Gyrokinetic Equations for Strong-Gradient Regions

TL;DR

This paper develops a practical gyrokinetic theory for strong-gradient regions in tokamaks, enabling accurate simulations of edge and transport barrier physics with large perturbations.

Contribution

It introduces a new set of gyrokinetic equations valid for large perturbations in strong-gradient plasma regions, suitable for numerical implementation and conservation properties.

Findings

Equations are valid for large perturbation amplitudes in edge regions.

The theory simplifies under specific orderings relevant to tokamak edge physics.

Applicable to nonlinear fluctuations at mixing-length levels.

Abstract

A gyrokinetic theory is developed under a set of orderings applicable to the edge region of tokamaks and other magnetic confinement devices, as well as to internal transport barriers. The result is a practical set equations that is valid for large perturbation amplitudes [q{\delta}{\psi}/T = O(1), where {\delta}{\psi} = {\delta}{\phi} - v_par {\delta}A_par/c], which is straightforward to implement numerically, and which has straightforward expressions for its conservation properties. Here, q is the particle charge, {\delta}{\phi} and {\delta}A_par are the perturbed electrostatic and parallel magnetic potentials, v_par is the parallel velocity, c is the speed of light, and T is the temperature. The derivation is based on the quantity {\epsilon}:=({\rho}/{\lambda})q{\delta}{\psi}/T << 1 as the small expansion parameter, where {\rho} is the gyroradius and {\lambda} is the perpendicular wavelength. Physically, this ordering requires that the E\times B velocity and the component of the parallel velocity perpendicular to the equilibrium magnetic field are small compared to the thermal velocity. For nonlinear fluctuations saturated at "mixing-length" levels (i.e., at a level such that driving gradients in profile quantities are locally flattened), {\epsilon} is of order {\rho}/L, where L is the equilibrium profile scale length, for all scales {\lambda} ranging from {\rho} to L. This is true even though q{\delta}{\psi}/T = O(1) for {\lambda} ~ L. Significant additional simplifications result from ordering L/R =O({\epsilon}), where R is the spatial scale of variation of the magnetic field. We argue that these orderings are well satisfied in strong-gradient regions, such as edge and screapeoff layer regions and internal transport barriers in tokamaks, and anticipate that our equations will be useful as a basis for simulation models for these regions.