Numerical Implementation of the Improved Sugama Collision Operator Using a Moment Approach

TL;DR

This paper presents a numerical implementation of the improved Sugama collision operator using a gyro-moment approach, demonstrating its enhanced accuracy in approximating Coulomb collisions in gyrokinetic simulations.

Contribution

The paper introduces a novel numerical implementation of the improved Sugama collision operator using a gyro-moment approach, enabling better approximation of Coulomb collisions in plasma models.

Findings

The IS operator better approximates Coulomb collisions than the OS operator for TEM in H-mode.

The IS operator predicts a zonal flow residual between Coulomb and OS results.

The IS operator's parallel electrical conductivity closely matches Coulomb's within 1%.

Abstract

The numerical implementation of the linearized gyrokinetic (GK) and drift-kinetic (DK) improved Sugama (IS) collision operators, recently introduced by Sugama et al. [Phys. Plasmas 26, 102108 (2019)], is reported. The IS collision operator extends the validity of the widely-used original Sugama (OS) operator [Sugama et al., Phys. Plasmas 16, 112503 (2009)] to the Pfirsch-Schl\"uter collisionality regime. Using a Hermite-Laguerre velocity-space decomposition of the perturbed gyrocenter distribution function that we refer to as the gyro-moment approach, the IS collision operator is written in a form of algebraic coefficients that depend on the mass and temperature ratios of the colliding species and perpendicular wavenumber. A comparison between the IS, OS, and Coulomb collision operators is performed, showing that the IS collision operator is able to approximate the Coulomb collision operator in the case of trapped electron mode (TEM) in H-mode pedestal conditions better than the OS operator. In addition, the IS operator leads to a level of zonal flow (ZF) residual which has an intermediate value between the Coulomb and the OS collision operators. The IS operator is also shown to predict a parallel electrical conductivity that approaches the one of the Coulomb operator within less than 1%, while the OS operator can underestimate the parallel electron current by at least 10%. Finally, closed analytical formulae of the lowest-order gyro-moments of the IS, OS, and Coulomb operators are given that are ready to use to describe collisional effects in reduced gyro-moment fluid models.