Plasma-photonic spatiotemporal synchronization of relativistic electron and laser beams

Modern particle accelerators and their applications increasingly rely on precisely coordinated interactions of intense charged particle and laser beams. Femtosecond-scale synchronization alongside micrometre-scale spatial precision are essential e.g. for pump-probe experiments, seeding and diagnostics of advanced light sources and for plasma-based accelerators. State-of-the-art temporal or spatial diagnostics typically operate with low-intensity beams to avoid material damage at high intensity. As such, we present a plasma-based approach, which allows measurement of both temporal and spatial overlap of high-intensity beams directly at their interaction point. It exploits amplification of plasma afterglow arising from the passage of an electron beam through a laser-generated plasma filament. The corresponding photon yield carries the spatiotemporal signature of the femtosecond-scale dynamics, yet can be observed as a visible light signal on microsecond-millimetre scales.


Introduction
The experimental use of intense, femtosecond-duration particle beams together with similarly short laser pulses becomes increasingly important in exciting and probing ultrafast processes 1,2,3 occurring in plasma, molecular, atomic, and nuclear structures. For example, modern light sources such as free-electron-lasers require precise spatiotemporal control of laser-electron beam interactions for seeding 4 and diagnosis 5 . Inverse Compton scattering acting as a light source 6,7,8,9 as well as a beam diagnostic 10,11 has similar demands. An emerging class of high field plasma accelerators 12,13,14,15,16 also strongly benefits from the spatiotemporal coordination of electron and laser beams for driving plasma waves, control of injection processes, and (staged) acceleration of high-quality particle beams. This demand, extending across multiple fields of research, has given rise to a broad range of synchronization and alignment techniques, such as electro-optic sampling 17,18 (EOS), beam time-of-arrival monitoring measurement techniques based on excited cavities 19 , coherent transition radiation 20 , cross-correlated THz radiation from undulators 21 , and various schemes in free electron lasers 22 . These techniques individually Page 3 of 20 offer either measurement of temporal synchronization or spatial alignment of electron and laser beams. To measure both, combinations of diagnostics must be implemented separately along the beamline, e.g. by using EOS for temporal overlap measurement at one position and optical transition radiation beam profile monitors for spatial overlap at another one. Further, damage thresholds prohibit the use of intercepting diagnostics for most intense and focused laser and electron beams, such that they must be employed away from the beam focus and/or at reduced beam power levels. The same reasons prevent application of these diagnostics in the presence of plasma.
Addressing the demand for measuring spatial and temporal coordination directly at the interaction point and the current limitations outlined above, we report on a novel plasmabased approach allowing for precise synchronization and spatial alignment of intense laser and electron beams. This method provides an online diagnostic applicable in conventional and plasma-based accelerator schemes. Figure 1a shows the layout of experiments conducted at the Facility for Advanced Accelerator Experimental Tests (FACET) at the SLAC National Accelerator Laboratory 23 , where a focused ultra-relativistic 20 GeV electron beam with root-meansquare (r.m.s.) length of z  64 µm propagates through a mixed H2 and He gas reservoir at sub-atmospheric pressure of 5.3 mBar. The setup employs a Ti:Sapphire laser pulse with duration of L  60 fs full-width-at-half-maximum (FWHM). Several metres upstream of the electron beam focus a collimated, low intensity laser fraction split-off from the source laser pulse is superimposed with the electric field from the electron beam on an EOS crystal. It provides relative time-of-arrival measurement and, being an established diagnostic, benchmarks the new effects we describe here. The main laser pulse arm is focused perpendicularly to the path of the electron beam to a spot size of w0  38 µm (FWHM) in the immediate vicinity of the electron beam focus position. By tuning the energy of this laser pulse to yield intensities in the range I  10 14 -10 15 Wcm -2 in the gas, a Page 4 of 20 millimetre-long H2/He cold plasma filament of width dplasma  100 µm is generated by tunnelling ionization 24 . A CCD camera monitors the interaction region and integrates radiation from the characteristic He plasma afterglow line 25 He  587 nm. The purely laser-generated plasma afterglow signal results from hydrodynamic expansion and subsequent recombination and relaxation processes 26 in absence of the electron beam and is shown in Fig. 1b. The electron beam alone, in contrast, does not generate plasma: at a peak electron density of nb0 = Nb / (2) 3/2  2 xz  3.5 -5  10 16 cm -3 its corresponding radial electric fields Er (r) = [Nb e / (2) 3/2 0zr] [1exp (-r / 2 2

Experimental setup
x)] are in the multi-GV/m range, below the tunnelling ionization threshold for hydrogen 27 . Here, r is the radial coordinate, Nb is the number of beam electrons, x is its transverse r.m.s. beam size, e is the elementary charge and 0 the vacuum permittivity. Impact ionization of the gas by the transient electron beam is negligible due to the low cross sections associated with highly relativistic energies 28,29 . As such, if the electron beam is switched off, is substantially misaligned with respect to the laser pulse axis, or passes before the laser pulse, only the laser-generated plasma afterglow signal is observed.
If, however, the electron beam intersects the laser path after the laser pulse has passed, it interacts with the thin laser-generated plasma filament of electron density ne  1.9×10 17 cm -3 (nb0  0.1 ne) instead of neutral gas. Then, the unipolar transverse electric field of the focused electron beam briefly couples with this seed plasma filament for the duration of their geometrical overlap, and transfers energy into the plasma. This initial kick accelerates plasma electrons to moderate, non-relativistic, broad-band velocities with peak energies Wmax  π[eEpeakz /βc] 2 / me  100's of keV and expels them partially from the initial plasma volume. Here, Epeak denotes the peak radial electric field of the beam, me is the electron mass, and βc the velocity. The interaction of electron beam and plasma filament distinctively changes the observed afterglow signal, as shown in Fig. 1c, by increasing its volume and intensity substantially compared to the signal displayed in Fig. 1b. Figure 2 shows the corresponding plasma dynamics modelled in three-dimensional (3D) particle-in-cell (PIC) simulations using VSim 30 (see Methods).

Particle-in-cell simulations
The strong electric fields of the electron beam are rapidly screened inside the plasma, so that significant energy transfer occurs only if beam and plasma volumes overlap. In this The result of this expansion can be seen by comparing Fig. 1 B and C, as the afterglow intensity is distributed well beyond the initial laser-only boundaries.
Summarising, the kinetic energy originating from the fast initial energy transfer from the electron beam to the seed plasma filament is thus gradually transferred into the creation of additional plasma. Eventually, recombination and atomic relaxation processes produce the emissions of the plasma afterglow 31,32,33,34 , which exhibits intense lines in the optical spectrum for helium and can be observed by the CCD camera.
Page 6 of 20 Experimental measurements We apply these findings to measure spatial alignment and time-of-arrival between electron beam and laser pulse. In both the spatial and temporal measurement modes, changing the geometric overlap varies the fraction of the beam fields transferring energy into the plasma, and thus the intensity of the resulting afterglow amplification.
The first measurement mode scans spatial alignment with fixed relative time-of-arrival (TOA) tdelay = TOAlaser -TOAe-beam = 2.1 ps between laser and electron beam to ensure interaction of the electron beam with a fully formed laser-generated seed plasma. By introducing translations y between electron beam and laser axis, the radial electric field of the electron beam intersects to a lesser degree with the pre-formed plasma region, thus reducing the total amount of energy transferred. Consequently, the integrated afterglow signal peaks for central overlap y = 0 and decreases with larger offsets |y|>0.
Eventually, the amplification ceases completely, yielding only the afterglow from the unperturbed filament. Fig. 4 presents a y-alignment scan that reveals a Gaussian distribution of amplified plasma afterglow with characteristic width σy = 64.8 µm r.m.s. This curve agrees well with PIC simulation results and exhibits a linear relation between the energy transferred into the plasma and the afterglow amplification in the given interaction regime. Comparing experiment and simulation, the central peak position corresponds to optimal overlap of electron beam and plasma axes and can, therefore, readily be established within the accuracy of the imaging system. From the 99 shots in the given dataset, the central overlap between beam and plasma can be determined within 4.1 µm accuracy, which is substantially smaller than the dimensions of electron beam and plasma. This plasma afterglow response constitutes a multi-shot alignment diagnostic with accuracy dependent on the number of shots per setting. If, furthermore, the dependency shown in Fig. 4 is sufficiently well characterized either from experiment or theory, it represents a gauge curve for the given electron and laser beams. In this case, the method can quantify the absolute alignment between electron and laser beam on a single-shot basis. To improve the accuracy, it is desirable that the sources of parametric jitter, e.g.
laser and electron beam size and duration, energy and charge, intensity and beam density, respectively, are well known, can be co-recorded and/or are substantially reduced.
In the second measurement mode, the spatial translation is fixed and the timing between electron and laser beam is varied. Setting the spatial overlap to the central position y = 0, a delay scan in a series of consecutive shots from -2.5 ps < tdelay < 4.0 ps reveals a strong dependence between TOA and afterglow signal, as shown in Fig. 5. The signal drops sharply when the electron beam arrives at the same time or earlier than the laser pulse because the seed plasma volume is not yet fully formed or not present at all. As result, the scan yields a sigmoid transition with a width of ~315 fs (r.m.s.) between zero and maximal afterglow amplification. This region allows to determine the degree of temporal coincidence between laser and electron beam. On the steep quasi-linear transition region around tdelay ~ 0, the afterglow signal reacts sensitively to small changes in the TOA and therefore allows for determining the synchronisation with high resolution. In the given experimental setup, the raw data yields an all-optical TOA synchronization measurement from the quasi-linear transition region with shot-to-shot accuracy of 55 fs. This measurement represents a multi-shot TOA diagnostic, and its shot-to-shot accuracy can be further improved by increasing the number of shots per setting as discussed earlier. As in the alignment measurement, the experimentally achieved TOA accuracy also results from the shot-to-shot variations of electron beam and laser pulse parameters and relative alignment jitter between laser and electron beam. Most critically, the system-inherent shot-to-shot TOA jitter between electron beam and laser beam of ~109 ± 12 fs r.m.s. has large influence on the obtainable accuracy. This jitter results to a significant degree from the strong longitudinal compression of the electron beam in the magnetic chicanes of the SLAC linac. Calibrating the data with EOS time stamps partially removes the effect of this shot-to-shot TOA jitter, and enhances the combined TOA resolution to 16 fs. It shall be noted that while this first experimental demonstration benefits strongly from an EOS benchmarking the relative TOA jitter, the amplified plasma afterglow can serve as standalone diagnostic and uniquely offers absolute TOA measurements at the interaction point. We find good agreement between measurement and simulation, and the sigmoid shape of the temporal dependence curve supports the hypothesis of a linear relation between transferred energy and afterglow amplification in the parameter regime explored (see Supplemental Figure 1). This relationship implies that the plasma effectively samples the beam envelope, which allows for precise TOA determination. As discussed above, characterizing the gauge curve shown in Fig. 5 sufficiently precise can allow for single- shot TOA measurements provided that other sources of parameter jitter are low or measured independently.
The sensitivity and multi-parameter dependency of the amplified plasma afterglow thus enables a versatile diagnostic which can measure various parameters of the interaction.

Discussion
The transient overlap of electron beam fields with a laser-generated plasma filament can be exploited as highly sensitive and versatile diagnostic system. The laser-gated seed plasma acts as spatiotemporally amplifying detector medium. The initial femtosecondmicrometre-scale interaction is transformed through localized plasma dynamics, eventually manifesting as amplified plasma afterglow light emissionan observable on the microsecond and millimetre scale in the visible spectrum. We have used this approach for synchronization and alignment of intense electron and laser beams directly at their interaction point with a single setup. Here, their intensities exceed the permissible measuring range and damage thresholds of many conventional diagnostics, while plasma as already ionized medium is sensitive to varying interaction parameters at such intensity levels, while not being destroyed in the process. In the context of these measurements, this capability was exploited in a first application to facilitate a plasma photocathode injection experiment 35 , which relies on precise spatiotemporal alignment and synchronization on the micrometre and femtosecond-scale to release electrons inside a small fraction of a ~100 µm long plasma wave via tunnelling ionization.
The plasma afterglow-based measuring process is minimally intrusive and highly efficient.
Both the energy required for generation of the seed plasma as well as the energy transferred by the electron beam to the seed plasma are of the order of 1 mJ, corresponding to ~0.001% of the total electron beam energy at FACET. This suffices to boost the afterglow signal by approximately a factor of ~50 during a spatiotemporal overlap scan.
Benchmarking of the data to predictions of PIC simulations shows that the experimentally observed afterglow amplification scales linearly with the total energy transferred by the beam into the plasma. In this study, we operate in the linear (overdense) beam-plasma Page 9 of 20 interaction regime, as nb,0 / ne < 1. The electron beam duration is longer than the width of the plasma filament; both attributes of the interaction ensure a quasi-adiabatic plasma response. At underdense working points, the energy transfer into plasma may significantly change the plasma dynamics and subsequent recombination rates depending on the degree of nonlinearity of the interaction 36 . One must still verify that the linear relation between initially transferred energy and plasma afterglow amplification holds in these regimes.
The obtainable resolution of the technique depends on the dynamic range of the experimental detector setup, the maximum afterglow amplification, and the gradient of the transition. The latter, in turn, profits from rapid Debye screening of the electric field of the electron beam inside the plasma due to its transverse size x,y >> λD, with λD = (ε0 kBT/ne 2 ) 1/2 being the Debye length, kB denotes Boltzmann's constant and T the electron temperature. Therefore, the coupling volume inside the filament is confined, and allows the plasma volume to sample the beam precisely. Simulations (see Suppl. Fig. 1) show that the transitions can become substantially steeper for shorter and narrower electron beams such as those expected e.g. from FACET-II, or from state-of-the-art plasma-based accelerators. For FACET-II, for example, the transition slope for a comparable parameter regime is expected to steepen by a factor of 4 compared to current measurements at FACET, thus improving resolution equivalently. Another, simple approach improving the resolution on the transition region decouples the amplifying neutral gas from the seed plasma. For example, reducing the laser energy can avoid ionization of helium such that only the laser-generated hydrogen filament receives energy from the electron beam. In this case, helium only gets ionised by heated hydrogen electrons and secondaries. As this procedure allows for much higher helium densities, the signal-to-noise-ratio can be substantially increased.
Development of a closed analytic description of electron-beams partially overlapping bounded plasmas, the complex long-term dynamics and their influence on the afterglow signal is beyond the scope of this work and will be subject to further research. Particularly, investigating the plasma afterglow amplification spatially and temporally resolved could identify and quantify the individual processes of energy conversion between the electronic dynamics investigated by PIC and the recombination timescale of the heated plasma.
As shown by measurement and simulations, the amplified afterglow signal is notably sensitive to various interaction parameters: electron beam duration, size, and charge; laser Page 10 of 20 beam intensity and power; and gas density. This multi-parameter sensitivity promises further optimized resolution and represents a valuable attribute of the approach as it enables broad versatility. On the other hand, the latter in turn means that the resolution of the quantity to be measured is susceptible to the shot-to-shot jitter of other interaction parameters. Full exploitation of the versatility and sensitivity of this method therefore requires, as is true of many diagnostics, minimization of jitter contributions, and/or their simultaneous measurement with auxiliary diagnostics. The former is a general goal of any particle accelerator and is subject to intensive development, e.g. in context of freeelectron-laser facilities. The latter can be addressed by simultaneous composite measurements. While in our proof-of-concept experiments we have exploited the plasma afterglow in two different measurement modes for two different series of shots sequentially, these modes can be applied to the same electron beam shot by generating multiple seed plasma filaments side by side considering the negligible energy loss in each filament. Such composite measurements could isolate and deconvolve the parametric dependencies, yielding a comprehensive characterization of laser beam, electron beam, as well as their spatiotemporal relation. At advanced stability and reduced shot-to-shot jitters as attainable at modern photocathode-based facilities such as free-electron-lasers, subfemtosecond and sub-micrometre resolution may be ultimately obtainable.
We emphasize the applicability of the effect for intense and focused beams, as plasmabased techniques are not limited by conventional damage thresholds, and its applicability directly at the interaction point of such beams and even in the presence of plasma. This opens numerous experimental doors e.g. for pump-probe experiments, for the optimization of seeded free-electron-lasers, inverse Compton scattering light sources, advanced and staged plasma accelerator schemes, and beam-laser experiments probing quantum electrodynamics.

Materials and Methods
Experiment The laser-plasma-electron beam interaction experiment at FACET is conducted within a large gas volume separated from the SLAC beamline vacuum. The homogeneously distributed gas mixture consists of H2 and He in 1:1 ratio at pressure p = Page 11 of 20 5.3 mBar corresponding to hydrogen and helium gas densities of nH2  nHe  6.3×10 16 cm -3 . The SLAC linac provides an ultra-relativistic electron beam at 1 Hz repetition rate with energy W  20.4 GeV ± 2 % (FWHM), total charge Q = 3.0 nC ± 0.6% (r.m.s), length z  64 µm ± 1.9 % (r.m.s.) and transverse size x  22 µm and y  44 µm (r.m.s.). The laser pulse is compressed to a FWHM duration of τL  60 fs and its energy is adjusted to 4.9 ± 0.1 mJ by polarized beam splitters. An f/22.9 off-axis parabola (OAP) mounted on a motorized stage with five degrees of freedom focuses the laser to w0  38 µm (FWHM) and provides a mean intensity I  3×10 15 Wcm -2 to generate a plasma filament perpendicular to the electron beam axis (see Fig. 1 b). A CCD installed along the laser propagation direction measures the spatial alignment between electron beam and laser pulse. To achieve precise overlap of laser and electron beam propagation axes, a motorized optical transition radiation (OTR) screen placed at the interaction point yields the electron beam position and allows alignment of the laser centroid with the OTR screen removed. The electron orbit in y-direction varies with an average shot-to-shot jitter of 6.6 µm (r.m.s.) characterized by ~100 shots observed on an OTR screen and the laser pointing in this direction jitters by 7.6 µm (r.m.s). The relative time-of-arrival between electron beam and laser pulse is tuned by a linear stage with ~333 ps delay range. A second CCD (see Fig. 1 b) images the recombination/atomic relaxation radiation originating from the interaction with 25 ms integration time, using a spectral band pass filter of range 589.3 ± 5.0 nm. A low-intensity pulse split off before the OAP is used to measure the relative system-inherent electron beam-laser pulse synchronization jitter for every shot by electrooptic sampling. The electro-optic sampling (EOS) consists of a 100 µm thick gallium phosphide crystal, placed a few millimetres from the electron beam orbit and irradiated by the laser at an angle of 45°. The signal is analysed by a polarization filter and imaged onto a CCD camera. The resulting image is background-subtracted and calibrated by altering the path length of the laser-beamline averaged for every step over the intrinsic timing jitter. This EOS maps the relative TOA between laser and electron beam to physical delays. The EOS temporal calibration is res = 25.8 ± 2.5 fs px -1 . Furthermore, the EOS measures the relative TOA jitter between electron beam and laser pulse as 109 ± 12 fs r.m.s 37 .

Data analysis
The experimental timing data shown in Fig. 5 correlates each image produced by the z-x-CCD with an individual relative TOA determined by the EOS unit, Page 12 of 20 which accounts for temporal jitter between laser and electron beam. Projections of recorded plasma afterglow images are then sorted by EOS TOA. Integrating all pixels per shot and subsequent normalization yields the red scatter plot for the delay scan in Fig. 4.
We model the corresponding transition with a sigmoid function s(t) = a / (1 +exp((t -t0)· k)) . The average camera background noise level of 707 counts limits the resolution of our imaging system. Error propagation of the detector function s(t) -1 yields the TOA accuracy of the experiment for raw data (54.7 fs) and for the data set calibrated by EOS time stamps (15.8 fs).
For the alignment scan, the collected signals are correlated with the vertical focus position determined by the centroid of the imaged focus. The integrated counts per shot are fit by a bi-Gaussian distribution f(y)=a1·exp(-((y-b1)/c1) 2 ) + a2·exp(-((y-b2)/c2) 2 ). The first term describes the amplified plasma afterglow signal from the interaction with the electron beam and agrees well with PIC simulations. The second one results from systematic aberration errors due to movements of the OAP which reduces the plasma volume with increasing misalignment. In Fig. 4 we subtract the aberration from the signal to make simulation and experiment comparable. From the amplified signals detector function f(y) -1 we obtain best measured accuracy of 4.1 µm at the peak of the curve from error propagation.  Fig. 4 and 5, the total energy transferred from the electron beam into the plasma is evaluated for each delay and alignment. The maximal energy transferred into the plasma amounts to 0.93 mJ, a negligible fraction of the total beam energy of ~67 J. Since as EOS time stamps do not provide absolute timing information, the measured integrated counts in in Fig. 4 D are shifted on the TOA axis such that the curve agrees with the simulated data.   28 29 Competing interests: 30 The authors have no competing interests. 31 32 Data and materials availability: 33 34 Data associated with research published in this paper will be available at publication.