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arXiv · 1004.1299

Perturbation analysis of trapped-particle dynamics in axisymmetric dipole geometry

F. -X. Duthoit·A. J. Brizard·Y. Peysson·J. Decker
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Abstract

The perturbation analysis of the bounce action-angle coordinates $(J,ζ)$ for charged particles trapped in an axisymmetric dipole magnetic field is presented. First, the lowest-order bounce action-angle coordinates are derived for deeply-trapped particles in the harmonic-oscillator approximation. Next, the Lie-transform perturbation method is used to derive higher-order anharmonic action-angle corrections. Explicit expressions (with anharmonic corrections) for the canonical parallel coordinates $s(J,ζ)$ and $p_{\|}(J,ζ)$ are presented, which satisfy the canonical identity $\{s,\; p_{\|}\}(J,ζ) \equiv 1$. Lastly, analytical expressions for the bounce and drift frequencies (which include anharmonic corrections) yield excellent agreement with exact numerical results.

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F. -X. Duthoit, A. J. Brizard, Y. Peysson, J. Decker. 2010-04-08. Perturbation analysis of trapped-particle dynamics in axisymmetric dipole geometry. https://doi.org/10.1063/1.3486554

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