Partially relaxed magnetic field equilibria in a gun-injected spheromak

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 (nabla x B -μB, μ not= constant), by solving a non-linear Grad-Shafranov equation in SPHEX geometry. It is demonstrated mathematically that in certain circumstances there exist two equilibria for the same boundary conditions. It is also shown that if μ 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. (author)