Physics-based description of gas breakdown

This paper develops an efficient method for simulation of breakdown in a gas, which explicitly makes use of the real underlying physics, in a case where standard numerical schemes are likely to fail. We develop a 'time-dependent capacitor model' (TDCM) for 2D or 3D, which ensures that the ionization rate is consistent with energy conservation and which disallows almost all numerical diffusion (and hence allows larger (Δx, Δt)). To avoid spurious ionization in the TDCM, density is only added in a cell when the density and electric field are high enough so that the density could physically grow to the expected final density within the cell. Numerical diffusion is negligible in the TDCM, in part because we only inject density into cells/capacitors when enough time has elapsed for density to be physically present. The direction of injection is controlled, so if, for example, density from cell [i, j] in reality moves to cell [i ± 1, j ± 1], it goes there directly, giving a physically correct direction of propagation. A simple scheme for accelerating convergence, exploiting the very different time scales which arise, is also discussed