A Geometrical Version of the Maxwell-Vlasov Hamiltonian Structure

ORAL

Abstract

We present a geometrization of the Hamiltonian approach of classical electrodynamics, via (non-canonical) Poisson structures. This relativistic Hamiltonian framework (introduced by Morrison, Marsden, Weinstein) is a field theory written in terms of differential forms, independently of the gauge potentials. This algebraic and geometric description of the Vlasov kinetics is well suited for a perturbation theory, in a strong inhomogeneous magnetic field (expansion in 1/B, with all the curvature terms...), like in magnetically confined plasmas, and in any coordinates, for instance adapted to a Tokamak (toroidal coordinates, or else...).

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Authors

  • Michel Vittot

    Centre de Physique Theorique (CPT), C.N.R.S. UMR 7332 - Aix-Marseille Universite, Luminy, 13288 Marseille - FRANCE

  • Philip J. Morrison

    The University of Texas at Austin, Institute for Fusion Studies and Department of Physics, University of Texas at Austin, Austin, TX 78712, The University of Texas at Austin, Physics Department, Austin, TX 78712-1192 - USA, Institute for Fusion Studies and Department of Physics, The University of Texas at Austin, Institute for Fusion Studies, The University of Texas at Austin, University of Texas at Austin, Department of Physics, Institute for Fusion Studies, Austin - TX 78712, USA