Calculation of effective work-function and average cooling energy of electrons emitted from an arc cathode root

This paper proposes several equations to calculate the effective work-function and the average cooling energy of electrons emitted from an arc cathode root in both the high temperature region and the high electric field region. It is shown that the average cooling energy consists of the effective work-function and the kinetic energy carried by escaping electrons due to their motion normal to the cathode surface. The numerical results of average cooling effect agree well with Lee's results (1960) which were calculated under other assumptions. From numerical solutions of these simple equations, it is evident that the average cooling energy and the effective work-function are strongly dependent on the temperature and the electric field at the position of electron emission, and the normal work-function of the cathode material.