The influence of the cathode field enhancer on the conditions for the transition of electrons to the runaway mode

The influence of field enhancers (pointed protrusions on the cathode) on the conditions for the transition of electrons emitted from them to the runaway mode in high-pressure gas is studied analytically. It is shown that the classical directly proportional dependence of the critical runaway field on pressure is replaced by the weaker root dependence in the presence of protrusions of sufficient height. A simple criterion for electron runaway, taking into account the field distortion near the enhancers, is formulated. The minimum height of the protrusions required for a noticeable reduction in the runaway threshold is determined depending on the gas pressure.