Complete characterization of ultra-intense laser pulses in radiation damping regime

We report the first closed, analytical expression for the scattering angle of an electron bunch ponderomotively scattered from a counter-propagating, ultra-intense laser pulse, also accounting for radiation reaction (RR). The found formulation depends nontrivially on the laser intensity, pulse duration, beam waist, and energy of the electron bunch. For various laser and bunch parameters the proposed formula is in excellent quantitative agreement with full, relativistic test particle simulations in a realistic electromagnetic field configuration of a focused laser pulse. We also demonstrate how in the radiation dominated regime a simple rescaling of our model's input parameters yields excellent quantitative agreement with numerical simulations based on the Landau-Lifshitz model. Finally, we discuss how the model can be applied for an in-situ characterization of current and future ultra-high power laser systems, but also to experimentally probe fundamental properties of RR during ultra-intense laser electron interaction.