Destruction of adiabatic invariance at resonances in slow-fast Hamiltonian systems

Details Destruction of adiabatic invariance at resonances in slow-fast Hamiltonian systems Destruction of adiabatic invariance at resonances in slow-fast Hamiltonian systems

2005-11-23

arxiv.org/abs/nlin/0511050v1

Nonlinear Sciences

Chaotic Dynamics

The paper is based on a talk given at the COULOMB'05 Workshop on High Intensity Beam Dynamics, 7 pages

Scientific paper

10.1016/j.nima.2006.01.008

There are many problems that lead to analysis of dynamical systems in which one can distinguish motions of two types: slow one and fast one. An averaging over fast motion is used for approximate description of the slow motion. First integrals of the averaged system are approximate first integrals of the exact system, i.e. adiabatic invariants. Resonant phenomena in fast motion (capture into resonance, scattering on resonance) lead to inapplicability of averaging, destruction of adiabatic invariance, dynamical chaos and transport in large domains in the phase space. In the paper perturbation theory methods for description of these phenomena are outlined. We also consider as an example the problem of surfatron acceleration of a relativistic charged particle.

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