  The General Spectral Modeling (GSM) code employs the quasi-static
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 also allows for some states to be treated only as
contributions to effective rates. 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 LANL 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 K$\alpha$ emission spectra are presented for Ni, Fe,
and Ca, in order to gauge the effect of both approximations 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 high densities; we obtain quantitative limits that are
significantly higher than previous works. This work demonstrates that, while
the range of validity for both approximations is sufficient to predict the
density-dependent quenching of the z line, the approximations break down at
higher densities. Thus these approximations should be used with greater care
when modeling high-density plasmas such as those found in inertial confinement
fusion and electromagnetic pinch devices.
