On the stability of a rigid body in a magnetostatic equilibrium

V. A. Vladimirov, H. K. Moffatt, P. A. Davidson, K. I. Ilin

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Abstract

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.

Original languageEnglish
Pages (from-to)511-523
Number of pages13
JournalEuropean Journal of Mechanics, B/Fluids
Volume22
Issue number5
DOIs
Publication statusPublished - Sep 2003

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ASJC Scopus subject areas

  • Mechanical Engineering

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