Growth rates and spectra for a particular axially symmetric equilibrium

Abstract

An axially symmetric ideal magnetohydrodynamic equilibrium akin to a mirror machine with currents only in the ignorable direction is considered. In order to study the spectrum of modes and growth rates of unstable modes, an expansion is performed in the small parameter, the ratio of plasma radius to axial periodicity length. Many stable continuous spectra and both stable and unstable point spectra are found. Growth rates are computed after a second expansion is made in the small parameter, the fractional distortion of the flux surfaces from cylinders. The high beta wall stabilization effect first noted by Haas and Wesson in their free boundary model is not found in this distributed pressure model which is not a good approximation to theirs. Aside from this one difference, the growth rates here are quite comparable to the sharp boundary model and give further indication of the utility of that model.