When can Fokker-Planck Equation describe anomalous or chaotic transport?

The Fokker-Planck Equation, applied to transport processes in fusion plasmas, can model several anomalous features, including uphill transport, scaling of confinement time with system size, and convective propagation of externally induced perturbations. It can be justified for generic particle transport provided that there is enough randomness in the Hamiltonian describing the dynamics. Then, except for 1 degree-of-freedom, the two transport coefficients are largely independent. Depending on the statistics of interest, the same dynamical system may be found diffusive or dominated by its L\'{e}vy flights.Comment: 4 pages. Accepted in Physical Review Letters. V2: only some minor change

Variabilité des blazars détectés par le télescope spatial Fermi-LAT Etude de 3C 454.3 et développement d'une méthode de génération de courbes de lumière optimisées.

The Fermi Gamma-ray Space Telescope was launched on 2008 June 11, carrying the Large Area Telescope(LAT), sensitive to gamma-rays in the 20 MeV - 300 GeV energy range. The data collected since then allowed to multiply by a factor of 10 the number of Active Galactic Nuclei (AGN) detected in the GeV range. Gamma-rays observed in AGNs come from energetic precesses bringing into play very high energy charged particles. These particles are confined in a magnetized plasma jet rising in a region close to the supermassive black hole in the center of the host galaxy. This jet moves away with velocities as high as 0.9999c, forming in many cases radio lobes on kiloparsec or even megaparsec scales. Among the AGNs, those whose jet inclination angle to the line of sight is small are called blazars. The combination of this small inclination angle with relativistic ejection speeds leds to relativistic effects : apparent superluminal motions, amplification of the luminosity and modification of the time scales. Blazars are characterized by extreme variability at all wavelengths, on time scales from a few minutes to several months. A temporal and spectral study of the most luminous of those detected by the LAT, 3C 454.3, was done so as to constrain emission models. A new method for generating adaptive-binning lightcurves is also suggested in this thesis. It allows to extract the maximum of information from the LAT data whatever the flux state of the source.Dédié à l'étude du ciel en rayons gamma, le satellite Fermi comporte à son bord le Large Area Telescope (LAT), sensible au rayonnement gamma de 20 MeV à 300 GeV. Les données recueillies par le LAT depuis son lancement en 2008 ont permis de multiplier par 10 le nombre de noyaux actifs de galaxie (NAG) détectés dans le domaine du GeV. Les rayons gamma observés dans les NAGs proviennent de processus énergétiques faisant intervenir des particules chargées de très haute énergie. Ces particules sont confinées dans un jet de plasma magnétisé qui prend sa source dans une région proche du trou noir supermassif habitant la zone centrale de la galaxie hôte. Ce jet s'éloigne à des vitesses aussi élevées que 0.9999c, formant dans de nombreux cas des lobes radio sur des échelles du kiloparsec voire du mégaparsec. Les NAGs dont le jet fait un angle faible avec la ligne de visée sont appelés blazars. La combinaison de cette très faible inclinaison du jet par rapport à la ligne de visée et de vitesses d'éjection relativistes donne lieu à des effets relativistes : mouvements apparents superluminiques, amplification de la luminosité et modification des échelles de temps. Les blazars sont caractérisés par une extrême variabilité à toutes les longueurs d'onde, sur des échelles de temps allant de quelques minutes à plusieurs mois. Une étude temporelle et spectrale du plus brillant d'entre ceux détectés par le LAT, 3C 454.3, a été réalisée afin de contraindre les modèles d'émission. Une nouvelle méthode de génération de courbes de lumière à échantillonnage adaptatif est également proposée dans cette thèse. Celle-ci permet d'extraire le maximum d'information des données du LAT quel que soit l'état de flux de la source

Roundabout relaxation: collective excitation requires a detour to equilibrium

Relaxation to equilibrium after strong and collective excitation is studied, by using a Hamiltonian dynamical system of one dimensional XY model. After an excitation of a domain of $K$ elements, the excitation is concentrated to fewer elements, which are made farther away from equilibrium, and the excitation intensity increases logarithmically with $K$. Equilibrium is reached only after taking this ``roundabout'' route, with the time for relaxation diverging asymptotically as $K^\gamma$ with $\gamma \approx 4.2$.Comment: 4 pages, 5 figure

An adaptive-binning method for generating constant-uncertainty/constant-significance light curves with Fermi-LAT data

We present a method enabling the creation of constant-uncertainty/constant-significance light curves with the data of the Fermi-Large Area Telescope (LAT). The adaptive-binning method enables more information to be encapsulated within the light curve than with the fixed-binning method. Although primarily developed for blazar studies, it can be applied to any sources. This method allows the starting and ending times of each interval to be calculated in a simple and quick way during a first step. The reported mean flux and spectral index (assuming the spectrum is a power-law distribution) in the interval are calculated via the standard LAT analysis during a second step. The absence of major caveats associated with this method has been established by means of Monte-Carlo simulations. We present the performance of this method in determining duty cycles as well as power-density spectra relative to the traditional fixed-binning method.Comment: 17 pages, 13 figures, 5 tables. Submitted to A&

Fermi observations of gamma-ray outbursts from 3C 454.3 in December 2009 and April 2010

The flat-spectrum-radio-quasar 3C 454.3 underwent an extraordinary outburst in December 2009 when it became the brightest gamma-ray source in the sky for over one week. Its daily flux measured with the Fermi Large Area Telescope at photon energies E > 100MeV reached 22 ± 1 × 10−6 ph cm−2 s−1. It again became the brightest source in the sky in April 2010, triggering a pointedmode observation by Fermi. The γ-ray temporal and spectral properties during these exceptional events are presented and discussed

An equilibrium model for RFP plasmas in the presence of resonant tearing modes

The equilibrium of a finite-beta RFP plasma in the presence of saturated-amplitude tearing modes is investigated. The singularities of the MHD force balance equation JXB=grad(p) at the modes rational surfaces are resolved through a proper regularization of the zeroth-order (equilibrium) profiles, by setting to zero there the gradient of the pressure and parallel current density. An equilibrium model, which satisfies the regularization rule at the various rational surfaces, is developed. The comparison with the experimental data from the Reversed Field eXperiment (RFX) gives encouraging results. The model provides an easy tool for magnetic analysis: many aspects of the perturbations can be analyzed and reconstructed.Comment: Final accepted version. 36 page

Hamiltonian Dynamics and the Phase Transition of the XY Model

A Hamiltonian dynamics is defined for the XY model by adding a kinetic energy term. Thermodynamical properties (total energy, magnetization, vorticity) derived from microcanonical simulations of this model are found to be in agreement with canonical Monte-Carlo results in the explored temperature region. The behavior of the magnetization and the energy as functions of the temperature are thoroughly investigated, taking into account finite size effects. By representing the spin field as a superposition of random phased waves, we derive a nonlinear dispersion relation whose solutions allow the computation of thermodynamical quantities, which agree quantitatively with those obtained in numerical experiments, up to temperatures close to the transition. At low temperatures the propagation of phonons is the dominant phenomenon, while above the phase transition the system splits into ordered domains separated by interfaces populated by topological defects. In the high temperature phase, spins rotate, and an analogy with an Ising-like system can be established, leading to a theoretical prediction of the critical temperature $T_{KT}\approx 0.855$.Comment: 10 figures, Revte