| Abstract: | Starting from the conventional theory of thermo-field emission of electrons from metal surfaces, the range of validity and the errors of several approximate emission formulae are examined that are additive or harmonic combinations of the limiting thermionic (Richardson) and field emission (Fowler—Nordheim) equations. An optimization of such kinds of equations results in the simple dependence (for example)  (iTF electron current density, T temperature, F field strength, k, A, B etc. are constants), or  (dependent on only one variable Y = T + β′F β′ = const.). If the emission equations are applied to arc cathodes, both T and F must be expressed as functions of the ion current (Ii) and the ion current density (ji); a simple interpolating formula of the electron current density je adapted to numerical results in the case of Cu cathodes becomes  (ā, B?, C?: constants). |
