The ion channel laser (ICL) is an ultra-compact version of the free-electron laser (FEL),with the wiggler replaced by an ion channel. Given its small size and the large wiggler field that can be created within a small volume, it has enormous potential for generating high-frequency coherent radiation. Previous studies of the ICL [1,5], however, have assumed transverse momentum amplitudes that are unrealistically small for experiments, and thus concluded that high-gain high-frequency coherent radiation generation using the ICL is infeasible.In contrast, this thesis shows 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 . Both steady-state and spatio-temporal analyses of the resulting scaled equations show a realistic prospect of building a compact ICL source for fundamental wavelengths down to the UV, with harmonics potentially extending to X-rays. The gain parameter ρ can attain values of the order of 0.01-0.1, which permits driving an ICL with electron bunches with realistic emittance and achieving a radiation power gain comparable to FEL over a small distance.In addition, we present the first results of superradiant simulations for the ICL, also within the framework of the scaled formalism for the FEL, taking into account propagation effects, as well as a full SASE simulation using shot noise as the startup.