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Hamiltonian in guiding center theory: a symplectic structure approach

journal contribution
posted on 12.01.2021, 13:55 by Anatoly Neishtadt, Anton Artemyev
The guiding center approximation represents a very powerful tool for analyzing and modeling a charged particle motion in strong magnetic fields. This approximation is based on conservation of the adiabatic invariant, magnetic moment. Hamiltonian equations for the guiding centre motion are traditionally intoduced using a non-canonical symplectic structure. Such approach requires application of non-canonical Hamiltonian perturbation theory for calculations of the magnetic moment corrections. In this study we present an alternative approach with canonical Hamiltonian equations for guiding centre motion in time-dependent electromagnetic fields. We show that the derived Hamiltonian decouples three types of motion (gyrorotation, field-aligned motion, and across-field drifts), and each type is described by a pair of conjugate variables. This form of Hamiltonian and symplectic structure allows simple introduction of adiabatic invariants and can be useful for analysis of various plasma systems.

History

School

  • Science

Department

  • Mathematical Sciences

Published in

Proceedings of the Steklov Institute of Mathematics

Volume

310

Issue

1

Pages

214-219

Publisher

Springer

Version

AM (Accepted Manuscript)

Rights holder

© Pleiades Publishing, Ltd

Publisher statement

This is a post-peer-review, pre-copyedit version of an article published in Proceedings of the Steklov Institute of Mathematics. The final authenticated version is available online at: https://doi.org/10.1134/S008154382005017X

Acceptance date

29/05/2020

Publication date

2020-12-04

Copyright date

2020

ISSN

0081-5438

eISSN

1531-8605

Language

en

Depositor

Prof Anatoly Neishtadt. Deposit date: 30 May 2020

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