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

Abstract

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.

Authors:
 [1]
  1. Courant Institute of Mathematical Sciences, New York University, New York 10012 (United States)
Publication Date:
OSTI Identifier:
22113427
Resource Type:
Journal Article
Journal Name:
Physics of Plasmas
Additional Journal Information:
Journal Volume: 20; Journal Issue: 2; Other Information: (c) 2013 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1070-664X
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; CONFINEMENT; DENSITY; ELECTRONS; EQUILIBRIUM; MAGNETIC FIELDS; MAGNETOHYDRODYNAMICS; MASS; PLASMA; SHOCK WAVES; STABILITY; TOKAMAK DEVICES; TOPOLOGY

Citation Formats

Hameiri, Eliezer. Generalized shock conditions and the contact discontinuity in the Hall-magnetohydrodynamics model. United States: N. p., 2013. Web. doi:10.1063/1.4792258.
Hameiri, Eliezer. Generalized shock conditions and the contact discontinuity in the Hall-magnetohydrodynamics model. United States. https://doi.org/10.1063/1.4792258
Hameiri, Eliezer. 2013. "Generalized shock conditions and the contact discontinuity in the Hall-magnetohydrodynamics model". United States. https://doi.org/10.1063/1.4792258.
@article{osti_22113427,
title = {Generalized shock conditions and the contact discontinuity in the Hall-magnetohydrodynamics model},
author = {Hameiri, Eliezer},
abstractNote = {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.},
doi = {10.1063/1.4792258},
url = {https://www.osti.gov/biblio/22113427}, journal = {Physics of Plasmas},
issn = {1070-664X},
number = 2,
volume = 20,
place = {United States},
year = {Fri Feb 15 00:00:00 EST 2013},
month = {Fri Feb 15 00:00:00 EST 2013}
}