Accurate calculation of radiation damping parameters in the interaction between very intense laser beams and relativistic electron beams

Abstract

We prove that the radiation damping force and the rate of change of the damping energy, in the Landau-Lifshitz forms, in interactions between very intense laser beams and relativistic electron beams, are periodic functions of only one variable, that is the phase of the electromagnetic field. The property is proved without using any approximation, in the most general case, when the degree of polarization of the electromagnetic field, the initial phase of the incident field and the initial energy of the electron have arbitrary values. This property leads to a strong simplification of the calculation of the radiation reaction parameters and of their dependence on the initial electron energy and angular frequency of the laser beam. Our analysis is performed in the proper inertial system of the electron. The radiation reaction is significant for laser beam intensities of the order 10 22 W/cm 2 , and for electron energy greater than 1 GeV. The calculations reveal limitations of the method of generating hard radiations by interactions between laser beams and relativistic electron beams.