Ohmic dissipation and relaxation of force-free magnetic fields

Abstract

A study is made of the process of passive ohmic dissipation of a force-free magnetic field in a low-pressure plasma with inhomogeneous conductivity. It is shown that the force-free field (curl ..-->..H = ..cap alpha -->..H) preserves its geometrical shape in the process of the dissipation if the ratio ..cap alpha../sup 2//sigma does not depend on the coordinates. The process of topological resistive relaxation of a force-free field in a twisted magnetic loop to the state with least magnetic energy is investigated. It is found that for fixed external pressure and given moment of the forces at the ends of the magnetic loop a uniformly twisted magnetic filament corresponds to this state. Taylor's relaxation model is analyzed critically. It is shown that a force-free field of variable sign with ..cap alpha.. = const corresponds to a minimum of only the ratio epsilon/K, where K is the spirality of the field, and not to a minimum of the total magnetic energy epsilon /sub m/ of the system.