Nonlinear Sciences – Chaotic Dynamics
Scientific paper
2006-04-13
Chaos in press (2006) in press
Nonlinear Sciences
Chaotic Dynamics
remplacement des figures 7, 8, 9 par rapport au premier depot
Scientific paper
10.1063/1.2216850
We report the experimental observation of a "devil's staircase'' in a time dependent system considered as a paradigm for the transition to large scale chaos in the universality class of hamiltonian systems. A test electron beam is used to observe its non-self-consistent interaction with externally excited wave(s) in a Travelling Wave Tube (TWT). A trochoidal energy analyzer records the beam energy distribution at the output of the interaction line. 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 for increasing excitation amplitude, due to the nonlinear forcing by the second wave on the pendulum-like motion of a charged particle in one electrostatic wave.
Doveil Fabrice
Elskens Yves
Macor Alessandro
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