Influence of beam waist radius and initial phase on spectrum and spatial spectrum

Based on Thomson scattering classical theory and single-electron model, we study the spatial spectrum and spectrum of laser driven high-energy electron radiation corresponding to different waist radius and initial phase. With the help of MATLAB software to complete the numerical simulation, we find that with the initial phase is unchanged, when the beam waist radius b(0) increases, the trajectory of the electron does not change significantly. The main peak of the threedimensional spectrum will rise slightly near b(0) = 2:2?(0), and then decline sharply, and the corresponding harmonic number is also declining. While the secondary peak keeps rising, and its corresponding harmonic frequency also keeps rising. When the initial phase value is larger, the sharp drop of the main peak and the sharp rise of the secondary peak in the spectrum will be more obvious, and the secondary peak is more sensitive to the change of polar angle. In the spatial spectrum, the angle range will increase with the increase in b(0), and the collimation will become worse. In addition, when the beam waist radius is unchanged and the electron collides at the focus, the monochromaticity of the scattering spectrum and the highest harmonic number of energy are not affected by the initial phase, and the change of the initial phase makes the maximum single harmonic energy of the scattered light change periodically, with its period of p, and the curve is approximate to a trigonometric function curve. When the initial phase increases, it can be seen from the top of the spatial spectrum that the maximum radiation direction rotates counterclockwise. When the pulse width increases, the monochromaticity of the spectrum becomes worse, the width becomes narrower, and a redshift phenomenon occurs. These results will be helpful to understand the nonlinear Thomson scattering.