Analytical results for non-linear Compton scattering in short intense   laser pulses
  We study in detail the strong-field QED process of non-linear Compton scattering in short intense plane wave laser pulses of circular polarization. Our main focus is placed on how the spectrum of the back-scattered laser light depends on the shape and duration of the initial short intense pulse. Although this pulse shape dependence is very complicated and highly non-linear, and has never been addressed explicitly, our analysis reveals that all the dependence on the laser pulse shape is contained in a class of three-parameter master integrals. Here we present completely analytical expressions for the non-linear Compton spectrum in terms of these master integrals. Moreover, we analyse the universal behaviour of the shape of the spectrum for very high harmonic lines. 
Daniel Seipt, Vasily Kharin, Sergey Rykovanov, Andrey Surzhykov, and   Stephan Fritzsche
hep-ph physics.atom-ph physics.plasm-ph