Laser chirping in inverse Compton sources at high electron beam energies and high laser intensities

The onset of nonlinear effects, such as ponderomotive broadening, increases the radiation bandwidth and thereby places a stringent limitation on the laser intensity used in inverse Compton sources. Recently, we have shown that a judicious longitudinal laser frequency modulation ("chirping") can perfectly compensate for this ponderomotive broadening and restore the narrow band property of scattered radiation in the Thomson regime, when electron recoil during the collision with the laser can be neglected. Consequently, using QED, the laser chirping has been extended to the Compton regime, where electron recoil is properly accounted for. Here we present a new, semiclassical model for computation of scattered spectra in the Compton regime. We also derive a comprehensive generalization of the expressions for chirping prescription for linearly polarized laser pulses in 1D plane-wave approximation with arbitrary shapes and arbitrary scattering angle in the Compton regime. We use these new expressions to show that the higher-order harmonics in sources with high laser fields and high electron beam energies (nonlinear Compton regime) will be nonlinearly redshifted when compared to those with lower beam energies (Thomson regime). The chirping prescription will act to correct ponderomotive broadening in very high harmonics.