Compact formulas for bounce/transit averaging in axisymmetric tokamak geometry

TL;DR

This paper derives compact formulas for bounce and transit orbit averaging in axisymmetric tokamak geometry using elliptic functions, facilitating calculations in bounce-gyrokinetic microturbulence theory and accurately reproducing known residual zonal flow expressions.

Contribution

It provides new, simplified formulas for bounce and transit averaging in tokamak geometry, enhancing computational efficiency in gyrokinetic turbulence analysis.

Findings

Formulas expressed in Jacobi elliptic functions and integrals.

Applicable to neoclassical susceptibility calculations.

Recovers Rosenbluth-Hinton residual zonal flow expression.

Abstract

Compact formulas for bounce and transit orbit averaging of the fluctuation-amplitude eikonal factor in axisymmetric tokamak geometry, which is frequently encountered in bounce-gyrokinetic description of microturbulence, are given in terms of the Jacobi elliptic functions and elliptic integrals. These formulas are readily applicable to the calculation of the neoclassical susceptibility in the framework of modern bounce-gyrokinetic theory. In the long-wavelength limit for axisymmetric electrostatic perturbations, we recover the expression for the Rosenbluth-Hinton residual zonal flow [Rosenbluth and Hinton, Phys.~Rev.~Lett.~{\bf 80}, 724 (1998)] accurately.