A theoretical study of electron trajectories and gain in a planar wiggler free electron laser (FEL) with ion-channel guiding is presented. A kinetic description is given. The linearized Vlasov–Maxwell equations are solved to investigate the growth rate in a tenuous-beam limit for perturbation about a general beam equilibrium distribution function, and generated harmonics are discussed. Linear gain corresponding to FEL resonance for the case of mono-energetic beam is derived and continuous tuning by varying the ion-channel density, for the fundamental mode, is illustrated.