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Effects of nonlinearity in Thomson scattering of a high intensity laser pulsefrom electrons are analyzed. Analytic expressions for laser pulse shaping inamplitude and frequency are obtained which control spectrum broadening forarbitrarily high laser pulse intensities. These analytic solutions allowprediction of the spectral form and required laser parameters to avoidbroadening. The predictions are validated by numerical calculations. Thiscontrol over the scattered radiation bandwidth allows of narrow bandwidthsources to be produced using high scattering intensities, which in turn greatlyimproves scattering yield for future x- and gamma-ray sources.

Controlling the spectral shape of nonlinear Thomson scattering with proper laser chirping