Analytical theory and control of the longitudinal dynamics of a storage-ring free-electron laser
Abstract
A comprehensive analytical description is given of the longitudinal dynamics of a storage-ring free-electron laser in the presence of a finite light-electron beam temporal detuning. Closed analytical expressions for the main statistical parameters of the system (i.e., beam energy spread, intensity, centroid position, and r.m.s. value of the laser distribution) as a function of the detuning are provided. The transition between the stable “cw” regime and the unstable steady state is shown to be a Hopf bifurcation. This allows us to introduce a feedback procedure which suppresses the bifurcation and significantly improves the system stability. The critical value of the detuning above which the bifurcation occurs is analytically derived as a function of the electron energy and of the beam optics parameters. Results are compared to experiments and display good agreement. Comparisons with other theoretical models are also drawn.
- Publication:
-
Physical Review E
- Pub Date:
- July 2004
- DOI:
- 10.1103/PhysRevE.70.016503
- Bibcode:
- 2004PhRvE..70a6503N
- Keywords:
-
- 41.60.Cr;
- 29.20.Dh;
- 05.45.-a;
- Free-electron lasers;
- Storage rings;
- Nonlinear dynamics and chaos