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On the analytic solution of the helical equilibrium equation in the MHD approximation

Published online by Cambridge University Press:  13 March 2009

M. L. Woolley
Affiliation:
Euratom-UKAEA Association for Fusion Research, Culham Laboratory, Abingdon, Oxfordshire, OX14 3DB, England

Abstract

The second-order elliptic partial differential equation, which describes a class of static ideally conducting magnetohydrodynamic equilibria with helical symmetry, is solved analytically. When the equilibrium is contained within an infinitely long conducting cylinder, the appropriate Dirichiet boundary-value problem may be solved in general in terms of hypergeometric functions. For a countably infinite set of particular cases, these functions are polynomials in the radial co-ordinate; and a solution may be obtained in a closed form. Necessary conditions are given for the existence of the equilibrium, which is described by the simplest of these functions. It is found that the Dirichlet boundary-value problem is not well-posed for these equiilbria; and additional information (equivalent to locating a stationary value of the hydrodynamic pressure) must be provided, in order that the solution be unique.

Type
Research Article
Copyright
Copyright © Cambridge University Press 1975

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References

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