Free Electron Laser Based on a Multi-Stage System of RF Wigglers
One of the key problems in realization of short-wavelength FELs is a small efficiency determined the so-called FEL parameter, which is typically ~0.001 for existing X-ray FELs. Evidently, a similar condition limits the spread in initial energy of particles forming the operating electron bunch.
A well-known way for a significant increase in the FEL efficiency is the use of tapered undulator and realization regime of trapping and adiabatic deceleration of electrons [1-3]. In this approach, the undulator parameters (period and/or undulator field) are profiles so that the resonant energy [the electron energy corresponding to the exact resonance] decreases slowly with the increase of the axial coordinate. A fraction of electrons is trapped by a potential well created by the field of the combination wave, end energies of the trapped particles are decreased together with the resonant energy. In principle, it is possible to exceed the FEL parameter limitation on the basis of this approach. However, it is difficult to provide trapping of a significant fraction of the electron beam in the case of a significant energy spread, as only electrons which are close enough to the resonance with the wave can be trapped.
In this work, we develop an idea of the “non-resonant” trapping regime [4,5], which, in principle, can provide an effective trapping of an electron beam with a great energy spread. In this case, at the beginning of the interaction the resonant energy is not close to the averaged initial electron energy but significantly higher. Different energy fractions of the beam are trapped in different points of the electron-wave interaction region, where their initial energy becomes close to the resonant energy. However, such non-resonant trapping is effective, if the wave is amplified fast enough during the trapping process (when the FEL parameter is big enough). We propose to avoid this difficulty by means of the use of a multi-stage (or “multi-pulse”) character of the trapping process, when the non-resonant trapping it provided several times in several consecutive undulator sections. In each act of the trapping (in each section) only a relatively small fraction of the electron beam is trapped by the amplified wave and pass their energy to the wave. However, repetition of this process from section to section involves in the electron-wave interaction almost all particles of the beam. As a result, an great electron efficiency (significantly exceeding the FEL parameter) can be achieved for an electron beam with a big (in the scale of the FEL parameter) spread in initial energy.
An important feature of the “multi-stage” trapping regime is the following: when the electron beam enters into a new undulator section, the trapping process starts from the very beginning. This means that any phase correlation between undulator sections is not needed. In the case, when every operating section represents an rf undulator, this means that every undulator section can be driven by independent (non-synchronized) rf-power sources.
As an example of the rf undulator, we consider the so-called “flying” undulator . This is an rf pulse co-propagating with the electron beam in a helical corrugated waveguide. A benefit of the Doppler up-shift of Compton scattering is not lost due to the mode having strong -1st spatial harmonic transverse fields at axis of the corrugated waveguide. A 30 GHz, 10 ns, 1 GW relativistic backward wave oscillator can power a 10 m long rf undulator with effective undulator strength K = 0.3 and the effective undulator period 5 mm. Multi-stage trapping is appealing for XFELs driven by high-current bunches having large energy spread. The laser-plasma accelerator presently provides electron beams with a typical current of a few kA, a bunch length of a few fs, energy in the few hundred MeV to several GeV range, and energy spread of 1%-10% . In simulations, we consider an example of XFEL on a base of the described principles with a 250 MeV, 100 pC electron bunch of 20m length and 5 m radius aimed to produce radiation at 11 nm wavelength. The energy spread is 1%-3%. Simulations predicts a possibility to achieve the saturated efficiency of several percent, which it is several times more than the FEL parameter of this system.
The work is supported by IAP RAS Project 0035-2014-0012, and Russian Foundation for Basic Research Project 18-02-00765.
 P. Sprangle, C.M. Tang, and W. M. Manheimer, Phys. Rev. Lett. 43, 1932 (1979).  N. M. Kroll, P. L. Morton, and M. N. Rosenbluth, IEEE J. Quantum Electron. 17, 1436 (1981).  T. Orzechowski et al., Phys. Rev. Lett. 54, 889 (1985).  A.V. Savilov, Phys. Rev. E 64, 066501 (2001).  A.V. Savilov, I.V. Bandurkin, N.Yu.Peskov, Nucl. Instr. Meth. Phys. Res. A 507, 158 (2003).  S. V. Kuzikov, A. V. Savilov, and A. A. Vikharev. Applied Physics Letters 105, 033504 (2014).  M. E. Couprie et al., Plasma Phys. Control. Fusion 58 034020 (2016).