Studies on convergence and scaling law of Thomson backscattering spectra in strong fields

Abstract

With the saddle point analysis method for the Bessel function structure and property, the convergence problem and the scaling laws of Thomson backscattering spectra are solved and studied in both cases that are for the plane wave laser field without and with applied external constant magnetic field. Some unclear points appeared in previous work are clarified. The extension of the method to a general situation for the laser field with an arbitrary polarization is discussed. We also make a simple analysis and discussion about the optimal spectra dependence of field parameters and its implication to practical applications.

Analytical Thomson backscattering spectra and new scaling laws in laser and magnetic fields

“…For example, He et al [14] initially solved the Thomson backscattering spectra in the case of linearly polarized laser field by using the asymptotic expansion method and obtained the simple scaling laws. Recently Xie et al [15] proved the convergence and the scaling law of the Thomson backscattering spectra, and they also obtained the harmonic order corresponding to the maximum radiation intensity in the case of linearly and circularly polarized laser fields by using the saddle point method. Also four fundamental laws related to the scale invariance of the radiation spectra are revealed for amplitude modulation of laser field with a uniform magnetic field [16].…”