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Analytical solutions for the current driven by a rotating magnetic field in a spherical plasma

Published online by Cambridge University Press:  13 March 2009

Peter A. Watterson
Peter A. Watterson
Affiliation:
School of Physical Sciences, The Flinders University of South Australia, Bedford Park, South Australia 5042, Australia
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Abstract

The steady currents driven in a spherical plasma by a rotating magnetic field via the Hall effect are studied analytically. The total field is shown to be symmetric across the origin. Integral relationships are obtained between Ohmic dissipation, angular momentum and the oscillating axial current density. The topology of the sum of a Hill's vortex field and a rotating field is documented. Analytical solutions for the driven current are obtained by expansion for the limits corresponding to small rotation frequency, to small number density, to large rotating-field magnitude, to small resistivity, and to small rotating-field magnitude combined with very small resistivity. The latter solution, relevant to the reactor limit, indicates that, with control of the vertical field magnitude, an MHD equilibrium can be generated with total current any fraction of the currentcorresponding to synchronous rotation of the electrons. Oscillating currents sufficient to drive the synchronous current are determined.

Type
Research Article
Information
Journal of Plasma Physics , Volume 46 , Issue 2 , October 1991 , pp. 271 - 298
Copyright
Copyright © Cambridge University Press 1991

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