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 ω
res
. The main resonance frequency is shown to depend on the initial conditions of the electron, and in particular on its initial transversal coordinate x
0
. This dependence
\omega_{res} (x_{0})
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 x
0
. 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.