Analytical model of cold-cathode breakdown in helium at extremely high electric field and low pressure

An analytical model is developed for gas ionization breakdown at extremely high values of reduced electric field (the ratio $E/n$ of electric field to gas density) between parallel-plate electrodes in helium. The value of $E/n$ under investigation \quad varies in the range of 70--6600 kTd (1~kTd $=$ 10$^{\mathrm{-18}}$ Vm$^{\mathrm{-2}})$ for \textit{pd }\textasciitilde \quad 0.5 Torr-cm, where $p$ is the gas pressure and $d$ is the electrode separation. The model includes anisotropic scattering for all species and fast neutral atom backscattering at electrodes, as well as fast-neutral impact ionization. The results are compared to those from a detailed Particle-In-Cell/Monte Carlo (PIC/MCC) simulation (Liang Xu et. al., “Investigation of the Paschen Curve for Helium in 100-1000 kV Range”), and to experimental measurements. Analytical model results are sufficiently accurate for $E$/$n$ \textasciitilde 1000~kTd if the model treats the electrons as a single beam and assumes that charge exchange is the dominant collision process which determines the local distributions of ions and fast neutral atoms.