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

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.