Effective charge state

The effective charge state of ions in a plasma $Z_{eff}$ is important to many physical processes.

$Z_{eff}={\frac {\sum _{i}n_{i}Z_{i}^{2}}{\sum _{i}n_{i}Z_{i}}}$

where $n_{i}$ is ion density for species $i$ and $Z_{i}$ is the charge state of species $i$.

$\sum _{i}n_{i}Z_{i}=n_{e}$ by quasi-neutrality, so

$Z_{eff}={\frac {\sum _{i}n_{i}Z_{i}^{2}}{n_{e}}}$

$Z_{eff}$ would be 1 for a plasma composed purely of hydrogen isotopes, but in practice is always higher due to impurities from plasma facing components. $Z_{eff}=2$ is a common baseline assumption for carbon-walled tokamaks, and some multi-device databases are restricted to cases with low-ish $Z_{eff}$, making their scaling laws valid for $Z_{eff}<3$ and questionable for higher $Z_{eff}$. The 1999 ITER physics basis estimates $Z_{eff}=1.8-1.9$; higher than this will dilute the fuel too much.