Generalized Miller Formulae

We derive the spectral dependence of the non-linear susceptibility of any order, generalizing the common form of Sellmeier equations. This dependence is fully defined by the knowledge of the linear dispersion of the medium. This finding generalizes the Miller formula to any order of non-linearity. In the frequency-degenerate case, it yields the spectral dependence of non-linear refractive indices of arbitrary order.Comment: 12 pages, 1 figure (4 panels

Higher-order Kerr terms allow ionization-free filamentation in gases

We show that higher-order nonlinear indices ($n_4$, $n_6$, $n_8$, $n_{10}$) provide the main defocusing contribution to self-channeling of ultrashort laser pulses in air and Argon at 800 nm, in contrast with the previously accepted mechanism of filamentation where plasma was considered as the dominant defocusing process. Their consideration allows to reproduce experimentally observed intensities and plasma densities in self-guided filaments.Comment: 11 pages, 6 figures (11 panels

Spectral dependence of purely-Kerr driven filamentation in air and argon

Based on numerical simulations, we show that higher-order nonlinear indices (up to $n_8$ and $n_{10}$, respectively) of air and argon have a dominant contribution to both focusing and defocusing in the self-guiding of ultrashort laser pulses over most of the spectrum. Plasma generation and filamentation are therefore decoupled. As a consequence, ultraviolet wavelength may not be the optimal wavelengths for applications requiring to maximize ionization.Comment: 14 pages, 4 figures (14 panels

On negative higher-order Kerr effect and filamentation

As a contribution to the ongoing controversy about the role of higher-order Kerr effect (HOKE) in laser filamentation, we first provide thorough details about the protocol that has been employed to infer the HOKE indices from the experiment. Next, we discuss potential sources of artifact in the experimental measurements of these terms and show that neither the value of the observed birefringence, nor its inversion, nor the intensity at which it is observed, appear to be flawed. Furthermore, we argue that, independently on our values, the principle of including HOKE is straightforward. Due to the different temporal and spectral dynamics, the respective efficiency of defocusing by the plasma and by the HOKE is expected to depend substantially on both incident wavelength and pulse duration. The discussion should therefore focus on defining the conditions where each filamentation regime dominates.Comment: 22 pages, 11 figures. Submitted to Laser physics as proceedings of the Laser Physics 2010 conferenc

Linear theory and violent relaxation in long-range systems: a test case

In this article, several aspects of the dynamics of a toy model for longrange Hamiltonian systems are tackled focusing on linearly unstable unmagnetized (i.e. force-free) cold equilibria states of the Hamiltonian Mean Field (HMF). For special cases, exact finite-N linear growth rates have been exhibited, including, in some spatially inhomogeneous case, finite-N corrections. A random matrix approach is then proposed to estimate the finite-N growth rate for some random initial states. Within the continuous, $N \rightarrow \infty$, approach, the growth rates are finally derived without restricting to spatially homogeneous cases. All the numerical simulations show a very good agreement with the different theoretical predictions. Then, these linear results are used to discuss the large-time nonlinear evolution. A simple criterion is proposed to measure the ability of the system to undergo a violent relaxation that transports it in the vicinity of the equilibrium state within some linear e-folding times

Emergence of a non trivial fluctuating phase in the XY model on regular networks

We study an XY-rotor model on regular one dimensional lattices by varying the number of neighbours. The parameter $2\ge\gamma\ge1$ is defined. $\gamma=2$ corresponds to mean field and $\gamma=1$ to nearest neighbours coupling. We find that for $\gamma<1.5$ the system does not exhibit a phase transition, while for $\gamma > 1.5$ the mean field second order transition is recovered. For the critical value $\gamma=\gamma_c=1.5$, the systems can be in a non trivial fluctuating phase for whichthe magnetisation shows important fluctuations in a given temperature range, implying an infinite susceptibility. For all values of $\gamma$ the magnetisation is computed analytically in the low temperatures range and the magnetised versus non-magnetised state which depends on the value of $\gamma$ is recovered, confirming the critical value $\gamma_{c}=1.5$

Development of Magnetohydrodynamic Modes During Sawteeth in Tokamak Plasmas

A dynamical analysis applied to a reduced resistive magnetohydrodynamics model is shown to explain the chronology of the nonlinear destabilization of modes observed in tokamak sawteeth. A special emphasis is put on the nonlinear self-consistent perturbation of the axisymmetric m = n = 0 mode that manifests through the q-profile evolution. For the very low fusion-relevant resistivity values, the q-profile is shown to remain almost unchanged on the early nonlinear timescale within the central tokamak region, which supports a partial reconnection scenario. Within the resistive region, indications for a local flattening or even a local reversed-shear of the q-profile are given. The impact of this ingredient in the occurrence of the sawtooth crash is discussed.Fil: Firpo, Marie C.. Ecole Polytechnique; Francia. Centre National de la Recherche Scientifique; FranciaFil: Ettoumi, W.. Ecole Polytechnique; Francia. Centre National de la Recherche Scientifique; FranciaFil: Farengo, R.. Comision Nacional de Energia Atomica. Gerencia del Area de Investigaciones y Aplicaciones no Nucleares. Gerencia de Fisica (CAB); Argentina. Comisión Nacional de Energía Atómica. Gerencia del Area de Energía Nuclear. Instituto Balseiro; ArgentinaFil: Ferrari, Hugo Emilio. Comision Nacional de Energia Atomica. Gerencia del Area de Investigaciones y Aplicaciones no Nucleares. Gerencia de Fisica (CAB); Argentina. Comisión Nacional de Energía Atómica. Gerencia del Area de Energía Nuclear. Instituto Balseiro; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Garcia Martinez, Pablo Luis. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Lifschitz, A. F.. Ecole Polytechnique; Francia. Centre National de la Recherche Scientifique; Franci

Transport in the barrier billiard

International audienceWe investigate transport properties of an ensemble of particles moving inside an infinite periodic horizontal planar barrier billiard. A particle moves among bars and elastically reflects on them. The motion is a uniform translation along the bars' axis. When the tangent of the incidence angle, alpha , is fixed and rational, the second moment of the displacement along the orthogonal axis at time n , , is either bounded or asymptotic to K n2 , when n -->&infin; . For irrational alpha , the collision map is ergodic and has a family of weakly mixing observables, the transport is not ballistic, and autocorrelation functions decay only in time average, but may not decay for a family of irrational alpha 's. An exhaustive numerical computation shows that the transport may be superdiffusive or subdiffusive with various rates or bounded strongly depending on the values of alpha . The variety of transport behaviors sounds reminiscent of well-known behavior of conservative systems. Considering then an ensemble of particles with nonfixed alpha , the system is nonergodic and certainly not mixing and has anomalous diffusion with self-similar space-time properties. However, we verified that such a system decomposes into ergodic subdynamics breaking self-similarity

Redistribution of high energy alpha particles due to sawteeth with partial reconnection

The redistribution of high energy alpha particles due to internal kink modes is studied in plasmas with ITER-like parameters. The exact particle trajectories in the total fields, equilibrium plus perturbation, are calculated. The equilibrium magnetic field is obtained by analytically solving the Grad–Shafranov equation and the perturbed electric and magnetic fields are reconstructed using ideal MHD and the experimental information about the displacement eigenfunction. The (1, 1), (2, 2) and (2, 1) modes are included and the effect of changing their amplitude and frequency is determined. The results show that if the conditions are similar to those reported in Igochine et al (2007 Nucl. Fusion 47 23), the peak density of counter-passing particles decreases between 25% and 40% (depending on the energy); the peak of the trapped particles density shifts outwards by approximately 10% of the minor radius and the total on axis density decreases by more than 25%. This redistribution occurs inside the q = 1 surface. The addition of a (2, 1) mode, which can produce the stochastization of the magnetic field, significantly increases particle redistribution and allows particles to spread beyond the q = 1 surface. Different groups of particles (co-passing, counter-passing, trapped) respond differently to the perturbations.Fil: Farengo, Ricardo. Comisión Nacional de Energía Atómica. Gerencia del Area de Investigación y Aplicaciones No Nucleares. Gerencia de Física (centro Atómico Bariloche); Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Comisión Nacional de Energía Atómica. Gerencia del Area de Energía Nuclear. Instituto Balseiro; ArgentinaFil: Ferrari, Hugo Emilio. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Comisión Nacional de Energía Atómica. Gerencia del Area de Energía Nuclear. Instituto Balseiro; Argentina. Comisión Nacional de Energía Atómica. Gerencia del Area de Investigación y Aplicaciones No Nucleares. Gerencia de Física (Centro Atómico Bariloche); ArgentinaFil: Garcia Martinez, Pablo Luis. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Firpo, M. C.. Centre National de la Recherche Scientifique; FranciaFil: Ettoumi, W.. Centre National de la Recherche Scientifique; FranciaFil: Lifschitz, A. F.. Centre National de la Recherche Scientifique; Franci