Adiabatic Time Development of Linear Theta-Pinch Plasma Profiles

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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, Ir = ∮ Pr 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 Bz to the center of the plasma to cause β to be significantly less than one. The resulting plasma angular momenta are obtained.