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.