Counterpropagating radiation emitted by an electron in the field of a Gaussian laser pulse

The transition from the nonlinear Thomson scattering (electron initially at rest) to the classical limit of Compton scattering (electron moving towards the laser pulse) is considered. The radiation emitted by an electron in the form of plane waves in the far zone is analyzed, and the intensity distribution over the solid angle is obtained. By constructing radiation diagrams, we find numerically the dependences of the intensity and power of radiation on the initial energy of the electron The backscattering intensity as is find analytically is proportional to six power in initial energy and to the peak power of the laser pulse. It is shown that as the initial energy of the electron increases, the effective solid angle of the scattered radiation decreases monotonically and becomes constant.