Approximate atomic models for fast computation of the Fokker-Planck equation in fusion plasmas with high-Z impurities and suprathermal electrons

Abstract

With the choice of tungsten as a material for the ITER plasma facing components, the suprathermal electron interaction with non-fully ionized impurities emerged as an important issue in plasma modeling. Microwave heating and current drive systems, especially lower hybrid current drive, can generate a significant population of suprathermal electrons in the plasma. Also, in the case of the runaway electron generation and mitigation by massive gas injection, the collisions with impurities can have a significant impact on the electron drag force. A correct description of the fast electrons collisions with non-fully ionized impurities requires calculation of the atomic form factor. This can be done with ab initio models that are accurate, though time consuming in practical applications. In this paper, we compare existing approximations of the form factors, based on the Thomas-Fermi or Pratt-Tseng models. Ab initio density functional theory (DFT) calculations are used as a reference method to determine the accuracy of the compared models. Based on this analysis, we propose some modifications of the existing models, tuned with numerical parameter optimization, which provide a higher accuracy while maintaining a short computation time. These modifications include multiple exponents in the Pratt-Tseng model and fitting the parameters of the form factor equation to the DFT-based results. Some applications of the presented models to the calculation of the elastic and inelastic collision frequencies for Fokker-Planck equation are presented, showing a good agreement between the results obtained with the DFT method and the proposed models.