Superlattice crystal accelerator: Acceleration beyond GeV/m

Here, an idea of using a visible light wave to accelerate relativistic particles via the inverse FEL mechanism is explored. A strain modulated crystal structure -- the superlattice, plays the role of a microscopic undulator providing very strong ponderomotive coupling between the beam and the light wave. Purely classical treatment of relativistic protons channeling through a superlattice is performed in a self consistent fashion involving the Maxwell wave equation for the accelerating electromagnetic field and the relativistic Boltzmann equation for the protons. It yields the accelerating efficiency in terms of the negative gain coefficient for the amplitude of the electromagnetic wave -- the rate the energy is extracted from the light by the beam. Presented analytic formalism allows one to find the acceleration rate in a simple closed form, which is further evaluated for a model beam -- optical cavity system to verify feasibility of this scheme