Effect of Tensor Conductivity on Collisionless Magnetogasdynamic Flows

Tang, J. Y. T.; Seebass, R.

doi:10.1063/1.1692492

Cited by 4 publications

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“…The detailed solution for a specific biconvex profile has been carried out to confirm the qualitative predictions made here [6].…”

Section: Introductionmentioning

confidence: 75%

The effect of tensor conductivity on continuum magnetogasdynamic flows

Tang¹,

Seebass²

1968

Quart. Appl. Math.

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Introduction.In recent years much work, both theoretical and experimental, has been done in the exploration of magnetogasdynamic or plasmadynamic phenomena, their engineering applications and their astrophysical implications. A good deal of this work, however, has included the approximation that the electric current always flows in the direction of the electric field vector. In reality, charged particles in a magnetic field do not move in straight lines, but rather tend to drift in a direction perpendicular to both the electric and magnetic fields, giving rise to the so-called Hall current or Hall effect. Because of the Hall effect, Ohm's law is modified in such a way that the electrical conductivity becomes a tensor quantity. The usual approximation of scalar conductivity is valid only when the collision frequency of the particles is so large that the particles have negligible time to drift across the magnetic field lines between collisions, i.e. when the cyclotron frequency of the particles is much less than their collision frequency. For cases where this condition is not met, the Hall effect must be taken into consideration. This paper extends our earlier results [1] to account for this phenomenon. We consider a dense plasma with a plasma frequency much greater than the cyclotron frequency of the particles present which, in turn, is much larger than the inverse of the characteristic flow time (i.e. the ratio of the free stream velocity to the characteristic length of the obstacle). In addition, the cyclotron frequency for the electrons is assumed to be of the same order of magnitude as the collision frequency between electrons and ions. We begin Sec. 2 by stating the equations pertinent to this problem. After linearization

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“…The detailed solution for a specific biconvex profile has been carried out to confirm the qualitative predictions made here [6].…”

Section: Introductionmentioning

confidence: 75%

The effect of tensor conductivity on continuum magnetogasdynamic flows

Tang¹,

Seebass²

1968

Quart. Appl. Math.

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Effect of Tensor Conductivity on Rotating Superposed Plasmas

Kathuria

Kalra

1974

Z Angew Math Mech

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Die Stabilitat einer Wirbeljhhe zwiechen zwei rotierenden hydromagnetiacln Fliiaeigkeiten ?nit Lenaorieller Ledfahigkeit wird uniersucht. Ebenso wird die Stabilitiit dea Systems fur den Fall diskutiert, dab es anjanglich ruhf. aber einer zur Trennflkhe senkrechten Beschleunigung unterliegt. Man findet, dab die tensorielle Leitfahigkeit dus System destabilisiert, dap aber die Rotation je nuch der G n g e der Storungswellen stabilisierend oder destabilisierend wirken kann.The stability of a vortex sheet between tzvo hydromagnetic, rotating liquids having tensor conductivity i s examined.The stability of the system without initial motion but subject to an acceleration perpendicular to the interface is also discussed. It is found that tensor condudivity destabilizes the system but rotation might be stabilizing or destabilizing depending upon the wave length oj perturbation. ~CCJle;lyeTCR CTa6UJbHOCTb BUXpeBOfi IIOBepXHOCTU Memay SByMR BpaUlaIOUlUMMCJl rUZpOMarH€iTIlblMU iKU,lKOCTJlMki C TeH30pHOfi npOBOaHMOCTblo. IIOnBepI'aeTCH TalC Hie UkiCKYCCHR CTa6ki.lbHOCTb Cki CTeMM HOCTU pa3nena yCKOpeHUlo. HatkneHo, '(TO TeH30pHaR IIpOBOnkiMOCTb IIPMBOSUT CMCTeMy K HeYCTOfilIU-BOCTM U 'IT0 BpaUeHMe B 3aBMCMMOCTki OT RJlMHLI BOJIII ~MpKyJIRIUiki MOmeT OKa3aTI. KaK M c~a6nnki3u-nnrr cayqaH, ecmi m a , iraxonrrcb nepBoHa4anbrio n noKoe, IionnemuT nepneHnuriyJirrpnoMy K nonepxpyloqee TaiC H ~e c~a 6~~1~3~p y w i i~e e BnuHHue. Basic Equations and the Dispersion RelationConsider two incompressible, inviscid, homogeneous hydromagnetic fluids separated by a plane interface z = 0. The fluids occupy the semi-infinite regions z 2 0 and are respectively denoted by the suffixes +, -.We assume the system t o be subjected t o an acceleration g (0, 0, -g) which may account for the gravitational field or the curvature of the field lines. The whole configuration is rotating uniformly with angular velocity f,,(O, Q, 0). Both thc fluids carry a uniform impressed magnetic field H and have initial streaming velocities U* in the zy-plane. The equations for each fluid in a rotating frame of reference are [lo]:

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