### 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 |
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Pages (from-to) | 511-523 |

Number of pages | 13 |

Journal | European Journal of Mechanics, B/Fluids |

Volume | 22 |

Issue number | 5 |

DOIs | |

Publication status | Published - Sep 2003 |

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### ASJC Scopus subject areas

- Mechanical Engineering

### Cite this

*European Journal of Mechanics, B/Fluids*,

*22*(5), 511-523. https://doi.org/10.1016/j.euromechflu.2003.08.002