Relaxed states in a spheromak with inhomogeneous boundary fields

Force-free equilibrium solutions of the MHD equations in a spherical geometry for the case in which magnetic flux crosses the boundary of the containing vessel are considered. The main motivation is to model more faithfully actual spheromak experiments in the laboratory, for which boundaries are unlikely to be magnetic surfaces. It is shown how a general inhomogeneous boundary field may be constructed from individual components. In particular, the cases of a boundary field of dipolar form and one of quadrupolar form are considered. Solutions for fields embedded in point or ring electrodes using the 'general solution', some of which can be used to model experiments such as the PS-1- or CTX-type spheromaks are discussed. (author)