Strong field approximation to the relativistic channeling of electrons in the presence of electromagnetic waves

We present a study of the interaction of a relativistically planar channeled electron with an intense electromagnetic field. Using a S-Matrix approach in the Strong Field Approximation, it is shown that the crystal periodicity affects drastically the excitation process, suppressing the possibility of multiphoton absorption except for some particular cases. This selective excitation opens the possibility to control the dynamics of the channeling process by means of an external field. Explicit expressions for the S-matrix N-photon excitation rates together with the corresponding conservation laws are obtained from the relativistic quantum mechanical Dirac equation.