Thermo-field emission and the Nottingham effect

The thermo-field emission current and Nottingham effect are calculated for a wide range of temperatures (<or=6000 K), field strengths (<or=10¹⁰ V m^-1) and work function (2-5 eV) of the emitter. The ranges of validity of known approximations are given and it is shown that the simple approximation formulae commonly used may give incorrect results to several orders of magnitude. New easy-to-use fit formulae for the emission current, the Nottingham heat and some important functions in the theory of electron emission are proposed. The main application of these approximations lies in the field of numerical modelling of the development of arc cathode spots.