Linearized model Fokker-Planck collision operators for gyrokinetic simulations. I. Theory

TL;DR

This paper introduces a new analytically and numerically manageable collision operator for gyrokinetic turbulence simulations, satisfying physical constraints and improving small-scale behavior in phase space.

Contribution

It develops a novel collision operator that conserves key quantities, obeys thermodynamic principles, and is suitable for gyrokinetic turbulence modeling.

Findings

The model operator conserves particles, momentum, and energy.

It satisfies Boltzmann's H-theorem.

It dissipates small-scale velocity space structures effectively.

Abstract

A new analytically and numerically manageable model collision operator is developed specifically for turbulence simulations. The like-particle collision operator includes both pitch-angle scattering and energy diffusion and satisfies the physical constraints required for collision operators: it conserves particles, momentum and energy, obeys Boltzmann's H-theorem (collisions cannot decrease entropy), vanishes on a Maxwellian, and efficiently dissipates small-scale structure in the velocity space. The process of transforming this collision operator into the gyroaveraged form for use in gyrokinetic simulations is detailed. The gyroaveraged model operator is shown to have more suitable behavior at small scales in phase space than previously suggested models. A model operator for electron-ion collisions is also presented.