Interaction of a Charged Particle with Strong Plane Electromagnetic Wave in Vacuum

Abstract

What can we expect from particle–strong wave interaction in vacuum? It is well known that the radiation or absorption of photons by a free electron in vacuum is forbidden by the energy and momentum conservation laws, which means that the real energy exchange between a free electron and plane monochromatic wave in vacuum is impossible, isn’t it? Then, is it worth considering the interaction of a free electron with strong monochromatic wave in vacuum? In other words, what can we expect from the strong wave fields in nonlinear theory with respect to the weak ones described by the linear theory? For example, what are the changes in cross section of the major electrodynamic process of electron–photon interaction, that is, Compton effect (which in the one-photon approximation within quantum electrodynamics is described by the Klein–Nishen formula) at a high density of incident photons? Lastly, how strong should a wave field be for revelation of nonlinear effects in vacuum? What are the criteria of the strong field? To answer these questions one must first study the dynamics of a charged particle in the field of a plane electromagnetic wave of arbitrary high intensity in vacuum on the basis of the classical and quantum equations of motion. Then, with the help of the classical trajectory of the particle and dynamic wave function in the quantum description, the nonlinear radiation in the scope of the classical and quantum theories—the Compton effect in the field of electromagnetic wave of arbitrary high intensity—will be treated. We will start from the relativistic equations, because in the field of a strong wave even a particle initially at rest becomes relativistic. Then, the amplitude of a strong wave will be assumed invariable, i.e., the radiation effects do not influence the magnitude of a given strong wave field.