  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.
