# SCIENTIFIC ABSTRACT POLOVIN, R.V. - POLOVIN, R.V.

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CIA-RDP86-00513R001341830001-0

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S

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100

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Publication Date:

December 31, 1967

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SCIENTIFIC ABSTRACT

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'AUTHORS. Akhiyezer, I. A., Po-lovin R. SOV156-37-3-25162
Tsintsadze, N. L.
TITLE: Simple Waves in the Chew, Goldberger, and Low Approximation
PERIODICAL: Zhurnal eksperimentallnoy i teoreticheskoy fiziki, 1959,
Vol 37, Nr 30), Pp 756-759 (USSR)
ABSTRACT; Chew, Goldberger, and Low showed that a dilute plasma in a
magnetic field in which collisions play an important role, may
be defined by a system of magnetohydrodynamic equations with
anisotropic pressure. It is of interest to use these equations
for investigating the nonlinear motions of a plasma (above all,
of simple waves). The present paper deals with this problem.
The system of magnetohydrodynamic equations has the following
form in the Chew, Goldberger, and Low approximation;
I ik 3H
+ curl F curl
F H
dt H xk t H
div H = 0 + div v (p,1 - p.L)h,h
Card 1/4 bt (?' ) = 0 Pik = P., c~,k + k
Simple Waves in the Chew, Goldberger, and SOV/56-37-3-25/62
1,ow Approximation
_91 __O~ d d 2
h Tt-(S!LF) o
H/H _~_t ?H
The author investigates one 9dimensional plane waves in which all
magnetohydrodynamic quantities are functions of one of these
quantities (e.g. of 9 ). 9 on its part aepends on the
coordinate x and on the time t: x - V ( Ot = f( ?). V
denotes the translation velocity of the point where density
has a given va lue; f( 9) - a function which is reciprocal to the
density distribution 9 (x) in the initial instant of time t= 0.
f(~) a 0 holds for the self-simulating waves in the ranges of
compression fr(?)---o and in the ranges of expansion fq(~)> 0
The simple waves are closely connected with the waves o small
amplitudes. Like in magnetohydrodynamics with scalar pressure,
there exist 3 types of -waves. The partly very extensive
differential equations of the Alfv6n waves and magnetic sound
waves are written down explicitly. The Alfv6n waves propagate
without changing their shape. Investigation of the equations of
the magnetic sound waves in general form frequently meets with.
Card 2/4 considerable difficulties. The authors deal only with the most
Simple Waves in the Chew, Goldberger, and SOV/56-37-3-25/62
Law Approximation
interesting case in which hydrostatic pressure is considerably
lower than magnetic pressure. In the ranges with expansion the
density gradient decreases, and in the ranges of compressior. it
increases. In the ranges with expansion (f'>0) and in the
self-simulating waves (f - 0) density decreases. In the ranges
of the compression (fle--O) density increases until a certain
expression written down by the authors becomes negative.
As soon as this expression equals zero, a compression shock
wave is formed. In a fast magnetic sound wave, the quantities
PU 9 P.L 9 11 9 1',/P,, change in the same way as in the magnetic
sound wave. The authors then investigate a slow magnetic sound
wave. There are two possibilities: (1) In the normal case,
density changes in the same way as in a fast magnetic sound
wave. Shock waves are formed especially in the ranges of
compression, and the self-sImulating waves are expansion waves.
Card 3/4
Simple Waves in the Chew, Goldberger, and SOV/56-37-3-25/62,.
Low Approximation
(2) In the abnormal case the density gradient decreases in the
ranges of compression and increases in the ranges of thinning
In the ranges of expansion a shock wave is formed. In contrast
to magnetohydrodynamics with scalar pressure, expansion shock
waves may form in this case. The authors thank A.I. Akhiyez.er
and G.Ya. Lyubarskiy for useful d'-scussions. There are
8 references, 5 of which are Soviet.
ASSOCIATION.- Fiziko-tekhnicheskiy institut Akademii nauk Uk-rainskoy SSR
(Physical-technical Institute of the Academy of Sciences,
Ukrain-skaya SSR) Institut fiziki Akademii nauk Graz. SSR
(Physics Institute of the Academy of Sciences of the
Gruzinskaya SSR)
SUBMITTED: April 3, 1959
Card 4/4
Z1 (7)
AUTHORS: Lyubarskiy, G. Ya., Polovin, R. V'o SOV/20-128-4-13/65
TITLE: On the Piston Problem in Magneticillydrodynamics
PERIODICAL: Doklady Akademii nauk SSSR, 1959, `101 128, NT 4, pp 684-687
(USSR)
ABSTRACT: The theorem of Chapman-Zhuge which remained a hypothesis for
a long time, was first investigated by Ya. B. Zelldovich
(Ref 1) by detonation in a cylinder. The present investiga-
tion aims at a qualitative examination of the simplest piston
problem in magneto-hydrodynamics while the piston is moving
with a constant velocity. The motion of the substance ahead
of the piston must be more complicated in magnet b -hydrodynamics
than in hydrodynamics as the state of the compressible con-
ducting fluid is characterized by 7 instead of 3 quantities.
The authors investigated the semi-space x> 0; it is filled
with an ideal conductive fluid which is in a magnetic field
and is at rest at the time t 0. The fluid's state is char-
acterized by the density 30 the pressure p 0, and the com-
ponents H X, H 0y , Hoz - 0 of the magnetic field. The thermo-
Card 1/4 dynamical state equation of the fluid is optional and the
On the Piston Problem in Mfagnetic Hydrodynamic3 SOV/20.-128-4-13/65
validity of the
es k -,)-a 1- 7., 0
is assumed. The fluid is bounded on the left by the piston
which is in the plane x = 0. At the time t the piston begins
moving with a constant velocity parallel to the Ox-axis. The
motion of the fluid will be described by application of
similarity and therefore all quantities depend solely on
the ratio x/t. The developing discontinuity should be stable
as related to a splitting up. According to A. I. Akhiyezer,
G. Ya. Lyubarskiy, R. V. Polovin (Ref 4), V. M. Kontorovich
(Ref 5), and S. I. Syrovatskiy (Ref 6) there are 3 types of
steady shock waves, i.e. fast and slow magneto sound waves
and Alfve"n waves. Only the magneto sound wave can run ahead
(shock wave or a wave by application of similarity), followed
by the Alfven wave and finally by the slow magneto sound
wave (sho ck wave or wave by application of similarity).Some
of these waves may be missingi there is a total of 17 variants.
But actually there only are 2 variants, a slow and a fast
magneto sonic wave in case the piston is moving against the
fluid and a fast and a slow "self-modelling" wave when the
Card 2/4 piston moves in opposite direction. The Alfve"n wave is missing
On the Piston Problem in Magnetic Hydrodynamics SOV/20-128-4-13/61,
in both cases. In this way the peculiar phenomenon of the
"electrodynamic viscosity" is obtained. A tangential magnetic
field in magnetic sound waves does not change the direction
(L. D. Landau, Ye. M. Lifshits Ref 7; A. I. Akhiyezer,
G. Ya. Lyubarskiy, R. V. Polovin Refs 8,9). The tangential
magnetic field increases in fast shock waves and decreases
in slow ones. Infen the tangential component equals zero on
one side of the shock wave or of the magneto sonic wave ob-
tained by application of similarity then it is parallel to
the tangential component of the magnetic field on the other
side. The density increases im shock-like magneto sound
waves and remains constant in Alfvdn waves. The tangential
magnetic field turns in an AlfvL-n wave about an arbitrary
angle without changing its magnitude. The corresponding
mq"matical relations are written down and briefly discussed.
The authors express their gratitude for the suggestion of
the theme to L. I. Sedov, to A. 1. Akhiyezer and A. S. Kom-
paneyets for discussing the results of this investigation.
There are 13 references, 12 of which are Soviet.
Card 3/4
On the Piston Problem in Magretic Hydrodynamics SCIV "20- 11 28- 1-1, 7/~' 5
1 ? "; ,
ASSOCIATION: Kharlkovskiy gosudarstvennyy universitet im. A. M. Gorlkogo
(Kharlkov State University imeni A. M. Gor'kiy).
Fiziko-takhnichenkiy institut Akademii nauk USSR (Physical-
technical Institute of the Academy of Sciences, VkrSSR)
PRESEPTED: May 27, 1959, by L. 1. Sedov, Academician
SUBMITTED: May 16, 1959
Card 4/4
AKHIYEZE-R, A.I.; LYUBARSKIY, G.Ya.; POLOVIN, R.V.
fivolutional discontinuities in magnetobydrodyn.--ics~' E '-
j
llutsionrWe razryvy v magnitnoi gidrodinamike. Khartkov,
Fiziko-tekhn. in-t AN USSR, 1960. 8-24 P. MIRA 17:3)
POLOVIN, R.V*; DEYjUTSKIY, V.P.
I
[Shock adiabats in magnetohydrodynamics] Udarnaia
adiabata v magnitnoi gidrodinamike. Kha-rlkov, Fiziko-
tekhn. in-t AN USSR, 1960. 25-34 P. (MIRA 17:2)
LYUBILRSYdY, G.Ya.; FOLOVD-1, H~V,
Y.
[Theory of' simple waves] K teorii prostykh voln. Khar'lmv.
Fiziko-tokhn. in-t JUI USSR, 1960. 1+0--1#3 p~ (MIRA 1,7~1)
(Shock waves) (Magnetohydrodpamics)
UUBARSKIY, G.Ya.; POLOVIN, R.V.
[The piston problem in magnetobydrodynar-L.'es) Zadacha
o porshne v magnitnoi gidrodinamike. Kharfkov, Fiziko-
tekhn. in-t AN USSR, 1960. 40-43 p. (MIRA 17:2)
ARHIYEZER, I.A.;,~OLOVIN, R.V.
[Motion of a conducting plane in a magnetobydrodymmic
medium] 0 dvizhenii provodiashchei ploskosti v magnito-
gidrodingmicheskoi srede. KharIkov, Fiziko-tekbn. in-t
AN USSRt 1960. 44-53 p. (MIRA 17:2)
AMYEZERI I.A.; POILVIN, R.V.; TSINTSADZE, N.L.
[Simple waves in Chewls, Goldberger's and Low's approxima-
tions] Prostye volny v priblizhenii Chliu, Golldbergera i
Lou. KharIkov, Fiziko-tekhn. in-t AN USSR, 1960. Page 57.
(MIRAL 17:3)
AKHIYEZER, I.A.; POLOVIN, R.V.
(Theory of relativistic magnetohydrod),namic waves] K tearii
reliativistskikh magnitogidrodinamicheskikh voln. KharIkov,
Fiziko-takhn. in-t AN USSR, 1960. 54-55 p. (MIRA 17:1)
86803
10 ID00
3/185/60/005/001/001/018
A151/AO29
1~~ 6, /1/ 0
AUTHORS: Polovin, R.V.; Demutskiy, V.P.
TITLE: The Shook Adiabatic in Magnetic Hydrodynamics.
PERIODICAL. Ukrayinslkyy Fizychnyy Zhurnal, 1960, Vol. 5, No. 1, PP. 3 - 11
TEXT: The aim of this paper is the investigation of the evolutionary parts
of a shock adiabatic within the limiting conditions of low-intensity shock waves,
as well as of the "almost parallel" and "almost perpendicular" shock waves of an
arbitrary intensity. The authors state that in the case of low-intensity shock
waves, the ineqi;alities (4) and (5) follow from the limiting conditions and Tsemp-
lents [ABSTRACTOR'S NOTE; The name Tsemplen is given as it appears in the Ukrain-
ian transliteration] theory (see Refs. 10, 8, 11, 12). The inequalities (4) and
(5) mean that the low-intensity shock waves are always evolutionary, i.e., resist-
ant to splitting. As to that shock wave, which in the limiting case 6p - 0 turns
into an 11al1fvenovs1ka" [ABSTRACTOR'S NOTE: the word "al'fvenovs'ka" ik, given in
the Ukrainian transliteration, since no English equivalent could be found] shock
wave it may be said that it is always non-evolutionary. Such a shock should not
be confused with an "al'fvenovs'kYy" discontinuity, in whichAp-O and the magrede
Card I/Y
8 6 6 () 3
S/185/6o/005/001,/001 1'~
The Shock Adiabatic in Magnetic Hydrodynamics. A151/AO29.
field turns around the normal at a certain angle not changing its valiv-. 'Bie "al~
fvenovslkyy" discontinuity ~z always evolutionary (Ref. 5). nie f-.j--)wj_jig two
types of shock waves are possible in the case when in front of the snock wav- tj--~
magnetic field is directed along the normal toward the surface of the
(Ref. 6): 1) the "sonic" shock wave, in which H2 = 0, 2) a particular shor'
wave, in which H2 -~ 0 (Ref. 10). On the sonic sK 0ck wave, the correlations L,,
tween the jumps of the magneto-hydrodynamic values are such as they appear in '.ne
absence of the magnetic field. The presence of a normal magnetic field, however.,
narrows the evolution zone (Ref. 5). In the plane ~Vl,,V20 the sonic shock wa7ie
is represented by the line abeg in Figure 1, and by ~he line fg in Figure '7no.!
Figures 1,2 correspond to the case Vlx> cl, the Figures 3,4 - to the case VJX 0. (6)
a-U/
from which it follows that a distribution function having only one maximum
is stable. This stability condition was observed by P. L. Auer (Ref-7:
Phys.Rev.Lett.,1,411,1958)- If the distribution function has two maxima,
the function will not be stable. A further condition is that any
.spherically symmetrical distribution function P (jvj) which is nowhere
00
vanishing is stable. Since f0 (U) FO (V) dvj. 2ff ~ F. (v-u-r--Fo.L) vi-dv.L, (A)
holds, where vL is the velocity component of the electron which is
Card. 2/7
22147
S/056 61/040/003/027/031
Stability condit ions of ... B113/33202
~peryendidular to
fl(u) es on the:.
-2nuF (Jul) is obtained. Henoe (3) tak
o rm 0 0
Go
21 du- (7)
coo
.from'which 0, (1
u du 2AW. (I s 1) (8)
2%
S-U
~',---'follows. The stability cond ition leads to the fulfillment of the in-
CD
eq ualityl F
(Jul)du