Coherent and spontaneous emission in the quantum free electron laser

We present an analysis of quantum free electron laser (QFEL) dynamics including the effects of spontaneous emission. The effects of spontaneous emission are undesirable for coherent short-wave generation using FELs and have been shown in previous studies to limit the capabilities of classical self amplified spontaneous emission (SASE)-FELs at short wavelengths ∼1 Å due to growth of electron beam energy spread. As one of the attractive features of the QFEL is its potential as a relatively compact coherent x-ray source, it is important to understand the role of spontaneous emission, but to date there has not been a model which is capable of consistently describing the dynamics of both coherent FEL emission and incoherent spontaneous emission. In this paper, we present such a model, and use it to show that the limitations imposed by spontaneous emission on coherent FEL operation are significantly different in the quantum regime to those in the classical regime. An example set of parameters constituting a QFEL using electron and laser parameters which satisfy the condition for neglect of spontaneous emission during coherent QFEL emission is presented