On the bunching effect of electrons in spatially periodic resonance fields

Abstract

The spatial relaxation of the electron distribution function (EDF) in uniform and spatially periodic electric fields is considered. The analysis is based on the Boltzmann kinetic equation containing spatial gradients and operators of elastic and inelastic collisions. We demonstrate that the presence of a discrete spectrum of excited states due to the process of electron back scattering leads to the appearance of a quasicontinuous flux of energy in the elastic region, similar to the flux created by means of energy loss in elastic impacts. In the absence of channels of energy dissipation connected with energy loss in elastic impacts and in the presence of several excited states, information about the initial EDF injected in a field of arbitrary configuration, can be transmitted over an unlimited distance.The process of the relaxation has the nature of undamped oscillations. The introduction of channels of energy dissipation results in a damped oscillatory relaxation character of the EDF injected into a uniform field and in the establishment of a homogeneous EDF in this field. The relaxation of an EDF injected into a spatially periodic resonance field results in the distribution function having specific maxima which change in energy and coordinates along the resonance paths in accordance with the potential distribution (the so-called bunching effect). This effect can be used for the interpretation of EDF formation in S- and P-striations in inert gas discharges at low pressures and currents.