We investigate how the Fraunhofer diffraction pattern produced by a slit is modified under a Lorentz transformation. Starting from the diffraction of a monochromatic wave in the slit rest frame, we analyze the angular redistribution of the diffracted intensity in a second inertial frame moving uniformly perpendicular to the slit axis. Two configurations are considered: normal incidence and oblique incidence of the incoming wave.In the laboratory frame, the diffraction pattern exhibits the usual symmetric distribution of minima around the central maximum when expressed in the appropriate angular variable. After transformation to the moving frame, this symmetry is generally lost: the diffraction profile becomes asymmetric with respect to the direction of maximum intensity. We show that this effect arises from relativistic aberration of light and reflects a nonlinear reparametrization of the angular coordinates rather than a modification of the diffraction process itself. In particular, the positions of the diffraction extrema remain well defined under Lorentz transformation, even though their angular spacing becomes distorted in the boosted frame.We further show that the sinc-type functional form of the Fraunhofer diffraction pattern is preserved under the Lorentz transformation. The observed asymmetry therefore originates entirely from the relativistic mapping between observation angle and transverse wave-vector component. These results provide a simple illustration of how a familiar wave-optics phenomenon is reshaped by special relativity, and they may be relevant to numerical or experimental studies of radiation patterns in moving optical or plasma systems.

Multiple filamentation poses a significant challenge for laser pulse propagation in the atmosphere. The purpose of this article is to explore how atmospheric turbulence influences the development of modulational instability, which results in multiple filamentation. We confirm a result that we previously published. We show through multiple analytical approaches that the growth rate of this instability decreases when the refractive index displays stochastic behavior.

Multiple filamentation is a major problem for laser pulse propagation in the atmosphere. In this article, we study the influence of a turbulent atmosphere on the growth of the modulational instability which is the cause of multiple filamentation. It is shown that the growth rate of this instability decreases when it is considered that the index of refraction has a stochastic behavior. A good qualitative agreement between the analytical and numerical results is obtained.

The analysis of observational data sequences in Geophysics consists of characterizing the underlying dynamics. An important preliminary step aims to analyze the variability related to the observed dynamic. The specific objectives related to this step are to remove noise, to determine the overall trend of the observational time series and to identify the relevant components contributing significantly to the original time series variability knowing that their number determines the dimensionality of the observed dynamics. Most of the observational time series have characteristics of non-stationarity and present fluctuations at all-time scales. In this context, variability analysis consists in representing time series in the time-frequency space and requires the development of specific numerical signal decomposition methods. The most commonly used techniques are adaptive and data-driven and among the most cited in the literature are the empirical mode decomposition, the empirical wavelet transform, and singular spectrum analysis. In this work, we describe all of these techniques and evaluate their ability to remove noise and to identify components corresponding to the physical processes involved in the evolution of the observed system and deduce the dimensionality of the associated dynamics. Results obtained with all of these methods on experimental total ozone columns and rainfall time series will be discussed and compared.

Most observational data sequences in geophysics can be interpreted as resulting from the interaction of several physical processes at several timescales and space scales. In consequence, measurement time series often have characteristics of non-linearity and non-stationarity and thereby exhibit strong fluctuations at different timescales. The application of decomposition methods is an important step in the analysis of time series variability, allowing patterns and behaviour to be extracted as components providing insight into the mechanisms producing the time series. This study introduces empirical adaptive wavelet decomposition (EAWD), a new adaptive method for decomposing non-linear and non-stationary time series into multiple empirical modes with non-overlapping spectral contents. The method takes its origin from the coupling of two widely used decomposition techniques: empirical mode decomposition (EMD) and empirical wavelet transformation (EWT). It thus combines the advantages of both methods and can be interpreted as an optimization of EMD. Here, through experimental time series applications, EAWD is shown to accurately retrieve different physically meaningful components concealed in the original signal.

The plasma refraction index can be calculated by different methods. In this paper, a physical approach is presented and applied to non-linear situations. We have particularly focused on the case where the mass of the electrons subjected to the wave becomes relativistic. In the case of a circularly polarized high intensity wave, ionization is considered.

Throughout scientific research, the state space reconstruction that embeds a non-linear time series is the first and necessary step for characterizing and predicting the behavior of a complex system. This requires to choose appropriate values of time delay T and embedding dimension dE. Three methods are applied and discussed on nonlinear time series provided by the Rössler attractor equations set: Cao's method, the C-C method developed by Kim et al. and the C-C-1 method developed by Cai et al. A way to fix a parameter necessary to implement the last method is given. Focus has been put on small size and/or noisy time series. The reconstruction quality is measured by using a criterion based on the transformation smoothness.

Optimization of the beam quality and electronic trapped charge in the cavity are key issues of laser wake field acceleration. The effect of an initially applied uniform magnetic field, parallel to the direction of propagation of the pump pulse, on the laser wakefield is explored. First, an analytic model for the laser wakefield is built up in the case when such an external magnetic field is applied. Then, simulations are performed with a 3D quasi-cylindrical particle in cell code in the blowout (or bubble) regime. Transverse currents are generated at the rear of the bubble which amplify the longitudinal magnetic field. For several plasma and laser parameters, the wake shape is altered and trapping can be reduced or cancelled by the magnetic field. When considering optical injection, and when two counterpropagating waves interact with a rather high plasma density, trapping is not affected by the magnetic field. In this range of plasma and laser parameters, it is shown that the longitudinal magnetic field can reduce or even prevent self-injection and enhance beam quality.

It is shown that stochastic heating can play an important role in Laser Wake Field Acceleration. When considering low density plasma interacting with a high intensity wave perturbed by a low intensity counterpropagating wave, stochastic heating can provide electrons with the right momentum for trapping in the wake field. The influence of stochastic acceleration on the trapping of electrons is compared to the one of cold injection by considering several polarizations of the colliding pulses. For some value of the plasma density and pulse duration, a transition from an injection due to stochastic acceleration to a cold injection dominated regime – regarding the trapped charge – has been observed from PIC code simulations. When the plasma density exceeds some value, stochastic heating becomes important and is necessary in some circumstances to get electrons trapped into the wakefield.

The enhancement of trapping and the optimization of beam quality are two key issues of Laser Wakefield Acceleration (LWFA). The effect of a homogenous constant magnetic field B0, parallel to the direction of propagation of the pump pulse, is studied in the blowout regime via 2Dx3Dv Particle-In-Cell simulations. Electrons are injected into the wake using a counter-propagating low amplitude laser. Transverse currents are generated at the rim of the bubble, which results in the amplification of the B0 field at the rear of the bubble. Therefore the dynamics of the beam is modified, the main effect is the reduction of the transverse emittance when B0 is raised. Depending on beam loading effects the low energy tail, observed in the non-magnetized case, can be suppressed when B0 is applied, which provides a mono-energetic beam.

The influence of an external static field applied in the direction parallel to the direction of propagation of a high intensity driving laser pulse on the electron trapping in laser wakefield acceleration is explored.

The dynamics of a charged particle in a relativistic strong electromagnetic plane wave propagating in vacuum is studied first, the problem is shown to be integrable when the wave propagates in vacuum. One particle in a high-intensity wave, propagating in a vacuum, perturbed by a low-intensity traveling wave is considered next. Resonances are identified, and conditions for resonance overlap are studied. Stochastic acceleration is shown by considering a single particle. It is confirmed in plasma in realistic situations with particle-in-cell code simulations. Finally, it is shown that when considering a low-density plasma interacting with a high-intensity wave perturbed by a low-intensity counter-propagating wave, stochastic heating can provide electrons with the right momentum for trapping in the wakefield and efficient acceleration.

Filamentation in air with ultraviolet pulses is reviewed. Channels of considerably more energy than in the visible/near IR can be generated.

Summary form only given. The propagation of intense laser pulses in the atmosphere is relevant to a wide range of applications: Lidar, lightening protection, wave guides in air, directed energy. Due to the nonlinear part of air refraction index, high power laser pulses can self-focus during their propagation through the atmosphere. Beyond critical power, self-focusing overcomes diffraction and the beam collapses. When self focusing is balanced by creation of plasma, a stable filament can form. Much of the theoretical work on filaments has been conducted in the infrared (IR), typically with wavelengths near 800 nm and pulse durations of the order of hundreds of fs. Since the peak intensity in these filaments exceeds 100 TW/cm 2 , nonlinear effects can be substantial. Some researches have begun to investigate the possibility of creating self-guided pulses in the ultraviolet (lambda ~ 250 nm ). In this case, peak intensity is only of the order of 1 TW/cm 2 . Consequently most of the higher order nonlinear effects can be neglected. It has been recently proposed by Schwarz and Diels that the UV filaments should scale with respect to increasing the pulse duration. This should result in long distance propagation of long duration pulses carrying a high energy. The present paper addresses the long UV pulses (tau ~ 1 ns ) propagation. It appears that the values of two of the parameters chosen by Schwarz and Diels in their model are wrong. It has been shown that attachment must be taken into account. The new equations obtained to describe the propagation of the filament tend to those published by Schwarz and Diels when the attachment mechanism is neglected.1 We will compare the results obtained with the new parameters and equations to those obtained by Schwarz and Diels. The domain of validity for a steady state analysis will be discussed. The feasibility of long UV filaments is also being studied experimentally. The laser system used to create UV filaments is based on a ND:YAG mode-locked oscillator. It produces up to 300 ps pulses at 1064 nm that are amplified in several Nd:YAG amplifiers. Their wavelength is then converted from 1064 to 266 nm by two second harmonic generations. The resulting duration is close to 200 ps, and will be further increased by using a Michelson interferometer with polarization separation. Our very first results should be presented at the conference.

We present two simplified models for the propagation of a long pulse UV filament in air, predicting the evolution of the beam diameter with distance, and the beam profile.

Recently, PIC simulations results published by Tajima et al. and Sheng et al. have shown that chaos can play an important role in the efficient electron heating observed in laser-plasma interaction at very high intensities. These results led us to investigate the condition under which significant stochastic heating is likely to take place. First, we shall consider the dynamics of a single charged particle in the field of a high intensity wave propagating in an unmagnetized vacuum or plasma. In a second part, the effect of a constant homogeneous magnetic field will be discussed. Third, in the case of a plasma interacting with several electromagnetic waves, the use of Chirikov's criterion to predict the conditions favouring stochastic heating will be presented. Finally, it will be shown that when considering a low density plasma interacting with a high intensity wave perturbed by a low intensity counterpropagating wave, stochastic heating can provide electrons with the right momentum for trapping in the wake field and efficient acceleration.

The effect on parametric instability growth of pump wave incoherence is treated by deriving a set of equations governing the space-time evolution of the ensemble-average coupled-mode amplitudes and intensities. Particular attention is paid to establishing the regions of validity of the statistical description. Thresholds, growth rates, and amplification rates are given for both spatially and temporally incoherent pump waves. Both absolutely and convectively unstable modes are considered. The statistical results are verified where appropriate by numerical integration of the coupled-mode equations with different models of pump incoherence.

The possibility of producing a low emittance energetic proton beam by means of a high intensity laser interacting with a solid target has been demonstrated experimentally and extensively investigated theoretically over the past years. These proton beams are very promising for applications related to inertial confinement fusion, plasma diagnostics, isochoric heating of matter or medical applications. There is now an increasing need to work out new setups capable of improving the proton beam properties. Configurations coupling two targets, two lasers, or both, look particularly encouraging in this respect. We have performed 2D PIC simulations with the code Calder (1) to study new setups and determine favorable parameters. The main proton acceleration mechanism at work with nowadays lasers is Target Normal Sheath Acceleration (2). The lasers heats electrons at the irradiated surface and these hot electrons cross the target and create a strong electrostatic field when they exit the target. This field then accelerates protons from the back surface. There are different ways to improve proton acceleration with this mechanism. All targets used in this study are 1 ∝m thick and at a density of 10 times the critical density (nc). For cases with one laser, the pulse has a duration of 36 fs and an intensity of 1020 W/cm2. When two pulses are used, they have the same intensity but a duration of 18 fs. By combining two lasers with one target it is possible to increase the duration of the acceleration phase. This setup only presents a sharp increase of the maximum proton energy for small delays between the two pulses. For a delay of 15 fs, this increase reaches 36.2%. The evolution with time of the maximum proton energy is not very different from the one with only one laser. It is also possible to combine one laser with two targets. By placing a secondary target behind the first one, hot electrons leaving the primary target can create a second accelerating field behind