| Summary: | Many Free Electron Lasers (FEL) are driven by short electron pulses which create equally short optical pulses. At saturation, the strong optical fields present in the undulator result in the trapped particle instability which drives the carrier wave unstable and modulates the optical pulse. The trapped particle instability coupled with the short optical pulses can result in periodic oscillations of the pulse shape. This results in oscillations of the output power even though all input parameters are constant. The effect is known as limit cycle behavior. The character of the oscillation is highly nonlinear and is dependent on the physical input parameters of the current density, resonator losses, electron pulse length, and desynchronism of the resonator cavity. These power oscillations affect the operation of the FEL requiring better insight into their cause and control. Using simulations based on a self consistent Maxwell Lorentz theory of FEL operation, the dependence of the limit cycle oscillations on these physical parameters is examined.
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