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ABSTRACT: The Hamiltonian description of the self-consistent interaction between an electromagnetic plane wave and a copropagating beam of charged particles is considered. We show how the motion can be reduced to a one-dimensional Hamiltonian model (in a canonical setting) from the Vlasov-Maxwell Poisson brackets. The reduction to this paradigmatic Hamiltonian model is performed using a Lie algebraic formalism which allows us to preserve the Hamiltonian character at each step of the derivation.
Physical Review E 10/2008; 78(3 Pt 2):036407. · 2.26 Impact Factor
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ABSTRACT: A numerical and experimental study of a control method
aimed at channeling chaos by building barriers in phase space is
performed on a paradigm for wave-particle interaction, i.e., a
traveling wave tube. Control of chaotic diffusion is achieved by
adding small apt modifications to the system with a low additional
cost of energy. This modification is realized experimentally
through additional waves with small amplitudes. Robustness of the
method is investigated both numerically and experimentally.
The European Physical Journal D 02/2007; 41(3):519-530. · 1.48 Impact Factor
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ABSTRACT: The saturated dynamics of a Single-Pass Free Electron Laser is considered within a simplified mean-field approach. A method is proposed to increase the size of the macro-particle, which is responsible for the oscillations of the intensity of the wave. This approach is based on the reconstruction of invariant tori of the dynamics of test particles. To this aim a dedicated control term is derived, the latter acting as a small apt perturbation of the system dynamics. Implications of these findings are discussed in relation to the optimization of the laser source.
Communications in Nonlinear Science and Numerical Simulation. 02/2007;
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ABSTRACT: We consider a diffusion model with stochastic porosity for which the average solution exhibits an abnormal transport. In this paper we investigate the relation of such an anomalous diffusive property of the mean value with the behavior of the solution corresponding to each realization of the stochastic porosity. Such a solution will correspond to the actual measurements in an experiment made on a particular tube. The most relevant result of our work is that, although the concentration corresponding to each realization diffuses normally for large times, it experiments on large deviations from the mean value during intermediate times.
Chaos An Interdisciplinary Journal of Nonlinear Science 01/2007; 16(4):043101. · 2.08 Impact Factor
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ABSTRACT: We consider a stochastic model for the diffusion in a porous media. For a case where the average satisfies an anomalous diffusion equation, we investigate the behavior of the realizations around the mean value. The most relevant result of our work is that, although the concentration corresponding to each realization diffuses normally for large times, it experiences large deviations from the mean value during intermediate times. As a consequence, the experimental measurements will always depart from the average value of the realizations (with respect to the stochastic process) for unpredictable times.
Chaos An Interdisciplinary Journal of Nonlinear Science 10/2006; 16(3):033128. · 2.08 Impact Factor
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ABSTRACT: Chaotic diffusion often represents a severe obstacle for the setup of experiments, e.g., in fusion plasmas or particle accelerators. We present a complete test of a method of control of Hamiltonian chaos, with both its numerical test and its first experimental realization on a paradigm for wave-particle interaction, i.e., a travelling wave tube. The core of our approach is a small apt modification of the system which channels chaos by building barriers to diffusion. Its experimental realization opens the possibility to practically achieve the control of a wide range of systems at a low additional cost of energy.
Physical Review Letters 03/2005; 94(7):074101. · 7.37 Impact Factor
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ABSTRACT: We present a technique to control chaos in Hamiltonian systems which are close to integrable. By adding a small and simple control term to the perturbation, the system becomes more regular than the original one. We apply this technique to a forced pendulum model and show numerically that the control is able to drastically reduced chaos.
12/2003;
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ABSTRACT: We describe a method of control of chaos that occurs in area-preserving maps. This method is based on small modifications of the original map by addition of a small control term. We apply this control technique to the standard map and to the tokamap.
Physica D: Nonlinear Phenomena.
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ABSTRACT: The interaction of a wave with a beam of particles is of paramount importance in a great number of physical appli-cations. We here focus on the case of a Free Electron Laser and review two control strategies aimed at re-shaping the inner topology of the single-particle phase-space to stabi-lize the oscillations of the laser intensity in the deep satu-rated regime.
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ABSTRACT: The E× B drift motion of charged test particle dynamics in the Scrape Off Layer (SOL)is analyzed to investigate a transport control strategy based on Hamiltonian dynamics. We model SOL turbulence using a 2D non-linear fluid code based on interchange instability which was found to exhibit intermittent dynamics of the particle flux. The effect of a small and appropriate modification of the turbulent electric potential is studied with respect to the chaotic diffusion of test particle dynamics. Over a significant range in the magnitude of the turbulent electrostatic field, a three-fold reduction of the test particle diffusion coefficient is achieved.
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ABSTRACT: We present an application of a method of the control of Hamiltonian chaos to a system of chaotic advection in hydrodynamics. The aim is to create barriers to diffusion of passive tracers by adding a small and simple control term to the stream function of the system.
