looking at the eigenvectors. For a given $T$, the eigenvector corresponding to the minimum $n_{\mathrm{e}}t$ eigenvalue is a linear combination of the abundances from the lowest charge states. The eigenvector corresponding to the maximum $n_{\mathrm{e}}t$ is mainly made up of components from the charge states that are abundant in CIE at that temperature. Thus, EIMI influences the ion balance by significantly increasing the ionization rate from the lowest charge states. However, for charge states that are already close to equilibrium, the EISI cross sections are larger and so EIMI has little additional influence.

Figure \[fig:mintime\] can be compared to Figure 2 of @Smith:ApJ:2010, where a similar calculation was carried out that included only single-ionization rates. There is a clear resemblance between the shape of the dependence of the scale on temperature. However, there are differences in magnitude. At low temperatures these differences are almost an order of magnitude, while at high temperatures the two calculations are nearly the same. These differences are probably due to the different ionization rate coefficients used in the calculations. @Smith:ApJ:2010 used the ionization and recombination rate coefficients from @Mazzotta:AAS:1998, whereas we have used those from CHIANTI [@Dere:AA:2007; @Landi:ApJ:2013]. @Bryans:ApJ:2009 performed CIE calculations using the same 