Motion of a charged particle in slowly varying electromagnetic fields.

*(English)*Zbl 0505.76128The motion of a charged particle in specified electric and magnetic fields is studied by use of repeated canonical transformations of a Hamiltonian system. In addition to the usual assumptions that the electromagnetic fields vary slowly in space and time, it is also assumed that the fields vary even more slowly in a distinguished direction. The existence of first and second adiabatic invariants is discussed and the results are applied to a standard plasma configuration, a long, thin mirror machine.

Reviewer: Harold Weitzner

##### MSC:

78A35 | Motion of charged particles |

70H05 | Hamilton’s equations |

70H15 | Canonical and symplectic transformations for problems in Hamiltonian and Lagrangian mechanics |

82B05 | Classical equilibrium statistical mechanics (general) |

##### Keywords:

repeated canonical transformations; existence of first and second adiabatic invariants; long, thin mirror machine
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\textit{H. Weitzner}, Commun. Pure Appl. Math. 36, 695--704 (1983; Zbl 0505.76128)

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