### Abstract

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 language | English (US) |
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Article number | 082513 |

Journal | Physics of Plasmas |

Volume | 19 |

Issue number | 8 |

DOIs | |

State | Published - Aug 2012 |

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### ASJC Scopus subject areas

- Condensed Matter Physics

### Cite this

*Physics of Plasmas*,

*19*(8), [082513]. https://doi.org/10.1063/1.4747700

**The complete set of Casimirs in Hall-magnetohydrodynamics.** / Kawazura, Yohei; Hameiri, Eliezer.

Research output: Contribution to journal › Article

*Physics of Plasmas*, vol. 19, no. 8, 082513. https://doi.org/10.1063/1.4747700

}

TY - JOUR

T1 - The complete set of Casimirs in Hall-magnetohydrodynamics

AU - Kawazura, Yohei

AU - Hameiri, Eliezer

PY - 2012/8

Y1 - 2012/8

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84865743439&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84865743439&partnerID=8YFLogxK

U2 - 10.1063/1.4747700

DO - 10.1063/1.4747700

M3 - Article

VL - 19

JO - Physics of Plasmas

JF - Physics of Plasmas

SN - 1070-664X

IS - 8

M1 - 082513

ER -