Effects of collisions on conservation laws in gyrokinetic field theory

TL;DR

This paper investigates how collisions affect conservation laws in gyrokinetic plasma theory, deriving modified conservation equations and transport fluxes that include collisional and turbulent effects.

Contribution

It introduces a novel gyrokinetic collision operator and systematically derives modified conservation laws incorporating collisional and turbulent transport.

Findings

Derived collision-modified conservation laws using a new gyrokinetic collision operator.

Formulated particle, energy, and momentum balance equations including collisional and turbulent fluxes.

Showed agreement of derived transport fluxes with conventional formulations.

Abstract

Effects of collisions on conservation laws for toroidal plasmas are investigated based on the gyrokinetic field theory. Associating the collisional system with a corresponding collisionless system at a given time such that the two systems have the same distribution functions and electromagnetic fields instantaneously, it is shown how the collisionless conservation laws derived from Noether's theorem are modified by the collision term. Effects of the external source term added into the gyrokinetic equation can be formulated similarly with the collisional effects. Particle, energy, and toroidal momentum balance equations including collisional and turbulent transport fluxes are systematically derived using a novel gyrokinetic collision operator, by which the collisional change rates of energy and canonical toroidal angular momentum per unit volume in the gyrocenter space can be given in the conservative forms. The ensemble-averaged transport equations of particles, energy, and toroidal momentum given in the present work are shown to include classical, neoclassical, and turbulent transport fluxes which agree with those derived from conventional recursive formulations.