Flexible and Coherent Soft X-ray Pulses at High Repetition Rate: Current Research and Perspectives

: The successful realization of high gain free-electron lasers has opened new possibilities to X-ray scientists for investigating matter in different states. The availability of unprecedented photon properties stimulated the development of new experimental techniques capable of taking full advantage of these options and has started a virtuous collaboration between machine experts and photon users to improve further and optimize the generated X-ray pulses. Over the recent years, this has led to the development of several advanced free-electron laser (FEL) schemes to tailor the photon properties to speciﬁc experimental demands. Presently, tunable wavelength X-ray pulses with extremely high brilliance and short pulse characteristics are a few of the many options available at FELs. Few facilities can offer options such as narrowband or extremely short pulses below one fs duration and simultaneous pulses of multiple colors enabling resonant X-ray pump—X-ray probe experiments with sub fs resolution. Fully coherent X-ray radiation (both spatial and temporal) can also be provided. This new option has stimulated the application of coherent control techniques to the X-ray world, allowing for experiments with few attoseconds resolution. FELs often operate at a relatively low repetition rate, typically on the order of tens of Hz. At FLASH and the European XFEL, however, the superconducting accelerators allow generating thousands of pulses per second. With the implementation of a new seeded FEL line and with an upgrade at FLASH linac, all the new features will become available in the soft X-ray spectral range down to the oxygen K edge with unprecedented average photon ﬂux due to the high repetition rate of pulses.


Introduction
The advent of high gain single-pass free-electron lasers (FEL) [1][2][3] and the sub- 22 sequent development of FEL user facilities [4][5][6][7][8][9][10] have led the scientific progress in 23 many fields making completely new options available to scientists. Using the unique 24 capabilities of FELs, light pulses with extremely high brightness and short time duration 25 can be produced over the spectral range going from the VUV down to the hard X-ray 26 range and are often combined with secondary sources with longer wavelengths across 27 the visible, infrared, and THz domains. 28 Since the first FEL pulses became available to users at FLASH (DESY Hamburg, 29 Germany) [4] more than 15 years ago, there has been continuous technological and 30 scientific progress allowing to extend the parameter range accessible by these sources. 31 The use of higher energy accelerators combined with high brightness electron beams has 32 allowed exceeding the 25 keV of photon energy [11]. Moreover, the recognizable progress 33 in the undulator design has made features such as variable polarization available [12,13]. 34 The latter, in combination with the accurate control of the beam dynamics, supported 35 parameters (temperature, external fields, positions, orientations, ...). Especially the 90 field of spectroscopy benefits from the increased longitudinal coherence, i.e., the smaller 91 energetic bandwidth of the pulses, where pulse parameters can come close to the optimal 92 point in the trade-off between energy and temporal resolution at the Fourier limit. Here, 93 FLASH will be operated in a regime with sufficient temporal resolution to visualize 94 electronic processes while still providing sufficient spectral resolution to selectively 95 study specific chemical elemental resonances as well as the respective chemical shifts. 96 Fully coherent pulses are also a prerequisite for transferring modern coherent 97 (spectroscopy) techniques from the laser world to the X-ray realm. Here, first steps have 98 been achieved, but it is becoming apparent that higher-order optical constants are even 99 weaker at shorter wavelengths than in the optical regime. Nevertheless, such techniques 100 often provide information that is unavailable to more traditional methods, like the spatial 101 motion of excitations in transient grating methods [53,54]. Some of those experiments 102 can be performed in a quasi-background-free manner, but full harvesting of results from 103 such novel X-ray methods requires fully coherent beams at high repetition rate in order   Xseed experiment [55] and on plasma wake field acceleration with FLASHForward [56].

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The unique use of a superconducting linac allows RF flat-tops of up to 0.8 ms running 125 with a repetition rate of 10 Hz enabling the acceleration of several hundreds of bunches 126 at the repetition rate of the injector laser (1 MHz). The bunch train can be divided into adapted to the specific requirements of the experiments in the two beamlines [33]. In 132 addition, charge and bunch spacing can be adjusted to different needs. Currently, the 133 generation of FEL radiation at FLASH is based on the SASE process [36,37]   The new FLASH1 will combine seeding with variable gap undulators of APPLE III type, 193 allowing to not only adjust wavelength but also polarization of the generated soft X-ray 194 radiation.

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The current FLASH accelerator uses a long 6-dipole S-type chicane [60][61][62] as the 214 last compression stage. Recently, an additional bunch compressor section was added to 215 the FLASH2 beamline to apply more flexible compression schemes that reduce the peak 216 current in the extraction section from the FLASH linac to the FLASH2 beamline.Therefore, 217 the final compression for FLASH2 is performed just before the undulator section, which 218 leads to better overall electron and SASE performances. As part of the upgrade plans, 219 the S-type compression section is redesigned to improve the overall compression in 220 the FLASH machine, increase the flexibility of compression schemes, and realize an 221 additional second matching section.

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In order to accommodate the beam emittance and optics measurement devices,the 223 S-type chicane will be replaced by a shorter 4-dipole D-type chicane (BC2 in Fig. 1).

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The need to balance the request for moderately compressed bunches, with reduced 225 micro-bunching, for seeding (∼600 -800 A) and stronger compression (∼1 -2 kA) with 226 significant residual energy chirp for the ultra-short SASE bunches, requires a flexible 227 chicane design which is capable of a variable momentum compaction R 56 .

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With the design of the new chicane [63], it has also been considered to allow a  Our studies (Fig. 2) show that with a small energy spread introduced by the laser 248 heater, the microbunching gain at the end of the linac is limited to a few tens for the FLASH2020+ design and comparable to the one estimated for the typical configuration 250 of the FERMI linac [71]. module and 3rd harmonic linearizer [76]. Since the undulator is located in the straight  Recent results have shown that Echo Enabled Harmonic Generation (EEHG) [79] 283 can be used efficiently to produce highly coherent soft X-ray FEL pulses [80]. The EEHG 284 scheme planned at FLASH uses two UV laser beams, seed laser 1 and seed laser 2 ( Fig.   285 3) [40] .
Bunching chicane (R56_2) is used to convert the energy modulation produced by the two lasers in the two modulators (Mod1,2) into bunching before the beam enters the final radiator (Rad1, ...).
In order to avoid a change of electron beam energy to modify the FEL radiation 287 wavelength, as is the case for the present fixed-gap undulator system, the new APPLE-III 288 radiators will allow a remote adjustment of the K-parameter in each radiator segment. 4 nm with an ideal beam can produce more than 5% initial bunching at the radiator The use of a very long radiator (∼10 gain lengths) with a well bunched beam 316 requires a proper undulator tapering to exceed the FEL saturation power (Fig. 4-b) while 317 maintaining a well-defined and narrow frequency spectrum (Fig. 4-d). However, the 318 extra power extracted from the electron beam after saturation (at ∼17 m) comes with 319 a slightly increased FEL pulse length with respect to the optimal case (Fig. 4-c). From 320 ongoing studies, it is also evident that a different optimization of the tapering could be 321 exploited to emphasize the leading super radiant spike and generate very short (few fs) 322 pulses [84]. studies along the FLASH2020+ linac [85]. However, previous works have shown that 327 EEHG bunching at very high harmonic can be smeared by intra-beam scattering, incoher-328 ent synchrotron radiation, and coherent synchrotron radiation occurring in between the 329 first modulator and the radiator [86][87][88]. In contrast to other schemes [87], in our setup a 330 second seed laser is used that is much shorter than the electron beam and the first seed 331 laser beam. Consequently, the sensitivity to these effects is significantly reduced and is 332 expected not to affect the bunching content and coherent properties dramatically [89]. At longer wavelengths, EEHG can easily generate bunching as high as 10% or more. 337 Consequently, parameters need to be adjusted to keep the bunching at a 5% level to avoid 338 quick over-bunching in the long radiator. Moreover, since the gain length is significantly 339 shorter at the long-wavelength (∼1.2 m at 10 nm), FEL amplification develops much 340 faster in the radiator and makes the undulator tapering crucial [90].  seed laser that is thus required to provide short pulses (50 fs) and tunable wavelength.

365
Moreover, it has also been shown that EEHG spectral properties and coherence critically 366 depend on the quality of the second seed laser beam that is required to be as close as 367 possible to the Fourier limit [91]. The seed laser parameters required for external seeding 368 using the HHGH and EEHG method are summarized in Table 7. The high laser pulse 369 energy required includes some margin to take into account possible losses along the 370 complex laser transport line described in the next section. The fixed wavelength of the seed laser 1 pulse is generated straight forward via 389 third harmonic generation of a 0.3 mJ portion of the compressed high energy output.

390
Simulations and preliminary experiments showed that we can generate more than 100 µJ 391 pulse energy of approximately 600 fs duration which fulfils the requirements for the 392 seed laser 1 pulse.

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The generation of the tunable seed laser 2 relies on an efficient chirped sum fre-394 quency generation scheme [93]. First the short IR pulse output drives a white-light  actively control of critical parameters is essential.

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After the generation of the seeding lasers in the laser laboratory, the two seed lasers, 420 seed laser 1 and seed laser 2, will be transported to the interaction regions via dedicated 421 laser beamlines. Seed laser 1 travels a distance of ∼22 m from the laser lab to the center 422 of the first modulator, seed laser 2 a distance of ∼30 m to the center of the second 423 modulator.

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In-coupling of both lasers to the electron beamline axis in the modulators will be 425 done through injection chicanes (see Fig. 3 and Fig. 6), allowing the electron beam to Traveling within the vacuum pipes the two laser pulses pass through 2 meters of 439 radiation protection wall that separates the laser laboratory from the accelerator tunnel. With the goal of reducing the energy density exposed on optical elements, the 474 electron beamline has been designed such that the distance between the injection mirrors 475 and the modulators is as large as reasonably possible. Moreover, grazing incidence The following abbreviations are used in this manuscript: