The various manifestations of collisionless dissipation in wave propagation

The propagation of an electrostatic wave packet inside a collisionless and initially Maxwellian plasma is always dissipative because of the irreversible acceleration of the electrons by the wave. Then, in the linear regime, the wave packet is Landau damped, so that in the reference frame moving at the group velocity, the wave amplitude decays exponentially with time. In the nonlinear regime, once phase mixing has occurred and when the electron motion is nearly adiabatic, the damping rate is strongly reduced compared to the Landau one, so that the wave amplitude remains nearly constant along the characteristics. Yet, we show here that the electrons are still globally accelerated by the wave packet, and, in one dimension, this leads to a non local amplitude dependence of the group velocity. As a result, a freely propagating wave packet would shrink, and, therefore, so would its total energy. In more than one dimension, not only does the magnitude of the group velocity nonlinearly vary, but also its direction. In the weakly nonlinear regime, when the collisionless damping rate is still significant compared to its linear value, this leads to an effective defocussing effect which we quantify, and which we compare to the self-focussing induced by wave front bowing.Comment: 23 pages, 6 figure

A predictive inline model for nonlinear stimulated Raman scattering in a hohlraum plasma

In this Letter, we introduce a new inline model for stimulated Raman scattering (SRS), which runs on our radiation hydrodynamics code TROLL. The modeling follows from a simplified version of a rigorous theory for SRS, which we describe, and accounts for nonlinear kinetic effects. It also accounts for the SRS feedback on the plasma hydrodynamics. We dubbed it PIEM because it is a fully PredIctivE Model, no free parameter is to be adjusted \textit{a posteriori}~in order to match experimental results. PIEM predictions are compared against experimental measurements performed at the Ligne d'Int\'egration Laser. From these comparisons, we discuss PIEM ability to correctly catch the impact of nonlinear kinetic effects on SRS

Integrated random processes exhibiting long tails, finite moments and 1/f spectra

A dynamical model based on a continuous addition of colored shot noises is presented. The resulting process is colored and non-Gaussian. A general expression for the characteristic function of the process is obtained, which, after a scaling assumption, takes on a form that is the basis of the results derived in the rest of the paper. One of these is an expansion for the cumulants, which are all finite, subject to mild conditions on the functions defining the process. This is in contrast with the Levy distribution -which can be obtained from our model in certain limits- which has no finite moments. The evaluation of the power spectrum and the form of the probability density function in the tails of the distribution shows that the model exhibits a 1/f spectrum and long tails in a natural way. A careful analysis of the characteristic function shows that it may be separated into a part representing a Levy processes together with another part representing the deviation of our model from the Levy process. This allows our process to be viewed as a generalization of the Levy process which has finite moments.Comment: Revtex (aps), 15 pages, no figures. Submitted to Phys. Rev.

‘My language … I don’t know how to talk about it’: children’s views on language diversity in primary schools in France and England

This article investigates the ways in which children from immigrant backgrounds view the place of ‘other’ languages in primary schools in France and England. This article draws on findings from a cross-national ethnographic study, which investigated the experiences of 10- and 11-year-old children of immigrants in two primary schools, one in France and one in England. It shows how, in both schools, children had to negotiate the symbolic domination of a single legitimate language and viewed their other languages as inferior, undesirable or illicit. Building on the work of Pierre Bourdieu, findings in this paper contribute insights into the complex debates around language diversity, multilingualism and intercultural communication in schools in France and England