Limit cycle behaviour in FELIX

Abstract

The free electron laser for infrared experiments (FELIX) operates at wavelengths up to λ = 110 μm. A radio-frequency linear accelerator is used to produce electron micropulses with a duration of about 3 ps. With N = 38 undulator periods, this puts FELIX well into the regime where the slippage length, Nλ, exceeds the electron micropulse length, and prominent short pulse effects are expected. One of these effects, stable limit cycle oscillations of the pulse energy, has not been detected experimentally before. Such oscillations occur when the saturated optical pulses move away from the electron pulses, due to the changing balance between lethargy and desynchronism, while new subpulses grow periodically. In FELIX, limit cycle behaviour is clearly demonstrated. The observations are in agreement with numerical simulations of the pulse propagation, and the oscillation period is given by a simple formula containing the slippage length and the desynchronism between optical and electron pulses. We also show how lethargic behaviour can be used to reduce the optical bandwidth of the FEL and to store optical energy in the optical cavity without saturation limiting the energy stored.