TEMPORAL EVOLUTION OF THE INVERSION CONDITION FOR THE X-RAY BALMER-ALPHA TRANSITION IN IONS OF SHORT-LASER-PULSE PRODUCED RECOMBINING PLASMAS

When generating population density inversion and X-ray gain in the ion s of a recombining plasma produced by short laser pulses it is essenti al to consider the energy level occupation as explicitly time-dependen t. In the framework of a four-level model with time-dependent pumping terms, the inversion condition for the Balmer-alpha transition in H-li ke ions is derived in closed form, dependent, apart from specified ini tial conditions, on the atomic number Z, with the free-electron densit y N-e, the electron temperature T-e, the Lyman-alpha escape probabilit y E(21), and the time t. In particular, at a short time after the init ial time chosen near the time of the onset of recombination the Balmer -alpha inversion requires that N-e must be larger than some critical v alue depending on T-e and Z.