Two methods are developed to solve an equation describing the equilibrium magnetic field associated with an E-layer in an Astron device. Because of problems related to bifurcation, all solutions are not obtainable by standard numerical means. Two methods are developed which enable one to find all solutions. The appearance of bifurcations and the difficulties in computing solutions past points of bifurcation are typical of finite beta plasma equilibrium problems and the methods proposed should have some general usefulness.