From classical to quantum radiation reaction effects in ultra high intensity laser plasmainteraction

Radiation reaction (RR) in the interaction of ultra-relativistic electrons with a strong external
electromagnetic field is investigated using a kinetic approach in the non-linear moderately quantum
regime. Analyzing the system of kinetic equation for the electron and photon distribution functions,
we deduce three complementary descriptions depending on the average quantum parameter of
the electron population : a deterministic one relying on the quantum-corrected radiation reaction
force in the Landau and Lifschitz (LL) form, a linear Boltzmann equation for the electron
distribution function, and a Fokker-Planck (FP) expansion in the limit where the emitted photon
energies are small with respect to that of the emitting electrons.
Quantum RR effects can affect significantly the electron distribution function. Both the average quantum parameter and the initial shape of the electron distribution function are important to determine the influence of quantum RR on the system. This has important implications for the experimental observation of quantum RR effect both regarding the final electron energy distribution and the emitted radiation spectrum. In particular, the features of RR are much more subtle on the radiation spectrum than on the electron energy distribution.