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Scattering of intense laser pulses on high-energy electron beams allows oneto produce a large number of X and gamma rays. For temporally pulsed lasers theresulting spectra is broadband which severely limits practical applications.One could use linearly chirped laser pulses to compensate that broadening. Weshow for laser pulses chirped in the spectral domain that there is the optimalchirp parameter at which the spectra has the brightest peak. Additionally, weuse catastrophe theory to analytically find this optimal chirp value.

Towards high photon density for Compton Scattering by spectral chirp