# Nonlinear Gyrokinetic Coulomb Collision Operator

## TL;DR

This paper derives a nonlinear gyrokinetic Coulomb collision operator suitable for plasma edge regions in magnetic confinement fusion, enabling accurate modeling of far-from-equilibrium collisions at small spatial scales.

## Contribution

It introduces a novel gyrokinetic Coulomb collision operator expressed in gyrocenter coordinates, with a numerical implementation framework and expansions in velocity space.

## Key findings

- Operator accurately describes far-from-equilibrium collisions
- Provides a gyroaverage formula in gyrocenter phase space
- Includes Hermite-Laguerre velocity space expansion

## Abstract

A gyrokinetic Coulomb collision operator is derived, which is particularly useful to describe the plasma dynamics at the periphery region of magnetic confinement fusion devices. The derived operator is able to describe collisions occurring in distribution functions arbitrarily far from equilibrium with variations on spatial scales at and below the particle Larmor radius. A multipole expansion of the Rosenbluth potentials is used in order to derive the dependence of the full Coulomb collision operator on the particle gyroangle. The full Coulomb collision operator is then expressed in gyrocentre phase-space coordinates, and a closed formula for its gyroaverage in terms of the moments of the gyrocenter distribution function in a form ready to be numerically implemented is provided. Furthermore, the collision operator is projected onto a Hermite-Laguerre velocity space polynomial basis and expansions in the small electron-to-ion mass ratio are provided.