Application of Townsend avalanche theory to tokamak startup by coaxial helicity injection

The Townsend avalanche theory is employed to model and interpret plasma initiation in NSTX by Ohmic heating and coaxial helicity injection (CHI). The model is informed by spatially resolved vacuum calculations of electric field and magnetic field line connection length in the poloidal cross-section. The model is shown to explain observations of Ohmic startup including the duration and location of breakdown. Adapting the model to discharges initiated by CHI offers insight into the causes of upper divertor (absorber) arcs in cases where the discharge fails to start in the lower divertor gap. Finally, upper and lower limits are established for vessel gas fill based on requirements for breakdown and radiation. It is predicted that CHI experiments on NSTX-U should be able to use as much as four times the amount of prefill gas employed in CHI experiments in NSTX. This should provide greater flexibility for plasma start-up, as the injector flux is projected to be increased in NSTX-U. (paper)