Adiabatic Time Development of Linear Theta-Pinch Plasma Profiles

Abstract

The formation of a θ‐pinch plasma sheath is studied under the assumption that the sheath is initially relatively thin and must therefore contain a radial E field but that later it relaxes to a thickness of the order of the ion gyroradius because of line shorting. A family of the resulting self‐consistent equilibria are computed for a Maxwellian plasma under the additional assumption that the radial adiabatic invariant, I_r = ∮ P_r dr, is conserved for all ions during the relaxation. These solutions predict that for particle line densities less than about 5 × 10¹⁶ cm⁻¹, this relaxation will allow enough penetration of B_z to the center of the plasma to cause β to be significantly less than one. The resulting plasma angular momenta are obtained.