Reflection from the earth's surface is not considered in the
present paper - the result of including it is simply to change
slightly the effective scattering volume. Since the mean field
value dies away exponentially, the fluctuations, in comparison,
grow rapidly. It should be noted, however, that they also depend
an the factor R-2(n+l) where, according to the experimental data
(Ref.6: D.I. Vysokovskiy, book "Some Problems of Long Distance
Propagation of Ultrashort Waves" (Nekotoryye voprosy dallnego
raspostraneniya ulltrakorotkikh voli), Izd. AN SSSR, M., 1958),
n zd2. Eq.(8) was derived under the condition of small
fluctuational these do noto therefore, tend to.infinity as the
equation otherwise Implies. The authorsthank A.V. Men' for
his opinion of the manuscript.
There are I figure and 6 Soviet references.
ASSOCIATION: InstItut radiofizikI I elektroniki, AN USSR
(Institute of RadiophysIcs and Electronics, AS
Ukr,SSR)
SUBMITTED.- October 21, 1960
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C/1 E192/F,382
AUTHOR: Bass, F.G.
TITLE: Fluctuations of the parameters of an electromagnetic
field propagating in a magnotically-active plasma
having a randomly-varying electron concentration and
magnetic field
PERIODICAL: Izvestiya vysshikh uchebnykh zavedeniy,
Radiofizika,
v- 4, no- 3, 196le 465 - 475
TEXT: The problem of the fluctuations of an electromagnetic
field Ju a magnetically-active me'dium was studied in R*f. 1 -
F.G. Bass and-S.I. Khankina - this journa1,._3_T__384, 1960'-
and,
Ref. 2 - N.G. Denisov, this journal, 3, 619, 1960, but it
appears that the generalization of the results obtained in
those
works is of some interest. This is done in the following by
using the perturbation method. The statistical characteristics
of an electromagnetic field which passes through a magneto-
active plasma are calculated; the fluctuations of the electron
concentration and the external magnetic field as well as the
field reflected from the layer of plasma are determined.
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Fluctuations of the parameters of *.*.E192/E382
The equations describing the propagation of electromagnetic
waves in a magnetically active plasma aret
1W Ur
rot H=--E+--&Nw
iW
rot B H
-iWW + !EH
m me IwHoj
where E and H are alternating electric and magnetic
fields, c is The velocity of light In vacuum, e is the
electron charge, N is the electron concentration in the
magnetically active plasma, Ho is the external magnetic field
and v is the velocity of the elactrons. It is assumed that
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Fluctuations of the parameters of ~-i92/F-382
all the quantities are sinusoidal functions of timeo Each of the
quantities In'Eqs. (1) can be represented as a sum of its mean
value and Its fluctuation;
3 = I + C ; 11 . j! + (t; no = Ro + h; N = N + p (2)
where the horizontal line above the symbol signifies statistical
averaging* It is assumed that the fluctuations are small so that,
by using the perturbation.m6thod, the fluctuation compmut of
the electric field of Eqs9 (1) is described by an equation of
the type:
;x 2
6ik k2s ik Ck - Ji (3)
where is a vector. The propagation of the non-perturbed
electromagnetic field is in the direction of the axis Oz and
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Fluctuations of the parameters of ... E192/9382
the plane Ozy coincides with 11 0 . In this coordinate system
the tensor v ik of the gyrotropic medium is expressed by.,
v iu 1/2 v Cos a
xx u xy YX I - u
V(l U sin2a) uv coo sin a
yy U yz zy u
VU U 0082 a) (5)
azz
where a is the angle between R 0 and the axis Oz
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Muctuations of the parameters ... E192/;;582
The solution of Eqs. (3) is assumed to be in the form of the
Fourier integral of the coordinates x, y : I
ei (Xxx + Xyy J(r)= 0i(X:j+Xyy) Z(x,z)dx (6)
If the thickness of the layer where the fluctuations occur is. L
and the layer in perpendicular to the axis z the-expressions
for the compo nents 4 for the plane z L are given byi
0..) A (Z) UJ2 (z)] dt +
2qjO (qj'r-q;'O)
0
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Fluctuations of the parameters...El92/E382
L
If.(L-S) a,,-ql,) (z)-aJ2 (z)] d2;
+ a
2q20 (q' -q'10)
20
I
V ell. (L-s) [atf, (z) + (a, -- q" f2 (z)) d2 +
1, (L) 2qjO (qI10- q210)0 1.0)
L (8)
[a2f, (z) + (a qI ft (z) I dz;
+ 20-ql
2q2a (Iq2 10)
U
tax
M - - - E, (L) - L-y- Ey (L).
where the various functions are defined by:
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Fluctuations of the parameters 1-92/E382
A (Z) 9.1 (Z) + !1-11 9,A (Z) + !Y-' g' (2);
#zz
a, as k' (oxy -
Olt
'Y
as k1 4YY
In the above the index i can-assume the value of 1 which
corresponds to.an ordinary wave or a value of 2 corresponding
to the extraordinary wavee Bqs. (8) are derived under the
assumption thAt X/211' = l/k