We discuss radiation reaction effects on charges propagating in ultra-intense laser fields. Our analysis is based on an analytic solution of the Landau-Lifshitz equation. We suggest to measure radiation reaction in terms of a symmetry breaking parame
ter associated with the violation of null translation invariance in the direction opposite to the laser beam. As the Landau-Lifshitz equation is nonlinear the energy transfer within the pulse is rather sensitive to initial conditions. This is elucidated by comparing colliding and fixed target modes in electron laser collisions.
We develop a numerical formulation to calculate the classical motion of charges in strong electromagnetic fields, such as those occurring in high-intensity laser beams. By reformulating the dynamics in terms of SL(2,C) matrices representing the Loren
tz group, our formulation maintains explicit covariance, in particular the mass-shell condition. Considering an electromagnetic plane wave field where the analytic solution is known as a test case, we demonstrate the effectiveness of the method for solving both the Lorentz force and the Landau-Lifshitz equations. The latter, a second order reduction of the Lorentz-Abraham-Dirac equation, describes radiation reaction without the usual pathologies.
We discuss intensity effects in collisions between beams of optical photons from a high-power laser and relativistic electrons. Our main focus are the modifications of the emission spectra due to realistic finite-beam geometries. By carefully analyzi
ng the classical limit we precisely quantify the distinction between strong-field QED Compton scattering and classical Thomson scattering. A purely classical, but fully covariant, calculation of the bremsstrahlung emitted by an electron in a plane wave laser field yields radiation into harmonics, as expected. This result is generalized to pulses of finite duration and explains the appearance of line broadening and harmonic substructure as an interference phenomenon. The ensuing numerical treatment confirms that strong focussing of the laser leads to a broad continuum while higher harmonics become visible only at moderate focussing, hence lower intensity. We present a scaling law for the backscattered photon spectral density which facilitates averaging over electron beam phase space. Finally, we propose a set of realistic parameters such that the observation of intensity induced spectral red-shift, higher harmonics, and their substructure, becomes feasible.
