A self-consistent model of electron emission from metals

We 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 the Grad method electron distribution function, the emission boundary is expressed consecutively in terms of its hydrodynamic moments: temperature, average velocity, heat flux density. These hydrodynamic moments are caused by the emission itself and thus need a self-consistent determination. New easy-to-use equations 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) and work function (3.0 to 4.5 eV) of the emitter. A considerable deviation from the Fowler-Nordheim (FN) theory was found at high current density (>10 ⁹ A/cm²)