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

Eliezer Hameiri

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Article number022112
JournalPhysics of Plasmas
Issue number2
StatePublished - Feb 2013

ASJC Scopus subject areas

  • Condensed Matter Physics


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