2009
DOI: 10.1103/revmodphys.81.693
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Hamiltonian theory of guiding-center motion

Abstract: Guiding-center theory provides the reduced dynamical equations for the motion of charged particles in slowly varying electromagnetic fields, when the fields have weak variations over a gyration radius ͑or gyroradius͒ in space and a gyration period ͑or gyroperiod͒ in time. Canonical and noncanonical Hamiltonian formulations of guiding-center motion offer improvements over non-Hamiltonian formulations: Hamiltonian formulations possess Noether's theorem ͑hence invariants follow from symmetries͒, and they preserve… Show more

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Cited by 303 publications
(500 citation statements)
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“…The system also contains an electrostatic wave propagating along this magnetic field. Thus, transverse particle motion (gyrorotation around magnetic field) is not perturbed by the wave field-aligned electric field, and we can use a guidingcenter approximation for the particle Hamiltonian [52]:…”
Section: Hamiltonian Equationsmentioning
confidence: 99%
“…The system also contains an electrostatic wave propagating along this magnetic field. Thus, transverse particle motion (gyrorotation around magnetic field) is not perturbed by the wave field-aligned electric field, and we can use a guidingcenter approximation for the particle Hamiltonian [52]:…”
Section: Hamiltonian Equationsmentioning
confidence: 99%
“…For nonrelativistic particles, g % 1. In the relativistic case, g remains nearly constant (i.e., B m changes little during the drift) because the potential energy becomes orders of magnitude smaller than the kinetic energy term (In guiding-center formulation, the electric potential term is an order of magnitude smaller than the terms with B, otherwise the second adiabatic invariant would not be conserved [Brizard and Chan, 1999;Tao et al, 2007;Cary and Brizard, 2009].). Therefore, particles move along straight lines in (U, B m ) space while preserving the second adiabatic invariant, J.…”
Section: Methodsmentioning
confidence: 99%
“…His work was subsequently extended on many occasions. We encourage the reader especially to the paper by Brizard (1995), and to the paper by Cary & Brizard (2009) (and the references therein) where also the history of the guiding-center theory is outlined in detail. In this contribution, we are mostly following these aforementioned works.…”
Section: About Lie-transformationsmentioning
confidence: 99%