SCIENTIFIC ABSTRACT SILIN, V.P. - SILIN, V.P.

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• Collection: Scientific Abstracts
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• Release Decision: RIF
• Original Classification: S
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• Document Creation Date: November 2, 2016
• Document Release Date: August 23, 2000
• Sequence Number: 11
• Publication Date: December 31, 1967
• Content Type: SCIENTIFIC ABSTRACT

sc;685
S/056 /:: 60/038/oo6/027/049/yyl
Bo06~BO710
0 (V, V, -C, fa-
I apt
ap, ~
J. (p, 0 -00 +
(V'. V, f., (P" t
apt
au r +
V, V" dr --T,-, "a',
H, I dk4l..- M C"'a X
/till, cosil.t-eirni- sin F2--? ~
HIHI + '11- ) H Mn (14)
H, Hi) Cos jI.,r - et,.l
+
5/6

S/056/60/038/006/027/049/XX
B006/BO70
(V, V, , 't, 1) x
a as
x (!~~ + (81/- ~11 H, )cos f1st - e1., "m sin %,c)
If
(v [H v sin Q. -c
I
V, sin R.. -r cos fl,.r V' I - cos
Iffl + [v
t+T . t'+T e,;, Cos Q. (-r + P
dt, H (HE (1')) +
+ dil
It M, Hs
e., Cos + 0
Iff JE (I-) HII
M,, 112
tJE (I-) sin D. (-r + t' - I') - - ee sin
p-
Card*6/6

-'
"
-
6
6 ~ 7
%UTHORS: Klimontovichg Yu._L., Silin_j V. P. S/053/60/070/02/005/1'016
B006/BO07

TITLL: The Spectra of' Systems of Interacting-ParticleAnd the
Collective Losses in the Passage of Charged Particles Through

I
atter
M
?ERIODICAL: Uspekhi fizicheskikh nauk, 1960, Vol 70, Nr 2, pp 247-286 (USSR)
ABSTRACT; The present survey deals with two essentially closely connect-
ed problems: The spectra of collective excitations in systems
of interacting'particles, and the energy losses in the excita-
tion of collective oscillations when charged particles pene-
trate matter. In the case of a system of strongly interacting
particles (liquid, solid, plasma, or nuclear matter) energy
levels and states for the system as a whole may be investigat-
ed; the investigation of such level spectra is, in itself,
rather complicated; the simplest case is that of weakly excit-
ed states, i.e. of minor deviations from equilibrium, e.g.
ion oscillations relative to the lattice points in a crystal
(phonons). Phonons, plasmons and the like are called quasi-
particles in quantum mechanics; the momentum dependence on its
Card 1/4 energy and the dependence of frequency on the wave number is ~

6,6',7
The Spectra of' Systems of Interacting Particles S/053/60/070/02/005/016
and the Collective Losses in the Passage of B006/BO07
Charged Particles Through Matter
in the following called excitation spectrum, Such excitations
occur as sound waves in solids, as phonon-roton-excitations
in superfluid helium, and as spin waves. The latter are an
example of Bose excitations occurrinj; in a particle system
concurring with Fermi statistics. The analogs of the elementary
Bose excitations in classical physics are the wave processes,
as e,g, the propagation of longitudinal plasma waves. Paragraphs
5 - 5 of the present paper deal with the investigation of
excitation spectra in systems of charged particles; the inves-
tigation is based upon the equations of the quantum-distribu-
tion function (density matrix)derived in paragraph 1. In para-
graph 6 the problem of energy losses during the passage of
fast charged particles through matter, which are due to the ex-
citation by collective oscillations,is Investigated. In matter,
electromagnetic oscillations are excited whose spectra are
fixed by the dielectric constant of the medium. The formulas
derived in paragraph 6 for the purpose of describing the energy
losses do not. however, in all cases reproduce the experimental
Card 2/4 results obtained, as, e.g., not in the case of the Langmuir- /

C
,)or,
,~tie SpectrF.~ of :5.ynterms of Interacting Particles S/053/60/070/02/r
and the Collective Losses in the Passage of B006/BO07
-harged Particles Through Matter
paradox. In order to be able to investigate also such cases,
a further possibility was dealt with in paragraph 2, which makes
it possible to investigate theanergy losses of charged particles
passing through a plasma; this possibility is based upon the
use of equations of motion which describe also the energy los-
ses of particles for the excitation of collective oscillations.
If the particles entering the plasma do not essentially influ-
enceits properties, the expressions derived here for the stop-
ping power coincide with those of paragraph 6. This condition
is, however, not satisfied when an intense electron beam enters
the plasma; and the system of nonlinear equations for the elec-
trons of the beam and th6ae of the plasma must be satisfied
simultaneously. In paragraph 7 the solution of such a special
case is discussed. The results obtained essentially describe
the conditions found by Langmuir. The individual paragraphs
deal with the following: Paragraph 1: Derivation of the equation
for the quantum-distribution function (Bose statistics); para-
graph 2; the equation of motion for the quantum-distribution
function; paragraph 3: the spectra of collective oscillations
Card 3/4 in self-conoistent field approximation; paragraph 4- the influence

jqW -

PHASE I BOOK EXPLOITATION SOV/5782
Silin, Viktor Favlovich, and Anri Amvroslyevich Rukhadze
Elektromagnitnyye svoystva plazmy I plazmopodobnykh ared (Electro-
magnetic Properties of Plasma and Plasma-Lik: Media) Moscow,
Gosatomizdat, 1961. 243 P. Errata slip inn rted. 6,500
copies printed.
Ed.: A. V. Matveyeva; Tech. Ed.: S. N. Popova.
PURPOSE; This book is intended for scientists concerned with
the physics of plasma,
COVERAGE; The authors consider the current theoretical and
experimental literature on problems of space dispersion of the
dielectric constant in its application to material media to
be inadequate. Analyzing the latest development in kinetic
presentations on plasma and the discovery and interpretation
of the abnormal skin effect, they conclude that these develop-
ments clearly Indicate that under specific conditions space
C ard 1/6

Electromagnetic Properties of Plasma (Cont.) SOV/5782
dispersion of the dielectric constant appears to be extremely
strong. In this sense# space dispersion of the dielectric
consta6t enters the field of electrodynamics by the same right
an frequency dispersion. Ch. I-presents the fundamentals of
electromagnetic media with spade dispersion and describes the
latest developments in the field. Basic material necessary
for comprehension of the theoretical presentation of the
electromagnetic properties of solid-state media in the follow-
ing chapters id included. Cho. II and III discuss the appli-
cation of the macroscopic approach to the study of plasma
physics; Ch. IV is concerned with the quantum plasma of metals;
and Ch. V deals with the theory of space dispersion of the
dielectric constant, Because space dispersion manifesto itself
with special intensity in plasnat the authors have originated
the term "plazmopodobnaya sreda"(plasma-like modiun)to describe
a medium possessing considerable space dispersion. Sees. 1,
4s 5, 10 to 18, 24, 26 to 30P and the Appendix were written
by V. P. 811in; Sees. 2P 3p to 9. 19 to 23, and 25 by A. A.
Rukhadze; and See. 31, jointly. The authors thank M. A. LeontovicN
Card 2/6

f Ile 0/ 1 qA 24927' S/181/61/003/006/r24/031
4.7 P 10 (11317 X B102/B214
AUTHORSt Ginzburg, V. L., Rukhadze, A. A., and Silin, V. P.
TITLEt Electrodynamics of crystals and the exciton theory
PERIODICALt Fizikd"tverdogo tela, v- 3, n6. 6; 1961, 1833 1850
TEXTt The present paper gives a detailed theoretical treatment of the
general problem of the ap~,Iication of the electrodynamics of matter iNith.
spatial dispersion to crystals. The'authors confine themselves particu-
larly to tehe invez'Vigation of the approximations one obtains when one
works with si,(*111,i), the t-ensoT of the cvmplex dielectric constant.
First the fundamental equations of the vlectrodynamics of matt*er with,
spatial dispersion are written down. They are in the usual notationst
1 aD 1 47c a3
c ur 1 B Tt + d i v ; div)? - 0; F' - e(9+ vB
CJO lm4T*-Q -T c
I cur t
0 c
the force acting on a point chaKge moving with velocity 1; for the
electric indugtion one has af'/at - a-2/at + 4rj_- For plane monochro-
matic wavez, D' and 11 are interrelated by3
Card 1/1

2 -`9 2 S/181/61/003/006/024/031
Blectrodynamics of... B102/B214
R, (k, k) Ej (k, E, (k, k) 4Yj k), (1, 6)
k) d, dR,41,ft- ~)Ajj (-,R). (1,7)
For crystals one has
D' , (r, w) f dety (-, r, r) E., (r'.
D~j (k, f dk'*,, (w. k, kj Ej (k,
It is shown that in crystals in the optical region the tensor
dan be reduced to the tensor '~k((J'4) ~n the usual way. If the normal
k
electromagnetic waves have the form 'E-' e r BV, ei
-+ 1 orl
r, O'l constant, B 01 , constant (spatiallyohomogeAeous med:um) one has
for j 0,
Card 2~7

S/-81/61/003/006/024/031
Elect-rodynamics of... 3',C2/3214
Df 0 [0], B c (U],
DI (k!E - k (kE)),
,2
9ijEj - OE, -t- kAjEj -= 0.
C,_
2
2
or, in the determinantal representation ti(W,k) 6 +k k L
2 2 ij i ir-
!:~~ -k -3
- 0, or .2 j jj + k.-k11, ij ( In 1 (6 orlldenote the
c
determinants of the system of linear homogeneous equations~ Starting from
these equations the authors investigate in the following the properties
of the tensor ~- in crystals, as well. as the possibRity of calcu-
lating this tensor quantum-mechanically. First,, the effect of taking in-
to consideration the space inhomogeneity is inves tigated. (1.8) may be
written n the form k where n
j
is an arbitrary vector of the reciprocal lattice. The relation between
Card 3/7

S 181/61/003/006/024/031
B102/B214
Blectrodynamics of
D1 and E is given by
k,k'jEj (-, k) - k1E, k) -4- `2 k) E., (k 2--b, 0. (2, 3)
C,
whose do tercainant, leads to the dispersic,n equation [j(W,Q) - 0 with roots
(j a 6,;, (k) . If all ter=9 with b / 0 are eliminated from (2.3Xwhich is jus-
V _~,c/a)~ considered here one ob-
lified for the region with k,~brj1/a;G_-4.cb
f analosous t~~Q'0-13): k,(~E) - k E + (w2/c2)E
tains or b-O i ij (L) ?~)E i
Here in ij (f.)Ik) differs from 1-ij ((..;,k) only by terms of the order of (a/~,d~
~2
In optics, not only Is IRA. but it can also be assumed that s/)~
01
an/A :,l (a-lattice constnnt, ~, -vacuum This is done in'
0 0
the following, i. e.) the spatial disp-3rsion is assumed to be small. One
may then expand in stories of powers of and neglect 'termit of
ij
higher order than the second. Near the absorption lines where some com-
ponents of (w) b,!come very large one must exPan'd analogously the recip-
.1 -1 2-j2
rocal tensor of (1,6): + igijl- ns, + Vijl,((J1c) n
C 'a 3fM
Card 4/7

0,06/024/031
-7, 2 1
-1, h e r e k! n in"- n+ '~LhQse expansions are not justified in
np+
C
, I upole transi-
111.1 tho r-Ine" t 4!. nb:7or-.)1-'O-- lines (;aus,-d by a quadr
*4 4nd llnechancal excitons"
rtro ntudi4~d. vVv,.- .1;olhltion .~. (t.,, k 0
ij
thero eyis'. Qf t'JO111 'A'! t '0 NZ: to
"fictitive" "Lon 4 o it in, sufficit-rit to observe in
the domain of classical. crystal oPtics th~tt waves with 0 become
o rm 2 13 is inves tigat ed in this case in the
longitudinnl when n2_-D. -f~
:A - . ::',. , ~,,c - , , 'c ), 1.
k - - cc.) _a n d t h e relation
are different
0- 4r 4 Z: j e , D- an d z,
nly
A 3 is C 01
f r Om z r~ - o . f a n 1 1: 0, ccn~!-* t`c-n 0 must be
j
satisfied. The la~;t cnse i -3 t " i a tc, f o I t- r ~- z a t i C, n wa -; e S All three,
the lonjitudinal, the fictitiv,~ loneitudinal, !and the polarization waves
satis'v *the cond'tion 'div 0. -,inttlly the a,~;Ihor3 discuss some prob-
lems of the nu---intum thec,ry of t'he disp.~r;3-.on of in crystals during
which the choice of thf* "Vthod of quantum-zechanically calculating the
i -e trans-
tennor s a I e c . Tn:c- .1rr into consi. eration th
lational sym-7:-2try of tl-.-~ cr.yi~tai a is obtai-ed for the current
Card 5/7

s/181/61/003/oo6/024/031
3102/3214
Ejectrodynam;cS This r Iesult ist
'on of the pe-,turbaton theory.
density in the
~,,) - V C(*). b (w, k) Ej (k 2-b. (4,4)
Y , (k, -j j
b
k)
where k)
ikr -Mr.
p'
N W. -f. wo
A-
-4 Arl
1kra (4, 5)'
-4- W.
is determined by exciton
f
it may be aosa.Mr-'d thqt tlh4? anc.L in (4-5) are the frequencies
trazisition3t i. e.1 the frecut-,Ilci~'s n are quasi-
r,,!3ta-. 'he exclton states
of Itmechanical ofcitons~' In the c expand (4-5) or the tensor
re comnlCY- one can
stationary, i. e.. the a
-4 obtains formajas analogous to
C-1 into a series 0~. :Covers of k and V-1us
jj
Card 6/7

24927 3,
El-,,-trodyn,jm,icu of ... B'02/132 14
( -1. ~ ) ; in the neighborhocd of th-_ abocr-pti " r. 1 1 n P ( ; . _1-) hclds. T n
ir7-stigations show-*-d that the tensclrE~,,,W,i~ 'i"t" all properties
of the lln,~-mal` elactromagnetic waves in a is 6!1N11-
-:ieritly smail. Tnvj-*- -h,3v,?g ar,-. I.Ierti-ni wl*~.
in the crystals. namely those which are trRatpq
-1,~,Ttromagnetic interartion in the cxcit3n ~h-C!-v. 'h-r-t, V~' ~I
,-ytic3 contain3 a part of general exciton th,~~)ry i" 'h- )uatiil
1:3 *aken inte acco,int. S. 1. Ijek3Z' iz; Thtrt~ axe tu
'- S~viet-blo-: and 8 non-Snviet-bj~-_-. Pho? i-:*--r-
~--q to English-lans-
uage putlic~iticns r-au [is fo ;.;ws: T. Pr~),qr.
Th-Dr. Phys. Suppl., no. 12, 5, LV. Far_~, Fn-,;~ 10:'1, 3956;
.1. J. Hopfi-:!Id, Phys. Rev. 112, 1"135.
A5301,'TATICNt Fizicheskly in.-itilut P N~ L-Ir_,~ilt,vi AN SSSR Fcl~3kv,t
(Tratitut- of Pti-Isics imen~,. P. N., L-a',IeJev AS JTSSfj.
3 IRD '01 1 T11 i:. D IJ~111 U;Ary 25, I:m
Car,J 7/7

GINZBURG, V.L.; RUFIMZZ, A.A.; SILIN, V.P.
Correction to the article "Electrodynamics of crystals and
exciton theory? Fiz. tver. telIL 3 no.9:2890 S 161. (mLRA 14:9)
(Crystals-Electri.; properties)
(Excitons)

AUTHOR: Silin, V.P.
30688
s/i4i/WooVoo4/023/024
LIOWE3i4
T ITLE: Thermal Fmiss-ion in a Transparent i-ledium
PEIRIODICAL: Izvestiya vysshilch uchobnylih zavedeniy,
Radiofizilca, 1961, Vol. 11, 140- 'k, vp- 767 -769
T EXT: Published theories of thermal emission in a trans-
parent medium usually neglect spaticl variation in the
dielectric constant. The present author reports an attempt
to remove this limitation. In the came of-an isotropic
nongyrotropic medium, the dielectric-constant tensor
(A.A. Rulchadze, V.P. Silin - Electr:)magnetic Properties of
Plasma and Plasma-like lNedia, Atomizdat, Noscow, 1961)
is given by
kk k, ki
k) "I IL )", (1-1k) +4
I/ ( k' W
where ctr and C are the longitudinal and transverse
dielectric constants. In a previous pnper the present author
Card 1/7

Tilerm,11 Emission ....
30698
s/14i/61/004/004/023/024
LOO 3 23 1 It
ShOWC-d thit ill tjl(%
czlse of clectromaglietic-field fluctuations
12A Aw lint,(.. k)
Cth
WO)i (2)
i-
4h Aw I M air (w, k)
V, ~2~y- c1h WT- -1 , -"(-, k-) -- k 2 c2 1.2 1j7 (3)
In the limit of a transparent Medium theSe formulae become
C111 & k))
(2r.)2 2-L T
C11, a k)
(2r)2 2% T
Substituting theseexpressions into
I 1 2- 0 k2
0 G." ('... k) ) +
4r
Card 2/7

30688
vi4i/WooVoo4/023/024
Thermal emission .... !;,032/E314
which gives the spectral-energy density in a transparent medium,
one obtains the following expressions for the energy densities
of the longitudinal and transverse waves:
kc C11, Ake (7)
A 2 fill') (k) 2-,,Th(," (k)
Are A k c
A n(,') (k) TI. (,i.) (k)
The longitudinal (n and transverse (n' refractive indices
are given by t' (kc1rj I,') (k). k) - 0, (4
(9)
kcjW.L) (k). k) -(k) - 0.
(10)
It is frequently necessary to obtain the frequency dependence.
In this case, instead of Fqs. (9) and (10), one can use
0; (9a)
(10a)
nf!) (w) -!c) - n("' 0.
I
and the relations analogous to Eqs. (7) and (8) are
Card 3/7

S/141/ '9688
61/004/004/023/024
Thermal Emission .... E032/E314
1111r, A,3 A- (01 d IW?811,1 (-)I
n H
I;t CIC111 2,x T
1201, ("')d (12)
C(h 7 ' I
In the case of an arbitrary anisotropic medium Eq. (6) must
be replaced by (Ref. 1)
I a 0'.2 k k
W2 (13)
.2
The general case is not discussed in detail although it is
pointed out that the following solution of the field equations
.2 .2 k) - V 4
C2 All E C2 it k1ko IEl C2 KI
leads to the following expression for the fluctuation field,
C2 all
(E' El (16)
Card 4/7

30688
-;/ilji/61/004/004/023/024
Thermal Emission .... E '
.WZ314
where K i satisfies the relation (Ref.
(Kj K, A cth-'- [It, (15)
(UP 2%T
In principle, Eqn. (jL6) and (13) can be used to determine the
density of thermal radiation in an anisotropic medium. In the
case of a nonrelativistic electron plasma and for frequenci'es
close to the Langmuir frequency w L. the-longitudinal
dielectric constant of the plasma is of the*form
7- k'
k) or I - -1 1+1_
M 'W2 A
where it is assumed that the wavelength is much greater than the
Debye radius. In that case, Eq. (11) becomes
Card 5/7 d-VI. A-3 A. (11a)
_- ah
r TAT
dw 40 (,3 WIL

30688
s/14i/W004/00/023/0211
Thermal Emission .... r,032/.-,3i4
where vT = 1'/3~,T/, In this frequency region the spatial
dispersion of the transverse dielectric constant is unimportant
and hence
dW tr hw3 i1w 2 2
- = - cth II- L (12a)
dw 2vr2c3 2)tT W 2
Comparison of Eqs. (11a) and (12a) shows that in the region
under consideration the spectral-energy density associated with
the longitudinal field is considerably greater than that for the
transverse field. Acknowledgments are expressed to
V.L. Ginzburg for discussions.
f~bstracterls note - this is a slightly abridged translation.1
There are 2 Soviet references.
Card 6/7

30668
Thermal Emission .... .'/E314
ASSOCIATION: Fizicheskiy institut tin. P.N. Lebedeva AN SSSR
(Physics In5titute inj P.N. Lebedev of the
AS USSR)
SUBIMITTED: December 6, 1960
wr
Card 7/7

33 220
;-4-.2,12- 0
AUTHOR:
TITLE~
s/I.41/61/00/o06/006/017
E032/Eii4
~1. V. P.
The relativistic transport equation for rapidly
varying processes in an ionised gas
PERIODICAL: Izvestiya vysshikh uchebnykh zavedeniy,
Radiofizika, vA, no.6, 1.961, 1029-1034
TEXT; In a previous paper (Ref.l.- ZhETF, v,38, 1771 (1.960)
the author derived the transport equation for non-relativistic
.harged particles. In the present paper the equation is
generalised to cover relativistic particles also. In the
derivation of the transport equations it is assumed that the
interaction between the particles is weak and the fields E anq
B are so small that they have no effect on the particle
trajectories during collisions. This means that these vectors
r-an be neglected in the expression for the two body correlation
function g,,, The final form of the kinetic equation is
Card 1/4

The relativistic transport equation... S/14l/6l/oO4/006/oo6/ol7
E032/E.114
f f
fa
e ja (71~
,a t c Ya 84
where the collision integral Ja is of the form 0
Np a
d dr, E',, (r - r,, dT X
31 V ~ 'p- RP a --a
0 OL
x J, 171 (r ra + v0-va)x, v va (r a+ vaTI t+T) x
P 3vt
'P 'r (!:5 + v0 1
x t
. app apo ar,
4 F] (r r + (v v )'C,v v )f (r + v 1, t f 1) X
CLIO -a -0 Ct 0 -a -P -P -0 P
C, VS f ( )
ap ap art
Card 2/ 4 a a (X

F.d
The relativistic transport equation... s/l4I/6I/004/Oo6/oo6/oI7
E032/E 11.4
It is pointed out that strictly speaking not only the interaction
between the particles but also the electromagnetic field must be
taken into account. It is shown how a correction for the effect
of' the self-consistent field and the particle collisions can be
introduced into the above equations. It is established that the
correction term for the right-hand side of Eq (7) is in fact
= _ d.E, dr !~ j '�aj 6 F (rar 0 +
a V pa
+ Fa?p (r OL - rV Y., XP) a (15)
The transport equation may be used- pie, to obtain the
high-frequency dielectric constant of relativistic plasma to a
higher approximation than the usual self-consistent field
approximation. Acknowledgments are expressed to V.L. Ginsburg
for interest in this work, Yu.L. Klimontovich, S.T. Belyayev
and G,I. Budker are mentioned in the article.
Card 3/4

3320)
S/l4l/61/oO4/OO6/oo6/oI7
The relativistic transport equation.., E032/EI14
There are 5 Soviet-bloc references.
ASSOCIATION; Fizicheskiy institut im. P.N. Levedeva AN SSSR
(Physics Institute imeni P.N. Lebedev. AS USSR)
SUBMITTED. June 8, 1961
Card 4/4

SILIN) V.P.
Integrir6f electron collision with electrons* Pizo met, i
metalloved. 3-1 no. 5:805-807 My 161. (MIRA 14:5)
1. Fizichaskiy institut imeni P.N. Loebedeva Akademii nauk SSSR.
(Collisions (Nuclev, physics))

24h83
S/126/61/oli/006/01109/011
e) E032/E314
AtrPIORS: Yeleonskiy, V.M., Zyryanov, P.S. and Silin, V.P.
TITLE: The Collision Integral for Char-ed Particles in a
Magnatic Field
PERIODICAL: Fizilca motallov J metallovodoniye, 1961, Vol- 11,
No. 6, pp. 955 - 957
TEXT: The present note is concerned' with the derivation of
the collision into-ral for charged non-relativistZic particles
in a magnetic field. Results are given for the scattering of
charaed particles by each other and for the scattering of
electrons by fired im,~,uritios. The matrix element for the
scatte:eing of particles % and P ',)y each other is
(d q) 41t r, e0
qjqj U[(Ej- E% ~//WTq
Card 1/7

24483
S/126/6i/oii/oo6/ooq/ol1
The Collision Integral .... !':032/E314
where I X> ,17,1~ are the states of the particle X before
and after scatterIng. The wave function represontin '- a charged
particle in the magnetic field is then taken in the form
(Lnndau representation)
n, ) -(4x-.,j-'exp (14x+ tk,'z) X
x,*. Ry + .41 4)16) 1 (2)
45
where a2 = ch( 0 W-1 and i~ n(x) is the normalised-
x x *I
oscillator wave function. Eqs. (1).and (2) can then be uaed
to show that the collision integral is
Card 2/7

24483
S/126/61/611/006/009/011
Tho Collision integral .... E032/2314
(2-)-Sdk.,)'dk,')dOdk,"-dk'.PdkPBlh-p+hlm,]X
X 4 kx + A kPj 8 [A k" +AkP j 24
q. A k,' . k' 11
4x,, ep dq.Ff [q. Ae. . I,' A]
.
[q- + (A 4)1 + (& k')'] A ill + (a k"),
(f (XI) f 01) - f M/ (F)
-%.r' h er e
Card 3/7

The Collision Intef-ral ....
24h83
S/126/61/oll/oo6/009/011
E032/Z314
I Jolla
h fxf- Ex El (hkl.) /2p, + A k - A', -k.
F.,.fq. a k, k,'] + x
X exp I- [a A,2 + 1#] 0/4) V."- ([A k' + q1] .1/2) X
X exp 1 *2 qk; + 10 A kvq/2 + I (n - n') [art sin A k, [A k,2 + ql]-m - x/2]
AL, (.0 a-).
dO
In Eq. (3) e(w, qz1 q.L) is defined by qiqjr,j(w, q)
2 2
(q.L + qz)r(w, qz,ql_) According to Zyryanov, P.S.
(Rof. 3- ZhOTF) for spatial uniform distributions of particles
of type
Card 4/7

2103
S/126/61/011/oc6/009/011
The Collision Integral so** B032/E314
U 2
Jim p(.2p q2, /2) X
9" +91'.- 7-0 11 (!, :-P) I I
P. AP. A$
X A, r 01) - I (P)
P Ep' - Ep + h-iAj
where f(P) is the distribution function,
2s P + I and
8 is the spin of the particles of type
In the case of scattering of electrons by fixed-charged
impurities of a given type, which are uniformly distributed
in space with a density n 0 the collision integral becomes
Card 5/7

2W
S/126/ Voil/oWooq/oll
The Collision Integral E032/P.314
,(2.)-2 jdk; dk,' d9L' I(E: - ET) X
+Ak,2 ]',I [O.Ak,, Ah' +
where Q is the charge of the impurity. Since the energy
of the clectron is conserved when it is cattdred by the
impurity, one can put w = 0 in s(w, q) -, In the quasi-
classical appro.-.4mat ion the asymptot ic form of the function
iF n,n I (X)I for large n is
2 2 1/2
IF n,n' )I = inl-n C(2x(n, + n + 1)) 3 (5)
wh er e j2 (x) is the square of tho Bessel function of
n'-n
Card 6/7

2'0483
S/12'6/61/011/006/009/011
The Collision Integral .... E032/E314
order n' - n . Detailed analysis of Eqs* (3) and (4) will
be 6;iven. in another paper. Other information related to the
present topic is given by V.P. Silin (Ref. 1: ZhETF,
Ref. 2: MM) and Zyryanov, P.S. (Ref. 3). The results reported
in the present note were obtained while the present authors
attended the Theoretical Physics Winter School at Kourovka.'
S.V. Vonsovshiy is thanIced for inviting the authors to that
school. There are 3 Soviet references.
ASSOCIATIONS: Ural'shiy politekhnicheslciy institut
(Ural Polytechnical Institute)
Fizicheskiy institut im. P.N. Lebedeva
(Physics Institute im. P.N. Lebodev)
SUBMITTED: February 4, 1961
Card 7/7

RVKHADZE, A.A.; SILIN) V.P.
Energy loss in fast nonrelativistic electrons in metals.
Piz. met. i metalloved. 12 no.2:287-289 Ag 161. (MIRA 14:9)
(Electrons) (~Ietals-Electric properties)

51056-16-,104 0/002/034/047
'I 1r 0 4C.. ItZ"IS02 I
AUTHOR: Silin, V. P.
TITLE: Electromagnetic properties of a relativistic plasma. !I.
PERIODICAL: Zhurnal eksperimentallnoy i teoreticheskoy fiziki,
v. 40, no. 2, 1961, 616-625
TE7T: The present paper shows that the method used by G. E. F.. Reuter
and E. H. Sondheimer (Froc- POY- Soc. A IL, 336, 19W can be directly
applied to a plasma of relativistic electrons. This makes it possible
not only to study the case of x-irror reflection in a high temDerature
_Y v also
plasma (cf., e.g., K. N. Steparov, ZhETF, ~6 1457, 1959), bui
the diffuse reflection of electrons from the plasma surface. On the
L~33111mqtion of a plane wave being perpendicularly incident upon 'he
s,--face of a bounded Plasma, expressions are derived here for t~e surface
ImDedance
- -------------- mw
Z (w) E . (0) E, (0) (2)
Card 1/11

Electromagnetic properties ... 3102Y3201
,0"- 4n the case of relativistic and no-relati-.istic electron temperature.
t ~-_ ~
For the case of an ultrarelativ-'-stic plas'na, 'he asymptotic behavior of
the field inside the plasma, far from the boundary, has been studied.
The complex reflection factor rhich is eq-jal to the ratio of the complex
amplitudes of incident and reflected waves: r (C44n)Z~-)-l must be
(C/4,-,)Z (~,)+l
known to allow one to study 'he reflecticn and absorption of electro-
ma-r-netic waves by the plasma. Besides r and Z(,..) also the effective
complex penetration depth of a magnetic field
cc c E, (0) E, (0) CS
~ dzB, (z) =__Y__ - 4niw Z (3)
fiv (0)a - 7- y 01) - - E, (+ 0) = (3)
is introduced; :6 is an elect;-ic field strength. The plasma.-absorbed
energy is given by A w 1 - Ir4l. On the basis of these relations and
of the equation of electron motion in the plasma filling the semispace
z >, 0, an expression for the effective depth of penetration of the field
Card 2/11
S/05 61/040/002/034/047

3/056/61/040/002/034/047
Zlectromagnetic properties ... 31~2/3201
f 0
is obtained: + ~7 + a il-f, where f is the equilibrium
0
dr p
distribution furction (6) , cef a non-equil'brium additiont v the collision
frequency, N the number of electrons per unit volume, and K the
e 2
function. In the case of a Tirrorlike reflection (denoted by
,,he superscript k) 11 dp V'010 I OP,
to+iv-kv,
+kc I
dw' X
4wkric K2 to + iv - 03'
I (M" ) J ~he
I- --* MCI
,,,: exp
PICT C I
2.0"V, dk'
x
(Kil' (V - k)
xrV, AV 2 MCI
exp
_T Ck'Ev-_ ;ir YCIPZ (W T IV).
MC

S/05 61/040/002/034/047
~ ],041
B102%201
Electromagnetic properties ...
1(7)
rse dielectric constant by way Of (7)
for the transve ~kzdh
C11) k) - h
reflection (superscript
In the case of a diffuse -45+V0 -+00.dk' W)
(A) E, (0) Lk elk 2 exp ~-I- ~ In CIV
231
_it 00
0 cases are given by
The penetration depths in these tv,
Card

71ec~romac-netic PrOI-ert4os
A
-"), k) -
C2)
3 (W
or)
A
(10)
the effective
first' exaMined
Che case is jL_
equations, C--a-d 71 the free path and with the
d of oscillation
,Oy IC
e i n ar,C C 40
particle du--ng one Per-
pene jt_on dCDth
y .1
mean distance traveled b
of the -field. r, 0 rm, u
IC -cc
ic
IC a -
6)
Lc,,d 5.111
(24)
(25)

3/056/61/040/002/034/047
Electromagnetic properties 310.2/3201
are obtained with
&-"
rge
OQ* dx I/ I x I -,--x: x
Imcl
-VT
x cxP (20)
H ciyqae iiepenmauacxxx -re%l-,IePaTyp (irc2>%T,)
(21)
a Z.19 Y.IbTpapcuT',t3HCTCKIIX TemriepaTyp (Me -< XTJ
-L W% 1 W2. (22)
lyp
Card 6/ 11

6 1 f'0 4 0 i'O 0 2 /0 4 o,,+ 7
lectromar,netic propert ies 3201
(231)
The case is then examired of the dista-nce traveled by the particles
., one oscillation period beinC; small co-m-pared with the effective
durir,-
penetration depth, and the free path beinC larre compared with it. The
result is
Its Im eor (w. x (w -' h)jr) (29)
0 V" ~
WI j, [Re e(,r(w, xhY0 - 0 -. iv,'eW -Y212 + (lm P~')'
I*dr Im 1"V' (0. t+ iv)jr)
da -
:T C la Re et., (o), x (,(,) + i%')'C) - (I Im tf#r),
(30)

S/Or 61/040/002/034/047
Elect-romagnetic properties ... 310 2N712 0 1
W1 1 .00
Re et,' ((0, iv I J"- [K- MO) + dxP 1 x
C X) 2(a (w + iv) xT, X, x'-x
+ xT,
X
exp xT, x'-'. (31)
W4 i., A
fin et, W, x x
C
T
x exp
MCI (32)
- ~ T. 71 ~-V_
and in the ultrarelativistic case the foi1owing equations hold if
2
OP
3 cc do 3 x-'\
8%(,) Ic I !)In
,,~ !.(I - 1 1[1 +;g(- - x$]'+
x 1)"
+ (3.t/4x)l I
, YI too; (33)
Card 8/11

-Electromagnetic prorportics
S10561611 040/002/034/047
=1D2/33201
1-;I) In
c 4~~a~xdx(l--
,1)111 + -7 X+11 aj
0 1
3"
L
+ ( V), (1 0, 18 (34)
In the case of nonrelativistic temperatures
~-12 wL xr
8%(.,) i2 I/ - L i:Li (35)
A w incl)
6 M--cl
and
Card 9/11
(36)

Electromagnetic properties ...
S/056/61/040/002/034/047~~
B102/B201
2V
+ 4 VIE Ke (37)
L zt WS in?.
AW 2v .81 (38)
R MCI'
At a strong spatial dispersion, ii ine ei:ective penetration depth 16---
small compared with the free path and wit!, 'he mean distance travel
ed by
particles during one oscillation period, one obtains E tr (,-tk)
4-niC/clki p where
C ON, XT, + exp MOIXT.) (45)
2 m mel, 2 Ks 00197'e) (45), --
,~ e
At nonrelativistic temperatures C - n/2 and in the
nr m -ITC
Card 10/11

S/056/61/040/002/034/047
Electromagnetic properties ... B102/3201
ultrarelativi3tic case Cur ' 'Ire2Nec/4,,Te. The penetration depths are
given by
10) = 2 (1
'T '
%W =1 1 -,
The asymptotic behavior of the field at large z in an ultrarelativistic
Dlasma is studied in an appendix. L. V. Pariyskaya is thanked for
numerical integrations. There are 10 references: 6 Soviet-bloc and
4 non-So7iet-bloc.
SUBIJITTED: August 24, 1960
1--card 11/11

ELIYCNTCVICH, Yu.L.;_SILIII, V.P.
Magnetohydrodynamics for a nonisotbermal plasma without collisions.
Zbur. eksp. i tesr. fiz. 40 no.4:1213-1223 Ap '61. (M:ERA 14:7)
1. Moskjvskiy gosudarstvennyy universitet i Fizicheskiy institut
imeni P.N. Lebedeva All SSSR.
(Magnetohydrodynamics) (Plasma (Ioni2ed cases))

S C, /61/040/006/017/'031
:.TTHOR: Silin, V. P.
S'I'T' L E Collision integralfor charged particles
PERIODICAL: Zhurnal eksperimenta"noy i teoreticheskoy fiziki, v. 40,
no. 6, 19611 1768 - 1774
T*,-.c author solves-the equation for the correlative distribution
,"-jnctior ihich is giver, by
A',
-%6 __
(k, p., R-) = ' ii.
(k) G, T "
P Iv (k) v5, (k)V2 J%?O X
kp~, , m5 I V V
rn. _-
x (p,, 1, k2) 1, k ,2) (p,, h k / 2) h k 12))
(,V~ 'V) v,, (k) If. (p, 4- hk f 2) hk 12)] h3 k.
h.(k, p.) (1-3).
N V) v,,,,4 (k) I ~_, (p hk/2) (p~ hk 12)1
/V denotes the number of particiei; of kind a pe. unit volume. This
Card 1/6

Collision iritegrril for ...
S/056/61/040/0061/017/031
310e/ 13209
relation h'Lt; been derived by Yu. L. Klimontovich and S. V. Temko' (Ref. I.-
"h--TF, ~J, 13-, 1957) through a generalization of results obtained by
Yubov (Problemy dinamichl!skoy teorii v statisticheskoy fiziki'
(.Problems of Dynamica in Statistical Physics), Gostekhizdat, 1946). The
:~utlhor introduces the following fuiction of the complex variable Gii
I I d
H (w, k, - N' 1-- It. k, p.),
2n i k
.;arum 1 -3) one f inds
(kpa k. (2.3)
2
-i here
h. (P.)p (2.2)
H dp
I:az-d 2/6

rl
7r?.l for. . .
and F rl~~c t,.- limi":i c,.,, the o the f uncl-Lons
k) 1 2 IF (w, k. F ((a, k,-
F (w. k, dp. V.~ (k-),lV. f. (P. L) (2.5)
Eq. ~2.3) by 6(Q- P" m integrating over p and taking the
- \. / Z, a
3um czer t, one obtains the -,oris
Iff- k. H' (o), k. 4-) H- (w, k,-) I&- (o), k) - P,* (o), k) j
Pri h) I P N, k, -) F k, *+) -F+ (o), k, -L) F-(o), k,-) 1. (2.6)
a r., d k,-) - H* (m, k,-) I c" (w. k) - H+ (w. k, -,,) I-e- (w, k) - P,- (w, k)]
(2:6 / rt)l P ((j, k.- F" ((,), k, F* (ft). k, + k.- (2-7)
which det,~rmine- the f,.-.nction 'n'. -.'hen H(w,l) (2.10),-
the soluti-cn of Eq. has the fDllo---;in:,- form:
It (W. k) F ((a, k. +) + F (w, k. +
j--(w Ze (w. k
. k)
C,--ird 3/ /6 + dw' F+ W. k. F* W. k. +) - F- (w*. k, F- (to'. k..+)
2.tl W, - 6) -----let., - - k) c- (ta', k)

S/ /C;6/61/C)40/CO6/017/031
C '~'I I i :I t e gal f o r ... n C:~!32C9
21 Ci
B'; the formulas 12.12), (~'-3), and (1-3) or,., may find a simple
eyrross--f,n -for t-vi ccrrelative function in a system of charged particles.
th-~, h.-Ap of these formulas obtains the collision integral in the
N dp,
0 rM 'V. (Pa A dP' dpow.3 (P., P.) X
V V
(p, 2m,, - p2 - p2 2M,') x
+ pi .12m. 0
+ p; p. - p) I (p" / 2m.
x (P.) fA (Pd 12 (P.) t~ (P')
M'.A W., P,) =
I-P!
i.- a.P.-P.) 0 (3.2)
(
2 X7.
(3.2) goes over into
s'at,2s close to 1. equilibrium, Eq.
t'-e formu]a esta-blis*-,ed by 0. V. K=stantinov and Is'. 1. Perell (Ref. 3.'
861, 1960). The scre-m,.~ngr o-'" Coulomb interaction can be,
(~e3c-ibcll bt a compl~.-x dielec~tri. cuns-ant
4 a e2"" ~ d P- Vt (61, [ 1 (4.1)
k) 6j/ + 7- ::1-2 "
V q?-kVS w
Card 4/(

320"
int,,gral
~'or- - -
C.
2. (4.6)
I,-, (kva. k)
f 0l
v
d. (kv. kvD) a it
vjjth
V0
Of
0 r. If 0
wh i
a rn'
r t h~ e kv,,)
f 6 ~kv,
0.
v ") -
~kv,-k) ned
erMi
ki =a' det
e Cr J e-1 ELn
-1 PlyaY et -
on- Ovi
n
ar'd
C, ea aS fOllo'lm
!,,.,tions ys.9
1'ent;
...e 13 i a ngu,-e e, 0
fro= -rc-e
CC'S
C-42'
.-- C' ': -Lljj
oloc- -P. YS!
-
Bal, es(.:u-
'-rd

S/c)-,~6/61/040/006/0 17/031
I for ...
:,--ision e~;ra- nauk SSSi
bedeva- A ademii demy of
e
L
c,~S C)r',iIj -r -)N F i z-ic'- 01, the Aca
Fhysic~ Lebe
(InntitutC. ol
scien~-.e-3 USSR)
janufiry L., 1961
'arla (1/6

012 0
AUTHORS:
TITLE:
~-ERIODICAL:
17
c/051(~(
V.1 02/D214
Silin, V. P., Fetisov, Ye. F.
The electromagnetic properties of a relativistic plasma-III
Zhurnal eksperi--ientallnoy i teoreticheskoy fiziki, v. 41,
no. 1(7), 1961, 159-170
TEXT: This paper gives a detailed theoretical study of the reflection
and absorption of electromagnetic radiation incident obliquely on the plane
boundary surface of an electron plasma. The case of perpendicular '
incidence has been exhaustively investigated-already. A sem-i-infinite
isotropic plasma (Without constant.,field) with arbitrary (in the special
case: relativistic) distribution of particles ts considered. Not only
the losses related to the ajpearance of transverse fields in the plasma
are considered, but also the excitation of longitudinal waves and the
losses related to them. To*study the electromagnetic properties of the
electron plasma (the idna form a homogeneous backg~!ound) the usual
kinetic equation with self-conoistent field is used:
M +.V 061 + eE Of.
N
Card 1/7

26417
3/05 61/041/001/012/021
The electromagnetic properties of B102YI32114
where fo is the equilibrium distribution function of the electrons, f the
non-equilibrium addition, and v the collision frequency. In the casp of
mirror reflect-ior. of the electrons by the plasma.surface the solution of
(1) is e;iven by
dz' exp z %I YE (z), v, < 0,
V,
(3)
61 r dz' exp z VE (Z') + dz' exp I-+ X1 x
UZ
0 4
x (E.U, + E1'VM - EIM, V, > 0. .
where -iW(1-V sing/c), f, is an arbitrary equilibrium energy die-
y 0
tribution function, and 9 the angle of incidence. The longitudinal and
transverse dielectric constants are given by:
k) I + ' ~' (5)
dp
WA3 W + iv - kv
ef (W. k) I + , ~dp (6i
WO
Card 2/f7

26417
S/056/61/04 1// DO 1 /012/1,21
The elL4ctromaanetic properties of ... 3102/B214
In the following the case of a-polarization (electric vector of the
4
.ncident wave perpendicul,r to the plane of incidence) is.considered. For
the effective depth of penetration
m i r ic t t 29)-1/2
3 . 1..~ 0+U )(F-(o-;)-(1+U )sin with
at (w, k) - a (w) WOO w1 wo' / w1 wl + lvw.1 / wo;
I Val (9)
W2 4n,- W 0 dp.
3 dpt?r,. (it _T r
the contributions due to the existence of a branching point of*the
dielect-ric constant are given for relativistic, nonrelativistic, and
Ultra-relativictic cases (all for mirror reflection). The case of diffuse
reflection of the electrons by the plasma surface is analogous; one
obtains
cc
111 D) dq In [I (at k) sin' 6)]1-'. (19)
7y
Card.3/7

26,417
3/056/61/041/001/012/021
The electromu6netic properties of B102/B214
In the follow4n--, the p-polarization (electric vector of the incident.
wave in the olare of incidence) i3 considered. In-this case longitt%dinal
waves may appe,~r in the plasma which is not possible for 9-polarization.
Here, the field in the plasma is characterized by:
E,(2) Es" (Z) + E" (22)
W
Ellf (Z) = JE, (0) - ICsin OE,(O)j X
(24
2 2
[91 + 46 102 sin Oil(w1c) (W.A)-(W/C)'SjI?
dj sin' 0 #1q,
(2) (0) --1 sin OE, (0) (24)
(91 + (w / qI sin' 0 1 a' (w. k)
-go
the complex reflection coefficient is given by
Cos 0 - Z,, (C / 42t) (25)
COSO + Z,(c/4R-) I
Card 4/7

26417
S/056/61/041/001/012/021
The electromagnetic properties of ... B102/D214
Here, the effecllve depth of penetration is obtained additively from the
tranuverse and ion(~itudinal 0.110.11:
+00 dqqt
jq, + (w c)2 sin, 0 1 t(w I c), et (w.k)-(w I c)'.s1n'O-q1J ' (27)
dq
(q' + (w I c), siro Q I .' ((a. k) (28)
The contributions to the left-hand sides of these f,ormulas due to d'ielec-
tric constant branching are:
21 C
(I + IV /W) 4" 'X2 - sin- 0 ( (0 1 IM el (-. W+,Vx) x
-W+-i V)
+ C
x Re el w0 + 'V'x) I--(I + IV / W), X-J], + [IM of w 4- iv X)] 1 (36)
+( C + C
as--
bxlp 21 sint 0 dx I m z1+ x
A,-'(w.'O"vx)F" x
(37)
x [x- s1n2 0
Card 5/7

26417
3/056/61/041/001/012//0*21
The electromagnetic properties of ... B102/B214
Here again a siecial case is investigated. If a1 < E, (W)
2 4 2 2 2
254; eL /1' T eoin 9(1-,- Le/-~ ), where T. is the electron temperature in~oi,
1; the nunber of electYons per cm3, and L the Coulomb logarithm, one
obtains for the ;-,bsorptivity of the plasma
A(P) 4 Cos Q sin 26~ale"(W) (45)
%Cos 0 + KcJsinlo I, + (-I+ sinte -I e!)g'
3
If in add i t ion, one has
A (P) = 4 Y -GT'V -(') cm 0 swo;~
ft (46)
3ilro-5W)COS 0
The heat released per cm at a depth z oA account of the absorption of
transverse waves is given by:
W2
(47);
')!I + r. Hj (0) is exp
V 9.--t ( W
for transverse waves one has analogously
C.,rd 6/7

26417
S/056/61/041/001/012/021
The electromagnetic properties of Z102/B214
Qj I + r, I', I H., (0) 11 exp 20 . &1.
f- C 141-alsin611/1
2 (48).
ell + "10 exp WIM
WS C7 As (XT' / M)*/- 5rx-f
The asymptotic behavior of the field for large z is investigated in an
appendix. There are 7 references: 6 Soviet-bloc and 1 nonLSovfet-bloc.
AbSOCI.-';TIUI',: Fizicheskiy in3titut im. P. N. Lebedeva Akademii nauk SSSR
(Institute of Physics imeni P. N. L,2bedeV of the Academy
of Sciences, U4ibR)
SUM'.11'TED: January 4, 1961
Card 7/7

28769 S/056/61/041/003/012/020
.2 B125/BIO2
AUTHOR: Silin, V. P.
TITLE: High-frequency dielectric constant of a plasma
PERIODICAL: Zhurnal eksperimentalinoy i teoreticheskoy fizikil v. 41,
no. 3(9), 1961, 861-670
TEXT: The author derives an expression for the complex dielectric
constant of a totally ionized rarefied plasma with an accuracy to terms
which are quadratic with respect to the number of particles per unit
volume. This expression is valid for frequencies which considerably
exceed the Langmuir electron frequency. The author has studied an
isotropic plasma and also a plasma located in a magnetic field. The
calculations are based on the kinetic equation for stable, rapidly varying
processes. The equation fot a plasma located in a spatially hpogeneoue
alternating electric field E and in a constant magnetic field B is
written as
4.
Card 1/ 1

2 675 :;/05 61/041/003/012/020
High-frequency cLelectric constant ... B125YB102
e,, (E + 1- jv.Bj)~P. NA TP. dp, dr,
c
x d, U.3 (', R. I t + P- r. Rp, I t -j- r, p, r., X
x P.] opfl it + P.11
x (p.,jj + To tt p.1, R. It -r v, t, p., r,, 1, t
0 (po I, + pol , RA it + x, t, p5, rp 1.
x
(Bp.) 18 IBP.II
- Sill U.-t Cos +
P. It p.1 == B- B
B-
J
Card 2111

28759 S/056/61/041/003/012/020
High-frequency dielectric constant ... B125/B102
+ e. !"'~29siti P, (I
B3 B
is [Be (rill Cos + T (2~
Ir
i -Cos SJ.T I BV. iin U. V is JOV.11
+ B Lovi) Ir - +
___ "-[-- --fl- - Ri-
t BI
+ BE (t')) JOE (t-)] Sill Q, (t' - t*) -
dt'~WJB( B, B
Cos (3~
where ea Mat ratvaand Pa denote the charge, mass, coordinate,
velocity and momentum of an a-type particlel -e aB/mac represents the
gyroscopic frequency, Nathe number of a-type particles per unit volume.
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28759 S/056/61/041/003/012/020
High-frequOncy dielectric constant... B125/BI02
UOP (r). 9a00/ro Eq& (1) cannot be applied at small collision parameters.
Therefore, integrations with respect to the collision parameters are cut
off at ?min' Eq. (1) also dote not take into account the shielding of the
Coulomb interaction at large distances. Without magnetic field the
distribution of an isotropic plasma is assumed to be qatially homogeneous.
For small deviations from the Maxwell distribution f (0) t'h* 61lowing
a
equation is obtained when linearizing the kinetic equation:
dr r,-rs + (v,,
Ev. No dp, dr,
y JU.0 (r. - ro) a af"; (P3, ' + T) + 6f. (P., t + -1) MI
M,
I(Q) 1(0) OU
a A Uo (I r. - r.3 + (v. - vo),r 1) x
(X,r),
x (ev. -~,- eAv3, E (t + x))I
(4)
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38759
S/05 61/041/003/012/020
High-frequency dielectric constant... B125YB102
This equation is solved by assuming a small collision integral. w~-v eff
has to be valid for a periodic time dependence. The solution in first
approximation reads:
6f(i ) i ea Ev a f(o)
a -;"T- - 7a
and the one in second approximation:
ag(ts) NA dPA dro dw-'- x
M.
r,,, -I (Y~ - v,,) r 1) (0) I(q e,3eEl.
X (xT)tf. fl~ (6)
Eqs. (5) and (6) furnish the current density
d 4. 6f
j e- (7)
Pa a
and the tensor of the complex dielectric constant Fij- 6ij + 4xid ij /(J.
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High-frequency dielectric constant.#. B125/BI02
Further,
4W dp. dp, x
aim-, + -,-r Q
as M, W'-' x 7,
x (0) dre-lo, A exp (ik (v, v;) -v),
tM trI ~ (__25nt_)I Us
where k X.T/ e e and k -1 r -1 Debye radius).
max min a min 0 Amax ~~t D (rD
Neglecting in (8) the terms containing positive powers of the ratio of
electron to ion mass,
+ 2- F
Z;v (0" 3 1/-- (XT)'!t
M
dr
and F el-I [4) ~ r
2M
(10)
(1) (X) e- dt.
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2P?59 S/056/61/041/003/012/020
High-frequency dielectric constant... B125/B102
will follow if only one type of ions are present. For io.4co La'
~ ~2
L
where + ~~) + '.W 3 'eff
")(0) ~'~X (ee if Ni T
In r (14),
jeeil
eff 3 'IF-m- (Y~T) 3/2 D,
and )2
4 V21t (ee i Ni
3 -
Im (.(T) 3/2 '-'La
where w denotes the Langmuir frequency. For the following
La
expression is obtained: 2
(I ) 4 V2x (eed Ni (),T)3/2
eff - 3 1-M (,T)3/2 In Y") ~C:f~ I e eil (18).
The corrections to the real part of vary considerably for the ranges
I _~ ~La and La' The new frequency dependence which occurs at w>> w La
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S/056/61/041/003/012/020
High-frequency dielectric constant ... 9125/BI02
allows, in principle, the calculation of the corresponding correction.
The complex dielectric constant of a plasma located in a constant magnetic
field is given by
tit (W) - ail iAj; (w, Q.) At, (W. - Q,) X
W"IX W
X [L. Al, (w, Q.) Ap ((o. (4.-seep)' dre-4- x
M, M's XT
Amal A k,k
!

X eXP
j53i_)3 70

.k'-7 SMI (Q.
(26)
2xT ,-
M
V I
and its Hermitian part is represent ed by
S21 BIBf - 6i/ W +
B
e
J - 1l,
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2~759 S/056J61/041/003/012/020
High-frequency dielectric constant ... B125/B102
If the collision integral is neglected. For the complex dielec-
tric constant is given as
6,, (G) . L. Yj ,_L~ (34).
ij ) 7_3 ff "effj B2 ij ~
For W, the Hermitian part of the correction to the tensor of the
_e
complex dielectric constant reads as follows:
2 &0 B2
rH_ < W < (45)
M1
B B 4T,
3 , 1+1 In-
be (m) -1 sign (o B-A 2 M
W3
(46)
M1
11B fit
680) 3 sign (a + In to