Dispersion relation and growth in a free-electron laser with ion-channel guiding

Abstract

A theory of a helical wiggler free-electron laser with ion-channel guiding is presented. Electron motion has been analyzed using single particle dynamics and regimes of orbit stability have been discussed. With the help of these trajectories, source currents have been obtained and the linear dispersion equation showing coupling of electromagnetic and space-charge waves by the wiggler field has been set up for a monoenergetic electron beam. Growth rates have been obtained for different ion-channel frequencies. The variation of resonant frequencies and peak growth rates with ion-channel frequency has been illustrated. Substantial enhancement in peak growth rate is obtained as the ion-channel frequency approaches the wiggler frequency.

Relativistic Raman backscattering in an electron beam with ion-channel guiding and its application in free-electron laser

“…͑54͒ with the previously found results in the laboratory frame by Jha and Kumar, 9 Eq. ͑54͒ should be Lorentz transformed to the laboratory frame.…”

“…However, due to inconsistency in the approximation used in Ref. 9, these results will not agree. Therefore, in this section, we will derive the dispersion relation, in the laboratory frame, for a FEL in the absence of ion channel, using the present method.…”

“…The approximations on the relativistic terms, in Ref. 9, are inconsistent and, therefore, many second-order terms in their dispersion relations ͑DRs͒ are omitted.…”

“…In the high-gain regime, in Ref. 9, the space-charge wave is treated relativistically to first order in the wiggler amplitude. However, the radiation is treated under the relativistic mass correction approximation, i.e., nonrelativistic treatment with the mass of an electron replaced by ␥ 0 m where ␥ 0 is the constant relativistic factor of an electron in the undisturbed equilibrium.…”

The Effect of Ion-Channel Guiding on the Chaotic Electron Trajectories in a Free Electron Laser

“…Ion-channel guiding of the relativistic electron beam in a FEL has been employed as an alternative to guiding by axial magnetic field [3,4]. Recent study of the electron trajectories in a helical wiggler and planner with ion-channel guiding has been carried out [5,6].…”