Numerical validation of a self-absorption model for plasma radiation

This paper investigates the reliability of deducing the emissivity at the peaks of a self-reversed emission line from a simple empirical one-parameter approximation for the source function. The theory of spectral line shape formation owing to self-absorption in inhomogeneous axially symmetric plasma layers was reformulated and readily calculable expressions were obtained. In the case of self-reversed lines, the emissivity at the line maximum was calculated using different relative distributions for the densities of the absorbing and independently emitting atoms. The results were compared with those calculated using a source function described by a simple exponential law, the exponent of which is known as the inhomogeneity parameter. The obtained difference in the emissivity is less than 3%, which implies a difference in the (density-ratio) temperature between the line-levels better than 0.5%. Therefore, if the inhomogeneity parameter is known, the line emissivity can be deduced from the one-parameter approximation for the source function with reasonable accuracy. The effect of the structure of the plasma layer on the emissivity as well as the lateral dependence of the inhomogeneity parameter was also studied through numerical simulation