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December 31, 1967
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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. 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