Charged-particle scattering in a magnetic and a laser field and nonlinear bremsstrahlung

A nonrelativistic theory of charged-particle scattering by a background potential $V\left(r\right)\mathrm{}$ in the simultaneous presence of a magnetic and a laser field is developed. The particle motion in the magnetic and laser field in dipole approximation is treated exactly. Transitions between exact quantum-mechanical states of the charged particle are considered to lowest-order Born approximation in $V\left(r\right)\mathrm{}$. Conservation laws and selection rules for the scattering are derived for the case of laser light circularly polarized in the plane perpendicular to the magnetic field direction. It is shown that nonlinear bremsstrahlung may occur accompanied by a corresponding change of the electron's angular momentum component along the magnetic field axis. Transition amplitudes for these cases are presented in closed form and their electric and magnetic field dependences are discussed in the limiting cases of weak and strong magnetic and laser fields. The connection of this approach to previous work is established.