Spontaneous radiation emitted from relativistic electrons undergoing betatron motion in a plasma-focusing channel is analyzed, and applications to plasma wake-field accelerator experiments and to the ion-channel laser (ICL) are discussed. Important similarities and differences between a free electron laser (FEL) and an ICL are delineated. It is shown that the frequency of spontaneous radiation is a strong function of the betatron strength parameter $a_{\beta },$ which plays a role similar to that of the wiggler strength parameter in a conventional FEL. For $a_{\beta }\gtrsim 1,$ radiation is emitted in numerous harmonics. Furthermore, $a_{\beta }$ is proportional to the amplitude of the betatron orbit, which varies for every electron in the beam. The radiation spectrum emitted from an electron beam is calculated by averaging the single-electron spectrum over the electron distribution. This leads to a frequency broadening of the radiation spectrum, which places serious limits on the possibility of realizing an ICL.

• Received 18 April 2001

DOI:https://doi.org/10.1103/PhysRevE.65.056505