Electron–photon backscattering lasers

In this work a scheme is investigated such that a laser with its wavelength λ_f is produced by backscattering of incident laser with its wavelength λ_i and an incident electron beam with its velocity v₀ passing through a magnetic field with its period λ_W. According to the scheme, the coherent conditions are nλ_f = c/v₀ − 1 λ_W, λ_W = lλ_i = lmλ_f and s < 1 + v₀/c λ_i/4, where s is the longitudinal length of an effective backscattering region, n, l and m are integers. When v₀ is large enough, λ_f ≪ λ_i. The condition σ < λ_f is no longer necessary, here σ is the longitudinal length of a clustering. Waggle magnets covered by superconductivity sheets can markedly decrease s. A laser resonator parallel with an incident electron beam can produce an incident laser with large enough intensity. It is possible that the power of the output laser beam is larger than that of the incident laser beam, although the number of the photons of the output laser beam is less than that of the incident laser beam. (paper)