Systematics of inner-shell photo-ionization X-ray lasers with constant pump rates

Population-rate equations are analytically solved for constant pump rates. Conditions for population inversions are developed for this simplified case. Numbers appropriate for inner-shell photo-ionization of magnesium and neon are used. These allow back-of-the envelope calculations for predicting lasing duration. Pump-rate thresholds are also given which permit lasing for the duration of the pumping. Blackbody-source temperatures associated with such pump rates are calculated. A method of using the solution of the small-signal population-rate equations to determine the saturated intensity when the lower lasing level has a decay channel is given. This method is applied to the case of constant pump rates. An analytic expression for the saturated intensity is developed for this case.