Stochastic heating of free electrons in multiple electromagnetic waves: A simple physical analysis.

It is established that charged particles crossing the interference field of two colliding electromagnetic (EM) waves can behave chaotically, leading to a stochastic heating of the particle distribution. A fine understanding of the stochastic heating process is crucial to the optimization of many physical applications requiring a high EM energy deposition to these charged particles. Predicting key stochastic heating features (particle distribution, chaos threshold) is usually achieved using a heavy Hamiltonian formalism required to model particle dynamics in chaotic regimes. Here, we explore an alternative and more intuitive path, which makes it possible to reduce the equations of motion of particles to rather simple and well-known physical systems such as Kapitza and gravity pendulums. Starting from these simple systems, we first show how to estimate chaos thresholds by deriving a model of the stretching and folding dynamics of the pendulum bob in phase space. Based on this first model, we then derive a random walk model for particle dynamics above the chaos threshold, which can predict major features of stochastic heating for any EM polarization and angle θ_{i}.

Pseudospectral Maxwell solvers for an accurate modeling of Doppler harmonic generation on plasma mirrors with particle-in-cell codes.

With the advent of petawatt class lasers, the very large laser intensities attainable on target should enable the production of intense high-order Doppler harmonics from relativistic laser-plasma mirror interactions. At present, the modeling of these harmonics with particle-in-cell (PIC) codes is extremely challenging as it implies an accurate description of tens to hundreds of harmonic orders on a broad range of angles. In particular, we show here that due to the numerical dispersion of waves they induce in vacuum, standard finite difference time domain (FDTD) Maxwell solvers employed in most PIC codes can induce a spurious angular deviation of harmonic beams potentially degrading simulation results. This effect was extensively studied and a simple toy model based on the Snell-Descartes law was developed that allows us to finely predict the angular deviation of harmonics depending on the spatiotemporal resolution and the Maxwell solver used in the simulations. Our model demonstrates that the mitigation of this numerical artifact with FDTD solvers mandates very high spatiotemporal resolution preventing realistic three-dimensional (3D) simulations even on the largest computers available at the time of writing. We finally show that nondispersive pseudospectral analytical time domain solvers can considerably reduce the spatiotemporal resolution required to mitigate this spurious deviation and should enable in the near future 3D accurate modeling on supercomputers in a realistic time to solution.