NIMROD Simulations of HIT-SI Plasmas

We present NIMROD simulation studies of current-drive, magnetic reconnection and relaxation behavior of the HIT-SI experiment. HIT-SI (Steady Inductive Helicity Injected Torus) is a spheromak that uses two semi-toroidal injectors to provide steady inductive helicity injection (SIHI). SIHI produces and sustains a spheromak by generating poloidal flux using relaxation current drive. The helicity injectors of the experiment are modeled as flux ($\psi_{\rm{inj}}$) and current ($I_{\rm{inj}}$) boundary conditions. Our study uses a zero $\beta$ resistive MHD model with uniform density. Lundquist number S and injector lambda, $\lambda_{\rm{inj}}(=\mu_{0}I_{\rm{inj}}$/$\psi_{\rm{inj}})$ characterize the parameter space. $S\left(=\sqrt{\frac{\mu_{0}}{\rho}}\frac{B}{2\pi R_{0}\eta\lambda_{sp}^{2}}\right)$ is the ratio of resistive diffusion to Alfv$\acute{e}$n transit time, $\rho$ and $\eta$ are the plasma density and resistivity, $R_{0}$ is the magnetic axis and $\lambda_{sp}(=\mu_{0} j_{//}$/$B)$ is the spheromak lambda, 10.3 m$^{-1}$ for HIT-SI. For our current simulations we set $\lambda_{\rm{inj}}$=30, and perform a scan in $S$ for low values ($\sim10-100$). Our results to date at $S=$ 22 and 35 show little relaxation during sustainement but growth of the $n$=0 magnetic energy and an increase in plasma current during the decay phase. Upon completion of this study at $\lambda_{\rm{inj}}$=30 we will repeat the resistive MHD simulations at a lower $\lambda_{\rm{inj}}$ ($\sim$ 20) in order to chart the relaxation behavior as a function of $\lambda_{\rm{inj}}$.