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.