Analytical calculation of the orbital spectrum of the guiding centre motion in axisymmetric magnetic fields
Open Access
- 20 January 2021
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of Plasma Physics
- Vol. 87 (1)
- https://doi.org/10.1017/s0022377820001506
Abstract
Charged particle motion in axisymmetric toroidal magnetic fields is analysed within the context of the canonical Hamiltonian guiding centre theory. A canonical transformation to variables measuring the drift orbit deviation from a magnetic field line is introduced and an analytical transformation to action-angle variables is obtained, under a zero drift width approximation. The latter is used to provide compact formulas for the orbital spectrum of the drift motion, namely the bounce/transit frequencies as well as the bounce/transit averaged toroidal precession and gyration frequencies. These formulas are shown to have a remarkable agreement with numerically calculated full drift width frequencies and significant differences from standard analytical formulas based on a pendulum-like Hamiltonian description. The analytical knowledge of the orbital spectrum is crucial for the formulation of particle resonance conditions with symmetry-breaking perturbations and the study of the resulting particle, energy and momentum transport.Keywords
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