High efficiency tapered free-electron lasers with a prebunched electron beam

In this paper we analyze the high gain, high efficiency tapered free-electron laser amplifier with a prebunched electron beam. Simple scaling laws are derived for the peak output power and extraction efficiency and verified using 1D simulations. These studies provide useful analytical expressions which highlight the benefits resulting from fine control of the initial conditions of the system, namely the initial electron beam bunching and input seed radiation. When time-dependent effects are included, the sideband instability is known to limit the radiation amplification due to particle detrapping. We discuss two different approaches to mitigate the sideband growth via 1-D time dependent simulations. We find that a more aggressive taper enabled by strong prebunching and a modulation of the resonance condition are both effective methods for suppressing the sideband instability growth rate.

Figure 1

Power transfer efficiency and trapping fraction for a seeded tapered FEL amplifier at constant resonant phase. The seed power is $1.6\rho P_{\text{beam}}$ and the taper starts at $z=0$ for the $N_u={10}^3$ period undulator. The theory estimate [Eq. (9)] is in good agreement with simulation and the trapping fraction is accurately given by the bucket width. Arrows show the axes belonging to the curves.

Figure 2

Analytic fit of the trapping fraction $f_t$ as a function of the modulation parameter $A\equiv h_b/{\sigma }_{\gamma }$ (ratio of the modulation bucket height and the electron slice energy spread) and the resonant phase between $\pi /16-7\pi /16$. The trapping fraction obtained with pre-bunching is larger than in the unbunched case leading to higher power transfer efficiency (see Fig. 3). The advantage of the double buncher compared to the single buncher scheme (see Appendix pp2) is largest for A $>10$ and ${\psi }_r<\pi /4$.

Figure 3

Analytic estimate (solid) and simulation (dots) of the efficiency with/without pre-bunching for three different values of the modulation strength A and the parameters of Table 1. The analytic formula is in good agreement for values of the efficiency $\eta <40\%$. For $\eta >40\%$ the assumption of constant trapping fraction breaks down as particles begin to detrap due to the bucket height ($h_b\propto \sqrt{KE}$) decreasing towards the end of the undulator.

Figure 4

(top) Spectra from 1-D time dependent simulations of a tapered FEL amplifier at constant resonant phase. The reduction in sideband intensity with resonant phase and the larger sideband growth length (bottom) reflects the scaling of the sideband gain $G\propto 1/\sin 2{\psi }_r$ from Ref. [18].

Figure 5

(Top) Undulator taper profile for a gain modulated tapered FEL. The modulation section at $N_u=750$ changes the synchrotron frequency and damps the sideband growth (see Fig. 6). (Bottom) The trapping fraction drops after the modulation section but remains constant compared to the unmodulated case which suffers from severe sideband-induced detrapping after $N_u=1500$.

Figure 6

Radiation spectrum (top) and temporal profile (bottom) with and without gain modulation showing sideband reduction for a gain modulated high efficiency FEL. The ratio of sideband to total power is 55% in the unmodulated case and 4% in the modulated case.

Figure 7

(not to scale) Schematic of the double-buncher set-up used for a high gain high efficiency FEL. The modulator sections are typically short (exact length depending on the beam energy) compared to the SASE and tapered undulators. The trapping fraction at the start of the tapered section is large (66% with the single buncher and 83% with the double-buncher) allowing quick and efficiency extraction of energy from the beam.