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In this paper we focus on WENO-based methods for the simulation of the 1D Quasi-Relativistic Vlasov–Maxwell (QRVM) model used to describe how a laser wave interacts with and heats a plasma by penetrating into it. We propose several non-oscillatory methods based on either Runge–Kutta (explicit) or Time-Splitting (implicit) time discretizations. We then show preliminary numerical experiments. [ABSTRACT FROM AUTHOR]

Abstract: We report on recent experimental results on electron acceleration using two counter-propagating ultrashort and ultraintense laser pulses. At the collision, the two pulses drive a standing wave which is able to pre-accelerate plasma electrons which can then be trapped in the plasma wave. Optical diagnostics of the collision reveal signatures of this standing wave. Electron acceleration results in this regime are reviewed: the use of colliding pulses enables the generation of stable, tunable and high quality electron beams at the 100–200 MeV level. Detailed comparisons with 3D Particle in Cell (PIC) simulations give deeper insight on the role of the nonlinear propagation of the pump pulse on the performance of the accelerator. This deeper understanding has allowed us to optimize the beam charge of the accelerator at high energy. To cite this article: J. Faure et al., C. R. Physique 10 (2009). [Copyright &y& Elsevier]