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Title: Direct observation of a 'devil's staircase' in wave-particle interaction

Abstract

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 traveling 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.

Authors:
; ;  [1]
  1. Physique des interactions ioniques et moleculaires, Unite 6633 CNRS-Universite de Provence, Equipe turbulence plasma, case 321, Centre de Saint-Jerome, F-13397 Marseille cedex 20 (France)
Publication Date:
OSTI Identifier:
20849473
Resource Type:
Journal Article
Journal Name:
Chaos (Woodbury, N. Y.)
Additional Journal Information:
Journal Volume: 16; Journal Issue: 3; Other Information: DOI: 10.1063/1.2216850; (c) 2006 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1054-1500
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; AMPLITUDES; CHAOS THEORY; CHARGED PARTICLES; ELECTRON BEAMS; ENERGY SPECTRA; HAMILTONIANS; NONLINEAR PROBLEMS; PARTICLE INTERACTIONS; PLASMA; PLASMA WAVES; TIME DEPENDENCE; TRAVELLING WAVE TUBES; WAVE FORMS; WAVE PROPAGATION

Citation Formats

Doveil, Fabrice, Macor, Alessandro, and Elskens, Yves. Direct observation of a 'devil's staircase' in wave-particle interaction. United States: N. p., 2006. Web. doi:10.1063/1.2216850.
Doveil, Fabrice, Macor, Alessandro, & Elskens, Yves. Direct observation of a 'devil's staircase' in wave-particle interaction. United States. doi:10.1063/1.2216850.
Doveil, Fabrice, Macor, Alessandro, and Elskens, Yves. Fri . "Direct observation of a 'devil's staircase' in wave-particle interaction". United States. doi:10.1063/1.2216850.
@article{osti_20849473,
title = {Direct observation of a 'devil's staircase' in wave-particle interaction},
author = {Doveil, Fabrice and Macor, Alessandro and Elskens, Yves},
abstractNote = {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 traveling 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.},
doi = {10.1063/1.2216850},
journal = {Chaos (Woodbury, N. Y.)},
issn = {1054-1500},
number = 3,
volume = 16,
place = {United States},
year = {2006},
month = {9}
}