Equivalence of two different approaches to global $\delta f$ gyrokinetic simulations

TL;DR

This paper derives a new set of flux tube gyrokinetic equations incorporating spatial variation effects and demonstrates their equivalence to traditional global $f$ gyrokinetic equations in the limit of small perpendicular turbulent structures.

Contribution

It introduces a flux tube gyrokinetic formulation that accounts for spatial variations and proves its equivalence to global equations at higher order accuracy.

Findings

New flux tube equations include density, temperature, and rotation gradient effects.

Equivalence to global equations established in the limit of small turbulent structures.

Higher-order accuracy in the $l_ot/L$ expansion compared to traditional flux tube models.

Abstract

A set of flux tube gyrokinetic equations that includes the effect of the spatial variation of the density, temperature and rotation gradients on the turbulence is derived. This new set of equations uses periodic boundary conditions. In the limit $l_\bot/L \ll 1$, where $l_\bot$ is the characteristic perpendicular length of turbulent structures and $L$ is the characteristic size of the device, this new set of flux tube gyrokinetic equations is shown to be equivalent to the traditional global $\delta f$ gyrokinetic equations to an order higher in $l_\bot/L$ than the usual flux tube formulations.