Evidence for a temperature law in non-LTE hot plasmas

Following a recent paper (Bauche J and Bauche-Arnoult C 2000 J. Phys. B: At. Mol. Opt. Phys. 33 L283), we investigate numerically the relation between the populations in the levels of an ionic configuration and individual level energies. It is found that for densities far from those for which local thermodynamic equilibrium is obtained, level populations still obey a decreasing exponential law for an effective temperature within the configuration. We begin by demonstrating the linear relationship between the collision-strength-weighted mean energies of the levels of a configuration and the energies of the final levels to which they are coupled. This linear relationship means that if the populations in the levels of the initial configuration are described by a distribution characterized by some temperature, then the populations in the levels of the final configuration are also characterized by the same distribution with a related temperature. We then look at the populations in the levels of the 3d⁴ and 3d³4p configurations of Fe V and Kr XV. We compute the populations in all levels of a large, detailed collisional-radiative model that involves nine configurations, then derive the effective temperatures for 3d⁴ and 3d³4p by fitting a line to the calculated level populations. We look at the cases of Fe V by itself and for Fe V coupled to equally detailed models of Fe IV and Fe VI, and similarly for Kr XV coupled to Kr XIV and Kr XVI. Finally, the effect of a Planckian radiation field on the level populations is considered.