The parameters of electron avalanches and the runaway of electrons in strong electric fields

A simple hydrodynamic model is suggested for the calculation of parameters of electron avalanches in a strong field, where the mean energy of electrons exceeds the ionization energy; this model is used to calculate the electron drift velocities and the coefficient of ionization and intensity of electric fields for cesium, helium, and xenon atoms in a wide range of variation of the mean energy of electron flow. It is demonstrated that, in a strong field, inelastic collisions make a determining contribution both to the loss of energy by electrons and to the loss of momentum. A criterion is suggested for the determination of the conditions of runaway of electrons. The dependence is obtained of the voltage, at which the runaway of electron with mean energy occurs, on the field intensity, mean energy, and the value of $pd$.