Bunching phase evolution of short-pulse FEL oscillator system

We studied numerically the short-pulse FEL oscillator system using properly defined bunching phase θB and ΨB. In stable operation, we have found that the optical field “locks” the phase to π/2 at the trailing edge, which gives the maximum gain. Moreover, electrons can be detrapped from ponderomotive bucket due to the spatial variation of the optical field, and this detrapping effect is a major cause of the limit cycle oscillation of the system. The `bump’ of the output power during the amplification usually exists at the near-perfect cavity synchronism regime, which can be explained as the change of the matching condition between electron micropulse and optical pulse.