Variational principles for the guiding-center Vlasov-Maxwell equations

TL;DR

This paper develops variational principles for the guiding-center Vlasov-Maxwell equations, deriving polarization, magnetization, and conservation laws, including a symmetric stress tensor, to enhance theoretical understanding of plasma dynamics.

Contribution

It introduces multiple variational formulations for guiding-center plasma equations, explicitly incorporating polarization and magnetization effects, and derives associated conservation laws.

Findings

Derivation of guiding-center polarization and magnetization effects.

Explicitly symmetric guiding-center stress tensor.

Conservation laws for energy, momentum, and angular momentum.

Abstract

The Lagrange, Euler, and Euler-Poincar\'{e} variational principles for the guiding-center Vlasov-Maxwell equations are presented. Each variational principle presents a different approach to deriving guiding-center polarization and magnetization effects into the guiding-center Maxwell equations. The conservation laws of energy, momentum, and angular momentum are also derived by Noether method, where the guiding-center stress tensor is now shown to be explicitly symmetric.