Three regimes of high-voltage breakdown in helium

A quasi-analytical model was developed to map out the low-pressure (left-hand) branch of the Paschen curve at very high voltage when electrons are in the runaway regime and charge exchange/ionization avalanche sustained by ions and fast neutral atoms becomes important. The model was applied to helium gas between parallel-plate electrodes, at potentials ranging in magnitude between 10 and 1000 kV. The respective value of reduced electric field E/n varied in the range of 50-6000 kTd (1 kTd = 10^-18 Vm²), with reduced density nd (where n is the gas density and d is the inter-electrode distance) on the order of 10²⁰ m^-2. Three regimes of the breakdown have been identified according to the relative share of impact ionization by electrons, by ions, and by fast neutrals. The analytically derived Paschen curve is compared to those obtained with a detailed particle-in-cell/Monte Carlo simulation, and also through experimental measurements (L Xu, A V Khrabrov, I D Kaganovich and T J Sommerer 2017 Phys. Plasmas 24 093511). The model provides accurate predictions for E/n up to ∼10³ kTd, constrained by availability and quality of required input data.