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Alessandro Macor , Fabrice Doveil

Alessandro Macor , Fabrice Doveil. ÉQUIPE TURBULENCE PLASMA Laboratoire de Physique des Interactions Ioniques et Moléculaires Marseille - France. Observation of Hamiltonian chaos and of its control in wave-particle interaction. Fabrice Doveil , Alessandro Macor, Anass Aïssi.

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Alessandro Macor , Fabrice Doveil

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  1. Alessandro Macor, Fabrice Doveil ÉQUIPE TURBULENCE PLASMA Laboratoire de Physique des Interactions Ioniques et Moléculaires Marseille - France

  2. Observation of Hamiltonian chaos and of its control in wave-particle interaction Fabrice Doveil, Alessandro Macor, Anass Aïssi email address: doveil@up.univ-mrs.fr ÉQUIPE TURBULENCE PLASMA Laboratoire de Physique des Interactions Ioniques et Moléculaires Marseille - France Séminaire, Ecole Polytechnique Fédérale de Lausanne, 30 novembre 2007

  3. in collaboration with: THALES ELECTRONIC DEVICES Paris – France ELETTRA synchrotron light laboratory Trieste - Italy CENTRE DE PHYSIQUE THÉORIQUE Marseille – France DRFC – TORE SUPRA – EURATOM CEA Cadarache – France Séminaire, Ecole Polytechnique Fédérale de Lausanne, 30 novembre 2007

  4. Outlines • beam - plasma system • experimental set up • TWT results • test beam case: 2) Why a Traveling Wave Tube in Plasma Physics ? • Hamiltonian chaos • principle of measurement • synchronization 3) Why are we interested in nonlinear and chaotic behavior ? • trapping • resonance/s overlap 4) How do we explore chaos ? • devil’s staircase • control 5) What are the main results ? 20 cm • conclusion and perspectives

  5. beam – plasma system resonant particles beam non resonant particles Dielectric support for wave propagation Weak Turbulence  : nb << npdispersion relation  : k(w). TWT to mimic beam plasma system Hsc Self-consistent Hamiltonian for N charged particles in M waves Outlines Velocity distribution function

  6. John R. Pierce Industrial TWTs March 27, 1910 - April 2, 2002

  7. Experimental set up 4 m 20 cm

  8. Outlines TWT results • Cold beam: Instability and beam trapping in a single wave • Warm beam: • Instability and beam diffusion in a broad spectrum of unstable waves • Quasilinear paradox • Test beam: • No instability • Investigation of Hamiltonian dynamics in 1, 2, M waves • Quasilinear diffusion in a broad spectrum of waves

  9. 3) Why are we interested in nonlinear and chaotic behavior ? S=0,5 1.2 1 0.8 0.6 0.4 0.2 0 -0.2 -0.4 v S=0,85 0 1 2 3 4 5 6 x Hamiltonian chaos modulation Integrable system a particle in one wave trapping Non integrable system a particle in two waves Overlap parameter v

  10. f(w) E B ∆w wr w d D l 4) How do we explore chaos ? principle of measurement amplitude phase frequency intensity vb frequency trochoidal analyzer

  11. 5) What are the main results ? Synchronization # 1/3 linear approx.: vb <vφ f b(v) modulation A beam (current, vb ) - 1 wave (↑A, f, φ, z) Doveil, Escande and Macor Experimental observation of nonlinear synchronization due to a single wave, Phys. Rev. Lett., 94 085003(2005) #

  12. 5) What are the main results ? Synchronization # 2/3 electrons motion helix damping + 2nd order estimate Doveil, Escande and Macor Experimental observation of nonlinear synchronization due to a single wave, Phys. Rev. Lett.,94 085003(2005) #

  13. 5) What are the main results ? vφ f p(v) f b(v) at the root of Landau Damping: Synchronization # 3/3 f b(v) typical error bar z beam (current, vb ) - 1 wave (A, f, φ, ↑z) Doveil, Escande and Macor Experimental observation of nonlinear synchronization due to a single wave, Phys. Rev. Lett., 94 085003(2005) #

  14. 5) What are the main results ? amplitude L=4 m Trapping f b(v) L=2,6 m 6 amplitude A beam (current, vb ) - 1 wave (↑A, f, φ, z)

  15. 5) What are the main results ? resonance overlap* 1/2 trapping vb f b(v) beam (current, ↑vb ) - 1 wave (A, f, φ, z) * Doveil, Auhmani, Macor, Guyomarc‘h Experimental observation of resonance overlap responsible for Hamiltonian chaos, Phys. Plasmas, 12 O10702(2005)

  16. 5) What are the main results ? S=1,5 S=0,63 resonance overlap* 2/2 v trapping trapping vb x f b(v) beam (current, ↑vb ) - 2 waves (A1, f1, φ1 , z), (A2, f2, φ2 , z) * Doveil, Auhmani, Macor, Guyomarc‘h Experimental observation of resonance overlap responsible for Hamiltonian chaos, Phys. Plasmas, 12 010702 (2005)

  17. 5) What are the main results ? experiment devil’s staircase simulation with different integration time t 2t beam (current, vb= vφ) - 2 waves (↑A1, f1, φ1 , z), (↑A2= αA1 ,f2, φ2 , z) Macor, Doveil, and Elskens Electron climbing a “devil’s staircase” in wave-particle interaction Phys. Rev. Lett., 95 264102(2005)

  18. 5) What are the main results ? beating wave: k1+ k2 ω1+ ω2 φ1+ φ2 Ampl.: 2 [(eA1/m) ∙ (eA2/m) ]/ (vφ1∙ vφ2)2 Econtrol / Esystem =0,1% Control of chaos @ Chandre, Ciraolo, Lima, and Vittot Control of chaos in hamiltonian system, Celest. Mech. (2004) @ Chandre, Ciraolo, Doveil, Lima, Macor and Vittot Channeling chaos by building barriers, Phys. Rev. Lett., 94 074101(2005) Comment in PhysicsWorld May 2005

  19. Conclusions & Perspectives Conclusions • resonance overlap • nonlinear synchronization • channeling chaos • fractal structure Work in progress • injection of electron packets Perspectives • introduce self-consistency • explore nonlinear phenomenon in trapping condition

  20. email address: doveil@up.univ-mrs.fr

  21. cold beam instability G. Dimonte, and J.H. Malmberg, Phys. Rev. Lett. 38, 401 (1977) T.M. O’Neil, J.H. Winfrey, and J.H. Malmberg, Phys. Fluids. 14, 1204 (1971)

  22. warm beam: quasilinear paradox S.I Tsunoda, F. Doveil, and J.H. Malmberg, Phys. Rev. Lett. 58, 1112 (1987)

  23. Kinetic coherence Phasecontrol + 180° Beam energy Macor et al. Channeling chaotic transport in a wave-particle experiment Eur. Phys. J. D 41 519-530(2007) Phasecontrol + 90°

  24. Resonance condition f [MHz] 3,08· 106 [m/s] 4,07· 106 [m/s] 2,51· 106 [m/s] 30 [MHz] k/2π [m-1]

  25. Self consistent Hamiltonian • Landau-Van Kampen theory recovered • Derivation of quasilinear equations for chaotic regime • Origin of chaotic diffusion elucidated • Statistical physics for 1 wave and N >>1 particles: - A 2nd order phase transition - comparison of Vlasovian and Hamiltonian approaches (effects associated to finite number of degrees of freedom) -link between microscopic reversible mechanics and irreversible evolution of an N-body problem Y. Elskens, D. F. Escande, Microscopic dynamics of plasmas and chaos (IoP Bristol 2003)

  26. Beam heating by a non-resonant wave

  27. Creation of short pulse with controlled phase vs. wave at 30 MHz

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