The complete set of Casimirs in Hall-magnetohydrodynamics

Yohei Kawazura, Eliezer Hameiri

Research output: Contribution to journalArticlepeer-review


A procedure for determining all the Casimir constants of motion in magnetohydrodynamics (MHD) [E. Hameiri, Phys. Plasmas 11, 3423 (2004)] is extended to Hall-MHD. We obtain and solve differential equations for the variational derivatives of all the Casimirs, which must be satisfied for any dynamically accessible motion in Hall-MHD. In an extension of the more commonly considered Hall-MHD model, we also include the electron fluid entropy. The most interesting case for plasma confinement, which is usually true for axisymmetric configurations but desirable in general, is when both the magnetic field and the ion velocity field form the two separate families of nested toroidal surfaces. The Casimirs are then three functionals for each surface, involving the fluxes of certain vector fields and the number of particles contained in each. We also determine a family of independent Casimirs in a general configuration.

Original languageEnglish (US)
Article number082513
JournalPhysics of Plasmas
Issue number8
StatePublished - Aug 2012

ASJC Scopus subject areas

  • Condensed Matter Physics


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