Energy Distribution of Electrons in High Frequency Gas Discharges

In this paper an equation for the energy distribution of electrons in a gas subject to a spatially constant high frequency field is obtained. The domain of applicability of the equation is limited (a) to situations in which the densities of electrons, ions, and excited molecules are very small compared to the density of normal molecules, (b) to electron energies such that the elastic collision cross section for electron-molecule collisions is large compared to the inelastic cross section, (c) to linear dimensions of the discharge region large compared to the mean free path for elastic collision, and (d) to frequencies of the impressed electric field larger than a certain lower limit determined by the pressure, type of gas, and linear dimensions of the discharge region. Methods for the solution of the distribution equation are presented in Section 5; simplified examples illustrating these methods are given in Section 7. The distribution equation for the d.c. case is also derived (Section 6); it agrees with those obtained by other authors. A comparison of the high frequency and d.c. distribution equations suggests a useful correlation between the two cases.