Evaluation of the Emission Current Density from Non-refractory Cathodes of Electric Arcs by means of the Transfer Matrix Method

The Transfer Matrix Method for solving the steady-state Schrödinger equation is applied in order to evaluate the emission current density from non-refractory cathodes. The transmission probability of the potential barrier is obtained without any analytical approximations since the method is applicable to arbitrary barrier shapes. The Fermi-Dirac distribution for the free electrons in the metal is used as a supply function. The emission current is obtained by a numerical integration. The results, obtained for a work function of the cathode material of 4.5 eV over a wide range of values of the surface temperature and the electric field strength, clearly show that with the increase of the electric field strength, the deviation from values obtained by the classical approximation is growing. Furthermore, a significant enhancement of the emission current is obtained as a result of ion presence near the metal surface.