We present a new paradigm for computation of radiation spectra in the non-linear regime of operation of inverse Compton sources characterized by high laser intensities. The resulting simulations show an unprecedented level of agreement with the experiments. Increasing the laser intensity changes the longitudinal velocity of the electrons during their collision, leading to considerable non-linear broadening in the scattered radiation spectra. The effects of such ponderomotive broadening are so deleterious that most inverse Compton sources either remain at low laser intensities or pay a steep price to operate at a small fraction of the physically possible peak spectral output. This ponderomotive broadening can be reduced by a suitable frequency modulation (also referred to as chirping, which is not necessarily linear) of the incident laser pulse, thereby drastically increasing the peak spectral density. This frequency modulation, included in the new code as an optional functionality, is used in simulations to motivate the experimental implementation of this transformative technique.
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