A Study of the Relevance of Simple Solutions to Nonlinear Rate Equations With Time-Varying Coefficients

The possibility of accounting for time-dependent coefficients in a non-linear rate equation, including a source term, is studied in circular cylindrical geometry. It is shown that the equation can be transformed to a form which allows for a simple particular solution, provided a certain combination of the time-dependent coefficients is a constant, or nearly a constant. The relevance of the solutions for describing the evolution of a plasma in the ionization phase is considered.