Elimination of the sideband instability in variable-parameter free-electron lasers and inverse free-electron lasers

A one-dimensional theory is given for the suppression of the sideband instability in a variable-parameter free-electron laser amplifier operating in the Compton regime. It is demonstrated that strong tapering can reduce drastically the intensity of sideband radiation because the frequency of the most unstable sideband mode varies continuously along the wiggler axis. Due to this continuous detuning effect, no single sideband mode can grow at a fixed maximal rate. Furthermore, the peak growth rate decreases gradually along the wiggler. Hence, only a suppressed but broadened sideband spectrum is obtained. In a particular numerical example, high efficiency (∼70%) with sideband intensities suppressed by eight orders of magnitude with respect to the intensity of the primary signal is obtained. The theory is also applied to an inverse free-electron laser in which sidebands are eliminated.