On the stability of a rigid body in a magnetostatic equilibrium

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

Research output: Contribution to journalArticle

2 Citations (Scopus)

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

Fingerprint

Magnetostatics
magnetostatics
rigid structures
Rigid Body
Magnetic Field
Magnetic fields
Fluid
Plasma Physics
Fluids
Potential Field
Nonlinear Stability
Stability criteria
Sudan
Magnetohydrodynamics
Stability Criteria
Small Perturbations
Variational Principle
conduction
Conductivity
magnetohydrodynamic stability

ASJC Scopus subject areas

  • Mechanical Engineering

Cite this

On the stability of a rigid body in a magnetostatic equilibrium. / Vladimirov, V. A.; Moffatt, H. K.; Davidson, P. A.; Ilin, K. I.

In: European Journal of Mechanics, B/Fluids, Vol. 22, No. 5, 09.2003, p. 511-523.

Research output: Contribution to journalArticle

Vladimirov, V. A. ; Moffatt, H. K. ; Davidson, P. A. ; Ilin, K. I. / On the stability of a rigid body in a magnetostatic equilibrium. In: European Journal of Mechanics, B/Fluids. 2003 ; Vol. 22, No. 5. pp. 511-523.
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