$\lambda_{j}$ of the diagonal matrix. Thus, the density-weighted timescales for equilibration are given by $1/\lambda_{j}$ in units of $n_{\mathrm{e}}t$. Note that the eigenvectors do not generally correspond to individual elements of $\vec{y}$ (i.e., charge states), but are instead linear combinations of those elements.

Figure \[fig:mintime\] presents the results for the minimum $1/\lambda_{j}$ as a function of temperature. This represents the scale $n_{\mathrm{e}}t$ for any significant changes in the ion population to occur. The bottom panel of Figure \[fig:mintime\] presents the ratio of the scale when EIMI is included versus when it is ignored. These results show that EIMI causes the plasma to evolve faster at high temperatures. For example, for $T=10^{7}$ K the CSD begins to change about 10% faster if EIMI is included in the calculation than when it is ignored. In contrast, the maximum $1/\lambda$ at a given temperature are nearly identical whether or not EIMI is considered in the calculation. Thus, EIMI causes changes to begin sooner, but the total time it takes for the system to asymptote to equilibrium is not significantly different when considering EIMI.

The reason the minimum $n_{\mathrm{e}}t$ is more sensitive to including EIMI channels compared to the maximum can be seen by 