Abstract
The motion of charged particle in longitudinal waves is a paradigm for the transition to large scale chaos in Hamiltonian systems. Recently a test cold electron beam has been used to observe its non-self-consistent interaction with externally excited wave(s) in a specially designed Traveling Wave Tube (TWT). The velocity distribution function of the electron beam is recorded with a trochoidal energy analyzer at the output of the TWT. An arbitrary waveform generator is used to launch a prescribed spectrum of waves along the slow wave structure (a 4 m long helix) of the TWT. The resonant velocity domain associated to a single wave is observed, as well as the transition to large scale chaos when the resonant domains of two waves and their secondary resonances overlap. This transition exhibits a “devil’s staircase” behavior when increasing the excitation amplitude in agreement with numerical simulation. A new strategy for control of chaos by building barriers of transport which prevent electrons to escape from a given velocity region as well as its robustness are also successfully tested. Thus generic features of Hamiltonian chaos have been experimentally observed.
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Doveil, F., Macor, A. & Aïssi, A. Observation of Hamiltonian chaos in wave–particle interaction. Celest Mech Dyn Astr 102, 255–272 (2008). https://doi.org/10.1007/s10569-008-9130-0
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DOI: https://doi.org/10.1007/s10569-008-9130-0
Keywords
- Hamiltonian chaos
- KAM tori
- Resonance overlap
- Devil’s staircase
- Traveling wave tube
- Large scale chaos (LSC)
- Control of chaos