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 initiate 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.
Employment of non-inductive plasma start-up techniques would considerably simplify the design of a spherical tokamak fusion reactor. Transient coaxial helicity injection (CHI) is a promising method, expected to scale favorably to next-step reactors. However, the implications of reactor-relevant parameters on the initial breakdown phase for CHI have not yet been considered. Here, we evaluate CHI breakdown in reactor-like configurations using an extension of the Townsend avalanche theory. We find that a CHI electrode concept in which the outer vessel wall is biased to achieve breakdown, while previously successful on NSTX and HIT-II, may exhibit a severe weakness when scaled up to a reactor. On the other hand, concepts which employ localized biasing electrodes such as those used in QUEST would avoid this issue. Assuming that breakdown can be successfully attained, we then apply scaling relationships to predict plasma parameters attainable in the transient CHI discharge. Assuming the use of 1 Wb of injector flux, we find that plasma currents of 1 MA should be achievable. Furthermore, these plasmas are expected to Ohmically self-heat with more than 1 MW of power as they decay, facilitating efficient hand-off to steady-state heating sources. These optimistic scalings are supported by TSC simulations.