Exact analysis of ultrahigh laser-induced acceleration of electrons by cyclotron autoresonance

We study the relativistic dynamics of a single electron in a plane-wave laser field and a static magnetic field oriented along the laser propagation direction. A set of exact solutions, that demonstrate acceleration to TeV energies in vacuum by the mechanism of resonance between the electron cyclotron frequency and the Doppler-shifted laser frequency, is presented. Forward velocity focusing is demonstrated, the radiation losses are shown to be negligible, and the frequency distribution of the weak radiation scattered by the electron undergoing the acceleration is discussed.