Dynamics and stabilization of the Elettra storage-ring free-electron laser

The ultimate performance of a storage-ring free-electron laser in terms of light stability and extracted power depends on the possibility of simultaneously controlling the electron-beam and laser dynamics. As a preliminary requirement, the level of longitudinal and transverse electron-beam stability must be high enough to guarantee the laser start-up and growth. This is usually obtained by means of dedicated feedback systems. Once such a requirement is satisfied, the possibility of establishing and maintaining a continuous-wave operation mode finally resides in a deep understanding of the strongly coupled laser-electrons dynamics. For this purpose, we have developed a simple theoretical model which has been proved to be able to provide insight into the evolution of the laser intensity. In this framework, we have also proposed the possibility of utilizing a derivative closed-loop feedback to create or enlarge the region of stable signal. A feedback of this type has been implemented on the Elettra storage-ring free-electron laser. The obtained results, which fully confirm our predictions, are discussed in this paper.

Figure 1

Schematic layout of a storage-ring free-electron laser.

Figure 2

Typical detuning curves (i.e., laser intensity as a function of detuning amount) obtained for the case of the Super-ACO (a) and Elettra (b) SRFELs.

Figure 3

(a) Typical temporal behavior of the Elettra FEL intensity close to the perfect laser-electron synchronism; (b) Fourier analysis of the signal shown in (a).

Figure 4

(a) Streak camera image of the electron beam circulating in the Elettra storage ring (energy: $0.9\mathrm{GeV}$, beam current: $0.5\mathrm{mA}$). Along the vertical axis one can follow the evolution in time of the temporal beam distribution, while a horizontal cut provides the beam distribution profile. (b) Evolution of the position of the beam centroid as obtained by the analysis of (a).

Figure 5

(a) Typical temporal behavior of the Elettra FEL intensity close to the perfect laser-electron synchronism; (b) Fourier analysis of the signal shown in (a).

Figure 6

Numerical results obtained with a modulation of the detuning parameter according to Eq. (4) with $f=50$, ${ϵ}_0=0$, and different values of the amplitude $A$.

Figure 7

Intensity and fast Fourier transform obtained combining Eqs. (1, 2, 3, 4) with ${ϵ}_0=0.05\mathrm{fs}$ and $A=0.18\mathrm{fs}$. Numerical results to be compared with the experimental ones shown in Fig. 3.

Figure 8

Intensity obtained with a modulation of the detuning parameter according to Eq. (5). In this case ${ϵ}_0=0.05\mathrm{fs}$, $A_1=0.14\mathrm{fs}$, and $A_2=0.1\mathrm{fs}$.

Figure 9

Schematic layout of the closed-loop derivative feedback: the laser light generated by the SRFEL is acquired by means of a photodiode (PD). The resulting signal is sent to the stabilization system, made of a simple device to obtain the signal derivative, followed by an inverting amplifier with a variable gain. The obtained output is then used to modify the electron-beam revolution period (via the modification of the radio frequency, rf), i.e., the value of the detuning $ϵ$.

Figure 10

(a) Temporal behavior of the Elettra FEL intensity without (left part) and with (right part) derivative feedback. (b) Fourier analysis of the signal shown in the left part of (a). (c) Fourier analysis of the signal shown in the right part of (a). FEL operated close to the perfect laser-electron synchronism.

Figure 11

(a) Temporal behavior of the Elettra FEL intensity without (left part) and with (right part) derivative feedback. (b) Fourier analysis of the signal shown in the left part of (a). (c) Fourier analysis of the signal shown in the right part of (a). FEL operated with a detuning of a few femtoseconds.

Figure 12

Numerical behavior of the laser intensity as obtained complementing Eqs. (1, 2, 3) with (7) (considering a two-frequency modulation). The following parameters have been used: ${ϵ}_0>{ϵ}_c$, $A_1=A_2=0.2\mathrm{fs}$, $f_1=50\mathrm{Hz}$, $f_2=100\mathrm{Hz}$; $\beta =0$ (left part of the picture) and $\beta =5\times {10}^{-3}$ (a), $\beta =3\times {10}^{-1}$ (b), $\beta =10$ (c) (right part of the picture).