A numerical model for resistive magnetohydrodynamic instabilities

Abstract

A hydromagnetic model has been developed to study resistive instabilities in cylindrical geometry, and the model is applied to study specific diffuse pinch configurations. The MHD equations include the effects of compressibility, finite resistivity, viscosity, and thermal conductivity. The plasma equilibrium configuration is assumed known and is specified by B θ 0 ( r), B z0 ( r), η 0( r), ϱ 0( r), T 0( r) and these functions can be chosen to describe a particular experiment. Perturbations of the form f 1( r, t)exp[ i( mθ + k 2 z)] are used for all plasma and field variables, and the resulting linear partial differential equations are solved numerically as an initial value problem using an implicit difference scheme. A set of seven equations for B r1 , B θ 1 , T 1 , ν r1 , ν θ 1 , ν z1 , ϱ 1, is obtained and the calculation is started by specifying an initial perturbation. For a particular problem, the parameters m, k z , and S = τ R / τ H , the ratio of resistive diffusion time to hydromagnetic transit time must be given, and for certain choices an exponential growth occurs and the growth rate p( m, k z , S) is calculated.