Zero-dimensional energy balance modelling of the CTX spheromak experiment

A zero-dimensional time-dependent energy balance model is used to explore the energy loss mechanisms of the CTX spheromak experiment at Los Alamos National Laboratory. A coupled set of model equations representing electron, ion, neutral, and impurity particle balance, electron and ion temperature, and magnetic field decay, are solved from initial values and the results compared to the time behaviour of experimentally measured average densities, temperature, and magnetic field. The energy balance model considers all the major atomic physics processes, especially the effects of radiation from a non-equilibrium distribution of impurity charge states evolving in time. The model includes the effects of a strong neutral-particle source which replaces by ionization the plasma being lost by a short particle confinement time. The neutral source is required in experiments to prevent the sudden termination of the discharge associated with low densities. A major new conclusion is that all the data from resistively decaying spheromaks can be effectively modelled, when the flux loss effects of a resistive flux conserver are also included, using plasma resistivity increased by a factor of 3.2+-0.6 over the Spitzer-Haerm value evaluated with the volume-average temperature. This factor appears to be constant for all discharges at all times. The analysis has determined that the power density associated with the particle replacement is the most important loss in the warm, non-radiation-dominated CTX spheromaks. (author)