# SCIENTIFIC ABSTRACT KOVNER, M. A. - KOVNER, M. S.

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CIA-RDP86-00513R000825630006-1

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RIF

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S

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100

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November 2, 2016

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6

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Publication Date:

December 31, 1967

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SCIENTIFIC ABSTRACT

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,f hydics.. bonds in dirn.ric organic acids.
X. UIT awl V. A. Churukuv (SAralov I'lliv 4
Ar
Irml. Ak4d. Noook S.S.S R,, Nier. Fis. 14,435 4](19f$))
Theoretical. A'-)mia. scheme of potcsitial eurve% is intra.
lured to explain the appm=cc of doublet fiftt~ in RamAn
4pectra, discovered by Hatucv. The distance Immeril the
fines dcpcndq on the height of the polewhil bArrier betwero
themin. Thisrctationshiph plotted Im formic, arctic, and
isovalerk acids. S. Pak%wur
3
O
I slolsiso -
O
9
o 7 Ti :e
7 Till 7 77
Z
1
U 11 i 0
t
li
U
V
!0.0112l"110 a a
LJ
A 4WD a I. V*M%#
Aus PVC04"'tS
eel
GA A 53 -00
ot
-00
539.133 1 M5.74-1
7WO Vibration spectrum and force constants of diacetylens. A. ~00
Xavnw and V. T. Salosin. Dokl. A)md. 1~6idc, SM. 75 (No. 5) Olv4 .94
(1050) In Rumfilan. .00
00 FroTtancles are calculated froin a valence force field which includes "s
'S IntarectIons of nei0bourlag borAs and of adjacent anRl6s. A commrison =*6
with kom freauenclea yields the corresponding force oonstalts. L -Thcobs.
ISIS' too
woo
LA SCIALON11CAL LITINATM CtAIMP11CATIP ~T,
1114101 "mini woo
S&SOMO .1p cow cat ##41111 OW Ov All
i
U AT so As U All A I I IM 0 4 9 1 V 99 6 A W
1; 4 on,
3: 2
e
0
0 o si o 0 0
l
is
. '
00 0 6 0
e
n- of twzT:lA=! Inethme and sim"r
1404"", M. R, Twinivills Whtlltv-
bbmkil Stlito Zhuf. Pit. Kbio. 23. 434 -,
(1951 The secalm apation for n3ethAne 6 obtaluvil
and 4--oorind by the vwmm bond metbW (Eyring. el
W., C-4. is. Ski), Prm g=p4hromtkal comidentAXIS.
the ftud;m rdft for wicumie-vibradonal tranoitions our
found; it b concluded dot tha abscom of vibrational 41ruc-
turc found In 0* OMMAC 4wtmm of methint (Cf. Dull.
can and Howlt, C.A. 29. OW) ealmot be attributed to thme
wiection rulm Howeva, mince the electronic Imb for
alkneed transitkm an d*pDmte the exdtod CHA mol.
inim I* unplabiv In tbt R;i~ confirmilon (theomi
of )*bvi and TWkr) and thus dWsocn, listo radicals N tv
Zftl ItAloliliq light abkwptkin (Unith, V.A. 32. Will 1.
" thI2 vitwout, the ADWOM of 1111lictum ill the VICT.
tn"lic Spreirum a C114 beemes c1mr. Mkhrl lkxj4i&rt
Cot
vactum modiLitics of the degenerate witirations of th
nitin
A" 14 ,, ndiSh ki ge
tLI, tilA
438-43(1951).-A comparimut between the quantuln-
mech. expression for the energy ll'ol C116. takinx into.1"
count the refinements of Linnat and Wheatley on the one
ham] (C-4.43, WA20and thersIrressiou ufStrmnuv(C,A..
36, 34(P, 64131) giving Was a function of the normal co-
ordinates anal the dynamic coeffs. k., a. and I an the other
hand, can be made conveniently only for the degenerate
vihFaLionsofthemol. Frornthiscomparisonandthevalues
giveri by Stepainiv (k. - 0.7165 X 10-0 per sq. cm., I - ,
0.039 X 10-4 per sq. cm.), it is possible to calc. the value of
the exchange integrals; in at. units N~ - -0.49 and
New - Nit m -3M. However, the value of a can Aso ix:
caled. directly froto the quantum-nurch, elprM11111S., Ilas
value Is 10 times that given by Stelianov. *nle dhCTtj)A11CV
can be part4fly explained by noting that a 6 very wusitive
to a small error In the ciptl. data which m:rvtd as the hasis
for Slepanoy's calca . The main source of error lies never-
theless in the assumption made in th resent work that the
exchange iltegrals are ladeMdect Wthe C-H distance.
It is known that, in the cast of water. an assumption of this
kind is not permissible. Michel Boudart
KOVIE'R, M.. A.
M. Al. Kovner an,'. V. A. Chuenkov. Theory of the hydrogen bond in diiners of carbonic acids.
P. 662
The N. G. Chernyshevskii State University
Chair of Theoretic Physics, Saratov
March 31, 1950
SO: Journal of Physical Chemistry, Vol. UV, No. 6. June 1951
6-0,0 0 V ; ; ; ~ x a
-TOO0990009696 ; ; ; wwwwrITI:
0100000000000000000
u a W
.. smu
"Is
00 it
ow ~i"
00 all,
W*mw "W ,law MIA ~SSX. 72
Ta"ll?*j. 1. .44
2)5-7 (1951 we Ilk the
lj~t absc 0 t " c 't vibm.
lion "WtFurn inc wit a CoW
It ,
tkyn lfwall I" twwSins
into In Ictfs.
timalm d p M%I$
00
P4
5.;
6--f
00 00 10
00 .
amt
31
6 1 w IM 9 A, Q
*go : ; 0 0 0 : :- 0 0 a a
*see
0_4 P
w
use
zoo
r. 0 0
Ice*
es
'Oe
U99
the-
Ag~a .
~ ~a6-14MM)Wqh~.C*- Me a-
SSSA 70. Z& a T=ww b-A
Pw Awc 32 (A;,, wm A.
nwW &G. 195-1) A, WA
,.*a - bor4
hft* 0. C_11
fi W2, onho.
avow4k -M~
whk6 ftj ;p
lb- ftot~ am
Of lb* A!~w .3
Iftb Of we ft"dmvy-.Xw
--kvft 15 Imm
A93ke'i ~-Qftq=m
and OY 2 C41
or
CO
-m% bdft
Ord* n" bg -Id ,
=Z;~~ LJA"w
Mistdcal Abstriots The theory of S~Utdnj the hrAf4nn frm"Pntv 4-IM
caused tunnel effecl. 0 er an
IL
25 P 1954
Iq4iiatropic , Pnenomena JzMjJ. AM. lVauk.Y.S..Y.R .561
Theoretical. . SeIgnettoclec. properties am now attributed
MA Spectra' to the presence of a H bond. The pmence of 2 ban& ijll~
Me Rainan spectrum of ICH&POA is attributed w a tu!mel
effect. A sotu. of the wave equation in Which the patentkl-~
en U corresponding to am OH bond Ims been Latro-
duCcteldyg in 9Md OgreeIntnt With the "pt. as far as the
pmition~of the doublet is coucerned, but gives. too-bigh-
values for the stpn. of the 2 lint%. 31 FAMM -
1~7/4
Akio Jqi-,.r Rsw!tf ZLoz, Fizika, No 2, 1.95'T, No 5038
K-0
Au'.boiz Koin~- M A. Irkhin, Yu.P.
State Univeraity, LT53R
Title Lhe Theory of Ultraviolet Spectra of Absorption of Methane
Rub a.. flapt-irim. I te.-or. flzlki, 19.54, 26, No 3, 317-3
A i.,s t i, ac-, tIJ_.& electron ex6rgy leveda of tie CH-JI CHLJ, and CI molecults are csLI.-
from the solution using the Aethod 6f the Zent palWof the
ed6kf -.s_Isctrcn problem of qa~~,.tvm mv--chanics. For molecules with a sym-
metry C , the classification of the electron levels with respect to
th'*7' is of the form 4A +-M +-4B. These representations cor-
_r=Epq;2d to 3.4 linerly indrz;p~zdent spin function. However, a total of
.~A n4f spin functions occur v&m the operations of symmetry of the C
'itze R
group applied to +.L~i gemaral _'tunctions of the eigbt-elect-ron
p z ~ o V11' em. These include tm. Iine~r rol9tionships. To determine the 14
Iine.~--ly indzpeadent baei.,: spin functigza one employs the analogy be-
tv,~~n the bebsvior of the spin functions and the oscillatory coordinat0i
C.6.~'d jI..J 7~
USEMI/Optice - Spectroscopy
Ri'f Mw - Fizi", No S) 1957j No 5036
11%..
K-6
in tbe~ ey=aetry opemtione. This makes it possible to employ the pro-
ctdur6 vhere the supplem!bntary relationships between the oscillatory
coordinates are taken into decouxit,la'$rocedure used to calculate the
cecillations of the molftules. Me 'mtiix pertur~htion elements are
*&Iculate-l using th4j graphic metbod iemployed earl*er by Sklar (Sklar, A.,
Joumal.apf MemicaV jjj - The resultant secular de-
0, 193 t) 2) 669) -
tszmimans contain'Sk energy in each term. In order for the un-
knawn 4be containiM orly in the diagonal elements, a transformation
vr.a ~Uea analogous to the introduction of the kinematic-coefficient
matrJa instead of the kinet-ic-energy matrix in the oscillatory~t~oblems.
The matrix elemients 6f the'6ecular equations contain the exchan86 inte-
gr6l's -of -the pairq and unpaired electrons of the C, H, and C-ahalide
atoms, samely K, A and dN ~ " S' I as well as the .excban~e integrals of
the eilfttrons of the'R, H and H, Hal atoms ( P' andf~ ' and the intra-
atomi exchinge integml of the C atom together with the exchange inte-
gr&I ~"' of the Hal'and gal electrions.''Based on the data by Parti
and'Samael (PartiI.Y.F.,' Smauea, R.1- Proceedings of'the'Phyiical Society~
London, 1937, ~~ 568) for the dissociation energy of OR I, CHI
3 3Y
d
KOYMM, M.A.
Computation and interpretation of the vibration spectra of some
monoalkyl- and polymethylbensenes. Izv.AW SS~R.Ser.Fiz.19 no.2:
218-219 Mr-Ap 155. (MLRA 9:1)
1.Saratovskiy gosudarstvanVy universitet imeni H.G.Chernychav-
skogo. (Tartu--Spectrum analysis--Congresses)
USM/ r-hysical Leaistry - Molecule. Chemical Bond. BA
Abs Jour Referat Zhur Khimiya, No 3, 1957, 7200
Author Kovner M A
Title ii~ ~ectra of Aromatic Compounds. III. Calcula-
tion and Interpretation of the Vibrational Spectra of
Mesitylene and Durene ,
Orig Pub : Optika i spektroskopiya, 1956, Vol 1, No 3., 348-363
Abstract : Geometrical models vith C3h and C symmetry are used
for mesitylene and durene, respec&ely. The force cons-
tants of benzene and ethane are used in the calculation
of the A-equencies. The calculated frequencies are com-
pared with 1"requencies observed in Baman spectra, fluores-
cence spectra, and IR spectra. The full interpretation
of the spectra is proposed on the basis of the calcula-
tions and selection rules. A classificatL on of the fun-
damental and component frequencies is given, based on the
symmetry of the point groups C3h and C2,6
Card 1/2 - 25 -
re, V IV Jz oo "'6< ,
3R/Opties K
Abs Jour: Referat Zhur-Fizika, 1957, No 4, 10451
Author : r,_M.A., Bogomolov, M.A.
-- UnIversity, 1JSSR
Inst : Saratav
Title : General Theory of Oscillation Spectra of Normal Mono-Alkylbenzols.
Orig Pub: Optika i spektroskopiya, 19561 1, No 3, 364-373
Abstract: The secular equations for the 46 oscillation frequencies of the
molecule of ethyl benzol vere setup and solved. An interpretation
is given for its oscillation spectra, and also for the vibration
spectra of the higher mon-alkylbenzols CH3 The
UP to C6H (CH ) ,
frequencies of the mono-alkylbenzols are comparea wiglge f'requen-
cies of the benzol itself. The frequencies that do not change upon
substitution, and also those that change and are independent or
dependent on the length of the alkyl chain are determined. The
frequencies of the valent vibrations C = C are calculated with the
aid of a simplified model of one dimensional zig-zag chain with
Card 1/2
V Y-
uw~nvsifti manistry Molecule.. CbsWcal Bond. B-4
Abs Jour: Refern't. &=a1 'hinlya, No 2, 1958, 3538.
Author a 9 -A. Novaer.
Inst v >/,ra&, a,: I
Title Vibration gpeetr% of Aronatic ComWvands- IT. Ca3patation
and: =erpretation, of.-Vibration SVictva of Dipbjftq1 and
Decadeuterodiphwyl,
Orig Pub**,Cptik& i spektro skopiYAP i956, 1) no 6, 749-751-
Abstract: A comiputati,on of basic frequencies"of Famn and infrared spectra
bf diphenyl sind decadC-dterqPUwwI vas carried out and'their com-
plete inter ff d.-Iollavini ai~praxinations were
pretation Was o ext
adnitteA: the Interaction -amidst arduo ne *asA=ed to be'zero,
all'tbe force cons S,Iof - ,Iw vere expressed by the ben-
zene force c6nstants dAUrnimA previously with the exception
of -the interaction'conati~its'ot.a-n'gles'prod:~ted-by the inter-
ring I ink with benzene rings. my~, and iyj p vhich vere accepted
Card 113
KOWNER, IN. A., Doc of Phys-'eiath Scl -- (diss) "Caletilation. and interpreta-
ti-)n of an oscilating spectra of benzol and Its derivatives." Vi-Insk, IP57
23 PP (Belorussian Stite University i-im V. 1. Lenin), 260 coi).Ies
M, '16-57, 103)
PRIK HOVKO. A. F.
3 PRAW I BOOK XVLOITATION SOV/1365
L'yov. Univeraytet
haterialy X VsveLyurnpgo wavosInchanlyk po spoktrovlopli. %. Ii
Holskulyamaya spvkt.Nm6#.npiya (tapers or the 10th All-Union
Conference on Spectr5aocpv. Vol. Is Mlecular Spectroscopy)
ILIvoy) W-vo L-vovskogo univ-ta, 195T. 499 p. 4 ooples
printed. (Sarleat Itai Piz7ohnyy %birvk, v".
Additional Sponsoring Agent7i Akademlys nbuk SSSR. KomIsAi7k PO
spektroakoplL. Ed.i Oscar, S.L.1 Tech. Ed.s Sararyuk. T.V.1
rA&tor&Ll tkox%%1% Lanvisterg G.S., koadavVlcloz (Reap. Ed.2 Deceased).
Neporent, U.S., Doctor or 6~slcal and Mathematical Sciences,
Fabelinakiy, I.L., Doctor of ftsical and Mathematical Sciences,
7sIP&k*rA' V.A.. Do4tdr or Physical and Kithe=tical Sciences.
KarAltakiv, V.Q., Candidate of -Technical Sciences, Rayakly, S.X.,
Candidate of Flqalea: and Math-t.11*1 Scl.noaa' Klutovskly, L.K.,
CandIdato of Physical And XZtber4tLCsl Science milly-huk. V.S.,
:
CwWldate of PhIstia! &M katSe=atical science
: &W Glaubermn,
A. Te.. Cand1dato of Physical and mathematical Soleness.
C&Td 1/30
71=aran, L.A. New O~tjnaj Phtht-I in Nggeopeo-
trosoopy 81
P%r, N A A X 13*gozolor. The Structure and
,
b
ti.
ra ~.'.j ;;:.ti% of So.. Ar~'.&tj. JVdrocarb...
84
Kamnatakly, V.D., AM B.M. Yavorakly. Mthod for the
Calculation of Absorpl-Ion Spectra or organic molecules. 88
logansen, A.V. Nozz-aal--elbratin:z Frequencies and the
Anh&rmoniolty Con. &tan' ta or Acetylene and Dautero-
acetylene %olvouleu 93
motulovich, 0J., end A.A. 8ruVin. Polvitation
Hathm for the mawxp$ ,r optioal c*nstsuts or
vatmay) In the L-4fra-04 Mugs 95
KIslcvsUiy, L.D. use *f a Ro.anator riode. With
VLacous Priation for the Representation or Optical
Ch&r ateristice of Absorbing media in the TMrare4
= 96
eft-4 76o
KOVMM. M.A.; BOGWOLOT, AsKs,
WPM- Structwe'and'vibration spectra of various aromatic h7drocarbono,
Piz. ebor. no.3:84-M '57. OEM 110)
1. Saratovskiy gowj&rstvenn~7 universitat im. II.T. Chemynhevokogo.
(Hydroaarbone-Speotra)
AUTHOR: Kovner. M.A.
51-3-4/24
TITLE: Metallic model and 'W- electron polarizability of the
benzene molecule. (Metallicheskaya model' i Ir-elektronnaya
polyarizuyemost' molekuly benzola).
PERIODICAL:"Optika i.Spektroskopiya" (Optics and Spectroscopy),
1957, Vol.2, No.3, pp.304-309 (U.S.S.R.)
ABSTRACT: This theoretical paper deals with quantum-mechanical
calculations of the fr-electron polarizability in the plane
of the ring of the benzene molecule. Three models were
considered: (1) free'eilectrons in a undimensional well with
infinitely hi5h walls, (2) electrons moving in a cosinusoidal
field, and (3 electrons in a rectilinear periodical potential
field.
(1) Free electron model.
The electrons were assumed 4W
-o be moving on a circle of
radius R L/2Tr, where L = 6a and a = the lenE~th of the
C-C bond. The energy levels of electrons are given by
n n h (n = 0, + 1, + 21
Card -.1/3 W ~ ~2m
The first four electrons occup, level W and the other four
W Only the transition to tp-e neares? free level was
Metallic model and 'or-electron polarizability of the
benzene molecule. (Cont.) 51-3-4/24
considered, i.e. + Il A# �2 , since the 0-->+ 2 transition
was forbidden. TEe polarizability for X = 4358 .9 was
found to be CL (-) ) - ~).40 X-), and the static value
Mir(O) = ?.63 73. The experimental val e, for -the C-C
bond in the plane of the ring,,is 8.16 0 and it includes
the effect of the a-electrons. Thus, the values calculated
are of the right order but too high.
(2) Cosinusoidal potential model.
Introduction of a periodic potential makes the energy level
gaps smaller and the frequency.131.of the first electronic
transition lower. Since a,, is inversely proportional to")
it follows that aff is larger. This was confirmed by
rough calculations. Since a lower value of cLehan that
obtained in (1) above is required, it is clear hat the
cosinusoidal potential is not a sufficiently accurate
approximation of the molecular field.
(3) Rectilinear Potentia'l model.
Card2/3 The potential along the circle of circumference L is given
by L % 1, it can be expressed by Eq. (1.14). Consequently,
3
the increment factor p is given by Eq. (1.15)9 where
is defined by Eq.' (1.16). In considering the ordinary and the
extraordinary waves outside the transition region the
expression for the increment factor is in the form of
Eq. (1.21). For the region which fulfils conditions expressed
by Eqs. (1.23) and (1.24),the increment factor is given by
Eq. (1-27). This formula coincides with the results obtained
by Rapoport (Ref. 8). In the transition region which fulfils
the conditions expressed by Eq. (1-30) the increment factor
is given by Eq. (1-31). The instability due to the magnetic
deceleration radiation can be investigated by considering the
Card 5/8
86850
s/141/60/003/005/003/026
E192/E382
Kinetic Analysis of the Diteraction of a Beam of Charged
Particles with Stationary Plasma in a Magnetic Field. 11.
growth (or attenuation) of the waves at the frequency
corresponding to the normal and the anomalous Doppler effect,
The condition of radiation in the region of the anomalous
Doppler effect is expressed bys
n(v0/C) Cos a = 1 + W H/W (2-1)
while for the normal Doppler effect it is given byg
n(v0/c) Cos a = 1 - WH /W . (2.2)
Provided the conditions of Eqs, (2.4) are fulfilled, Eq, (1.8)
can now be written as Eq. (2.5), where Ii is defined by
Eq. (2-3). By using the perturbation methods the expression
Card 6/8
S/14 M100/003/005/003/026
E192/E382
Kinetic Analysis of the interaction of a Beam of Charged
Particles with Stationary Plasma in a Magnetic Field. 11.
for determining ji+ is in the form of Eq. (2.6). Consequently,
lt:~ are given by E-qs. (2-7) and (2.8). From the above it
k
follows that the plasma wave in the region of the anomalous
Doppler effect is described by Eq. (2.9). The wave in the
region of the normal Doppler effect is characterised by
Eq. (2.19). The extraordinary and the ordinary waves in the
region of the anomalous Doppler effect are characterised by
Eqs. (2.21) and (2.22), respectively, where A and C are
determined by Eqs. (1-5). In the transition region which
fulfils the conditions of Eqs. (1.2) and (1-5), the increment
factors for the ordinary and the extraordinary waves are
represented by Eqs. (2.27) and (2,28); these are derived from
Eqs. (2.21) and (2.22). From Eq. (2.27), it is seen that the
instability occurs for U < I . On the other hand,
Eq. (2.28) shows that the instability is observed for u ~ l
Card 7/8
86850
s/141/6o/ool/005/003/026
E192/E382
Kinetic Analysis of the Interaction of a Beam of Charged
Particles with Stationary Plasma in a Magnetic Field. Ii.
The author expresses his gratitude to V.V. Zheleznyakov and
V.O. Rapoport for reading the manuscript and discussing the
results and also to B.N. Gershman for his interest in this
work. There are 15 referencesg 2 English and 13 Soviet.
ASSOCIATION: Nauchno-issledovatelvskiy radiofizicheskiy
institut pri Gorikovskom universitete
(Scientific Research Radiophysics Institute of
Gor?kiy University)
SUBMITTEDs March 25, 1960
Card 8/8
'I"!/ b1/0011/003/006/020
AUTHOR: Kovner,. M.S.
TITLE: Instability of low-frequ,~~ncy elz,~-fromagnetic waves
in a plasma with a beam of' chargad partitles passing
through it (propagatfon at an arb~~A:x-ary angle with
respect to the direction of the magnetic: f:Lel.d)
PERIODICAI,g Izvestiya~vysshikh uch-abny1ch 7,av;sd-?.niy, Radiofizika,
v. 4, n0o 3, 196.iv 444 -- 4,54
TEXT.- The stability-of a system consisting of a beam of
charged particles and plasma has beer) inve2tigatad on1y, as VIV/
regards the high-frequency waves but it appoars that little work
has been done as regards 1ovr-frequen,;*y wa-vzs (Ref. 9 - ,
V.P. Dokuchayev .- ZhETF, 39j 4.13, 196o, Ref~ .1.0 - G.V. Gordeyev,
ZhETF, 27, 1.9~ 1951f and Ref. 11 -.. the pratTurt author, ZhETF,
4o,
. 517~, 1961). In th4r4 follow!Ag, therefori~., a "netle approach
to the problem of the stability of a beam of -harged particles
in plasma, with respect to low-frequenc..y weore-; is pr"eented.
It is assumed that the wave.-s propagate in the 1.3,rsotion k
which forms an arbitrary ang.1.0 a with the aj.ra,,tion of thr.
Card 1/1-0
Instability of
S/ 14.1./61/ 004/003/oo6/o2o
E192/F-382.
constant magnetic field H , Th,.s plasma and the beam are
unlimited. quasi-neutral ana sing1,y-ionjzc_d,, The beam of the
particles moves along the external magnetic, fi,%ld H The
'0
basic equations for the system are the linearized kinetic
equations and the equations of electri.Aynami.,:~q: By following
the approach adopted in Refo 12 (1,,D,, Landau ZhFTF, 16, 571,
1946) and Ref. .1.4 (B.N. Gershman, ZhETV, 2.4. 659z 1953) and
assuming that all the physical quant-Ities - can be represented
as plane waves, the scattering equation foT tile syt~tem is in
YX
YX
0%
where
XY
VY
ZY
XM
Yz 0
zz
Card 2A0
T,istability of ....
I q
j,l -1--l-L/01/604/003/oWo2o
B,.L 92 E 3 8 2
2 -
�F 4ZZ + 0 - Ic Cos QL; fe = xy
xy
+ k2c2sin m cou m = a
byy yy+ w Ic0 Vyz ~= 'yz
- a + Ic2a2sin a cos a; G
zy = azy
+ w 2 k 2c2sin2a LX
zz zz
where:
4
ajp i w e yvjyCpy d-%,y
Card 3/10 Y=j
Instability of ....
B192/8332
in which dvT ~ VP dVF d-,,zd y
exp (2ne, costp, Cos
C.,,Y aWKj w ) VIP I I -exp(2-,rs, dj'+
2c
exp ( 27tal ) vot
C,,,, a (y)K, Vzj-'ZIOl v0sincEcosi'
11-exp(2m,) f (
0
VZT-VOT + vpj I? S1110t COS
e NI 1117 312 111 T (V, - VO,
K, -- exp
-WHy -Tj ( 2-,T, ) 1 27,
expj-j T + /.I Iiii y);
!kv,, - lui kvp, sin ot
Will Will
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Instability of .... i." i oo/ r3 8 2
The quantity C. yy is obtained from t1oo. -.-,-)ression for C xy
by replacing cosy by sin~~ . In the ;O)wvo i'orviiilcie the
quantities with indices y = 1, 2, 3, It rofor -to the ions of
the plasma, electrons of the plasma, ions and electrons of the
beain, respectively. The folloiing symbols are also introduced:
w w - _'-_~jj = - eH /Dic i-diere c and 'M are the charge
Hi ~ 1-13 0
and the mass of an ion; wH2 w 114 ~ IF1 = 1110 /nic , where e
and in are the charge and the mass of an'electron; N Y and
M
A, are the concentration and temperature of the corresponding
Y
particles, the temperature being measured in energy units;
Ic is the wave perturbation vector lying in the plane x, z
the direction of the magnetic field 1-1 0 and that of the
average velocity v 0y of the particles of the beam is assumed
to be the axis z . First, the instability is investigated
for the case when the thermal agitation of the particles can be
neglected. It is shown that in thio cw~o Vie scattering equation
is in the forizi:
Card 5A0-
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Instability of .... L;,i r,'3 8 2
k2C WOIEU- ftj(w - kv,)' +
(2-5)
2 2 0.
04 U) )01 U) Wo"I
k20 coslat +
(w-kV,),U)O'j 110
H
From this, it follows that the instability occurs at:
v0 > Ho (2.9)
where: cos,
N.44 = NN,
N+N, (2.10).
Card 6/L0
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Ilistability of .... )--/E382
Furtlicr investigation of Eq. (2-5) the extraordinary
wave is -table and that it obeys the relationship
(Ref. 19 - Ya.L. Allpert, V.L. Gii-t--.burZ-- and Ye.i, Foynberg-
- Propagation of Radic, Waves, Goste1--'.iizdat, 1-joscow, 1953):
0
11 V4,:~-Iu-lcoscc
If the roSion of anomalous Doppler effect is considered, the
instability of t1ic, lo-iii-frequency waves can be described by the
following scattering equation:
2
kv, + 211) k,C, COS2,7 + PC22)2~1
COSU)
(2.19)
4
04~1 m k*2i-2(i + COS'2)
0
L)2
11 ["
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Instability of .... L ~ L ~)-"/ L3 3' 2
w1lich is valid -.-;-hen the following conditions are met:
(02
-- t~! a(I + Cosla) 0
(02-02
-11 -~]
wh er e H2/ 11T-1,D1 IIt is of interest to tahe into account
V1.1-- 0 Vr
the thermal ag-itation of the particles since their influence
substantially changeithe nature of the 5-taijility of the system.
This problem is investigated under tlie assumption that the
thermal agritat ion in the beam is significant and 'L-.iat tile
stationary plasma can be considered as being "cold". For the
case i-.hen the phase-velocity of the i-.,nve is nonr to t"ic
velocity vo I and the thermal agitation is intense, t-lae
scattering equation for the system becomes:
card 8/1o
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lantnbility of .... Vr.58,2
2 2 -
2 (0011.1 T3 i I/ :T
I+- x
2V1 2 1
k 7-3 COS a T4 2 (Nil 3 COSOI)'
2 2 2
(1101 111
X k1c' c,,O,,~ + k1c' - 92
U)2
From this it is found that ins-Lability occurs vrhen
w (0) - kV 0 < 0 Now, the instability in the region of the
anomalous Doppler effect (under the conditions of thermal
a--itation) is described by the follo,.-Tin- scattering equation:
COS2a + kIC2 (1) 21 012 tj)(4
k1c 1 0 )1 ~JI,, +
W2 - Q 2 g2 ( )
H H If
(1103 Q11 2U 0)-
+ k2c'(1 + COS21) + 1, 0.
8 kV7'3 COS Or ",-Q11 d
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Instability of .... E19-2/B332
From this, it is possible to find the correction factor for
(0)
the frequency w
There are 20 references: 18 ~oviot-bloc and 2 non-Soviet-bloc.
The two English-language references mentioned are;
Ref. 2 R.Q. Tiviss, Phys. Rev., 34, 443, 1951 and
Ref. 15 1. BornsteirL, PhYs. Rev., 109, 10, 1958.
ASSOCIATION: Nauchno-issledovatellslziy radiofizicheskiy
institut pri Qor'I*zovsho.-.i universitete
(Scientific-research Hadiophysics Institute of
GorIkiy University)
SUB1,117f ED: October 21, 1960
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E032/r,3.i4
AUTHOR: Kovner, M.S.
TITLE: On One Case of Cherenkov Instability in Non-
equAlibrium Plasma
PERIOD7:CAL: Izvestiya vysshikh uchebnykh zavedeniy,
Radiofizika, i961, Voi. 4, No. 4, Pp- 765 - 766
T SXT: Publishedwork concerned with the instability of'
a boom of chargod particles in a non-equilibrium plasma
located in a magnetic field, is based on the assumption that
tho phaso velocity of the wave is much greater than'the
velocity disporsion due to thermal motion of the particles.
The present author considers the excitation of waves in a
plasma by a beam of charged particles, -whose phase velocity
satisfies the relation
VT1 Cox a