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Fabrice Doveil1, Alessandro Macor, Yves Elskens

  • 1Physique des interactions ioniques et moléculaires, Unité 6633 CNRS-Université de Provence, Equipe turbulence plasma, case 321, Centre de Saint-Jérôme, F-13397 Marseille cedex 20. doveil@up.univ-mrs.fr

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Area of Science:

  • Plasma physics
  • Nonlinear dynamics
  • Chaos theory

Background:

  • Hamiltonian systems exhibit complex dynamics, including transitions to chaos.
  • Understanding these transitions is crucial for various physics applications.
  • Traveling wave tubes (TWTs) offer a platform for studying wave-particle interactions.

Purpose of the Study:

  • To experimentally observe the
  • devil's staircase
  • in a time-dependent system.
  • To investigate the transition to large-scale chaos in the universality class of Hamiltonian systems.
  • To analyze the nonlinear interaction of an electron beam with externally excited waves in a TWT.

Main Methods:

  • Utilizing a test electron beam in a traveling wave tube (TWT).
  • Employing an arbitrary waveform generator to excite specific wave spectra.
  • Recording electron beam energy distribution with a trochoidal energy analyzer.

Main Results:

  • Observed the resonant velocity domain for a single wave.
  • Documented the transition to large-scale chaos when resonant domains of two waves and their secondary resonances overlap.
  • Demonstrated a
  • devil's staircase
  • behavior with increasing excitation amplitude.

Conclusions:

  • The
  • devil's staircase
  • is experimentally observed in a time-dependent Hamiltonian system.
  • Nonlinear forcing by a second wave drives the transition to chaos via pendulum-like particle motion.
  • This study provides a paradigm for understanding chaos transitions in related physical systems.