Analytical spectrum of nonlinear Thomson scattering including radiation reaction

Accelerated charges emit electromagnetic radiation and the consequent energy-momentum loss alters their trajectory. This phenomenon is known as radiation reaction and the Landau-Lifshitz (LL) equation is the classical equation of motion of the electron, which takes into account radiation-reaction effects in the electron trajectory. By using the analytical solution of the LL equation in an arbitrary plane wave, we compute the analytical expression of the classical emission spectrum via nonlinear Thomson scattering including radiation-reaction effects. Both the angularly resolved and the angularly integrated spectra are reported, which are valid in an arbitrary plane wave. Also, we have obtained a phase-dependent expression of the electron dressed mass, which includes radiation-reaction effects. Finally, the corresponding spectra within the locally constant field approximation have been derived.