Most realistic kinetic calculations for tokamak plasmas are now required to incorporate the effect of partially ionized high-Z elements arising either from uncontrolled influxes of metallic impurities, such as tungsten in high input power regimes or from mitigation of runaway electrons generated after possible major disruptions by massive gas injection. The usual electron–ion Fokker–Planck collision operator must therefore be modified, because all plasma atoms are not entirely ionized, as is the case for light elements. This represents a challenge, in order to perform fast but also accurate calculations, regardless of the type of element present in the plasma, but also their local levels of ionization while covering a wide range of electron energies in a consistent way, from a few keV to tens of MeV in plasmas whose electron temperature may itself vary from 10 eV to several keV. In this context, a unified description of the atomic models is proposed, based on a multi-Yukawa representation of the electrostatic potential calibrated against results obtained by advanced quantum calculations. Besides the possibility to improve the description of inner and outer atomic shells in the determination of the atomic form factor, this model allows one to derive analytical formulations for both elastic and inelastic scattering, which can then be easily incorporated in kinetic calculations. The impact of the number of exponentials in the description of the atomic potential is discussed, and a comparison with simple and advanced atomic models is also performed.
Effective ionization and emission rate coefficients of the helium atom in a plasma