On the stability of a rigid body in a magnetostatic equilibrium

P.A. Davidson; Konstantin Ilin; H.K. Moffatt; Vladimir A. Vladimirov

doi:10.1016/j.euromechflu.2003.08.002

On the stability of a rigid body in a magnetostatic equilibrium

P.A. Davidson, Konstantin Ilin, H.K. Moffatt, Vladimir A. Vladimirov

Mathematics

Research output: Contribution to journal › Article › peer-review

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 language	English
Pages (from-to)	511-523
Number of pages	12
Journal	European Journal of Mechanics - B/Fluids
Volume	22
Issue number	5
DOIs	https://doi.org/10.1016/j.euromechflu.2003.08.002
Publication status	Published - Sept 2003

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10.1016/j.euromechflu.2003.08.002

http://dx.doi.org/10.1016/j.euromechflu.2003.08.002

Cite this

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title = "On the stability of a rigid body in a magnetostatic equilibrium",

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.",

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T1 - On the stability of a rigid body in a magnetostatic equilibrium

AU - Davidson, P.A.

AU - Ilin, Konstantin

AU - Moffatt, H.K.

AU - Vladimirov, Vladimir A.

PY - 2003/9

Y1 - 2003/9

N2 - 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.

AB - 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.

U2 - 10.1016/j.euromechflu.2003.08.002

DO - 10.1016/j.euromechflu.2003.08.002

M3 - Article

SN - 0997-7546

VL - 22

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EP - 523

JO - European Journal of Mechanics - B/Fluids

JF - European Journal of Mechanics - B/Fluids

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