Statistical simulation of the energy spectra of field-emission electrons

Random energies of electrons that escape from the source in the course of field emission are simulated using energy spectra. A relationship of the random values of total energy and the energy related to the normal (with respect to surface) component of momentum is established. A family of quadrature formulas needed for the integration of the distribution density of particles is analyzed. A hypothesis on the compliance of selected random energies with desired distribution laws is statistically tested.