Stochastic heating in ultra high intensity laser-plasma interaction

The basic physical processes in laser-matter interaction, up to 1017 W/cm2 (for a Neodymium laser) are now well understood, on the other hand, new phenomena evidenced in particle-in-cell (PIC) code simulations have to be investigated above. Thus, the relativistic motion of a charged particle in a linearly polarized homogeneous electromagnetic wave is studied, in this paper, using the Hamiltonian formalism. First, the motion of a single particle in a linearly polarized traveling wave propagating in a non-magnetized space is explored. The problem is shown to be integrable. 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. After this short time, even when the plasma response is taken into account no chaos takes place at least when considering low densities and/or high wave intensities. The case of a charged particle in a traveling wave propagating along a constant homogeneous magnetic field is then considered. The problem is shown to be integrable when the wave propagates in vacuum. The existence of a synchronous solution is shown very simply. In the case when the wave propagates in a low density plasma, using a simplifying Lorentz transformation, it is shown that the system can be reduced to 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. Finally, stochastic instabilities are studied by considering the motion of one particle in a very high intensity wave perturbed by one or two low intensity traveling waves. Resonances are identified and conditions for resonance overlap are studied. PIC code simulation results confirm the occurrence of stochastic heating.