charge state distribution (CSD) of the plasma. The CSD is determined by the rates of ionization and recombination. In collisionally ionized plasmas, the ions are ionized by electron-impact ionization (EII). The electron-ion recombination is dominated by dielectronic recombination (DR) and radiative recombination (RR). These various processes have been reviewed by @Muller:Book:2008.

An electron-ion collision can also cause electron-impact multiple ionization (EIMI) — the ejection of multiple electrons due to a single collision. This process has generally been ignored in ionization balance calculations because, for a given charge state, multiple ionization usually becomes significant only at temperatures so high that the fractional abundance of that charge state is small [@Tendler:PhysLett:1984]. However, it has been argued that multiple ionization may become important in dynamic systems where the ions are suddenly exposed to higher electron temperatures [@Muller:PhysLett:1986]. Such non-equilibrium could occur, for example, in solar flares [@Reale:ApJ:2008; @Bradshaw:ApJS:2011], supernova remnants [@Patnaude:ApJ:2009], or merging galaxy clusters [@Akahori:PASJ:2010]. Nevertheless, calculations of these dynamic events have ignored multiple-ionization processes.

One reason for not considering multiple ionization, is that very little EIMI data exist. To theoretically calculate even double-ionization cross sections is very difficult. This is because the problem requires considering at least four charged particles in 