Method of Numerical Determination of the Electron Radiation Power in the Focus of an Ultrashort Laser Pulse

A new numerical method of integration over two angles of the radiation pattern of an electron moving with acceleration is presented. The method uses the representation of a two-dimensional integral in the form of a double integral sum over angular sectors, a linear approximation of the intensity function over the angular points of an elementary sector, taking the integral from the approximation in an analytical form. Using the new method, the problem of relativistic electrodynamics related to the calculation of the radiation power of an electron moving along a complex trajectory in the vicinity of the focus of a femtosecond laser pulse is solved.