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  • A HAMILTONIAN FORMULATION OF CHARGED PARTICLE MOTION IN A MAGNETIC FIELD AND OF THE DRIFT KINETIC EQUATION IN TERMS OF LOCAL SPATIAL COORDINATES

Abstract

The equations which describe the combined E X B, -B X B, and curvature drifts, the magnetic gradient force along magnetic field lines, the existence of the first adiabatic invariant, and the rapid cyclotron motion are shown to have a canonical Hamiltonian structure which relates directly to the local spatial coordinates. The use of Poisson brackets leads immediately to the drift kinetic equation, expressed in local spatial coordinates rather than magnetic field coordinates. When the magnetic field geometry is such as to give rise to mirroring, and the second and third adiabatic invariants exist, their physical identification follows at once from the canonical formulation. Consideration of the symplectic two-form and its exterior derivative in terms of non-canonical local spatial coordinates leads both to the well-known use of magnetic field coordinates as canonical variables, and to a compact geometrical formulation of the drift equations.

Additional information

Authors: DENDY R O CULHAM LABORATORY, ABINGDON (UK), CULHAM LABORATORY, ABINGDON (UK)
Bibliographic Reference: WRITE TO THE LIBRARIAN, UKAEA, CULHAM LABORATORY, ABINGDON, OXON, OX14 3DB (UK), MENTIONING REPORT CLM-P-781, 1986
Record Number: 1989125030600 / Last updated on: 1987-03-01
Category: PUBLICATION
Available languages: en