Breakdown of the quasistatic approximation at high densities and its effect on the heliumlike Kα complex of nickel, iron, and calcium

Recent work to include R-matrix data within a larger model comprised mostly of distorted-wave and plane-wave Born data has resulted in the general spectral modeling (GSM) code. It employs a quasistatic approximation, a standard, low-density methodology that assumes the ionization balance is separable from a determination of the excited-state populations that give rise to the spectra. GSM further allows for some states to be treated statistically as contributions to effective rates, instead of being included explicitly in the kinetics model. While these two approximations are known to be valid at low densities, this work investigates using such methods to model high-density, non-LTE emission spectra and determines at what point the approximations break down by comparing to spectra produced by the Los Alamos National Laboratory code ATOMIC which makes no such approximations. As both approximations are used by other astrophysical and low-density modeling codes, the results should be of broad interest. He-like Kα emission spectra are presented for three elements, Ni, Fe, and Ca, in order to gauge the effect of both the statistical methods and the ground-state-only, quasistatic approximation employed in GSM. This work confirms that at and above the temperature of maximum abundance of the He-like ionization stage, the range of validity for both approximations is sufficient for modeling the low- and moderate-density regimes one typically finds in astrophysical and magnetically confined fusion plasmas. However, a breakdown does occur for sufficiently high densities; we obtain quantitative limits that are significantly higher than previous works. Additionally, this work demonstrates that, while the range of validity for both approximations is sufficient to accurately predict the density-dependent quenching of the z line, the approximations begin to break down at higher densities. Thus, these approximations should be used with greater care when modeling high-density plasmas such as those found in laser-driven inertial confinement fusion and electromagnetic pinch devices