Simulations of SSPX Sustainment -- Toward a Standard Model for Spheromaks

SPHERE simulations calibrated to CTX are shown to predict the correct temperature (0.12 KeV) for SSPX sustainment Shot 4624. Agreement with the temperature suggests that the Rechester-Rosenbluth thermal diffusivity included in the SPHERE heat transport equation is essentially correct. Substituting parallel heat loss as suggested by NIMROD calculations gives a temperature four times too low, while omitting Rechester-Rosenbluth transport but retaining ion classical transport gives a temperature that is 50% too high. Less certain is the magnetic buildup equation in SPHERE representing the spheromak load as a resistance adjusted to give the correct magnetic field--as is essential to obtain the correct temperature by ohmic heating. While extrapolation for long pulses using the Shot 4624 resistance does give higher magnetic field and higher temperature, the actual resistance during sustainment is still highly uncertain. In Section 6, we present a new resistance model in rough agreement with Shot 4624, but much work remains to be done. Understanding the spheromak resistance during sustainment is the main theoretical challenge for the model