Radiation Scattering from Relativistic Electrons in Intense Laser Light*

Electrons in the focus of a high powered laser undergo relativistic motion. In its average center-of-mass frame, the electron follows a well-known figure-eight trajectory. The resulting radiation pattern of the scattered light is described by a nonlinear equation with an integral solution, as described by Sarachik and Schappert in 1970.  They approximated the integral with a series of Bessel functions. We compare the computational requirements of the approximation to performing the integral numerically. We also examine the accuracy and limitations of using a finite number of Bessel functions in the expansion.