Two-beam accelerator based on a Cherenkov wake amplified by an optical active medium

We develop the basic scaling laws for the design of a proof of principle two-beam accelerator based on a solid-state active medium (TBA-AM). The essence of the paradigm is to rely on a low-charge trigger bunch which will generate a weak intensity Cherenkov wake in a dielectric extraction structure. The wake consists of a discrete spectrum of eigenfrequencies, one of which is amplified by the active dielectric material. The exponential growth of the wake, behind the trigger bunch, continues as long as virtually all the energy from the medium is depleted. At this point, the electromagnetic field reaches saturation and thus its maximum value. Beyond this peak gradient, a trailing bunch may be placed and thus accelerated. Evidently, the major difference between the proposed paradigm and the existing ones is the energy source: in existing schemes the energy is stored in the driving bunch, whereas in ours, the required energy is stored in the active medium. Special attention is paid to three quantities which characterize the interacting mode: its initial amplitude generated by the trigger bunch, its exponential growth, and its saturation level. The latter indicates that accelerating gradients in excess of 1 GV/m are feasible in a less than 10 cm long structure.