On the Geometrical Gyro-Kinetic theory

Emmanuel Frénod; Mathieu Lutz

doi:10.3934/krm.2014.7.621

Article Contents

2014, Volume 7, Issue 4: 621-659. Doi: 10.3934/krm.2014.7.621

This issue Previous Article Time decay of solutions to the compressible Euler equations with damping Next Article A review of the mean field limits for Vlasov equations

On the Geometrical Gyro-Kinetic theory

Emmanuel Frénod^1, and
Mathieu Lutz^2,

1.
LMBA (UMR 6205) Université de Bretagne-Sud, F-56017 Vannes
2.
IRMA (UMR 7501) Université de Strasbourg, F-67094 Strasbourg Cedex

Received: June 30, 2014

Revised: June 30, 2014

Published: November 2014

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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.

Keywords:

Tokamak,
Stellarator,
Gyro-Kinetic Approximation,
Hyperbolic Partial Differential Equations,
Differential Geometry,
Hamiltonian Dynamical System Theory,
Symplectic Geometry,
Lie Transforms,
Partial Lie Sums.

Mathematics Subject Classification: Primary: 58Z05, 58J37, 58J45; Secondary: 82D10.

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