Enhanced seeded free electron laser performance with a “ cold ” electron beam

FERMI is a seeded free electron laser (FEL) based on the high gain harmonic generation (HGHG) scheme and has been generating intense and fully coherent extreme ultra-violet and soft x-ray pulses for several years. The high-degree performance of the FEL leans on a high brightness electron beam, with small transverse emittance ( ∼ 1 μ m) and a peak current of about 700-800 A. The main constraint on lasing at high harmonics of the seed is low electron time-slice energy spread. The optimization of the photoinjector and of some linac parameters has allowed a reduction of the relative slice energy spread to the level of few times of 10 − 5 . With these new conditions, the FEL can be operated without the need of a laser heater to suppress micro bunching instabilities and this “ cold ” beam has allowed generation of extreme UV pulses with pulse energy exceeding a mJ, and with peak power of about 10 GW. We describe the electron beam characterization and the FEL performance improvement, including the extension of the range of harmonics of the seed which can be amplified, up to


I. INTRODUCTION
Free electron lasers (FELs) can exceed by about 10 orders of magnitude the peak brightness of existing synchrotron sources. Their unique capability of producing very intense and short pulses, at wavelengths ranging from tens of nm to sub Ångström [1,2], are opening new scientific possibilities and enabling the access to new matter states [3]. Most of these FELs amplify the stochastic electronic noise of a high current beam passing through a long magnetic undulator. Such a self-amplified spontaneous emission (SASE) mode of operation, does not guarantee the generation of longitudinally fully coherent pulses. Each FEL pulse is typically composed of a burst of many short spikes, with random phases and amplitudes [4,5]. Longitudinal coherence can be improved by injecting a coherent seed radiation pulse to initiate the FEL amplification process. Several schemes implementing the seed have been proposed and demonstrated. These can be classified as externally seeded configurations [6][7][8][9] and self-seeded configurations [10][11][12][13][14].
FERMI [15] is a FEL based on the high gain harmonic generation scheme (HGHG) [6] where an optical seed is frequency multiplied and amplified, preserving some of the original pulse coherence properties. This scheme allows generation of temporally and spatially coherent pulses and control of the slowly varying phase along the FEL pulse [16]. Coherence is also preserved at higher orders [17], and it has been exploited in coherent control experiments as [18] and for the generation of multiple-color multiple pulses with a well determined and controlled phase relation in the EUV and soft x-rays [18][19][20][21][22][23].
This progress has stimulated a search for the ultimate limits of the HGHG scheme in the generation of high harmonics. The harmonic conversion efficiency of HGHG decreases at high harmonics (shorter wavelengths) [6,7] and the quality of the pulses is increasingly affected by the electron beam defects, such as phase space distortions [24,25] or microbunching instability. The latter is induced by the collective self-amplification of nonuniformities in the electron longitudinal distribution [26,27]. In fact, an initial density modulation in the beam current profile is converted into an energy modulation by longitudinal space charge forces. The energy modulation is in turn converted into density modulation when the electrons pass through dispersive sections such as magnetic compressors, leading to amplification of the initial modulation. The suppression of microbunching instability is of critical importance to avoid structures in the electron beam phase-space that affect the longitudinal coherence of FEL pulses.
Microbunching instability gain is sensitive to the slice energy spread (σ E ). A laser heater (LH) device [28] is used to properly increase σ E , damping the instability growth [29]. The use of a LH has shown the capability to improve the HGHG performances in terms of longitudinal coherence. Unfortunately, the LH-induced σ E increment prevents an efficient harmonic conversion, so that a trade-off between microbunching damping and FEL amplification at high harmonics has to be found. During routine operation of FERMI, a modest level of heating is sufficient to suppress the microbunching. The typical σ E at the undulator entrance is of the order of 100-150 keV [8,9], i.e., δ ¼ σ E =E ≈ 10 −4 . In these conditions, the single stage HGHG in FEL-1 can be operated for users up to harmonic 13-15 of the UV seed (260-240 nm), reaching a wavelength range 16-20 nm [8].
Among the various seeding schemes recently proposed [7,30,31], echo enabled harmonic generation [7] allows improvement of the high harmonic conversion efficiency and a reduction of the sensitivity to electron beam phase space modulations [24,25,[28][29][30][31][32]. However, also the performances of FERMI operating in HGHG can be also improved, if a solution to suppress microbunching instability without increasing the slice energy spread with a LH is found.
In this work, we report recent results obtained under conditions allowing transport of the electron beam up to the FERMI FEL-1 undulator without significant gain of the microbunching instability. In the following, we will focus on the improved performance of the FEL when such an electron beam is used for generating coherent HGHG radiation.
The first part of the paper is dedicated to the electron beam characterization, showing the measurements of the electron slice energy spread obtained by setting the FEL in SASE optical klystron mode and optimizing the dispersive section strength [33]. In the second part, we focus on the FEL performance obtained with this "cold" beam, both in terms of spectral purity and intensity at high harmonics.

II. ELECTRON BEAM
The FERMI electron beam is generated from a copper photocathode illuminated by an intense UV laser at 260 nm (namely, photoninjector laser, PIL) and immediately accelerated in a 1.6-cell rf gun cavity (S-band) up to about 5 MeV. The typical charge per bunch is in the range 600-700 pC, with a repetition rate of 10 Hz or 50 Hz [34].
Temporal modulation in the shape of the PIL can introduce modulations in the bunch current profile. In fact, the PIL is obtained from a 100 fs-long, large bandwidth pulse, that is stretched to a few ps. As a consequence, small modulations with periodicity of tens of micrometers (over a bunch length of about 2 mm) can be impressed onto the electron temporal profile and amplified by the microbunching instability.
In September 2019, a new copper cathode was installed and a careful optimization was done to preserve its transverse uniformity. The photoinjector laser was upgraded for an improved transverse uniformity and smoothness in the longitudinal direction. Furthermore, in order to limit the generation of undesired temporal modulation, the PIL bandwidth has been reduced by 30% by decreasing the bandwidth of the fundamental infrared pulses by about 20%, followed by the use of a combination of thicker second and third harmonic crystals in the UV generation setup. As a result of this upgrade, at the injector exit (∼100 MeV), a projected emittance of about 1.2-1.3 μm was measured in both planes for a bunch with a charge in the range 600-700 pC and a FWHM length of about 8 ps. The beam is routinely compressed to a nominal peak current of ∼700-800 A at about 300 MeV by means of a single compressor (BC1), as it has been proven that it is less affected by microbunching growth than the double compression scheme [35].
Concerning the beam optics, the typical strategy adopted to match the beam optics in the FERMI linac consisted of imposing predetermined Twiss parameters in three particular matching points: at the injector exit, after the first compressor BC1, and the end of the linac (see [36]), and then setting a quasi-FODO lattice in between them. This strategy has been recently revised. We increased the beam beta functions at the matching points, also relaxing the conditions to match to a beam waist at these positions. The beam optics in the spreader was also investigated to better control the residual dispersion and chromaticity after the spreader [37]. Moreover, this new tool allows exploration of different beam optics solutions in order to mitigate the microbunching instability growth by avoiding excessively strong focusing, i.e., high charge density, at lower energy. The combined effect of these changes led to the transport of a beam with minimal microbunching instability amplification and with a substantially lower energy spread, that will be referred to as the "cold" beam.

A. Characterization of the electron beam
Measurements of the time-slice energy spread of the electron bunch are routinely performed by using an rf deflector placed at the end of the linac, in combination with the energy spectrometer [38]. The measurement resolution depends on several parameters (beam optics, rf deflecting voltage, beam energy). In the specific case of FERMI, considering a beam energy in the range 1.0-1.5 GeV, the minimum energy spread value that can be resolved is about 100 keV [29]. The cold beam produced at FERMI after the mentioned changes has a slice energy spread well below this value and an alternative method is necessary to measure this parameter. FERMI FEL-1 can be operated in SASE as a high-gain optical klystron [33,39,40]. According to [39,41,42] the maximum FEL intensity is obtained when: where R 56 is the momentum compaction of the dispersive section, k r ¼ 2π λ r and λ r is FEL output wavelength. The SASE optical klystron is therefore a diagnostic tool to measure the beam energy spread that can be calculated from the value of the dispersion corresponding to the maximum FEL intensity.
The modulator and the radiator of FEL-1 were tuned to be resonant at λ ¼ 31.9 nm and the dispersive section strength between them has been scanned. Figure 1 shows the FEL pulse energy measured as a function of the dispersive section R 56 for different values of the laser heater intensity, and for a beam energy E ¼ 1.32 GeV. In order to have a high SASE intensity we initially compressed the electron beam more than in the nominal case reaching a peak current I p ∼ 1.1 kA.
The first indication of a reduced microbunching instability gain and of a low energy spread, is given by the fact that the best FEL performance, in terms of pulse energy, is obtained in the absence of the laser heater. This differs from what was observed in the past for a similar FEL configuration (see [33]). On that occasion, the FEL pulse energy was maximized for a low (but not zero) intensity of the laser heater, with an R 56 value of 75 μm (see vertical dotted line on the inset of Fig. 1). In contrast, in the present situation the maximum FEL pulse energy decreases and shifts toward smaller values of R 56 when the laser heater power is increased. This is a clear indication of a progressive and monotonic growth of the slice energy spread, without the typical minimum for nonzero heating. Similar measurements have been repeated for the nominal FERMI compressed beam, I p ∼ 0.8 kA, and for higher compression, Applying Eq. (1), σ E was retrieved in the mentioned cases and the results are summarized in Fig. 2. For the nominal case (I p ∼ 0.8 kA), a minimum σ E of about 40 keV was measured, a value much lower than what was usually obtained. Also in the strong compression case (I p ∼ 1.3 kA), σ E is minimized with the laser heater off. This suggests that no microbunching structures have been amplified along the machine, at least to a level that affects the energy spread. In terms of energy spread mitigation, the laser heater is actually not required with this electron beam condition.
As has been reported in the literature [30], the σ E parameter is of paramount importance. For a seeded FEL as FERMI based on the HGHG scheme, in order to be able to lase efficiently at a harmonic h of the seed laser frequency, the following condition has to be met: where ρ is the FEL parameter, i.e., Pierce parameter [43]. Figure 3 shows the maximum tolerable relative energy spread δ FEL calculated for FERMI FEL-1, from 40 nm to 10 nm, according to the inequality (2) that provides exponential gain. In the past, the FERMI FEL-1 gain suffered a strong reduction for harmonics (h) larger than 13-15, indicating a slice energy spread of the order of 100-150 keV, in agreement with the past energy spread measurements [8,29,33]. A beam slice energy spread of 40 keV fulfills the condition (2) up to harmonic  1.32 GeV. This condition corresponds to the measured value in the reported conditions, and stimulated an investigation of the FEL performances.

III. FEL PERFORMANCE AT FERMI
At FERMI, the LH has been exploited to control periodic structures in the electron beam, in order to generate stable spectral sidebands, i.e., multicolor FEL pulses, or to shift the lasing frequency with respect to an integer harmonic of the seed [44], but its main application is the suppression of the microbunching instability [29,45]. The LH is considered essential in the optimization of the FEL aiming at maximizing the FEL intensity while preserving a single moded, gaussian-shaped, stable from pulse to pulse, radiation spectrum. The impact of the LH on the FEL performance depends upon several parameters including the use of bunch compressor and the original content of microbunching structures and their amplification [46]. At FERMI, the absolute advantage provided by the LH, in terms of FEL intensity and spectral purity, has not been constant over the years, but a small amount of LH energy has been always necessary to optimize the FEL output.
A typical case is represented in Fig. 4, where the FEL intensity [ Fig. 4(a)] and the FEL spectrum [ Fig. 4(b)] at 22.5 nm (h ¼ 11) are reported as a function of the LH pulse energy controlled through an optical attenuator. When the LH energy is close to zero, the FEL presents a multispike spectrum and low pulse energy. It is necessary to increase the LH energy to about 1 μJ to get rid of the microbunching instability and maximize the FEL intensity with a "clean" spectrum.
After the recent changes mentioned in Sec. II, we observed a consistent reduction of the LH energy required to reach such a condition. Figures 4(d-f) show the same measurements in the new configuration: the FEL spectrum is a single line without evidence of microbunching induced sidebands, and the maximum FEL intensity is obtained at the minimum LH intensity. Apparently, the LH has the effect of increasing the electron slice energy spread and consequently, reducing the FEL gain and the output intensity. This is consistent with the measurements reported in Fig. 2, where the minimum slice energy spread was observed for the LH at zero intensity. Moreover, even in the case of the LH completely off, as shown in Fig. 5, the FEL at ∼21 nm is characterized by a shot-to-shot power stability of ∼10% (rms), with a bandwidth of 7 × 10 −4 (fwhm) averaged over 1800 shots. A small fraction of shots (∼10%) have been filtered out as they were associated with a large jitter of the relative arrival time between seed and electron bunch, as measured by the bunch arrival monitor [47]. The measured spectral bandwidth corresponds to a Fourier limited pulse duration δ ðfelÞ t of about 45 fs (fwhm). This is in agreement with the expected pulse duration (51 fs) calculated from a seed pulse of about 100 fs (fwhm) at 260 nm, according to the rule δ ðfelÞ t ¼ 7=6δ ðseedÞ t =h 1=3 , where h ¼ 12 is the harmonic order [48]. The residual difference may be due to a small chirp of the seed laser pulse that causes an increase of the time bandwidth product of the FEL pulse. Note also that the scaling relation with the seed pulse duration represents a rough estimate, since the effective pulse duration depends on the level of saturation reached by the amplifier. In fact, far away from the saturation the δ ðfelÞ t scales as δ ðseedÞ t =h 1=2 . In presence of time-dependent energy modulation along the bunch, the FEL wavelength output is slightly shifted shot-to-shot according to the temporal jitter between seed and electrons that is about 50 fs [49]. However, in Fig. 5 the shot-to-shot wavelength stability (rms ∼8 × 10 −6 ) is anyway two order of magnitude smaller than the FEL bandwidth, and this is another important signature that the beam has no microbunching structures.
It is worthwhile mentioning that because of the low resolution, a measure of the electron longitudinal phase space performed with rf-deflector and energy spectrometer does not show any difference in terms of microbunching content between this cold beam and the previous situation. Conversely, this difference is highlighted by the performance of the FEL operating at high harmonics in HGHG mode.
The use of a cold electron beam (with σ E ∼ 40 keV) without microbunching structures at the undulator entrance provides further advantages. As shown in Fig. 3, the low slice energy spread enables the amplification of shorter wavelengths, such as 14 nm (h ¼ 18). FEL operation in this wavelength range was reported in [50], but with a substantially lower pulse energy, and implementing an harmonic cascade scheme. In the present conditions, more than 10 μJ per pulse were measured, with a relative (fwhm) FEL bandwidth of about 6.4 × 10 −4 , as reported in Fig. 6. The measured FEL bandwidth corresponds to a Fourier limited pulse of about 32 fs (fwhm), in agreement with the aforementioned scaling law [48] that foresees an FEL pulse duration ranging from 24 fs to 45 fs depending upon the level of saturation. Note that data reported in Fig. 6 refer to linearly polarized light. More than a factor two of power increase is expected in the case of a circularly polarized undulator.
We measured the FEL pulse energy at various wavelengths, in particular from 35 nm (h ¼ 7) down to 10 nm (h ¼ 25). The measurements down to 20 nm were carried out with the FERMI intensity monitor [51]. At shorter wavelengths, the pulse energy was estimated from the intensity of the spectrometer camera image [52], crosscalibrated with the intensity monitor. An average energy of about 0.5 μJ at 10 nm was estimated, with shots up to 1.5 μJ. The results are shown in Fig. 7   significantly exceed the standard one in the whole range. Moreover, in this configuration we could measure a good signal down to 10 nm, thus extending the lasing range of FERMI FEL-1.
The lower beam energy spread can be also exploited to increase the beam current with a stronger compression. We operated the FEL with a bunch compressed by a factor 15 corresponding to a final peak current of about 1.3 kA. After optimization at h ¼ 7 (i.e., 37 nm) in circular polarization, the FEL intensity reached several hundreds of μJ. A taper of the final undulators and a careful optimization of the seeding parameters allowed to measure FEL pulses exceeding 1 mJ for the first time at FERMI. Taking into account the scaling law already mentioned [48], one can estimate an FEL pulse length of about 60 fs, and therefore an FEL peak power at 37 nm of about 16 GW. Figure 8(a) reports the FEL amplification (blue line) along the undulator chain, together with the energy offsets corresponding to the undulator taper (red line).
It must be noted that despite the stronger compression, only a small fraction of the bunch charge participates to lasing in a seeded FEL where the seed pulse is much shorter than the electron bunch. The energy offset of the resonance of the last radiator was 15 MeV, corresponding to more than 1% of energy loss for the emitting electrons. Considering a peak current of 1.3 kA and the mentioned energy loss, one can estimate an FEL peak power of about 20 GW, consistent with the previous estimation. Evolution of the FEL spectra as a function of the number of undulators is reported in Fig. 8(b). For each undulator setting, spectra are normalized to the corresponding maximum. This representation of the data allows identification of possible spectral structures even in case of weak spectra. Despite the very high compression and the fact that the laser heater was offline, FEL pulses show very stable and narrow spectra, without undesired features. The small sideband toward longer wavelength is expected to be the result of a combination between resonance tuning and FEL saturation.

IV. CONCLUSION
We have experimentally demonstrated at FERMI, the possibility to generate, accelerate and compress above 1 kA, an electron bunch with the nominal charge in the range 600-700 pC with an unprecedented small slice energy spread. This fact allowed significant improvement of the seeded FEL performance of FERMI. The output power increased by more than a factor two in the nominal range of operation of FEL-1. The standard operation range of the FEL was extended to higher harmonics, obtaining about 1 μJ at h ¼ 25 (i.e., 10 nm). The bunch, virtually free of microbunching heating has also allowed the FEL operation at higher compression, producing mJ-level pulses at 37 nm. This result represents a foundation to improve the capabilities of quantum optics experiments and nonlinear optics experiments with fully coherent EUV pulses. A number of the related techniques have been pioneered at FERMI; applications include precision two-photon spectroscopy [54,55], coherent control [18,56], pulse shaping [21,23], and four-wave mixing [57,58].

ACKNOWLEDGMENTS
Authors would like to thank all the FERMI Team for the support provided during the machine tuning and optimization. In particular they are grateful to Fatma Iazzourene for the development of the code to match the beam optics along the linac and the undulator line in a more