Thomson scattering in strong external fields

In the present paper we shall investigate relativistic Thomson scattering in two external fields. A free classical electron will be embedded in a strong, constant and homogeneous magnetic field and in a powerful electromagnetic field. Both fields will be considered in the Redmond configuration, in which case the electromagnetic wave is circularly polarized and propagates in the direction of the homogeneous magnetic field. The electron will be allowed to have arbitrary initial conditions and the electromagnetic wave will be switched on either suddenly or adiabatically. We shall present the exact solution of the Lorentz equation of motion in the above external field configuration and we shall evaluate the spectrum and cross sections of the scattered radiation. In particular, we shall consider scattering close to resonance and we shall compare our results with the findings of earlier work.