Computer simulation of discharge development under an induced toroidal electric field

This paper describes a computer simulation of the development of an electron avalanche under an induced toroidal electric field. The simulation was based on solving the continuity equations for electrons and positive ions. These equations were solved numerically by a two-dimensional treatment and the space-charge field was directly calculated using the net charges within a quarter of the torus in front of and behind the mesh point whose field was required. The time variation of the calculated instantaneous luminosity agreed well with the photomultiplier output of the corresponding experiment and the distribution of the particle densities in the discharge volume was obtained. Under the condition of a 'growing' avalanche (e.g. E 0 =86.8 V cm -1 and p=0.5 Torr) the space-charge field is negligible in the first half-circuit round the torus. When the avalanche develops near the end of the first full circuit, the radial space-charge field increases to a value giving an electron drift velocity comparable with the diffusion velocity. In the second circuit, a toroidal space-charge field of >25% of the induced field appears, and it promotes the discharge development.