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arXiv · 1403.3873

Canonical transformation for trapped/passing guiding-center orbits in axisymmetric tokamak geometry

Alain J. Brizard·Francois-Xavier Duthoit
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Abstract

The generating function for the canonical transformation from the parallel canonical coordinates $(p_{\|},s)$ to the action-angle coordinates $(J,ζ)$ for trapped/passing guiding-center orbits in axisymmetric tokamak geometry is presented. Drawing on the analogy between the phase-space portraits of the librating/rotating pendulum and the trapped/passing guiding-center orbits, the generating function is expressed in terms of the Jacobi zeta function, which can then readily be used to obtain an explicit expression for the bounce-center transformation for trapped/passing-particles in axisymmetric tokamak geometry.

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Alain J. Brizard, Francois-Xavier Duthoit. 2014-05-10. Canonical transformation for trapped/passing guiding-center orbits in axisymmetric tokamak geometry. https://doi.org/10.1063/1.4879811

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