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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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.
|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|
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|Deposited On:||18 Dec 2007|
|Last Modified:||26 Dec 2012 09:48|
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