Partially relaxed magnetic field equilibria in a gun-injected spheromak

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Abstract
The UMIST spheromak (SPHEX) is a gun-injected spheromak similar in design to the Los Alamos spheromak CTX. A numerical code was written to calculate the possible zero pressure gradient axisymmetric spheromak equilibria, which deviate from the minimum energy relaxed states ( Del *B= mu B, mu not=constant), by solving a nonlinear Grad-Shafranov equation in SPHEX geometry. It is demonstrated mathematically that in certain circumstances there exist two equilibria for the same boundary conditions. The authors also show that if mu is not a constant then the energy increases to infinity as a specified weighted average approaches a critical value. The relevant parameters of these equilibria (e.g. helicity, magnetic energy, etc.) are calculated and their interdependence studied.