The Field Emission Initiated Vacuum Arc. II. The Resistively Heated Emitter

Electrical breakdown between clean metal electrodes in high vacuum was observed when the field current density at the single crystal tungsten cathode exceeded a critical value of the order of ${10}^8$ amperes/${\mathrm{cm}}^2$. At current densities just below the critical value, an electron emission process was observed which apparently involved both high temperature and high electric field. Calculations are presented for the emitter temperature increase due to the resistive mechanism for both the steady state and the transient solution. Emitter geometries used for the calculations approximated those obtained from electron micrographs of several emitters. The calculations show that the resistive heating was sufficient to melt the emitter at the critical current density, assuming the accepted value of the physical constants for the polycrystalline metal.