EFFECT OF COMPRESSIBILITY ON THE NONLINEAR EVOLUTION OF THE FIXED-BOUNDARY M=1 MODES IN A Z-PINCH

The effect of compressibility on the nonlinear evolution of the fixed-boundary (internal) m = 1 modes in a pure Z-pinch (no axial magnetic field) is investigated. The work extends the result of a preceding paper, in which it was shown that, near marginal stability, all these modes are stabilized nonlinearly within incompressible, ideal MHD. In the present paper it is shown that essentially the same result is obtained in the case of a compressible plasma. Only a minor increase of the amplitudes of the bifurcated equilibria (i.e. slightly less nonlinear stability) is found for gamma = 5/3 as compared with the incompressible limit gamma --> infinity, where gamma is the exponent in the equation of state. The fact that the equation of state only plays a minor role for the nonlinear evolution of these modes indicates that nonlinear stabilization possibly may also occur in collisionless pinches, in spite of the fact that the ideal MHD model is not strictly valid for such plasmas.