Relativistic free-electron dynamics and light-emission spectra in the simultaneous presence of a superintense laser field and a strong uniform magnetic field

We present exact analytic trajectories for a relativistic electron in the presence of an elliptically polarized superintense laser field and a strong uniform magnetic field. Also derived are expressions for the velocity components of the electron and for its energy as functions of the phase of the laser field as a parameter. The analytic trajectory solutions are illustrated by numerical calculations employing laser-field parameters and magnetic-field strengths currently available for laboratory experiments. The trajectory solutions are useful for (among other things) the study of the related problem of emission of radiation in the combined laser and magnetic fields. An exact expression for the cross section of light scattered by an electron initially moving along the laser propagation direction and in a magnetic field is given. It is found that, for observation along the common direction of laser propagation and the magnetic field, light at two frequencies $\omega ={\omega }_0$ and ${\Omega }_0$ is scattered, where ${\Omega }_0={\gamma }_0(1+{\beta }_0){\omega }_c,$ ${\omega }_c$ is the cyclotron frequency of the electron motion in the magnetic field, ${\beta }_0$ is the initial speed of the electron normalized by the speed of light, ${\gamma }_0=(1\mathrm{}-{\beta }_0^2{)}^{-1/2}$, and ${\omega }_0$ is the laser frequency. Using the analytic solutions, we also study numerically the spectrum of radiation emitted along observation directions parallel to the electric and parallel to the magnetic components of the laser field. In each case, we present and discuss the dependence of the spectra on (a) the increase of the electron initial velocity, (b) the intensity and the frequency of the laser, and (c) the strength of the magnetic field.