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Second-order nonlinear gyrokinetic theory: from the particle to the gyrocentre

Part of: Focus on Fusion

Published online by Cambridge University Press:  05 June 2018

Natalia Tronko  and
Cristel Chandre
Natalia Tronko*
Affiliation:
Max-Planck Institute for Plasma Physics, 85748 Garching, Germany TU Munich, Mathematics Center, 85747 Garching, Germany
Cristel Chandre
Affiliation:
Aix Marseille Univ, CNRS, Centrale Marseille, I2M, Marseille, France
*
†Email address for correspondence: nataliat@ipp.mpg.de
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Abstract

A gyrokinetic reduction is based on a specific ordering of the different small parameters characterizing the background magnetic field and the fluctuating electromagnetic fields. In this tutorial, we consider the following ordering of the small parameters: $\unicode[STIX]{x1D716}_{B}=\unicode[STIX]{x1D716}_{\unicode[STIX]{x1D6FF}}^{2}$ where $\unicode[STIX]{x1D716}_{B}$ is the small parameter associated with spatial inhomogeneities of the background magnetic field and $\unicode[STIX]{x1D716}_{\unicode[STIX]{x1D6FF}}$ characterizes the small amplitude of the fluctuating fields. In particular, we do not make any assumption on the amplitude of the background magnetic field. Given this choice of ordering, we describe a self-contained and systematic derivation which is particularly well suited for the gyrokinetic reduction, following a two-step procedure. We follow the approach developed in Sugama (Phys. Plasmas, vol. 7, 2000, p. 466): In a first step, using a translation in velocity, we embed the transformation performed on the symplectic part of the gyrocentre reduction in the guiding-centre one. In a second step, using a canonical Lie transform, we eliminate the gyroangle dependence from the Hamiltonian. As a consequence, we explicitly derive the fully electromagnetic gyrokinetic equations at the second order in $\unicode[STIX]{x1D716}_{\unicode[STIX]{x1D6FF}}$.

Keywords

fusion plasmaplasma nonlinear phenomenaplasma simulation
Type
Tutorial
Information
Journal of Plasma Physics , Volume 84 , Issue 3 , June 2018 , 925840301
Copyright
© EUROfusion Consortium Research Institutions 2018 

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