A free electron laser (FEL) configuration utilizing a linearly polarized wiggler and ion-channel guiding has been studied for axial injection of the electron beam. The interaction results in an imperfect electron trajectory which is a superposition of two simple harmonic oscillations, one at the wiggler frequency and the other at the ion-channel frequency. The possibility of obtaining gain at the upshifted wiggler or the upshifted ion-channel betatron frequency and their odd harmonics has been shown. As a result the FEL can be tuned either by changing the electron energy or the ion-channel density.

A study of the spontaneous emission and gain in radiation of a free-electron laser having an elliptically polarised electromagnetic wiggler at the fundamental Doppler upshifted wiggler frequency and its odd harmonics using single particle dynamics is presented. "

The possibility of obtaining significant FEL gain at an upshifted Larmor frequency is examined with the help of single particle analysis in the small gain per pass limit.