Guiding Center and Gyrokinetic Theory for Large Electric Field Gradients and Strong Shear Flows

TL;DR

This paper extends guiding center and gyrokinetic theory to include large electric field gradients and strong shear flows, revealing modifications in particle orbits, drift velocities, and polarization while maintaining compatibility with existing simulation frameworks.

Contribution

It introduces a generalized gyrokinetic theory accounting for large electric field gradients and strong shear flows, applicable to high-performance tokamak edge conditions.

Findings

Larmor orbits deform into elliptical trajectories under large electric field gradients.

Guiding center drift becomes anisotropic with dominant flux surface gradients.

The modified theory can be integrated into existing simulation tools.

Abstract

The guiding center and gyrokinetic theory of magnetized particle motion is extended to the regime of large electric field gradients perpendicular to the magnetic field. A gradient in the electric field directly modifies the oscillation frequency and causes the Larmor orbits to deform from circular to elliptical trajectories. In order to retain a good adiabatic invariant, there can only be strong dependence on a single coordinate at lowest order, so that resonances do not generate chaotic motion that destroys the invariant. When the gradient across magnetic flux surfaces is dominant, the guiding center drift velocity becomes anisotropic in response to external forces and additional curvature drifts must be included. The electric polarization density remains gyrotropic, but both the polarization and magnetization are modified by the change in gyrofrequency. The theory can be applied to shear flows that are even stronger than those observed in the edge transport barrier of a high-performance tokamak (H-mode) pedestal, even if the toroidal field is as small as or even smaller than the poloidal field. Yet, the theory retains a mathematical form that is similar to the standard case and can readily be implemented within existing simulation tools.