Inverse FEL proton accelerator via periodically modulated crystal structure

Presented study explores the idea of using a visible light wave to accelerate relativistic protons via the inverse FEL mechanism. Here, a strain modulated crystal structure — the superlattice, plays the role of a microscopic undulator providing very strong ponderomtive 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 was 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 electromagnetive wave — the rate the energy is extracted from the light by the beam. Presented analytic formalism allows one to find the accleration rate in a simple closed form, which is further evaluated for a model beam optical cavity system cavity system to verify feasibility of our scheme.