Lifting particle coordinate changes of magnetic moment type to Vlasov-Maxwell Hamiltonian dynamics

P. J. Morrison, M. Vittot, L. de Guillebon
2013 Physics of Plasmas  
Techniques for coordinate changes that depend on both dependent and independent variables are developed and applied to the Maxwell-Vlasov Hamiltonian theory. Particle coordinate changes with a new velocity variable dependent on the magnetic field, with spatial coordinates unchanged, are lifted to the field theoretic level, by transforming the noncanonical Poisson bracket and Hamiltonian structure of the Vlasov-Maxwell dynamics. Several examples are given including magnetic coordinates, where
more » ... ordinates, where the velocity is decomposed into components parallel and perpendicular to the local magnetic field, and the case of spherical velocity coordinates. An example of the lifting procedure is performed to obtain a simplified version of gyrokinetics, where the magnetic moment is used as a coordinate and the dynamics is reduced by elimination of the electric field energy in the Hamiltonian.
doi:10.1063/1.4794828 fatcat:b2ee3igkavgtdfc3twtvb2jori