X-ray free-electron lasers (FELs) are state-of-the-art research tools to study matter with time and spatial resolutions at the atomic level.1^–3 The X-ray FEL radiation is produced by a high-brightness multi-GeV electron beam traveling through an undulator. Typical X-ray FEL pulses have peak powers at the gigawatt level and durations of a few tens of femtoseconds or shorter. Short FEL pulses at the femtosecond level and below, achieved with short electron beams or with spoiling approaches,4^–8 are necessary to analyze ultrafast atomic and molecular processes.9

The FEL performance and the properties of the resulting radiation are determined by the time-dependent properties of the electron beam, namely, the electron bunch duration, the current profile and the slice emittance, optics mismatch, trajectory alignment, energy, and energy spread. Therefore, it is fundamental to characterize and optimize such electron beam properties in X-ray FELs. Moreover, knowledge of the FEL power profile and pulse duration is highly beneficial for many scientific experiments. Considering that the FEL process results in an energy loss and energy spread increase at the regions of the electron beam that lase, the FEL power profile can be derived from the difference in the time-resolved energy and energy spread of the electron beam after the undulator between lasing-on and lasing-off conditions.10^,11

Radiofrequency (RF) transverse deflecting structures (TDSs) are standard diagnostics devices to measure the temporal properties of electron bunches in linear accelerators.10^–23 A TDS streaks (or, using the terminology for this type of devices, stretches, or shears) a charged beam in the transverse direction by imposing a correlation between the transverse momentum and the time coordinate of the beam. This correlation, which is linear to very good approximation when the RF operates at zero phase, can be employed to image on a screen the temporal distribution (or current profile) of the electrons. The slice emittance, optics mismatch, and trajectory alignment can be reconstructed by measuring the time-resolved transverse beam size and offset for different betatron phase advances, which are typically scanned by varying the magnetic strength of quadrupole magnets (see, e.g., Refs. 24 and 25). The time-resolved energy and energy spread of the electron beam can be accessed with a screen with transverse dispersion in the plane perpendicular to the streaking (see, e.g., Ref. 26) (e.g., a location with vertical dispersion if the streaking is horizontal).

Most TDS systems streak the electron beam in one fixed direction (either horizontal or vertical). In this context, a collaboration among CERN, DESY, and PSI was established to develop and build an advanced modular X-band TDS system called PolariX, which included the novel feature of providing variable polarization of the deflecting force.22^,27^,28 The possibility of changing the orientation of the streaking field to an arbitrary azimuthal angle opens new opportunities for extended beam characterization that makes particular use of the variable streaking direction, such as the measurement of the slice emittance in different transverse planes,27 the retrieval of the three-dimensional charge distribution,27 or 5D phase-space characterization.29

As an alternative to TDS systems, the electron beam can also be streaked with other methods, namely, with transverse wakefields30^–32 or dispersion.33^,34 Wakefield streaking is self-synchronized and cost-effective but results in no streaking at the head of the bunch and non-linear streaking for the rest of the beam, which does not allow the characterization of the head of the bunch with sufficient temporal resolution and renders the overall reconstruction difficult. Dispersion-based streaking is cost-effective but requires an electron beam with an energy chirp and cannot provide absolute time-resolved measurements.

Electron beam measurements with root mean square (rms) time resolution of less than one femtosecond have been reported twice before, on both occasions with TDS devices with fixed streaking direction: 0.8 fs with an X-band (with a frequency f of 11.4 GHz) RF TDS and an electron beam energy of 4.7 GeV at LCLS,11 and 0.87 fs with a C-band (with f=5.7GHz) and an electron beam energy of 5.2 GeV at the hard X-ray beamline of SwissFEL.23 Moreover, X-ray FEL rms pulse durations of 0.76 fs have been reconstructed with the SwissFEL X-band (12 GHz) TDS and an electron beam energy of 3.4 GeV at the soft X-ray beamline of SwissFEL,8 implicitly indicating sub-femtosecond resolution. The SwissFEL X-band TDS is one of the PolariX devices that resulted from the CERN-DESY-PSI collaboration and has the capacity to streak the electron beam in an arbitrary direction. This device has been used with horizontal streaking to reconstruct the FEL power profile for different FEL operation modes.8^,35^,36 For the sake of completeness, we mention that streaking with wakefields and dispersion have achieved resolutions of a few femtoseconds.32^,34

The FEL pulse duration can also be retrieved directly from photon measurements. One option is to reconstruct the pulse duration from FEL spectral information.37^,38 Such an approach has been used to estimate the duration of attosecond pulses,4^–6^,8^,39 but it requires assumptions on the energy chirp of the photon beam and cannot be used to obtain the FEL power profile. Photoelectron streaking with terahertz or infrared lasers39^–44 is another possibility that has been employed to reconstruct FEL pulses as short as 0.2 to 0.3 fs [full width at half maximum (FWHM) values].39^,44 Such measurements are extremely challenging, in particular for hard X-rays, because of their weak interaction with matter. The setup and analysis of photoelectron streaking are complicated in comparison to a TDS measurement, posing difficulties in obtaining reliable information on a shot-to-shot basis. The dynamic range, defined by the wavelength of the employed laser, is also limited (the laser wavelength must be much longer than the FEL pulse duration).

In this work, we present variable polarization and attosecond time-resolved measurements with the X-band TDS system at Athos, the soft X-ray beamline of SwissFEL. First, we demonstrate the device’s capacity to streak the electron beam in any transverse plane. Second, we present measurements indicating an electron beam rms resolution of 0.6 fs for a beam energy of 3.2 GeV and standard bunch charges of 200 pC. Third, for similar beam energies and low charge (10 pC) operation, we show FEL power profiles with rms durations as short as 0.3 fs or 300 attoseconds (as), indicating an effective resolution of at least 300 as. This is, as far as we know, the best time resolution ever achieved with electron beam streaking. The combination of the variable polarization feature with the capability of achieving attosecond temporal resolution allows new insights to be gained with multidimensional beam phase-space characterization at unprecedented resolution.

The streaking or calibration factor C between the transverse coordinates and the time coordinates within the electron beam is reconstructed by measuring the dependence of the transverse position of the centroid of the streaked beam on the RF phase of the TDS. The rms resolution R to measure the electron bunch duration is normally defined as the unstreaked beam size σ0 divided by the calibration factor C: R=σ0/C.13 For relativistic electrons and considering that the TDS operates around the zero-crossing, the time resolution can be obtained as23R=σ0C=εEmec2βsin(μ)eVck,(1)where ε is the normalized emittance of the electron beam in the streaking plane, E is the electron beam energy, mec2≈0.511MeV is the rest energy of an electron, β is the β function in the streaking plane at the TDS location, sinμ is the betatron phase advance in the streaking direction between the deflector and the profile monitor, e is the elementary charge, V is the deflector voltage, c is the speed of light, and k=2πf/c is the wavenumber of the TDS system with frequency f. The resolution can be enhanced on three fronts: first, hardware-wise, by increasing the TDS voltage and its k value (frequency); second, concerning the electron beam, by improving its quality (i.e., by reducing the transverse emittance) or by reducing its energy (although this option is limited for X-ray FELs); and third, by optimizing the beam optics, i.e., by increasing the β function at the TDS and by setting an appropriate betatron phase advance μ between the TDS and the profile monitor such that sinμ≈1.

The R defined in Eq. (1) is adequate to quantify the resolution in measuring electron bunch durations, but it represents an upper limit for the resolution of structures that can be measured within the electron bunch. This is because R takes into account the total or projected natural beam size σ0, which can be larger than the time-resolved or slice natural beam size because of beam correlations. This was reported in Ref. 28, where an R of 4.4 fs was reconstructed, but features as short as 3.3 fs could be measured within the bunch. The intrabunch time resolution could be obtained from Eq. (1) using the time-resolved or slice properties instead of the projected ones.

The energy resolution RE is the measured natural beam size in the dispersive plane divided by the dispersion. It can be expressed, excluding screen resolution effects, as26RE=βDεDEmec2/D, where εD is the normalized emittance of the electron beam in the dispersive plane, βD the β function in the dispersive plane at the profile monitor, and D the transverse dispersion at the profile monitor. Good energy resolution implies large dispersion and small β function values at the profile monitor location.

Figure 1 shows a schematic layout of the TDS diagnostics section, which is located after the undulator of the soft X-ray beamline of SwissFEL. It consists of two TDSs (TDS1 and TDS2), the waveguide network with the X-band barrel open cavity (XBOC) RF pulse compressor, and three phase shifters (PS1, PS2, and PS3). PS1 and PS2 are installed in one of the two inputs of each TDS and are used to change the polarization in the individual RF structure.22 PS3 is used to ensure synchronicity between the two TDSs. All waveguide RF components including the XBOC and phase shifters were designed and built at PSI. The TDS structures were also manufactured at PSI according to the tuning-free technology developed for the SwissFEL project (see Ref. 45 and references herein). They are constant-impedance, backward-traveling wave structures. Table 1 lists the RF parameters for the single cell, a single TDS, and for the whole system consisting of two TDSs with the XBOC. The high-power RF source comprises a high-voltage (HV) modulator and a CPI VKX-8311A 50 MW pulsed X-band klystron installed in the technical gallery. The HV modulator was built in-house and is capable of delivering a pulsed voltage of up to 400 kV with a pulse length of 1.5μs (FWHM). The maximum deflecting voltage V of the TDS system is 90 MV. The deflector wavenumber corresponding to a frequency of 12 GHz is k=251m−1. Figure 2 shows the two TDSs installed in the SwissFEL tunnel.

The post-undulator diagnostics section is designed to perform time-resolved diagnostics of the electron and photon beams with optimum resolution. Twelve quadrupole magnets, six before the TDSs and six after, are used to optimize the beam optics for the different types of measurements, e.g., current profile and slice emittance measurements in different directions at screen S1 in the straight section, or characterization of the longitudinal phase space (LPS) at the spectrometer screen S2. In the latter, the electron beam is streaked in the horizontal direction while the energy is measured via dispersion in the vertical plane. Besides the screens, there are a few beam position monitors (BPMs) downstream of the TDS system to measure the electron beam transverse position (both horizontal and vertical).

Figure 3 shows the measurement optics for current profile measurements at S1 (with streaking in any arbitrary direction) and for LPS measurements at S2 (horizontal streaking, vertical dispersion). To optimize the time resolution [see Eq. (1)], the β functions at the deflector are set to the relatively large value of 50 m in the horizontal and vertical planes to ensure good resolution in all streaking directions. Moreover, the betatron phase advance between the deflector and the profile monitors S1/S2 is set such that sinμ≈1. Finally, the β function at the profile monitors for the streaking plane (horizontal and vertical in S1, horizontal in S2) is set to the relatively large value of around 15 m (both for S1 and S2), so that the unstreaked beam size σ0 can be measured with decent resolution. Concerning the energy resolution optimization, the β function βD and the dispersion at S2 are set to 0.63 and 0.345 m, respectively.

Figure 4 presents the results of the experimental verification of beam streaking at multiple polarization angles. The adjustment of the phase shifters located in the waveguide network, as illustrated in Fig. 1, enables the changing of the streaking direction. Figure 4(a) shows a selection of beam images captured at screen S1 for varying phase-shifter set points, corresponding to distinct streaking field directions (polarization angles). Ultimately, the calibration parameter and the streaking angle can be estimated simultaneously through the scanning of the beam’s position on the screen as a function of the RF phase. During the scan, the beam centroid on the measurement screen exhibits a transverse displacement along the streaking direction of the structure. The angle of the streaking direction can thus be calculated by fitting the direction of the shift of the beam centroid, whereas the calibration parameter can be calculated by measuring the amplitude of the shift for a given change in the RF phase. Furthermore, Fig. 4(b) indicates the bunch centroid position on a BPM placed immediately downstream of the TDSs. Each color represents a distinct direction of the streaking field, with a 5-deg polarization angle increment and a full scan of the RF phase. From this figure, we can conclude that the streaking fields have amplitudes in the various polarization planes that differ by a maximum of about 10%.

Figure 5 shows a time-resolved measurement at the straight section screen S1 with sub-femtosecond resolution. The electron beam was streaked in the horizontal plane with a deflection voltage of 84 MV. The measurement was performed for an electron beam energy of 3.16 GeV and a standard bunch charge of 200 pC. The upper plots display single-shot images of the streaked beam for the different phases around one zero-crossing. The bottom-left plot shows a single-shot image for the unstreaked beam size, which has a value of 33.8±0.7μm. The error of the unstreaked beam size, as well as the errors shown later for different measured parameters, corresponds to the statistical uncertainty of the measured or reconstructed values.

The bottom-right plot shows the movement of the streaked-beam centroid as a function of the deflector phase. A linear fit to the data gives a calibration factor of 53.9±7.6μm/fs. The rms electron bunch duration is calculated as the ratio between the streaked beam size, obtained from Gaussian fits, and the calibration, resulting in 21.4±3.2fs. Dividing the measured natural beam size by the calibration, we obtain a resolution of R=0.63±0.09fs.

We can now calculate the expected natural beam size, calibration, and temporal resolution from Eq. (1), taking into account that the natural beam size is σ0=βpε/(mec2E), where βp is the β function at the profile monitor location. For the deflector parameters, we use V=84MV and k=251m−1, from our optics design β=50m, βp=14.5m, and sinμ≈1. We assume a normalized emittance of 400 nm (consistent with our measurements presented in Ref. 25). With these parameters, we expect an unstreaked beam size of 30.6μm, a temporal resolution of 0.57 fs, and a calibration of 54μm/fs. The measured calibration matches perfectly with the expected values. The measured resolution, although fitting well with the calculated values within error bars, is somewhat lower than expected. This is because of the slightly larger unstreaked beam size found in the measurements (33.8μm versus 30.6μm). The discrepancy could be due to profile monitor resolution, resulting in a measured natural beam size somewhat larger than in reality, or because the beam is not perfectly matched.

Figure 6 shows an FEL power profile measurement performed at screen S2 for short-pulse operation using an electron bunch charge of 10 pC. The electron bunch is fully compressed in the nonlinear regime, similar to what has been reported in Ref. 8. The electron beam energy was 3.4 GeV, and the photon energy was 665 eV.

The figure displays single-shot LPS images for lasing-on and -off conditions, and the FEL power profiles for 20 consecutive shots (excluding one shot containing invalid data). We can see the characteristic K-shape resulting from space-charge forces of a fully compressed beam, which has been observed in simulations as well as in previous measurements.6^,8 Evidently, only a small fraction of the electron bunch at the core of the bunch (for times t slightly below zero) is subject to an energy loss and an energy spread increase due to the FEL process. The energy axis is calibrated with the dispersion, which for this particular measurement was 0.16 m (we changed the last quadrupole magnet in the lattice before the screen to enhance the streaking, at the expense of reducing the dispersion and losing energy resolution, which was not critical for this measurement). The time calibration was measured to be 55.0±4.3μm/fs. For this case, the standard calibration scan as shown in Fig. 5 was difficult to perform because of a large jitter observed on the screen. As an alternative, we directly utilized the jitter by estimating the calibration from a linear fit to the centroid of the streaked beam and the RF phase recorded for thousands of shots. With Eq. (1), we obtain a reconstructed resolution from the time calibration and the natural beam size (46.5μm) of 0.85±0.07fs. The deflecting voltage was 85 MV.

The FEL power profile is calculated as the difference in the energy loss of the electron beam between lasing-on and -off conditions times the peak current of the electron beam. As a reference for lasing-off conditions, we use the median of the time-resolved energy and energy spread over 20 additional shots when lasing was disabled. This reference value is compared with the time-resolved energy of the lasing-on conditions on a shot-to-shot basis. The FEL peak power average over all shots is 5.1±1.8GW, and the average rms pulse duration, obtained by fitting Gaussian functions to the power profiles, amounts to 0.57±0.22fs. The minimum reconstructed rms pulse duration is 0.29 fs, or 290 as. The reconstructed average pulse energy by integrating the FEL power profiles is 8.4μJ, consistent with 7μJ measured with a gas-based photon pulse energy monitor.46

The reconstructed FEL pulse durations are significantly shorter than the measured resolution of 0.85 fs. This can be explained by the fact that the resolution along the bunch can be significantly better than R, as explained above, as the slice unstreaked beam size can be significantly smaller than the corresponding projected quantity. Although slice emittance is a rather robust property that stays fairly constant along the accelerator, the projected emittance may be increased significantly owing to compression and collective effects. At SwissFEL, where the bunch compression takes place in the horizontal direction, the horizontally projected emittance for compressed bunches has been measured to be up to twice as large as the slice emittance under standard conditions.25 For the measurements presented here, where we fully compress the electron beam, we can expect an even greater difference. With a slice emittance of 100 nm (consistent with measurements presented in Ref. 25), and for our electron bunch, optics, and deflector parameters, the expected resolution within the bunch would be 0.29 fs, consistent with our reconstructed pulse durations. For our parameters, we would need to have a projected emittance of 850 nm to arrive at a resolution R of 0.85 fs, as we have measured. The 850 nm projected emittance is consistent with what we would expect for a fully compressed electron bunch.

The estimated FEL pulse durations (0.57±0.22fs) are, to the best of our knowledge, the shortest ever measured in an X-ray FEL using the TDS approach. These values are an upper limit of the FEL pulse duration as the resolution elongates the observed profile. They are shorter than the 0.76±0.05fs cited in our earlier report8 for similar electron beam conditions. Besides the fact that the pulses reported here may indeed be shorter, we think that 0.76 fs in Ref. 8 was resolution-limited. Evidence of this is the smaller-than-expected variation in pulse duration from shot to shot (indicated by the error bars of the pulse duration), whereas now, as expected, we observe more shot-to-shot variation. This is due to better resolution, possibly improved by enhanced optics control. Nevertheless, further resolution improvements may be required to measure very short FEL pulses, such as 0.2 fs reconstructed in Ref. 8 from spectral measurements for a photon energy of 1.1 keV.

We have demonstrated attosecond resolution time-resolved measurements of electron and photon beams using a variable polarization X-band RF system. We have measured an electron bunch resolution of 0.6 fs. We have also presented FEL power profile measurements with average rms pulse durations of 0.57 fs and single shot durations down to 0.3 fs. The latter indicates that we have achieved an effective resolution equal to or better than 300 as, which represents, as we believe, a new record for electron beam streaking. The variable polarization capacity combined with the attosecond resolution gives access to measure the electron beam in all its dimensions at extremely high resolution. We think this advance will be crucial for future ultrafast experiments at X-ray FEL facilities.

The practically achieved resolution of 300 as is close to but still not at the same level as the resolution reported with photoelectron streaking.39^,44 Nevertheless, our approach has several important advantages: the capacity to measure both the electron and, indirectly, the photon beam, the simplicity in setup and analysis, the versatility (working over a large dynamic range of pulse durations and photon energies) and the capability to measure, in a reliable and straight-forward way, the pulse duration, and the FEL power profile on a shot-to-shot basis.

In the future, we plan to benefit from the variable polarization capacity of our system, for instance, by measuring the slice emittance of the electron beam in different planes. Moreover, we aim to push the resolution further by, for instance, increasing the β function at the deflector or by further improving the electron beam quality. When reconstructing the FEL power profiles, improving the resolution may be limited by FEL slippage effects, particularly for low photon energies.10

Eduard Prat is an accelerator physicist with expertise in beam dynamics for linac-based free-electron lasers (FELs). He received his PhD from DESY in Hamburg (Germany) between 2005 and 2009, where he served with the FEL facilities FLASH and European XFEL. Since 2010, he has been at the Paul Scherrer Institute in Switzerland, focusing on the design, commissioning, and development of SwissFEL. His research interests include novel FEL modes and advanced methods to measure electron and photon beams.

Zheqiao Geng is an electronic engineer at the Paul Scherrer Institute in Switzerland. He studied nuclear technology at Tsinghua University and received his PhD from the Graduate School of CAS in China. He has been serving on accelerator RF and beam control systems in different labs for various projects such as the European XFEL, LCLS, and SwissFEL. As an internationally acclaimed LLRF expert, he was appointed as a PSI Senior Expert in 2021.

Christoph Kittel has been an expert operator for the SwissFEL facility at the Paul Scherrer Institute since 2017 and currently pursuing his PhD studies on the commissioning of Apple X Undulators. Before, he served on improving magnetically shielded rooms at the Physikalische Technische Bundesanstalt, Berlin, and at the ETH Zürich from 2009 to 2011. Subsequently, he gained expertise in accelerator operation during his work as a proton synchrotron operator at CERN in Geneva, Switzerland, from 2011 to 2016.

Alexander Malyzhenkov is an accelerator physicist specializing in linear accelerators for FELs, irradiation facilities, and medical accelerators. He completed his PhD at Los Alamos National Laboratory (2012–2018). As a fellow at the Paul Scherrer Institute (2019–2021), he established the attosecond operation mode of SwissFEL. He joined CERN as a senior fellow in 2022 and, since 2025, has held a joint appointment at CERN (visiting scientist) and the Swiss International Institute Lausanne (director of research).

Fabio Marcellini is an electrical engineer with expertise in the design, commissioning, and operation of RF and diagnostic systems for particle accelerators. He worked for the DAFNE lepton collider at the Frascati Laboratory of INFN (Italy) from 1992 to 2012, when he joined the Paul Scherrer Institute (Switzerland), contributing to the SwissFEL and SLS 2.0 projects.

Sven Reiche received his PhD in 2000 from the University of Hamburg on modeling the free-electron laser process. He also contributed to the design and commissioning of the now-named European XFEL and FLASH. From 2000 Sven Reiche spent 8 years in the group of Prof. Claudio Pellegrini at the University of California, Los Angeles, to work on the linac coherent light source. Since 2008, he has been at the Paul Scherrer Institute, coordinating the design effort of SwissFEL and contributing to the commissioning of the facility and the development of new operation modes.

Thomas Schietinger started his career in particle physics, obtaining a PhD from the University of Basel on the subject of CP violation in the neutral K-meson system in 1998. After continuing his research into the origins of CP violation at SLAC and CERN, he moved to the Paul Scherrer Institute in 2006, where he soon joined the effort to build an X-ray FEL there. He led the commissioning of the SwissFEL facility and is currently the SwissFEL machine coordinator.

Paolo Craievich is currently serving as an RF engineer and accelerator physicist at the Paul Scherrer Institute (PSI) in Switzerland where he serves as a head of the RF System 2 group (RF linacs and R&D). He studied electronic engineering at the University of Trieste in Italy and received his PhD in applied physics from the University of Technology in Eindhoven, Netherlands. His expertise covers a broad range of topics for beam acceleration, diagnostic, and manipulation in particle accelerators.