GinzburgLandau model for a longpulse lowgain freeelectron laser oscillator
Abstract
The GinzburgLandau model for the radiation field of a freeelectron laser (FEL) was originally derived for a highgain amplifier (S.Y. Cai and A. Bhattacharjee, Phys. Rev. A 43 (1991) 6934). With a view to making precise comparisons with experimental data from the longpulse FEL oscillator at the University of California at Santa Barbara (UCSB) (L.R. Elias, G. Ramian, J. Hu, A. Amir, Phys. Rev. Lett. 57 (1986) 424), we have developed a new formulation of the GinzburgLandau model starting from the lowgain oscillator equations. We implement a smallamplitude expansion of the radiation field, and derive the coefficients of the GinzburgLandau equation by analysis as well as by Mathematica. Stability analysis of the GinzburgLandau equation produces results similar to those obtained by T.M. Antonsen and B. Levush (Phys. Fluids B 1 (1989) 1097). These include the stability of the main mode (no BenjaminFeir instability), phaseunstable offcentered modes (Eckhaus instability), as well as relaxation to the single mode which occurs much faster in amplitude than in phase. We obtain the saturated radiation amplitude a_{0} as functions of the detuning parameter p_{inj} and cavity loss, and determine the phase instability boundary in the a_{0} p_{inj} plane. The probability of realizing a single mode starting with random initial conditions is calculated and compared with spectral measurements from the UCSB FEL.
 Publication:

Nuclear Instruments and Methods in Physics Research A
 Pub Date:
 June 1999
 DOI:
 10.1016/S01689002(99)000777
 Bibcode:
 1999NIMPA.429...88N