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Conservation of canonical circulation and its relation to finite Hall term magnetohydrodynamics

Bellan, P. M. (1993) Conservation of canonical circulation and its relation to finite Hall term magnetohydrodynamics. Physics of Fluids B, 5 (7). pp. 1955-1961. ISSN 0899-8221. http://resolver.caltech.edu/CaltechAUTHORS:BELpofb93

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Abstract

The axisymmetric, compressible visco-resistive two-fluid plasma equations are examined under the constraint that the current is purely poloidal and the pressure is a function of density only ("barotropic"). For ideal plasmas (zero resistivity and zero viscosity) the Kelvin circulation theorem of fluid mechanics and the concept of frozen-in field lines turn out to be limiting cases of a more general concept, namely, that the canonical circulation Ssigma=[contour-integral] (msigmausigma+qsigmaA) ·dl of a toroidal fluid element, is exactly conserved as the toroidal element convects and/or is compressed. Appropriate linear combinations of the electron and ion fluid equations give a magnetohydrodynamic vorticity transport equation and an induction equation with a nonlinear Hall term. The finite Hall term is identical to the source term in the vorticity transport equation [P. M. Bellan, Phys. Rev. Lett. 69, 3515 (1992)], except for a constant factor related to the ion collisionless skin depth.


Item Type:Article
Additional Information:Copyright © 1993 American Institute of Physics. Received 25 January 1993; accepted 22 March 1993. Supported by National Science Foundation Grant No. ECS-8814184.
Subject Keywords:MAGNETOHYDRODYNAMICS, CONSERVATION LAWS, HALL EFFECT, VORTEX FLOW, PLASMA SWITCHES, COMPRESSIBLE FLOW, TRANSPORT, JET FLOW, PLASMA FLOW, VORTICITY
Record Number:CaltechAUTHORS:BELpofb93
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:BELpofb93
Alternative URL:http://dx.doi.org/10.1063/1.860783
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:9391
Collection:CaltechAUTHORS
Deposited By: Archive Administrator
Deposited On:18 Dec 2007
Last Modified:26 Dec 2012 09:48

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