Multiscale Gyrokinetics for Rotating Tokamak Plasmas II: Reduced Models for Electron Dynamics

TL;DR

This paper develops a rigorous reduced electron model for rotating tokamak plasmas by exploiting scale separation, eliminating fast electron timescales, and deriving transport equations within magnetic flux surfaces.

Contribution

It introduces a new multiscale gyrokinetic approach that derives reduced electron equations using scale separation and magnetic flux surface construction.

Findings

Ion-scale turbulence does not alter magnetic topology

Magnetic field lies on fluctuating flux surfaces to lowest order

Derived closed system of equations for electron response and heat transport

Abstract

In this paper, we extend the multiscale approach developed in [Abel et. al., Rep. Prog. Phys., submitted] by exploiting the scale separation between ions and the electrons. The gyrokinetic equation is expanded in powers of the electron to ion mass ratio, which provides a rigorous method for deriving the reduced electron model. We prove that ion-scale electromagnetic turbulence cannot change the magnetic topology, and argue that to lowest order the magnetic field lies on fluctuating flux surfaces. These flux surfaces are used to construct magnetic coordinates, and in these coordinates a closed system of equations for the electron response to ion-scale turbulence is derived. All fast electron timescales have been eliminated from these equations. We also use these magnetic surfaces to construct transport equations for electrons and for electron heat in terms of the reduced electron model.