Applications of Recombination

Abstract

This paper is concerned with recombination of free electrons with atomic ions. The applications of recombination to be described are in the study and analysis of various types of ionised plasmas. Although other recombination processes such as charge exchange can be very important in, for example, neutral beam heated plasmas they are not the subject of discussion in this work. In all studies of plasmas it is certainly necessary to know the ionisation state of the species in the plasma and probably also the total radiated power. We might introduce the term, ‘the standard model’, to describe a plasma collisionally excited by electrons, in equilibrium, at low density, in which free electron recombination balances collisional ionisation. That is $${N_e}{N^{(z + 1)}}\alpha (z + 1 \to z) = {N_e}{N^{(Z)}}S(z \to z + 1) $$ (1) with N e , the electron density, N (z), the number density of the element X in charge state z, α, the recombination coefficient and S the ionisation coefficient. In the standard model recombination does not take place on boundary surfaces and charge transfer processes with other atoms or ions do not play a role. The α and S apply in a non- stationary state as $$\begin{gathered}\frac{{\partial {N^{(z)}}}}{{\partial t}} + \nabla .{\Gamma ^{(z)}} = {N_e}{N^{(z - 1)}}S(z - 1 \to z) \hfill \\- Ne{N^{(z)}}\left\{ {\alpha (z \to z - 1) + S(z \to z + 1)} \right\} \hfill + {N_e}{N^{(z + 1)}}\alpha (z + 1 \to z) \hfill \end{gathered} $$ (2)