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Two-dimensional generalizations of the Newcomb equation

Published online by Cambridge University Press:  13 March 2009

R. L. Dewar  and
A. Pletzer
R. L. Dewar
Affiliation:
Department of Theoretical Physics and Plasma Research Laboratory, Research School of Physical Sciences, The Australian National University, G.P.O. Box 4, Canberra, ACT 2601, Australia
A. Pletzer
Affiliation:
Department of Theoretical Physics and Plasma Research Laboratory, Research School of Physical Sciences, The Australian National University, G.P.O. Box 4, Canberra, ACT 2601, Australia
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Abstract

The Bineau reduction to scalar form of the equation governing ideal zero-frequency linearized displacements from a hydromagnetic equilibrium possessing a continuous symmetry is performed in ‘universal co-ordinates’, applicable to both the toroidal and helical cases. The resulting generalized Newcomb equation (GNE) has in general a more complicated form than the corresponding one-dimensional equation obtained by Newcomb in the case of circular cylindrical symmetry, but in this cylindrical case we show that the equation can be transformed to that of Newcomb. In the two-dimensional case there is a transformation that leaves the form of the GNE invariant and simplifies the Frobenius expansion about a rational surface, especially in the limit of zero pressure gradient. The Frobenius expansion about a mode rational surface is developed and the connection with Hamiltonian transformation theory is shown. The derivations of the ideal interchange and ballooning criteria from the formalism are discussed.

Type
Research Article
Information
Journal of Plasma Physics , Volume 43 , Issue 2 , April 1990 , pp. 291 - 310
Copyright
Copyright © Cambridge University Press 1990

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References

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