Effects of collisions on impurity transport driven by electrostatic modes

S Buller,P Helander

doi:10.1017/s0022377820000537

Abstract

The turbulence-induced quasi-linear particle flux of a highly charged, collisional impurity species is calculated from the electrostatic gyrokinetic equation including collisions with the bulk ions and the impurities themselves. The equation is solved by an expansion in powers of the impurity charge number $Z$ . In this formalism, the collision operator only affects the impurity flux through the dynamics of the impurities in the direction parallel to the magnetic field. At reactor-relevant collisionality, the parallel dynamics is dominated by the parallel electric field, and collisions have a minor effect on the turbulent particle flux of highly charged, collisional impurities.

Highlights

Impurities are always present in fusion plasmas, either due to unavoidable plasma– wall interaction, or through deliberate impurity injection
Far less has been done to study turbulent particle transport – either of impurities or of the bulk ions and electrons – and most of these studies rely on quasi-linear transport theory (Mikkelsen et al 2014)
We have shown that impurity self-collisions have no effect on the quasi-linear particle flux of highly charged impurities

Summary

Introduction

Impurities are always present in fusion plasmas, either due to unavoidable plasma– wall interaction, or through deliberate impurity injection. The experimental observations may be consistent with recent theoretical calculations of the transport due to electrostatic turbulence (Helander & Zocco 2018), which, for heavy species, give transport coefficients independent of the impurity charge and mass (Angioni et al 2016; Helander & Zocco 2018). Previous analytical work has shown that collisions with the impurities themselves do not significantly affect the impurity flux in tokamaks (Pusztai et al 2013) In the limit where finite Larmor-radius effects can be neglected, we can use the expressions for the Fokker–Planck collision operator from collisional transport theory directly on gz This is justifiable for the impurities, which have a small. It is instructive to consider the limit where Czz[gz] Czi[gz], to demonstrate why impurity–impurity collisions cannot affect the impurity flux

Impurity–impurity collisions only

Effects of impurity–ion collisions

Summary and conclusions