Exact solution of rate equations for afterglow with ambipolar diffusion and electron attachment

The system of three coupled differential rate equations governing the growth and decay of positive and negative ion and electron concentrations in an afterglow with ambipolar diffusion and electron attachment is solved in the sense of reducing the problem to the solution of a single algebraic (albeit transcendental) equation. Approximate analytical solutions of this algebraic equation are obtained which are accurate well before and well after a certain transition time, t d , when the build-up of negative ions partially frees the electrons from charge neutrality constraint and allows them to diffuse more rapidly than before. Exact numerical solutions of this algebraic equation are defined in terms of iterative sequences.