Some improvements concerning the modelling of the cathodic zone of an electric arc (ion incidence on electron emission and the `cooling effect')

An accurate numerical calculation of the electron emission using the Numerov integration method of the Schrödinger eigenvalue equation is presented. Such a calculation eliminating the WKB approximation and the use of elliptic functions can give the corrections that have to be applied to the well-known Fowler - Nordheim [1] or Murphy and Good results [2]. Because the very intense electron emission that takes place in the cathode spot is greatly affected by those corrections, we give the results of the calculation of the Nottingham effect, which plays an important role in the energy balance equation at the cathode surface. Finally, an exploratory study is presented on the influence of ions within a distance of a few tens of ångström units in front of the cathode surface on electron emission.