I. First-order calculation of the pressure tensor for cylindrical, Z-pinch plasmas

Abstract

Calculations of the pressure tensor in a two-dimensional (2D), Z-pinch geometry are presented that extend calculations previously published [K. G. Whitney, Phys. Plasmas 6, 816 (1999)], which dealt with a spherical, Inertial Confinement Fusion geometry. In a cylindrically symmetric [(r,z)] plasma, the electron pressure tensor has three independent, but coupled, components (rather than one as in a sphere). There are a variety of nonlinear contributions to the electron pressure tensor that depend bilinearly on gradients in temperature and density and on the current density. A general presciption for calculating their magnetic field and ionization state dependence is described in this paper. It is found, for example, that the contribution that comes from gradients in temperature has the same form involving three η coefficients as the classical contributions to the Z-pinch pressure tensor that come from gradients in fluid velocity. Moreover, all three coefficients of the temperature gradient terms are found to be much larger than the corresponding fluid velocity coefficients. Explicit formulas for all first-order pressure tensor coefficients are given in the appendixes.