Abstract
The various analytic approaches to the solution of the electron Boltzmann equation in non-uniform glow discharge plasmas in atomic gases are presented. For slow electrons with kinetic energy w> epsilon 1, the approximation of continuous energy losses can be used. The simplest approximation corresponds to the neglect of scattering. In this case, simple analytic expressions for the distribution of the fast electrons, for the multiplication factor and so on can be derived, and the structure of normal and abnormal cathode regions for plane and hollow cathodes can be analysed.