MHD equilibria in a spheromak sustained by coaxial helicity injection*

Spheromaks sustained by coaxial helicity injection differ from unsustained spheromaks in the profiles of the ratio of current to magnetic field and of the safety factor. Ideal MHD modelling with Taylor relaxed profiles in the injector predicts that the safety factor in the confined region will generally lie between 0.5 and 1, with a divergence on the separatrix since the open field lines carry current from the injector. The safety factor can be single or double valued, depending on the current profile. The modelling predicts that there are no mode rational surfaces with m = 1 except very near the separatrix; this is expected to determine the unstable resistive tearing modes associated with the dynamo which drives the discharge current. The resulting low magnetic shear has a beta ( ~ 2%) at the Mercier limit, which can be improved by current profiles differing significantly from the Taylor state or by other effects such as plasma flow. Examples are presented for the Sustained Spheromak Physics Experiment recently constructed at LLNL.