A fully relaxed helicity balance model for an inductively driven spheromak

Abstract

Magnetic helicity balance and a fully relaxed Taylor-state model are shown to predict the magnitude of sustained equilibrium current in an inductively driven spheromak. The Helicity Injected Torus with Steady Inductive drive (HIT-SI) [T. R. Jarboe et al., Phys. Rev. Lett. 97, 115003 (2006)] forms and sustains spheromaks using two inductively driven helicity injectors. By assuming helicity is injected at a rate 2VΨ, and only decays through Spitzer resistivity using Te measured with a Langmuir probe, the magnitude of the sustained equilibrium current is predicted with no fitting parameters. The model correctly predicts a threshold helicity injection rate for spheromak formation. Although the experimental results suggest a higher effective helicity dissipation rate by a factor of ∼1.37 compared to the Spitzer value, the prediction is still within the uncertainties of the measured parameters.