Development of a general thermal-field-photoemission model and its relation to current density, emittance, and beam brightness

We have developed a methodology that combines the three emission mechanisms into one framework based on analytical, rather than numerical, methods. An account of the development shall be given. The approach demarcates "field-like" and "thermal-like" regimes dictated by which expansions of the current density integral dominate. Methods to regroup the expansions are shown, and the result exhibits a compelling symmetry as a function of the parameters used to characterize emission. The derivation of an equation for emittance and beam brightness from the methodology will be applied to a photocathode in particular.