Exact momentum conservation laws for the gyrokinetic Vlasov-Poisson equations

TL;DR

This paper derives exact momentum conservation laws for the nonlinear gyrokinetic Vlasov-Poisson equations using Noether's theorem, providing key insights into momentum transport in tokamak plasmas.

Contribution

It presents the first derivation of exact momentum conservation laws for gyrokinetic equations via a variational principle and Noether's theorem, including toroidal angular momentum in tokamaks.

Findings

Derived exact gyrokinetic momentum conservation laws

Established relation between momentum transport and gyrocenter polarization

Extended conservation laws to axisymmetric tokamak geometry

Abstract

The exact momentum conservation laws for the nonlinear gyrokinetic Vlasov-Poisson equations are derived by applying the Noether method on the gyrokinetic variational principle [A. J. Brizard, Phys. Plasmas {\bf 7}, 4816 (2000)]. From the gyrokinetic Noether canonical-momentum equation derived by the Noether method, the gyrokinetic parallel momentum equation and other gyrokinetic Vlasov-moment equations are obtained. In addition, an exact gyrokinetic toroidal angular-momentum conservation law is derived in axisymmetric tokamak geometry, where the transport of parallel-toroidal momentum is related to the radial gyrocenter polarization, which includes contributions from the guiding-center and gyrocenter transformations.