Spontaneous radiation emitted from an electron undergoing betatron motion is a plasma focusing channel is analyzed and applications to plasma wakefield accelerator experiments and to the ion channel laser (ICL) are discussed. Important similarities and differences between a free electron laser (FEL) and in an ICL are delineated. It is shown that the frequency of spontaneous radiation is a strong function of the betatron strength parameter a(sub (beta)), which plays a similar role to that of the wiggler strength parameter in a conventional FEL. For a(sub (beta)) (approx-gt) 1, radiation is emitted in numerous harmonics. Furthermore, a(sub (beta)) is proportional to the amplitude of the betatron orbit, which varies for every electron in the beam. This places serious limits on the possibility of realizing an ICL.