Temporal evolution of the inversion condition for the X-ray Balmer-α transition in ions of short-laser-pulse produced recombining plasmas

Abstract

When generating population density inversion and X-ray gain in the ions of a recombining plasma produced by short laser pulses it is essential to consider the energy level occupation as explicitly time-dependent. In the framework of a four-level model with time-dependent pumping terms, the inversion condition for the Balmer-α transition in H-like ions is derived in closed form, dependent, apart from specified initial conditions, on the atomic number Z, with the free-electron density Ne, the electron temperature Te, the Lyman-α escape probability E21, and the time t. In particular, at a short time after the initial time chosen near the time of the onset of recombination the Balmer-α inversion requires that Ne must be larger than some critical value depending on Te and Z.