The inversion condition for the X-ray Balmer-α transition in consideration of the modeled time-dependent Lyman-α reabsorption in a rapidly recombining laser-produced plasma

Abstract

The time-dependent condition for population inversion in the X-ray 3 → 2 transition in hydrogen-like ions of a recombining plasma produced by a short laser pulse is studied. The population densities of the energy levels are theoretically obtained in a collisional-radiative plasma model; the reabsorption of the 2 → 1 resonance line is taken into account via the escape probability. A new feature is first that the escape probability is treated as an explicitly time-dependent function,E21(r,t). On the basis of a four-level model of the H-like ions, the rate differential equations governing the time development of the population densities are considered, including time-dependent pumping terms and coefficients. Furthermore, specially modeling the time dependence ofE21(r,t), and assuming the other rate coefficients to be approximately constant with respect to time, via the explicit closed-form solution of the corresponding rate equations, the Balmer-α inversion condition ΔN32(r,t) > 0 is given in terms containing confluent hypergeometric functions and depends on rate coefficients, pumping terms, and explicitly on the time. For the free-electron densityNeof the recombining plasma, this relation means a condition depending on atomic and plasma state parameters and qualitatively changing in the course of time.