Analytical theory and control of the longitudinal dynamics of a storage-ring free-electron laser.
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.
Sincrotrone Trieste, 34012 Trieste, Italy.
Giovanni
G
De Ninno
Duccio
D
Fanelli