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. doi:10.1063/1.860783. https://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 | ||||||
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Additional Information: | © 1993 American Institute of Physics. Received 25 January 1993; accepted 22 March 1993. Supported by National Science Foundation Grant No. ECS-8814184. | ||||||
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Subject Keywords: | MAGNETOHYDRODYNAMICS, CONSERVATION LAWS, HALL EFFECT, VORTEX FLOW, PLASMA SWITCHES, COMPRESSIBLE FLOW, TRANSPORT, JET FLOW, PLASMA FLOW, VORTICITY | ||||||
Issue or Number: | 7 | ||||||
DOI: | 10.1063/1.860783 | ||||||
Record Number: | CaltechAUTHORS:BELpofb93 | ||||||
Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:BELpofb93 | ||||||
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: | 08 Nov 2021 20:58 |
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