On the classical similarity solutions of the continuity equation for electrons in microwave-afterglow plasmas

Abstract

In a recent work by the author, a model for the continuity equation for electrons in microwave-afterglow plasmas has been suggested. This equation reflects the dependence of the ambipolar diffusion and dissociative recombination coefficients on the number density of electrons. Here, Lie group analysis is used to generate classical similarity solutions of this equation. It is found that the general family of the group of characteristic trajectories not only leads to a classical similarity solution, already found by other ways, but also reveals a special class of similarity solutions. The existence and uniqueness for the solution of the ordinary differential equations obtained are proved. A qualitative behaviour of this solution is analysed. Also, some special forms of these equations are exactly solved. It is found that the solution of the continuity equation for the number density of electrons in the experiments carried out by Penetrante et. al (1986) and Hdang et al (1975) decreases or increases.