Eur. Phys. J. D 32, 361-376 (2005)
https://doi.org/10.1140/epjd/e2005-00010-4

Dynamics of a charged particle in a linearly polarized traveling wave

Hamiltonian approach to laser-matter interaction at very high intensities

Commissariat à l'énergie atomique, Direction Ile-de-France, Département de Physique Théorique et Appliquée, B.P. 12, 91680 Bruyères-le-Châtel, France

Corresponding authors: ^a alain.bourdier@cea.fr - ^b david.patin@cea.fr

Received: 10 June 2004
Revised: 4 October 2004
Published online: 1 February 2005

Abstract

The basic physical processes in laser-matter interaction, up to (for a neodymium laser) are now well understood, on the other hand, new phenomena evidenced in 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, here, 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, when the plasma response is taken into account no chaos take 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.