Steady-state description of an ion channel free-electron laser with varying betatron amplitude

The ion-channel laser (ICL) has been proposed as an alternative to the free-electron laser (FEL), replacing the deflection of electrons in an undulator by betatron oscillations in an ion channel. The aim of this study is to describe the ICL in terms of the well-developed formalism for the FEL in the steady-state, while taking into account the dependence of the resonance between oscillations and emitted field on the oscillation amplitude. Numerical solutions for experimentally relevant parameters show similarities and differences between both devices. The ICL has potential to replace FELs based on magnetic undulators, leading to very compact coherent X-ray sources. Furthermore, coupling the ICL with a laser plasma wakefield accelerator would reduce the size of a coherent light sources by several orders of magnitude.