Nonlinear stability of a Vlasov equation for magnetic plasmas

The mathematical description of laboratory fusion plasmas produced in Tokamaks is still challenging. Complete models for electrons and ions, as Vlasov-Maxwell systems, are computationally too expensive because they take into account all details and scales of magneto-hydrodynamics. In particular, for most of the relevant studies, the mass electron is negligible and the velocity of material waves is much smaller than the speed of light. Therefore it is useful to understand simplified models. Here we propose and study one of those which keeps both the complexity of the Vlasov equation for ions and the Hall effect in Maxwell's equation. Based on energy dissipation, a fundamental physical property, we show that the model is nonlinear stable and consequently prove existence

Modelling and numerical simulation of plasma flows with two-fluid mixing

13 pagesFor the modelling of plasma flows at very high temperature such the ones produced by laser beams, one must account for a bi-temperature compressible Euler system coupled to electron thermal conduction and radiative conduction. Moreover, mixing of two different fluids can occur, the two fluids occupying the same volume. For modelling such a phenomenon, instead of dealing with the conservation of mass, momentum and energy for each fluid, we propose here a simplified model which will be easier to implement in a multi-physics Lagrangian 2D code. The principle is to use a closure for expressing the relative velocity between the two fluids with the help of the gradient of the concentration. So, besides the classical system, the final model consists in a non-linear diffusion equation for the concentration and an equation for the mixing kinetic energy (analogous to the one used in turbulence models). We present also first numerical 2D simulations using this model

On the Boyd-Kadomstev System for a three-wave coupling problem and its asymptotic limit

article accepted for publication in Comm Math. PhysicsA paraitre dans Comm. Math. PhysicsWe consider the Boyd-Kadomstev system which is in particular a model for the Brillouin backscattering in laser-plasma interaction. It couples the propagation of two laser beams, the incoming and the backscattered waves, with an ion acoustic wave which propagates at a much slower speed. The ratio $\varepsilon$ between the plasma sound velocity and the (group) velocity of light is small, with typical value of order $10^{-3}$. In this paper, we make a rigorous analysis of the behavior of solutions as $\varepsilon$ goes to 0. This problem can be cast in the general framework of fast singular limits for hyperbolic systems. The main new point which is addressed in our analysis is that the singular relaxation term present in the equation is a nonlinear first order system

On the Boyd-Kadomstev System for a three-wave coupling problem and its asymptotic limit

A paraitre dans Comm. Math. PhysicsWe consider the Boyd-Kadomstev system which is in particular a model for the Brillouin backscattering in laser-plasma interaction. It couples the propagation of two laser beams, the incoming and the backscattered waves, with an ion acoustic wave which propagates at a much slower speed. The ratio $\varepsilon$ between the plasma sound velocity and the (group) velocity of light is small, with typical value of order $10^{-3}$. In this paper, we make a rigorous analysis of the behavior of solutions as $\varepsilon$ goes to 0. This problem can be cast in the general framework of fast singular limits for hyperbolic systems. The main new point which is addressed in our analysis is that the singular relaxation term present in the equation is a nonlinear first order system

On the slowing down of charged particles in a binary stochastic mixture

International audienceA kinetic equation is addressed for the straight line slowing-down of charged particles, the geometrical domain consists of randomly distributed spherical grains of dense material imbedded in a light material. The dense material is assumed to be a Boolean medium (the sphere centers are sampled according to a Poisson random field). We focus on the fraction of particles $P$ which stop in the light medium. After setting some properties of the Boolean medium, we perform an asymptotic analysis in two extreme cases corresponding to grain radius very small and very large with respect to the stopping distance of the dense material. A fitted analytic formula is proposed for the quantity P and results of numerical simulations are presented in order to validate the proposed formula

Laser Textured Black Silicon Solar Cells with Improved Efficiencies

International Conference on Intelligent Materials and Mechanical Engineering (MEE 2011), Guangzhou, PEOPLES R CHINA, SEP 24-25, 2011International audienceFemtosecond laser irradiation of silicon has been used for improving light absorption at its surface. In this work we demonstrate the successful implementation of femtosecond laser texturisation to enhance light absorption at Si solar cell surface. In order to adapt this technology into solar industry, the texturisation process is carried out in air ambient. The microstructure similar to what has been produced in vacuum can be made in air by using appropriate laser conditions. The texturised surface shows excellent optical properties with a reflectivity down to 7% without crystalline orientation dependence. Junction formation and metallisation proceeded after texturisation. Suns-Voc measurements are performed to evaluate the cell performance and decent electrical characteristics have been achieved

Equations de transport avec conditions aux limites de type reflexion

SIGLECNRS-CDST / INIST-CNRS - Institut de l'Information Scientifique et TechniqueFRFranc

Analyse asymptotique de l'equation de Poisson couplee a la relation de Boltzmann quasi neutralite des plasmas

Available at INIST (FR), Document Supply Service, under shelf-number : RP 12161 / INIST-CNRS - Institut de l'Information Scientifique et TechniqueSIGLEFRFranc