Generalized shock conditions and the contact discontinuity in the Hall-magnetohydrodynamics model

Journal Article · Fri Feb 15 04:00:00 EST 2013 · Physics of Plasmas

DOI:https://doi.org/10.1063/1.4792258· OSTI ID:22113427

Hameiri, Eliezer ^[1]

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1. Courant Institute of Mathematical Sciences, New York University, New York 10012 (United States)

It is shown that shocks and contact discontinuities in the Hall-magnetohydrodynamics (HMHD) model must satisfy solvability conditions that replace some of the familiar Rankine-Hugoniot jump conditions when the latter do not apply due to singular behavior of fluxes of conserved quantities. Some of these conditions depend on the larger topology of the plasma and magnetic field and are not merely 'local.' The contact discontinuity which separates two adjoining plasma regions or plasma and vacuum regions is the simplest case where the new jump conditions are applicable and is discussed for a toroidal plasma with sheared magnetic field such as the tokamak, but with no initial mass flow. It is proven that a static discontinuous tokamak-like equilibrium is linearly stable in the HMHD model if it is linearly stable within the ideal magnetohydrodynamics model, provided that the electron pressure depends only on the density, and some other restrictions on the ratio of pressure to density gradients also apply. When the electron pressure does depend on two thermodynamic variables, a sufficient condition for Hall-MHD plasma stability is derived as well.

• OSTI ID: 22113427
• Journal Information: Physics of Plasmas, Journal Name: Physics of Plasmas Journal Issue: 2 Vol. 20; ISSN PHPAEN; ISSN 1070-664X
• Country of Publication: United States
• Language: English

Related Subjects

70 PLASMA PHYSICS AND FUSION TECHNOLOGY
CONFINEMENT
DENSITY
ELECTRONS
EQUILIBRIUM
MAGNETIC FIELDS
MAGNETOHYDRODYNAMICS
MASS
PLASMA
SHOCK WAVES
STABILITY
TOKAMAK DEVICES
TOPOLOGY