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On the stability of a rigid body in a magnetostatic equilibrium

Vladimirov, V.A., Moffatt, H.K., Davidson, P.A. and Ilin, K.I. (2003) On the stability of a rigid body in a magnetostatic equilibrium. European Journal of Mechanics - B/Fluids, 22 (5). pp. 511-523. ISSN 0997-7546

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We study the stability of a perfectly conducting body in a magnetostatic equilibrium. The body is immersed in a fluid which is threaded by a three-dimensional magnetic field. The fluid may be perfectly conducting, non-conducting or have finite conductivity. We generalise the classical stability criterion of Bernstein et al. (Proc. Roy. Soc. London Ser. A 244 (1958) 17–40; I.B. Bernstein, The variational principle for problems of ideal magnetohydrodynamic stability, in: A.A. Galeev, R.N. Sudan (Eds.), Basic Plasma Physics: Selected Chapters, North-Holland, Amsterdam, 1989, pp. 199–227) and show that the body is stable to small isomagnetic perturbations if and only if the magnetic energy has a minimum at the equilibrium. For an equilibrium of a body in potential magnetic field, we obtain a sufficient condition for genuine nonlinear stability.

Item Type: Article
Institution: The University of York
Academic Units: The University of York > Mathematics (York)
Depositing User: York RAE Import
Date Deposited: 26 May 2009 14:59
Last Modified: 26 May 2009 14:59
Published Version: http://dx.doi.org/10.1016/j.euromechflu.2003.08.00...
Status: Published
Publisher: Elsevier
Identification Number: 10.1016/j.euromechflu.2003.08.002
URI: http://eprints.whiterose.ac.uk/id/eprint/6159

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