A self-consistent model of electron emission from metals at high current density

The authors present a model of electron emission from metals, which takes into account deviation of the electron distribution function from the Fermi equilibrium form inside the cathode under the emission effect. Using Grad´s method, the electron distribution function at the emission boundary is expressed consecutively in terms of its hydrodynamic moments (temperature, average velocity, heat flux density). As these hydrodynamic moments are caused by the emission itself and depend upon distribution function at the emission boundary, they need self-consistent determination. New easy-to-use formulae for the emission current density, emission heat flux and total energy distribution function of the emitted electrons are proposed. Consideration was made for a wide range of temperatures (⩽3500 K), field strengths (⩽1.5.10⁸ V cm^-1) and work function (3.0-4.5 eV) of the emitter. A considerable deviation from the Fowler-Nordheim´s theory results was found for high current density (>10⁹ A/cm²)