Conservation of canonical circulation and its relation to finite Hall term magnetohydrodynamics
- California Institute of Technology, Pasadena, California 91125 (United States)
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 [ital canonical] [ital circulation] [ital S][sub [sigma]]=[contour integral] ([ital m][sub [sigma]]u[sub [sigma]]+[ital q][sub [sigma]]A) [center dot][ital d]l of a toroidal fluid element, is [ital 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. [bold 69], 3515 (1992)], except for a constant factor related to the ion collisionless skin depth.
- OSTI ID:
- 6364255
- Journal Information:
- Physics of Fluids B; (United States), Vol. 5:7; ISSN 0899-8221
- Country of Publication:
- United States
- Language:
- English
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