Derivation of Hamiltonian magnetofluid models with gyroviscous-like contributions using a gyro-map

POSTER

Abstract

Ideal MHD and various reduced magnetofluid models exhibit a noncanonical Hamiltonian structure when expressed in Eulerian variables [1]. Extending the work of Ref.[2], we investigate the possibility of systematically including contributions due to finite ion gyro-radii in three dimensions while preserving a noncanonical Hamiltonian structure. Starting with the Morrison-Greene 3D ideal MHD noncanonical Poisson bracket[1] and a Hamiltonian including gyroviscous terms, we derive equations of motion using a three-dimensional generalization of the gyro-map introduced in Ref.[2]. The origin of the gyro-map is motivated and explained using an action principle formulation as in Ref.[3]. Through a systematic reduction procedure, we also recover the (noncanonical) bracket and the gyroviscous tensor, which are identical to the ones obtained via the Hamiltonian formalism. \\[4pt] [1] P.J.~Morrison and J.M.~Greene, Phys. Rev. A {\bf 45},790 (1980).\\[0pt] [2] P.J.~Morrison, I.L.~Caldas, and H.~Tasso, Z. Naturforsch. {\bf 39a}, 1023 (1984).\\[0pt] [3] P.J.~Morrison, M.~Lingam, and R.~Acevedo, arXiv:1405.2326 (to appear in Phys. Plasmas)

Authors

  • Alexander Wurm

    Department of Physical and Biological Sciences, Western New England University, Springfield, MA 01119

  • Manasvi Lingam

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

  • 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