Analysis of saturation phenomena in Cerenkov free-electron lasers with a planar waveguide

Abstract

In this paper, the operation of the stimulated emission in Cerenkov free-electron laser (CFEL) is studied on the basis of the modulations of electron velocity and density by the electromagnetic (EM) field. The influence of the electron relaxation, due to mutual electrons collisions, on the electron dynamics is taken into account. We investigate the growth characteristics of Cerenkov laser operating in the small-signal and saturation regimes. In the saturation regime, the effect of velocity reduction of the electron beam on the gain dynamics is demonstrated. We also show that our results match with those of other well-known treatments in the small-signal gain limit.

Unified analysis for calculating the amplification gain of Cerenkov laser in the single-particle and collective regimes

“…(13) reduces to that obtained in Ref. 10 when the space-charge correction is neglected (i.e., x p ! 0).…”

“…5 It is assumed that the EM wave can interact only with the space-charge wave when the phase velocities of these waves become equal, and the EM wave satisfies the dispersion relation for the waveguide. 5 On the basis of classical 9,10 and quantum [11][12][13] approaches, the authors have shown that due to the asymmetric separations between electrons accompanied with the beam bunching, the asymmetric Coulomb forces exerted on an electron by the neighboring electrons work to recover its initial position. Therefore, the unbalanced Coulomb forces work to weaken (relax) the bunching mechanism.…”

On the small-signal theory of stimulated Cherenkov emission in dielectric-lined waveguides

“…(5). [17][18][19] Also, the second term of the right-hand side of Eq. (6) corresponds to the damping phenomenon of the electron velocity to a timely averaged velocity v z .…”

“…[15][16][17][18] Let us now derive expressions for the velocity modulation and the resultant currentdensity modulation in the injected beam. For this purpose, assuming a plane wave dependence on the axial position z and time t, velocities v and charge current densities N can be written as v ¼ v z þ ½u i ðy; z; tÞe ðjb v z À1=sÞtÀjbz þ c:c:;…”

“…To the best of our knowledge, the majority of the published theoretical papers have neglected the Coulomb interactions among electrons. Exceptions were our contributions 17,18 in which we introduced relaxation phenomena into electron modulations using the single-particle formulations. However, the effect of electron relaxation on the operation of CFELs in the collective regime has not been yet studied.…”