Scattering of intense laser pulses on high-energy electron beams allows one to produce a large number of x and $\gamma$ rays. For temporally pulsed lasers, the resulting spectra are broadband which severely limits practical applications. One could use linearly chirped laser pulses to compensate for that broadening. We show for laser pulses chirped in the spectral domain that there is the optimal chirp parameter at which the spectra have the brightest peak. Additionally, we use catastrophe theory to analytically find this optimal chirp value.

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• Radiation from moving charges
• Synchrotron radiation & free-electron lasers
• Synchrotron radiation facilities
• Compton scattering