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Internal relaxation, ionization and recombination in a dense hydrogen plasma I. Application of singular perturbation theory

The master equation which describes internal relaxation, ionization and recombination in a dense hydrogen plasma at constant electron temperature is developed. An approximate solution is obtained by using singular perturbation theory based on the assumption that the internal relaxation time is much shorter than the time for ionization. The results show that there are two distinct time regimes in the relaxation of a given initial nonequilibrium population distribution to the final equilibrium distribution. The first phase, a fast initial transient, involves an internal redistribution of the atoms to form a new distribution. This new distribution decays slowly during the second and much longer phase to the equilibrium distribution. Only during this period is there any significant change in the electron number density. After the initial transient period the rate coefficient for ionization is related linearly to the smallest eigenvalue of the relaxation matrix, the rate-quotient law holds approximately and the ordinary differential equation describing the behaviour of the electron number density is the usual phenomenological rate equation.