Theory of the sideband instability in free electron lasers

Abstract

In a Compton-regime free electron laser a relativistic electron moves in the combined potential (ponderomotive potential) formed by the optical radiation field and the static magnetic field. If the energy of the electron, the wavelength of the light, and the period and strength of the static magnetic field are connected by the well-known resonance condition, the electron may exchange part of its energy with the radiation field during its transit through the interaction region (wiggler magnet). Whether the electron gains or loses energy is determined by the phase of its transverse motion with respect to the phase of the optical field. Satisfaction of the resonance condition implies that the relative phase between the light and the electron will vary slowly during the interaction time, thus allowing the possibility of net energy transfer. Consideration of the detailed dynamics of the electron motion shows that, as the electron's energy slowly changes, so does its phase with respect to the optical field. This motion may be described as an oscillation in the ponderomotive potential (synchrotron oscillation). The occurrence of synchrotron oscillations is a fundamental property of the theory of electron dynamics in a free electron laser at high optical intensities and therefore strongly affects the saturation properties of such a laser. In particular, such oscillations can couple the motion of an electron to light at other wavelengths and thus lead to the generation of sidebands on the frequency spectrum of the laser light. The appearance of such sidebands corresponds to a strong modulation of the temporal profile of the optical pulse and modifies the interaction of the light with the electron beam. A review of the theory of the sideband instability will be presented. Results from analytical and numerical studies on the growth and saturation of the instability will be reviewed. Modifications of the results due to two- or three-dimensional effects will be discussed, as will the effects of an imperfect electron beam. Experimental evidence of this effect will be reviewed.