research papers
Harmonic radiation contribution and Xray transmission at the Small Quantum Systems instrument of European XFEL
^{a}European XFEL, Holzkoppel 4, 22869 Schenefeld, Germany, ^{b}Deutsches ElektronenSynchrotron DESY, Notkestr. 85, 22607 Hamburg, Germany, ^{c}National Institute of Advanced Industrial Science and Technology (AIST), NMIJ, Tsukuba 3058568, Japan, and ^{d}Institut für Physik und CINSaT, Universität Kassel, HeinrichPlettStrasse 40, 34132 Kassel, Germany
^{*}Correspondence email: thomas.baumann@xfel.eu, michael.meyer@xfel.eu
Transmission measurements of the soft Xray beamline to the Small Quantum Systems (SQS) scientific instrument at the SASE3 undulator of European XFEL are presented. Measurements are reported for a wide range of photon energies (650 eV to 2400 eV), using Xray gas monitors as well as a bolometric radiometer. The results are in good agreement with simulations for the beam transport and show a transmission of up to 80% over the whole photon energy range. The contribution of second and thirdharmonic radiation of the soft Xray undulator is determined at selected photon energies by performing transmission measurements using a gas absorber to provide variable attenuation of the incoming
A comparison of the results with semianalytic calculations for the generation of freeelectron laser pulses in the SASE3 undulator reveals an influence of apertures along the beam transport on the exact harmonic content to be accounted for at the experiment. The secondharmonic content is measured to be in the range of 0.1% to 0.3%, while the thirdharmonic contributed a few percent to the SASE3 emission. For experiments at the SQS instrument, these numbers can be reduced through specific selections of the mirror reflection angles.Keywords: freeelectron lasers; Xray beam transport; harmonic radiation; atomic, molecular and optical science.
1. Introduction
The Small Quantum Systems (SQS) instrument is located behind the soft Xray undulator SASE3 of the freeelectron laser European XFEL (Decking et al., 2020). It is dedicated to studying the interaction of Xrays with atomic and molecular systems as well as nanoparticles and clusters, focusing particularly on nonlinear processes, timeresolved femtosecond dynamics and coherent imaging (Mazza et al., 2020; Eichmann et al., 2020; Jahnke et al., 2021; Boll et al., 2022; Feinberg et al., 2022; Grychtol et al., 2021; Rivas et al., 2022). Such studies require an extreme Xray photon density, which can uniquely be delivered by freeelectron lasers (FELs). Consequently, a good knowledge of the fluence, defined as the number of photons per unit area, is required for planning and performing such experiments.
The fluence is determined by the total energy in each FEL pulse and by the ability to focus these pulses onto the sample. In this article, we concentrate on the FEL pulse energy and investigate the transmission of the Xray optics delivering the FEL beam to the experimental station at SQS. The energy of the Xray pulses is measured by Xray gas monitor detectors (XGMDs), a technique based on et al., 2008). XGMDs are now routinely used at Xray FELs like LCLS (Tiedtke et al., 2014), SwissFEL (Juranić et al., 2018) and European XFEL (Grünert et al., 2019). Distributing several of these devices along a beamline is a tool to measure the transmission of the Xray optics, as previously done, for example, at FLASH (Wellhöfer et al., 2007) or LCLS (Moeller et al., 2015). An alternative approach for an absolute determination of the FEL intensity is bolometric techniques that measure temperature changes induced by the Xray radiation in an absorber (Kato et al., 2010; Tanaka et al., 2015, 2017). In this article we utilize both methods.
of a dilute gas that was established at FLASH (TiedtkeThe fluence at the experiment is dominated by the radiation at the fundamental wavelength of the FEL but also contains contributions from harmonics. For planar undulators as used at SASE3, the most prominent contribution is expected for the third harmonic (Saldin et al., 2006). However, also the second harmonic can occur at nonnegligible levels as calculated by Geloni et al. (2007) or measured at FLASH (Düsterer et al., 2006) and LCLS (Ratner et al., 2011). The harmonic radiation can be problematic for certain types of experiments, e.g. measurements of nonlinear multiphoton processes induced by the fundamental radiation competing with an inseparable onephoton channel of the harmonic (LaForge et al., 2021). Therefore, we deploy the techniques used for measuring the beamline transmission to investigate the harmonic contribution at the SQS instrument in the second part of this article.
2. SASE3 and SQS beamline layout
SQS is one of three scientific instruments at the SASE3 soft Xray undulator branch (Tschentscher et al., 2017). The photon beam transport section between the undulator and the SQS instrument is about 450 m long and is schematically shown in Fig. 1. It contains four grazingincidence Xray mirrors that are relevant for the photon beam delivery to SQS. Mirrors M1 and M2 introduce a horizontal chicane to prevent unwanted highenergy radiation propagating to the instrument. Their incidence angle can be tuned between 9 mrad and 20 mrad to change their geometric acceptance and highenergy cutoff. Furthermore, the surface of M2 is bendable, which allows for focusing the beam to an intermediate horizontal focus along the beam transport path. A second pair of mirrors (M3 and M4) is part of the soft Xray monochromator (Gerasimova et al., 2022). The cylindrical premirror M3 deflects the beam vertically and focuses it onto the exit slit at a distance of 400 m from the last undulator segment. Either a diffraction grating for monochromator operation or a flat mirror can be inserted in position M4. M3 can also be retracted completely to let the FEL pass to SQS without using M3 and M4. For all measurements described in this article, we utilize a beam transport configuration with M1 and M2 only. This configuration is intended to provide the highest number of photons for example for studies of nonlinear phenomena since transmission is maximized by using a minimum number of optical elements.
At the SQS instrument, the photon beam is microfocused by a pair of mirrors in Kirkpatrick–Baez (KB) configuration named vertical focusing mirror (VFM) and horizontal focusing mirror (HFM). After using a pair of interim mirrors with a fixed elliptical curvature during the first year of operation, a new set of bendable mirrors was installed in 2020. These bendable KB mirrors allow for moving the focus point between two experiment interaction zones at 1.8 m and 3.8 m distance from the second mirror by changing the curvature of the elliptical mirror surfaces. The measurements presented here were made using the bendable mirrors corresponding to the final configuration of the SQS beamline layout. A detailed description of the SASE3 and SQS photon beam transport can be found in the literature (Sinn et al., 2012; La Civita et al., 2014; Tschentscher et al., 2017). Mazza et al. (2023) describe and characterize the beam transport system including the fixedcurvature mirror KB setup.
3. Beamline transmission measurement
The transmission of the photon beam from the undulator to the interaction region at SQS is determined by two main factors: the reflectivity of the mirrors and the geometric aperture of the elements in the beam transport. M1, M2, VFM and HFM are made from large silicon substrates with an 800 mmlong reflective surface that was polished to a tangential height error of about 2 nm peaktovalley and coated with 50 nm of boron carbide (B_{4}C) (Vannoni & FreijoMartin, 2019). Depending on the incidence angle and photon energy, each mirror reaches a calculated reflectivity of above 90%. The geometric aperture of the mirrors becomes a relevant factor for photon energies below 1500 eV due to the increasing divergence of the FEL beam with decreasing photon energy, causing the FEL to overfill the reflective surface. This will not only reduce transmission but can also affect the wavefront purity and reduce the quality of the focused beam. One strategy to mitigate this factor is to increase the incidence angle to a maximum of 20 mrad for lower photon energies. Further parameters that can influence the transmission are the vacuum level throughout the beam transport as well as contaminations on mirror surfaces. The entire beam transport section is kept under ultrahighvacuum conditions with pressures between 1 × 10^{−9} mbar and 1 × 10^{−7} mbar, which minimizes photoabsorption by residual gas. Special care is taken for vacuum chambers housing mirrors, which are treated under particlefree conditions to prevent contamination from dust particles. The possible influence of contamination is discussed – to some extent – below.
We determined the transmission of the beam transport by comparing the FEL pulse energy coming from the undulators with the pulse energy measured downstream of the interaction region at SQS. An Xray gas monitor (XGM) is installed upstream of the SASE3 beam transport section to measure the incoming FEL pulse energy. The XGM is a larger version of the XGMD and was developed for hard Xray FELs like European XFEL (Maltezopoulos et al., 2019). The pulse energy measurement is based on of a noble gas. The XGM records a current of photoions under well known conditions and thereby allows for an absolute determination of the incoming FEL pulse energy using semiempirical ionization cross sections and photoion charge state distributions. Furthermore, it can provide a pulseresolved signal by recording the emitted photoelectrons, which is calibrated to the ionbased pulse energy measurement (Sorokin et al., 2019). The data described here solely rely on the ion measurement. A mobile version of the XGMD was installed downstream of the SQS interaction zone to record the FEL pulse energy after beam transport. Both gas monitors were operated with xenon as target gas at a pressure in the mid10^{−6} mbar range.
For a second, independent measurement a compact roomtemperature bolometric radiometer (CBR) was mounted downstream of the mobile XGMD, behind the SQS instrument. This device provides an absolute measurement of the average FEL power by measuring the temperature change in a gold absorber resulting from photon energy deposition (Tanaka et al., 2015, 2017). Using the known number of FEL pulses per second, the average pulse energy can be derived from this measurement. The radiometer has an aperture of 5 mm diameter, which puts a constraint on the measurement since under normal operation conditions the beam is larger at the position of the radiometer. Therefore, we closed a slit system upstream of the beamline (including the XGM, cf. Fig. 1), called the synchrotron radiation aperture (SRA), to an aperture of 1 mm × 1 mm to prevent an overfilling of the CBR aperture. This measure minimized the contribution of limited geometric apertures of the beamline elements to the transmission since only the center areas of the mirrors were illuminated. It reduced the incoming pulse energy of a few millijoules by about a factor of three.
Fig. 2(a) shows the resulting transmission for the incidence angle of the mirrors M1 and M2 set to 9 mrad as well as 20 mrad, while the M2 surface was kept flat (no intermediate horizontal focus). VFM and HFM were always operated under an incidence angle of 9 mrad. Each point represents the FEL pulse energy detected by the CBR or the XGMD, normalized to the incoming pulse energy measured in the upstream XGM, and averaged over several minutes. The FEL was operated with one pulse per pulse train and a train repetition rate of 10 Hz. The error of the transmission is dominated by the systematic uncertainty of the XGM and XGMD measurements, which lies between 5% and 10% depending on the photon energy (Sorokin et al., 2019). The uncertainty of the CBR measurement is below 1% (Tanaka et al., 2017).
A transmission between 70% and 80% was measured in the photon energy range between 650 eV and 2400 eV at the 9 mrad set point. The limits of this photon energy range were given by the K parameter range of the variablegap undulators at an electron beam energy of 14 GeV. At 20 mrad, the transmission at low photon energies was reduced to about 50% and a clear cutoff can be seen at 1400 eV. This also leads to the suppression of the higher harmonics at these higher incidence angles. The results from the XGMD and CBR are generally in good agreement, but show a discrepancy at lower energies due to yet unknown reasons. We calculate the reflectivity of the singlelayer mirrors using the CXRO database (Henke et al., 1993). The dotted lines in Fig. 2(a) represent the calculated transmission obtained from the nominal reflectivity of the mirrors for linear polarized light, using a single B_{4}C layer of 50 nm thickness coated on the silicon mirror substrates with a surface roughness of 0.3 nm. The calculations account for a coating density of 2.37 g cm^{−3}, as has been previously measured for these mirrors by Störmer et al. (2018). The transmission measurements for the 9 mrad incidence angle of M1 and M2 were taken in a monotonous regime resulting in about 90% of the transmission expected by the calculation. The FEL beam cutdown by the SRA only illuminates the center part of the mirrors, which has been irradiated the most during the past two years of FEL operation. The mirror coating might therefore already be slightly deteriorated in this center area by carbon contamination. To estimate the effect of such contamination, we utilize the twolayer calculation of CXRO and add a 5 nmthick layer of carbon on top of the B_{4}C for all mirrors. The resulting transmission is plotted as dashed lines in Fig. 2(a). Fig. 2(b) further shows the ratio between the data points and the contamination calculation. The choice of 5 nm thickness is based on measurements of the carbon contamination layer thickness on top of the previously used KB mirrors with fixed curvatures after they were taken off the beamline. The inclusion of a carbon layer improves the agreement between calculation and measurement. However, there is still a deviation especially for the data taken at the incidence angle of 20 mrad. Here we are also probing the transmission cutoff, a region where the calculation is very sensitive to its input parameters. The average ratio between measurement and calculation is thereby dominated by the deviation in the cutoff region. The actual B_{4}C layer thickness and density, but also the actual incidence angles of all mirrors, can differ from the numbers we use for the reflectivity calculation. This might be the reason for the remaining deviation.
Opening the SRA to 4.5 mm × 4.5 mm lets the full FEL beam enter the transport section and allows for measuring the beamline transmission including the contribution from its geometric acceptance. The results using only the XGMD are shown in Fig. 3. For this measurement, M1 and M2 were set to an incidence angle of 9 mrad and the bending mechanism of M2 was used to create an intermediate horizontal focus (IMFH) at a position of about 400 m along the beamline. The IMFH decreased the horizontal size of the beam to a few millimetres directly upstream of the KB system, making it smaller than the clear aperture of the HFM. This leads to a reduction of losses due to the limited aperture of the KB system. A calculation of the transmission for this scenario uses the product of mirror reflectivity and geometric mirror acceptance. The reflectivity is derived without (dotted line) and including (dashed line) carbon contamination, as discussed above. For calculating the geometric acceptance, a model of the FEL beam divergence derived by Schneidmiller & Yurkov (2011) is used. The result is shown as the dashed line in Fig. 3(a). When compared with Fig. 2, it becomes evident that using the full beam provides a lower transmission for energies below 1500 eV. This is due to the geometric aperture of the mirrors becoming smaller than the beam (which has a larger divergence at lower photon energies). This effect is included in the calculated transmission. However, as seen in Fig. 3(b), the measured transmission yields about 85% of the calculated one, which is a deviation larger than seen in the reflectivity measurements. This is possibly a result of the uncertainty in the calculation for the FEL divergence, which serves as a basis for the calculated geometric acceptance. Another source of uncertainty is the actual position of the IMFH, which might deviate from the one used in the calculation. Taking the deviation into account one can still use the reflectivity calculations as reference for the overall transmission of the beamline.
4. Harmonics contribution measurement
The contribution of the harmonics to the FEL radiation can be determined with the bolometric radiometer in combination with the gas attenuator in the SASE3 beamline, making use of the different photoabsorption cross sections for the harmonic and fundamental. The gas attenuator is a 15 mlong cell upstream of the beam transport mirrors (see Fig. 1), which is filled with a gas (in this case N_{2}) to a pressure of up to 10 mbar to attenuate the FEL beam (Sinn et al., 2012).
The transmitted intensity I through the gas attenuator can be described by
with incoming intensity I_{0}, photon energy E dependent absorption σ(E), gas pressure p, gas temperature T and length l of the gas attenuator as well as Boltzmann's constant k. We model the FEL fundamental and harmonics as a superposition of n discrete spectral components with a relative contribution P_{i} to the incoming intensity I_{0}. For calculating the transmission through the entire beamline, the energydependent mirror transmission M_{i} has to be included. Thus, the transmission in dependence of the attenuator pressure is
From this we can determine the contribution of the harmonics P_{i} by measuring the transmission using the XGM and the CBR at different pressures in the gas attenuator. In the following we will measure the harmonic contribution, which scales with the FEL fundamental energy, at a few selected points.
For investigating the secondharmonic contribution, the mirrors M1 and M2 were set to an incidence angle of 9 mrad, which suppresses photons of energies above 3500 eV [see red dashed line in Fig. 2(a)]. The undulators were producing FEL radiation at a fundamental energy of 1500 eV. The transmission was determined as the average ratio of the incoming FEL pulse energy and that measured in the CBR in dependence of the pressure in the gas attenuator. During these measurements, the FEL was operated with a gradually increasing number of pulses per pulse train, starting from one at low gas attenuator pressure up to 400 at high pressure. This was done to keep the measured average power and thereby the acquisition time roughly constant. The green stars in Fig. 4(a) show the results. Equation (2) describes the shape of the curve: at p = 0 the transmission is defined by the mirrors and corresponds to the results of the transmission measurement in Fig. 2. At low gas pressures, the slope is dominated by the absorption of the fundamental. At high pressures, the fundamental radiation is mostly absorbed in the gas attenuator and thereby the of the harmonic radiation determines the slope. To quantify the contributions under the assumption of two components, we derive a fit function from equation (2),
with the mirror transmission M_{i} taken from the transmission measurements. The attenuation coefficients B_{i} = σ_{i}l/(kT) are determined from the known length l and temperature T of the gas attenuator using the photoabsorption σ_{i} for N_{2} calculated with scattering coefficients from the literature (Henke et al., 1993) as shown in Table 1. This leaves two free fit parameters P_{f} and P_{h} that represent the contributions of the fundamental and harmonic. The dashed green line in Fig. 4(a) shows the result of the fit from which we obtain a contribution of P_{2}/P_{1} = 0.14 ± 0.02% for the second harmonic. The third harmonic is absorbed by the mirrors.

To measure the thirdharmonic contribution, the photon energy of the FEL was decreased to 1000 eV. The resulting pressure scan is shown as blue dots in Fig. 4(a). Applying the twoparameter fit containing the fundamental and third harmonic, we obtain a harmonic contribution of P_{3}/P_{1} = 4.4 ± 0.4%. The second harmonic is also present in this 1000 eV measurement, but is assumed to be at least an order of magnitude weaker than the third harmonic – as seen at 1500 eV. The fit method cannot extract the second harmonic contribution from this data by adding an additional term to equation (3); it might only contribute to the uncertainty of the result. An alternative approach to fit the 1000 eV data would be the use of a fourparameter fit with the additional free fit parameters B_{f} and B_{h} from equation (3). Such a fit yields a very similar result of P_{3}/P_{1} = 4.2 ± 0.4%. However, the fourparameter fit is not converging for any of the other data sets with fewer data points in the highpressure regime, therefore we use the twoparameter fit instead.
One data set was taken at 1800 eV, where the second harmonic is absorbed by the mirrors as well [red crosses in Fig. 4(a)]. Indeed, the transmission shows the exponential decrease of the fundamental intensity and does not indicate the contribution of a second energy component up to the maximum applicable pressure, yielding P_{2}/P_{1} = 0 in the fit.
Fig. 4(b) shows additional measurements taken at an incidence angle of 20 mrad on M1 and M2. The increased angle leads to an energy cutoff at about 1600 eV which allows for an investigation of the harmonic contribution at lower photon energies. Here, we measure a second harmonic contribution of P_{2}/P_{1} = 0.27 ± 0.04% at 730 eV and see that we can suppress the harmonics at 1000 eV.
The results of the harmonics measurements are summarized in Table 2. The error bars are statistical and result from the fits. Overall, we find the contribution of the third harmonic to be on the level of a few percent, while the second harmonic is within 0.1% to 0.3% of the fundamental. Compared with measurements made at LCLS (Ratner et al., 2011) around a FEL photon energy of 1 keV, our harmonic content is higher. In the following, we will further analyze the experimental results by comparison with calculations and show the dependence of the harmonic content on the fundamental photon energy.

5. Calculation of harmonics contribution
The harmonic content of the FEL emission with the FEL tuned at the fundamental pertains a radiation mechanism known as nonlinear harmonic generation (NHG) (Huang & Kim, 2000; Freund et al., 2000; Tremaine et al., 2002; Biedron et al., 2002). The FEL is driven by the fundamental, but the bunching develops higher harmonics, which then radiate. NHG on even harmonics follows a different mechanism compared with odd ones, with the angleintegrated power depending on the FEL diffraction parameter. Once the bunching is known, the generation of harmonic radiation is an electrodynamical process which can be calculated analytically from Maxwell's equations. A detailed derivation of the harmonic properties was carried out by Geloni et al. (2007), where the authors obtain the power P_{2} of the second harmonic relative to the fundamental P_{1} using
The thirdharmonic contribution can be derived in an analogous way to be
In the previous equations we used the following notation: K is the undulator parameter, λ_{u} the undulator period, L_{g} the gain length of the fundamental and N_{h} the Fresnel number for the radiation of harmonic h,
where the transverse size of the electron beam is σ, the speed of light c, and the frequency of the harmonic ω_{h0}. Moreover, for odd harmonics (h odd), we define
while for even harmonics (h even)
indicating with J_{n} the Bessel functions of the first kind and order n. The microbunching of the electrons in the field of the fundamental radiation is defined through the bunching factors a_{h}, which describe the density modulation level at the fundamental (h = 1) as well as at the target harmonic, and have to be known for solving the electrodynamical problem.
The bunching ratios a_{2}/a_{1} and a_{3}/a_{1} for the second and third harmonic can be retrieved from simulations of the FEL process using the experimental conditions as input. To this end, we utilize both the GENESIS (Reiche, 1999) as well as the SIMPLEX (Tanaka, 2015) codes. The bunching is averaged over the duration of the electron beam that is assumed to have a flattop current profile. From both codes we obtain similar results for the undulator tapering conditions used during the experiment, an electron beam with an energy of 14 GeV and a normalized emittance of 0.5 × 10^{−6} as well as an undulator period of 68 mm. These are applicable for all discussed photon energies,
With these bunching ratios we can use equations (4) and (5) to obtain an estimate of the harmonic contribution under the conditions of the experiment. We obtain a secondharmonic contribution of P_{2}/P_{1} = 0.12% at 730 eV and P_{2}/P_{1} = 0.06% at 1500 eV. The third harmonic contribution at 1000 eV is calculated to be P_{3}/P_{1} = 1.9%. The results are summarized in Table 2 in the `Analytical' columns.
These calculated harmonic contributions deviate from the measured ones by about a factor of two. As discussed above, the SRA slit system has been closed to a 1 mm × 1 mm aperture to prevent an overfilling of the CBR during the measurements. This has to be taken into account in the calculations. Fig. 5 shows the normalized transverse beam profiles for the fundamental as well as the harmonic radiation after the last undulator cell for three different fundamental photon energies. The profiles are calculated from the far field radiation obtained in the semianalytical model. When propagating the divergent beam 196 m further downstream to the SRA, it becomes larger than the aperture. The contributions of fundamental and harmonics are affected differently due to their spatial distributions. The thirdharmonic radiation has a smaller divergence than the fundamental and is thereby cut less. Including the aperture in the calculation yields P_{3}/P_{1} = 10.6% at 1000 eV. The second harmonic is emitted off axis, so the aperture leads to an underestimation in the experiment. The calculation results in P_{2}/P_{1} = 0.05% at 730 eV and P_{2}/P_{1} = 0.07% at 1500 eV. These results still deviate from the measurements.
The above calculation assumes the SRA to be exactly centered on the FEL axis. This was not the case during the measurements due to slight beam pointing variations between the different photon energy settings. Looking at the calculated beam profiles in Fig. 5, it is evident that shifting the aperture away from the center of the fundamental leads to a relative change of the harmonic contributions. This is quantified in Fig. 6, which shows the calculated dependence of the harmonic contributions on a horizontal and vertical center shift of the 1 mm × 1 mm SRA. The shaded areas represent a 2σ range around the values obtained from the measurements. The calculations for the third harmonic suggest an aperture shift of above 0.68 mm from the FEL axis to match the measured values. Such a shift in the horizontal direction also fits the second harmonic data. However, this would correspond to an angular beam shift of about 3 × 10^{−3} mrad and we cannot confirm such a large shift from measurements using beam imagers taken during the beamline preparation. These data show a shift of about 0.4 mm in the horizontal direction and, depending on the beamline configuration, between 0.1 mm and 0.4 mm vertically. In these positions, the calculation deviates from the measured values by about a factor of two.
In summary, the semianalytical model of the FEL process describes the harmonic content and the effect of a small aperture in the beam transport, reproducing the measurements within a factor of two. It also demonstrates a possibility of controlling the harmonic content with the aperture, at the cost of transmitted pulse energy.
We can further use the semianalytical model to calculate the second and thirdharmonic contribution for the entire energy range of the SASE3 undulator. The results are depicted in Fig. 7. These harmonic contributions are calculated for the undulator tapering conditions used above and do not include any aperture. They demonstrate values expected for typical experimental conditions at SQS, if the harmonics are not cut by the beam transport mirrors.
6. Conclusion
The transmission of the Xray optics in the beam transport section of SASE3 including the M1/M2 horizontal chicane as well as the bendable KB mirrors of the SQS instrument was determined using Xray gas monitor detectors and a bolometric radiometer. The measurements show a transmission between 50% and 80%, depending on photon energy and transport configuration, which is slightly lower than expected by calculations. The deviation from the calculation might partly be explained by carbon contamination on the mirror surface. Using the same detectors, the contributions of harmonic radiation were determined to be a few percent for the third and 0.1% to 0.3% for the second harmonic. These results can be described by a onedimensional semianalytical model of the FEL radiation emission in the undulator.
In general, the exact harmonic contribution depends on the tuning of the trajectory the electron beam takes through the undulators, which can change on a daytoday basis. Furthermore, apertures along the beam transport have an influence on the harmonic content. For experiments that are sensitive to the harmonic radiation the best option is to suppress their contribution with the Xray mirrors by choosing a steeper incidence angle. Alternatively, the contribution has to be assessed. The gas attenuator scans can be performed in preparation for an experiment using an XGMD or even a beam imaging unit with a scintillator screen as detector (Ratner et al., 2011). One option for generating an online signal for optimization and monitoring of the harmonic contribution would be photoelectron spectroscopy: electrons ionized from a rare gas atom by the harmonic radiation can be detected in a timeofflight spectrometer. The signal from these electrons could then be used to minimize the harmonic contribution. Such spectrometers are available at the SASE3 beamline (Laksman et al., 2019) as well as SQS (De Fanis et al., 2022).
Acknowledgements
The authors would like to acknowledge the support of all European XFEL staff during the installation and commissioning phase of the SQS instrument. We thank the operators at DESY for their commitment in tuning the FEL for our experiments. Data recorded for these measurements at the European XFEL are available at https://doi.org/10.22003/XFEL.EUDATA00268000. Open access funding enabled and organized by Projekt DEAL.
Funding information
MM and TM acknowledge support by the Deutsche Forschungsgemeinschaft (DFG) (SFB925, project No 170620586). Funding was also provided by: Volkswagen Foundation (PeterPaulEwald Fellowship to MI, VM, PS).
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