Classical theory of emission and amplification at high harmonics in the relativistic strophotron FEL

Relativistic strophotron is a system in which fast electrons move along a potential "trough" produced by quadrupole magnetic or electric lenses. Spectral intensity of a spontaneous emission and the gain of an external wave in the strophotron are given by a superposition of contributions from emission or amplification at different (odd) harmonics of the main resonance frequency ωres. The main resonance frequency is shown to depend on the initial conditions of the electron, and in particular on its initial transversal coordinate x0. This dependence is shown to give rise to a very strong inhomogeneous broadening of the spectral lines. The broadening can become large enough for the spectral lines to overlap with each other. The spectral intensity of a spontaneous emission and the gain are averaged over x0. The averaged spectral intensity is shown to have only a very weakly expressed resonance structure, whereas in the averaged gain, the resonance peaks are shown to be much higher than the nonresonant background. A physical nature of these resonances remaining after averaging is discussed. The maximum achieveable averaged gain and frequency of the strophotron FEL are estimated.