Electron dynamics and photon-emission spectra in an ultrashort laser pulse and a uniform magnetic field

We present exact trajectory solutions for a relativistic electron in the presence of a superintense linearly polarized laser pulse and a uniform magnetic field. To be concrete, the pulse envelope is taken in the form ${\sin }^2\left[\right(\kappa /2\left)\eta \right]$, where $\eta$ is the phase and $0<\mathrm{}\kappa <1\mathrm{}$. Using the analytical trajectories, we study numerically the spectra of radiation, emitted by the accelerated electron, along various observation directions. In particular, we find that light in the forward direction can be emitted essentially at two frequencies ${\omega }_0$ and $r{\omega }_0$, where ${\omega }_0$ is the laser frequency and r is related to the ratio of cyclotron frequency to the laser frequency. Spectra emitted in the directions of the electric and the magnetic components of the laser field are, in contrast, very rich in structure with highly irregular distributions of positions and strengths.