SIMPLE AND ROBUST FREE ELECTRON LASER DOUBLER*

We present the design of a Free-Electron Laser (FEL) doubler suitable for the simultaneous operation of two FEL lines. The doubler relies on the physical selection of two longitudinal portions of an electron bunch at low energy, and on their spatial separation at high energy. Since the two electron beamlets are naturally synchronized, FEL pumpFEL probe experiments are enabled when the two photon pulses are sent to the same experimental station. The proposed solution offers improved flexibility of operation w.r.t. existing two-pulse, two-color FEL schemes, and allows for independent control of the color, timing, intensity and angle of incidence of the radiation pulses at the user end station. Detailed numerical simulations demonstrate its feasibility at the FERMI FEL facility.


INTRODUCTION
We propose a scheme in which two longitudinal portions of the electron bunch (beamlets) are physically selected with a thick mask at low energy in the linac (beam scraping), and spatially separated with a septum magnet at high energy. Each beamlet is then sent to a distinct undulator line. Unlike any of the preceding schemes, ours allows the simultaneous operation of two FEL lines, naturally synchronized at (sub-)fs level, with continuously tuneable relative delay from few fs to ps. Since two undulator lines are used, full and independent control of color, timing, intensity and angle of incidence of the individual radiation pulses on the sample is ensured. If the two FEL pulses are directed to the same user end station, FEL-pump FELprobe experiments can be done with unprecedented flexibility, either in self-amplified spontaneous emission (SASE) [1,2] or in seeded configurations [3,4].

ELECTRON BEAM MANIPULATION
The scheme is sketched in Fig. 1, and typical parameters at FERMI [5,6] are considered in the following as a case study. A high brightness electron bunch is generated in a photo-injector (gun) and time-compressed in a magnetic chicane (BC1). The bunch length compression factor is

, with
2% the relative energy spread linearly correlated to the initial bunch duration , 2.8 ps. A mask with two apertures is installed in the middle of BC1, where the particles horizontal position w.r.t. the reference trajectory is ≅ , and betatron oscillations can be neglected. The mask, made of 10 mm thick copper, physically selects two transversally displaced beamlets, the rest of the bunch being scattered at large angles and absorbed in the chamber. Since the chicane is achromatic, the two beamlets exit BC1 separated both in energy and in time, but spatially aligned. With Vshape geometry, the vertical position of the mask determines both the width of the two apertures and their transverse separation. The beamlets duration at the exit of BC1, as well as their time separation, is estimated by [7] ∆ ∆ , , with x either the apertures width or the width of the central slit, respectively. For example, with C = 10 and x = 3 mm, t FWHM  320 fs.
Downstream of BC1, the linac RF phases are adjusted to ensure both a large relative energy offset of the beamlets ( f ), which is suitable for their spatial separation in the switchyard, and a small energy spread in each beamlet ( ,f ), as required for efficient lasing. The RF phasing takes into account the effect of the longitudinal wakefields excited by the leading beamlet on the trailing one. For example, we obtain in simulation  f = 0.9% and  ,f = 0.04%. Doing so, the final mean energy is lowered from 1.40 GeV for the standard whole bunch preparation, to 1.25 GeV (see  The FERMI switchyard (SW in Fig. 1) is a 40 m long line working in the energy range 0.9-1.5 GeV. It comprises two branches, each including two modified double bend achromatic cells. The first cell is in common, and the dipoles bending angle is 3 deg. The two branches lead to the FEL1 and FEL 2 undulator lines; these are parallel and separated by 1 m. Depending on the electron beam energy and on the resonant harmonic jump set by the variable gap undulators, FERMI covers the fundamental wavelength range 20-100 nm with FEL1, and 4-20 nm with FEL2, in high gain harmonic generation (HGHG) mode of operation [3].
For the purpose of separating the beamlets in the bending plane, the SW optics was modified. A dispersion function as large as -0.3 m is generated at the location of the third dipole magnet, i.e., at the entrance to the FEL2 branch line (see Fig. 1). The dipole magnet would be replaced by a thin septum magnet, having similar length of 0.5 m and the same bending angle. The beamlet at low energy-positive x coordinate is bent by the septum magnetic field and directed to-wards FEL2. The other beamlet continues its straight path towards the next double bend cell, and is eventually directed to FEL1. In order for the two beamlets to safely reach the present common dump at the end of the undulators, the FERMI dump line would be modified. This modification is not required in facilities where multiple dumps downstream of distinct undulators are already available. Figure 2 shows the beamlets longitudinal phase spaces at the entrance of the septum magnet, for different separations of the apertures in the mask. Particle tracking was carried out with the elegant code [8], including all major collective effects from the injector exit to the undulator. The main beam and mask parameters are listed in Table 1. In this simulation, the outer borders of the mask apertures are kept fixed, so that a larger apertures separation (larger energy offset of the two beamlets) implies a smaller apertures width (shorter beamlets duration). Figure 2 also shows the corresponding horizontal separation of the beamlets at the septum entrance, and their current profile. The horizontal separation of the beamlets at the septum entrance is  x  f 2.5 mm, and much larger than their individual betatron beam size. We thus consider a minimum septum thickness of 2 mm, which can be provided by an in-vacuum eddy-current septum magnet. We developed a septum design of 1525 mm 2 transversal acceptance. A maximum electric power of 100 W is expected to be safely dissipated, which translates into a repetition rate of 25 Hz at the beamlets' mean energy of 1.25 GeV. The beamlets' rms position jitter at the septum must be much smaller, say one-tenth, of 2 mm, which implies a relative rms energy jitter of 0.07%, and an overall trajectory jitter  50 m. This error budget is well within reach of x-ray FEL facilities [9].
The optics of the switchyard branches is achromatic. Although it is not isochronous (R 56 = -0.3 mm for FEL1, +2.9 mm for FEL2), the beamlets' duration is almost unchanged by virtue of their negligible correlated energy spread, i.e., ∆ ≅ , /  4 fs. The minimum relative delay of the beamlets at the undulator is determined by the difference in the transfer matrix of the two branches: ∆ ≅ ∆ ∆ / ≅ ′ / 67 5 75 fs = 147 fs in our case.  Figure 3 shows the result of time-dependent FEL1 and FEL2 simulations done with the Genesis 1.3 code [10], for the mask geometry and beam parameters in Table 1. The mask was chosen so as to make the beamlets long enough, approximately 300 fs full width, to accommodate an external seeding laser of 50 fs. The FEL input and output parameters are summarized in Table 2.

LASING
We also conducted an experiment with beam and mask parameters close to those in Table 1, but a single mask aperture as due to available hardware. Figure 4 shows the measured spectrum of the first HGHG stage of FERMI 39th Free Electron Laser Conf.
FEL2019, Hamburg, Germany FEL2, tuned at the 8 th harmonic of the seed laser wavelength. The seed laser duration was about 50 fs. The spectrum is measured as a function of the delay of the seed laser relative to the electron bunch arrival time. The top plot is without beam scraping; the bottom plot is for scraping in BC1 set to generate beamlet duration of approximately 330 fs. The extension of the lasing region as a function of the seed laser-electron bunch delay confirms the expected beamlet duration, and it highlights a region of efficient lasing in the beamlet as long as 150 fs. The spectrum intensity is normalized to the peak value in both plots: the average FEL pulse energy was 35 J for the whole beam, 15 J for the selected beamlet without further optimization of the spatial and temporal overlap of seed laser and electron beamlet.  Table 1.

CONCLUSIONS
In conclusion, we have demonstrated with detailed numerical simulations that two-pulse, two-color FEL emission synchronized at sub-fs level can be generated by splitting the electron bunch in two beamlets, and that these can be safely sent to distinct undulator lines. The scheme is suitable for the simultaneous operation of experimental beamlines receiving FEL pulses generated by very similar electron beam parameters, and can be implemented at existing facilities with limited cost and reduced impact on the infrastructure.
Unlike any HGHG option, the proposed scheme has no color limitation due to the harmonic up-conversion of the seed laser wavelength. Accordingly, this study is expected not only to pave the way to simultaneous operation of two synchronized FEL lines, but also to more flexible, robust and reliable two-color, two pulse schemes for, e.g., four wave mixing spectroscopy as well as a broader variety of FEL-pump FEL-probe experiments, including transient grating spectroscopic methods. Since pump and probe are generated with two different undulators, and for relative time separation of the two pulses up to 1 ps or so, there is no need of a large split-and-delay system for the photon beam, which can be costly, difficult to operate, and reducing the photon flux at the sample.
For future facilities with freedom of parameter choice, the two beamlets could be created using a double photoinjector laser pulse, accelerated at the same phase on different RF cycles, before being given small energy offsets in a subharmonic cavity so that they can be separated into two FEL beamlines by the septum with the same scheme presented above. Such double pulse option may offer some more flexibility in beam compression, and avoids relatively large beam power losses induced by scraping at high repetition rates.