Ultrahigh intensity laser-plasma interaction: a Hamiltonian approach

The basic physical processes in laser-matter interaction, up to 10^17 W/cm^2 , are now well understood, on the other hand, a large number of issues remain open in the study of the relativistic interaction regime above 10^18 W/cm^2. The relativistic motion of a charged particle in a linearly polarized homogeneous electromagnetic wave is studied using the Hamiltonian formalism. Conditions for stochastic instability resulting in electron quasilinear diffusion are investigated. First, the motion of a single particle in a linearly polarized traveling wave propagating in a nonmagnetized space is studied. The results obtained are compared to those derived considering a cold electron plasma model. When the phase velocity is close to c, it is shown that the two approaches are in good agreement during a finite time. The case of a traveling wave propagating along a constant homogeneous magnetic field is then considered. Using a simplifying Lorentz transformation in the case of superluminous waves, it is shown that the system can be described with a time-dependent system with two degrees of freedom. The system is shown to be nonintegrable, chaos appears when a secondary resonance and a primary resonance overlap. The problem is shown to be integrable when the wave propagates in vacuum. The analytic solution is derived. The existence of a synchronous solution is shown very simply. Then, the stability of a single particle interacting with a strong intensity electromagnetic wave and a se cond wave which is assumed to be a perturbation is studied. A resonance condition is derived by solving the Hamilton-Jacobi equation. Considering two electromagnetic low intensity waves, Chirikov criterium is used to predict stochastic heating. PIC code simulation results, confirming the existence of the stochastic heating for the electrons, are discussed. Finally, a new fast ignitor scheme is presented.