# A gyrokinetic model for the plasma periphery of tokamak devices

## TL;DR

This paper introduces a comprehensive gyrokinetic model for tokamak plasma periphery, capable of capturing complex electromagnetic fluctuations and flows, advancing the understanding of plasma behavior in fusion devices.

## Contribution

It develops a second order gyrokinetic model using Lie perturbation theory and expands the distribution function onto a Hermite-Laguerre basis for detailed plasma analysis.

## Key findings

- Accurately describes plasma behavior with strong flows and electromagnetic fluctuations.
- Derives a set of coupled fluid equations from the gyrokinetic Boltzmann equation.
- Provides a variational principle-based electromagnetic field evolution framework.

## Abstract

A gyrokinetic model is presented that can properly describe strong flows, large and small amplitude electromagnetic fluctuations occurring on scale lengths ranging from the electron Larmor radius to the equilibrium perpendicular pressure gradient scale length, and large deviations from thermal equilibrium. The formulation of the gyrokinetic model is based on a second order description of the single charged particle dynamics, derived from Lie perturbation theory, where the fast particle gyromotion is decoupled from the slow drifts, assuming that the ratio of the ion sound Larmor radius to the perpendicular equilibrium pressure scale length is small. The collective behavior of the plasma is obtained by a gyrokinetic Boltzmann equation that describes the evolution of the gyroaveraged distribution function and includes a non-linear gyrokinetic Dougherty collision operator. The gyrokinetic model is then developed into a set of coupled fluid equations referred to as the gyrokinetic moment hierarchy. To obtain this hierarchy, the gyroaveraged distribution function is expanded onto a velocity-space Hermite-Laguerre polynomial basis and the gyrokinetic equation is projected onto the same basis, obtaining the spatial and temporal evolution of the Hermite-Laguerre expansion coefficients. The Hermite-Laguerre projection is performed accurately at arbitrary perpendicular wavenumber values. Finally, the self-consistent evolution of the electromagnetic fields is described by a set of gyrokinetic Maxwell's equations derived from a variational principle, with the velocity integrals of the gyroaveraged distribution function explicitly evaluated.