View source for Effective charge state

The effective charge state of ions in a plasma <math>Z_{eff}</math> is important to many physical processes.
:<math>Z_{eff} = \frac{\sum_i n_i Z^2_i}{\sum_i n_i Z_i}</math>
where <math>n_i</math> is ion density for species <math>i</math> and <math>Z_i</math> is the charge state of species <math>i</math>.

<math>\sum_i n_i Z_i = n_e </math> by quasi-neutrality, so
:<math>Z_{eff} = \frac{\sum_i n_i Z^2_i}{n_e}</math>
<math>Z_{eff}</math> would be 1 for a plasma composed purely of hydrogen isotopes, but in practice is always higher due to impurities from plasma facing components.
<math>Z_{eff}=2</math> is a common baseline assumption for carbon-walled tokamaks,<ref>[[doi:10.1088/0029-5515/39/11Y/338|T.N. Carlstrom, et al., Nucl. Fusion '''39''' (1999) 1941]]</ref><ref>[[doi:10.1103/PhysRevLett.107.215001|T. Eich, et al., Phys. Rev. Lett. '''107''' (2011) 215001]]</ref> and some multi-device databases are restricted to cases with low-ish <math>Z_{eff}</math><ref>[[doi:10.1063/1.866892|ITER Physics Basis Chapter 2: Plasma confinement and transport, Nucl. Fusion '''39''' (1999) 2175]]</ref>, making their scaling laws valid for <math>Z_{eff}<3</math> and questionable for higher <math>Z_{eff}</math>.
The 1999 ITER physics basis estimates <math>Z_{eff}=1.8-1.9</math>;<ref>[[doi:10.1088/0029-5515/39/12/301|ITER Physics Basis Chapter 1: Overview and summary, Nucl. Fusion '''39''' (1999) 2137]]</ref><ref>[[doi:10.1088/0029-5515/39/12/304|ITER Physics Basis Chapter 4: Power and particle control, Nucl. Fusion '''39''' (1999) 2391]]</ref> higher than this will dilute the fuel too much.

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