Joule heating of an emitter on the cathode surface by field electron emission current with an account of the nonisolation of the apex

Abstract

This work is devoted to the investigation of the nonstationary problem of the thermal conductivity of a nanoemitter on the surface of a massive copper cathode when a field electron emission current passes through it. At the same time, the dependence of volume resistivity, thermal conductivity on temperature, and size effects have been taken into account. The influence of the Nottingham effect has been considered. The dependence of the equilibrium temperature of the emitter apex on the field enhancement factor for different values of the electric field strength has been found. Based on the assumption that the initial stage of the breakdown begins when the emitter apex melts, the conditions for the occurrence of a vacuum breakdown and the influence of the Nottingham effect have been analyzed.