Extended MHD Stabiliy Calculations of Spheromak Equilibria

Linear extended MHD calculations of spheromak equilibria in a cylindrical flux conserver are performed using the NIMROD code (Sovinec et al, JCP 195, 2004). A series of Grad-Sharfranov equilibria are generated with $\beta$ ranging from $0.4\%$ to $4.2\%$, corresponding to peak electron temperatures ranging 50 to 300 eV. These equilibria use a $\lambda$ profile representative of SSPX shot 14590, which measured a peak electron temperature of 325eV (McLean et al, POP 13, 2006). Resistive MHD calculations find that the $\beta = 0.4\%$ case is unstable to resonant resistive interchange modes with $\gamma \tau_A \leq 2.3\%$. These modes transition to ideal interchange as the equilibrium pressure is increased. Growth rates as large as $\gamma \tau_A = 20\%$ are calculated for the $4.2\%$ $\beta$ case. Calculations including ion-gyroviscosity show a minimal reduction of growth rate. Effects from including the Hall and Electron pressure terms in Ohm's Law and the cross-field diamagnetic heat flux are investigated. Results of related nonlinear simulations are also presented.