Variational formulations of guiding-center Vlasov-Maxwell theory

2016/02/16 by Alain J. Brizard, A. J. Brizard, Cesare Tronci +1 · 28 citations
Engineering · Physics and Astronomy · #Angular momentum #Cauchy stress tensor #Center (category theory) #Classical mechanics #Conservation law #Euler's formula #Guiding center #Lagrangian #Magnetic confinement fusion research #Magnetic field #Mathematical analysis #Mathematical physics #Maxwell stress tensor #Maxwell's equations #Noether's theorem #Particle accelerators and beam dynamics #Physics #Quantum mechanics #Superconducting Materials and Applications #Tensor (intrinsic definition) #Variational principle #physics.plasm-ph

paper · pdf · doi:10.1063/1.4953431

published in Physics of Plasmas 23(6) (American Institute of Physics) · 15 pages

arxiv created 2016/02/16 · openalex publication_date 2016/06/01 · arxiv updated 2016/06/13 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/06

Abstract

The variational formulations of guiding-center Vlasov-Maxwell theory based on Lagrange, Euler, and Euler-Poincaré variational principles are presented. Each variational principle yields 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.

Citations

• Variational Integrators in Plasma Physics
• Beyond linear gyrocenter polarization in gyrokinetic theory
• Neutral Vlasov kinetic theory of magnetized plasmas
• Variational formulation of particle algorithms for kinetic plasma simulations
• Hamiltonian description of the ideal fluid
• Geometric integration of the Vlasov-Maxwell system with a variational particle-in-cell scheme
• The Hamiltonian structure and Euler-Poincaré formulation of the Vlasov-Maxwell and gyrokinetic systems