Dependence on laser intensity of the number-weighted angular distribution of Compton-scattered photon beams

Inverse Compton scattering of an ultra-relativistic electron in the field of a high-intensity laser produces photon beams with angular and spectral distributions that are strongly dependent on the laser intensity. Here, we show that the laser intensity at the interaction point can be accurately inferred from the measurement of the angular number-density distribution of Compton-scattered photon beams. The theory, corroborated by numerical simulations, is accurate to within 10\% in a wide range of laser intensities (dimensionless intensity $5 \leq a_0 \leq 50$) and electron energies (250 MeV $\leq E \leq $ 15 GeV), and accounts for experimental features such as the finite transverse size of the electron beam, low-energy cut-offs in the photon detector, and the possibility of a transverse misalignment between the electron beam and the laser focus.