Plasma Equilibrium in a Magnetic Field

Abstract

An integral equality relating different kinds of energy (kinetic, thermal, gravitational, etc.) of some region with a volume V and a surface S, is commonly referred to as the virial theorem. It seems to have been proved for mechanical systems for the first time by Clausius. The derivation of the virial theorem for a mechanical system executing a motion in some finite region of space, velocities also being finite, can be found, for example, in Landau and Lifshitz (1960, Mechanics, Ch. 2, § 10). The generalization of the theorem to include the magnetic energy in the context of magnetohydrodynamics was achieved by Chandrasekhar and Fermi (1953).