Laguerre-Hermite Pseudo-Spectral Velocity Formulation of Gyrokinetics

TL;DR

This paper introduces a Laguerre-Hermite pseudo-spectral velocity formulation for gyrokinetics that bridges the gap between gyrofluid and gyrokinetic models, enabling efficient and accurate turbulence simulations in fusion devices.

Contribution

It presents a novel spectral velocity-space basis projection of the gyrokinetic equation, accommodating various collision operators and capturing key turbulence phenomena.

Findings

Reproduces linear instability results

Accurately models zonal flow dynamics

Compatible with diverse geometries

Abstract

First-principles simulations of tokamak turbulence have proven to be of great value in recent decades. We develop a pseudo-spectral velocity formulation of the turbulence equations that smoothly interpolates between the highly efficient but lower resolution 3D gyrofluid representation and the conventional but more expensive 5D gyrokinetic representation. Our formulation is a projection of the nonlinear gyrokinetic equation onto a Laguerre-Hermite velocity-space basis. We discuss issues related to collisions, closures, and entropy. While any collision operator can be used in the formulation, we highlight a model operator that has a particularly sparse Laguerre-Hermite representation, while satisfying conservation laws and the H theorem. Free streaming, magnetic drifts, and nonlinear phase mixing each give rise to closure problems, which we discuss in relation to the instabilities of interest and to free energy conservation. We show that the model is capable of reproducing gyrokinetic results for linear instabilities and zonal flow dynamics. Thus the final model is appropriate for the study of instabilities, turbulence, and transport in a wide range of geometries, including tokamaks and stellarators.