Paschen’s law for a hollow cathode discharge

Abstract

An expression for the breakdown voltage of a one-dimensional hollow cathode discharge has been derived. The breakdown condition which corresponds to Paschen’s law contains, in addition to the first Townsend coefficient, and the secondary electron emission coefficient two parameters which characterize the reflecting action of the electric field and the lifetime of the electrons in the discharge. The breakdown voltage for a hollow cathode discharge in helium was calculated and compared to that of a glow discharge operating under similar conditions.