Nonlinear Thomson scattering of an ultrashort laser pulse

The nonlinear scattering of an ultrashort laser pulse by free electrons is considered. The pulse is described in the “Mexican hat” wavelet basis. The equation of motion for a charged particle in the field of a plane electromagnetic wave has an exact solution allowing, together with the instant spectrum approximation, the calculation of the intensity of nonlinear Thomson scattering for a high-intensity laser pulse. The spectral distribution of scattered radiation for the entire pulse duration is found by integrating with respect to time. The maximum of the emission spectrum of a free electron calculated in 10¹⁹–10²¹ W/cm² fields lies in the UV spectral region between 3 and 12 eV. A part of the continuous spectrum achieves high photon energies. One percent of the scattered energy for the field intensity 10²⁰ W/cm² is concentrated in the range ħω > 2.7 × 10² eV, for a field intensity of 10²¹ W/cm² in the range ħΩ > 7.9 × 10² eV, and for an intensity of 10²² W/cm² in the range ħΩ > 2.45 × 10⁵ eV. These results allow us to estimate nonlinear scattering as a source of hard X-rays.