Making spectral shape measurements in inverse Compton scattering a tool for advanced diagnostic applications.

Interaction of relativistic electron beams with high power lasers can both serve as a secondary light source and as a novel diagnostic tool for various beam parameters. For both applications, it is important to understand the dynamics of the inverse Compton scattering mechanism and the dependence of the scattered light's spectral properties on the interacting laser and electron beam parameters. Measurements are easily misinterpreted due to the complex interplay of the interaction parameters. Here we report the potential of inverse Compton scattering as an advanced diagnostic tool by investigating two of the most influential interaction parameters, namely the laser intensity and the electron beam emittance. Established scaling laws for the spectral bandwidth and redshift of the mean scattered photon energy are refined. This allows for a quantitatively well matching prediction of the spectral shape. Driving the interaction to a nonlinear regime, we spectrally resolve the rise of higher harmonic radiation with increasing laser intensity. Unprecedented agreement with 3D radiation simulations is found, showing the good control and characterization of the interaction. The findings advance the interpretation of inverse Compton scattering measurements into a diagnostic tool for electron beams from laser plasma acceleration.