Diapositiva 1

1
Observation of a devils staircase behavior and
experimental control of chaos in wave-particle
interaction
Yves Elskens, Alessandro Macor , Fabrice Doveil
,
Université de Provence / CNRS équipe
turbulence plasma Marseilles -
FRANCE
2
Experimental set-up
4 m
20 cm
macor_at_up.univ-mrs.fr
3
Principle of the experiments
4) How do we explore chaos ?
amplitude phase frequency
Probe/s
Interaction lenght
Helix
Intensity vb
Electron beam gun
Trochoidal analyzer
Trochoidal analyzer
macor_at_up.univ-mrs.fr
macor_at_up.univ-mrs.fr
4
Hamiltonian chaos
modulation
Integrable system Particle with one wave
trapping
Non integrable system Particle with two waves
Chirikov parameter
macor_at_up.univ-mrs.fr
macor_at_up.univ-mrs.fr
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devils staircase
(n,m) m k / (nm k ) where k vf / vb
beam (current, vb vf) - 2 waves (? A1, f1, f1 ,
z), (? A2 aA1 ,f2, f2 , z)
Macor, Doveil and Elskens Electrons climbing a
devil's staircase in wave-particle interaction,
Phys. Rev. Lett., 95 264102 (2005)
macor_at_up.univ-mrs.fr
macor_at_up.univ-mrs.fr
6
Robustness of a control method
Chandre, Ciraolo, Doveil, Lima, Macor and
Vittot Channeling chaos by building barriers,
Phys. Rev. Lett., 94 074101 (2005)
Commented in PhysicsWorld May 2005
The control term beating wave k1 k2 ?1 ?
2 f1 f 2 Ampl. 2 (eA1/m) (eA2/m) / (vf1
vf2)2
macor_at_up.univ-mrs.fr
macor_at_up.univ-mrs.fr
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Robustness of a control method
(Econtrol / Esystem 0,1)
Amplitude of the control term
Phase of the control term
Initial beam velocity
s 1,27
Kinetic coherence var (f (v)ref)/ var (f (v)m)
macor_at_up.univ-mrs.fr
macor_at_up.univ-mrs.fr
8
Conclusions perspectives
conclusion

• observation of a fractal structure

• new method to control hamiltonian chaos has
  been tested

• self-concistency are being explored

perspectives

• pulsed beam

• exploit the analogies with Free Electron Laser

macor_at_up.univ-mrs.fr
macor_at_up.univ-mrs.fr
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Selected publications
Doveil, Macor and Elskens, Direct observation of
a devil's staircase" in wave-particle
interaction, Chaos, 16 033103 (2006)
devil's staircase
Macor, Doveil and Elskens, Electrons climbing a
devil's staircase in wave-particle
interaction, Phys. Rev. Lett., 95 264102 (2005)
Chandre et al., Channeling chaos by building
barriers, Phys. Rev. Lett., 94 074101 (2005)
control
Macor et al., Channeling chaotic transport in a
wave particle experiment, submitted,
arXivphysics/0608119
macor_at_up.univ-mrs.fr
macor_at_up.univ-mrs.fr