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 gener ally lie between 0.5 and 1, with a divergence on the separatrix since the o pen field lines carry current from the injector. The safety factor can be s ingle or double valued, depending on the current profile. The modelling pre dicts that there are no mode rational surfaces with m = 1 except very near the separatrix; this is expected to determine the unstable resistive tearin g modes associated with the dynamo which drives the discharge current. The resulting low magnetic shear has a beta (similar to 2%) at the Mercier limi t, which can be improved by current profiles differing significantly from t he Taylor state or by other effects such as plasma flow. Examples are prese nted for the Sustained Spheromak Physics Experiment recently constructed at LLNL.