A one-dimensional fluid model is developed for a numerical study of pre-ionization in a tokamak device under a given external inductive field. The calculation space is a magnetic field line connecting the bottom and the top limiters, and the spatial profiles of ion and electron densities and their time evolutions are calculated, assuming density growth by the Townsend avalanche. It was found that at a low initial density, electrons are evacuated and exponential growth can be stopped (i.e. stagnation phase), and at a high density, formation of an ambipolar diffusion state may suppress further avalanche by compensating the external inductive field. The numerical study revealed that these two obstacles for pre-ionization can be avoided or mitigated under a certain condition. A high ion impact secondary electron emission efficiency at the limiter, a long field line length and a large Townsend's coefficient are preferable to avoid the stagnation phase or to resume growth from the stagnation phase. The ambipolar diffusion state can be mitigated or avoided using the following four mechanisms: drift induced diffusion, and curvature drifts, a high ion impact secondary electron emission efficiency and AC inductive field. Among them, only the first is practically useful in weak inductive field large devices. Various analytical expressions describing these behaviors and the conditions for a successful pre-ionization are obtained.
Three-dimensional first principles simulation of a hydrogen discharge