Adiabatic Compression of 3-D Plasma Magnetic Field Configuration

Abstract

The work in this paper describes the formulation and computation of the adiabatic compression of a plasma in a realistic geometry such as a finite length θ-pinch or imploding liner device. The assumption of cylindrical symmetry allows us to make use of the techniques originated by H. Grad and coworkers for treating the resulting generalized differential equations. The nonlinear equilibrium equations are volume averaged over a flux surface and converted from PDE’s to ODE’s. This allows the adiabatic boundary conditions arising from the law of flux conservation to be taken into account. Calculations are presented for a field-reversed plasma configuration confined in either a finite length θ-pinch or liner device. Compression is obtained by increasing the external confining coil current (flux compression) and thereby increasing the pinching field or by collapsing the external wall (liner) under the assumption of constant flux. In both cases it is assumed that compression occurs on a time scale which is longer than the pressure equilibration time. Results of radial and accompanying axial contraction are presented for a series of initial plasma profiles and beta under varying compression schemes.