Dynamics of a charged particle in a linearly polarized traveling electromagnetic wave

Summary form only given, as follows. The relativistic motion of a charged particle in a linearly polarized homogeneous electromagnetic wave is considered using the Hamiltonian formalism. First, a single particle in a linearly polarized traveling wave propagating in a nonmagnetized space is studied. It is shown that the charged particle can have a high average velocity along the propagation direction of the wave. The same result is derived considering an electromagnetic wave in a cold electron plasma. The case of a traveling wave propagating along a constant homogeneous magnetic field is then considered and shown to be nonintegrable. Using canonical transformations, it is shown that the the equations of motion can be derived from an autonomous Hamiltonian. The system has three degrees of freedom and a formal solution is found for all the variables of the system. When the wave propagates in vacuum and when the particle is initially resonant and at rest, a set of equations is found coupling the energy of the particle and the phase of the wave. Then, the expression for the energy and the differential equation for the phase allow a solution in terms of quadratures. Asymptotic solutions for the phase, the energy and consequently all of the variables are found. Finally, the dynamics of a test particle in a traveling relativistically strong linearly polarized wave propagating in a plasma is studied. The form of the wave is a solution of the Maxwell equations and the Lorentz equation.