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Abstract
To investigate the influence of radiation reabsorption on the level populations of ions in an expanding laser-produced plasma of intermediate density, we start with the system of rate equations for the population densities coupled with the line-radiation transport equation, the dynamical Doppler effect due to the differential macroscopic velocity field included. In a physically motivated approximation, for spatially varying absorption and emission, and general three-dimensional plasma geometry, an integral equation describing the effect of Lyman-a radiation reabsorption on the spatial behavior of the population density of the upper resonance level is derived. Assuming a sufficiently large velocity gradient so that the Doppler-induced frequency shift dominates the linewidth, after asymptotically evaluating the frequency integral involved in the kernel we are led to a simplified integral equation exhibiting the reduction of radiation reabsorption by Doppler decoupling. In particular, in the case of a cylindrical, radially expanding laser plasma we discuss this Fredholm equation for the reabsorption-influenced population density.
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