The ion channel free-electron laser with varying betatron amplitude

The ion-channel laser (ICL) is an ultra-compact version of the free-electron laser (FEL), with the undulator replaced by an ion channel. Previous studies of the ICL assumed transverse momentum amplitudes which were unrealistically small for experiments. Here we show that this restriction can be removed by correctly taking into account the dependence of the resonance between oscillations and emitted field on the betatron amplitude, which must be treated as variable. The ICL model with this essential addition is described using the well-known formalism for the FEL. Analysis of the resulting scaled equations shows a realistic prospect of building a compact ICL source for fundamental wavelengths down to UV, and harmonics potentially extending to x-rays. The gain parameter ρ can attain values as high as 0.03, which permits driving an ICL with electron bunches with realistic emittance.