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Journal Articles Kinetic and Related Models Year : 2014

On the Geometrical Gyro-Kinetic Theory

Abstract

Considering a Hamiltonian Dynamical System describing the motion of charged particle in a Tokamak or a Stellarator, we build a change of coordinates to reduce its dimension. This change of coordinates is in fact an intricate succession of mappings that are built using Hyperbolic Partial Differential Equations, Differential Geometry, Hamiltonian Dynamical System Theory and Symplectic Geometry, Lie Transforms and a new tool which is here introduced : Partial Lie Sums.
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Dates and versions

hal-00837591 , version 1 (23-06-2013)
hal-00837591 , version 2 (17-07-2013)
hal-00837591 , version 3 (13-07-2014)

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Cite

Emmanuel Frénod, Mathieu Lutz. On the Geometrical Gyro-Kinetic Theory. Kinetic and Related Models , 2014, 7 (4), pp.621-659. ⟨10.3934/krm.2014.7.621⟩. ⟨hal-00837591v3⟩
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