2. Experimental set-up, relevant diagnostics and examples of data

In a previous publication (Storey et al. Reference Storey, Zhang, San Miguel Claveria, Cao, Adli, Alsberg, Ariniello, Clarke, Corde and Dalichaouch2024), we detailed the beamline configuration of FACET-II, the experimental set-up around the interaction point area and the diagnostics. Here, we discuss the set-up and relevant diagnostics pertinent to the results reported in this paper (figure 2) for the reader's convenience.

Figure 2. Sketch of the experimental set-up. The 10 GeV single-bunch driver propagates from left to right, being focused by a set of quadrupoles into a gas filled region, which is bounded by two beryllium windows (with beam-drilled holes). The gas pressure within this region is adjustable, maintained at less than 5 Torr and constrained by the capabilities of the differential pumping system (not shown in the sketch). The post-interaction electron bunch is analysed by the downstream diagnostics, which include an imaging spectrometer (composed of tuneable quadrupoles, a vertically dispersing dipole magnet and a large field of view (LFOV) gadolinium orthosilicate-based scintillator screen coupled with a camera) and X-ray detectors (GAMMA1, detailed in Claveria et al. Reference Claveria, Storey, Cao, Di Piazza, Ekerfelt, Gessner, Gerstmayr, Grismayer, Hogan and Joshi2023). Three cameras (topview, sideview1 and sideview2) capture the time- and spectral-integrated plasma light at various locations. The distance between these cameras is indicated in the figure.

As previously mentioned, FACET-II currently operates in a single-bunch configuration, delivering 10 GeV high brightness electron bunches with peak currents exceeding 50 kA. These peak currents are a factor of 2–3 higher than in previous experiments on FACET and at FFTB and thus have allowed ionization of higher ionization potential (IP) gases (such as hydrogen molecules ${\rm H}_2$ with IP 15.4 eV and He atoms with IP 24.6 eV) compared with previously used lithium (IP 5.4 eV). In the present experimental results reported here, the compressed bunch is focused by a set of quadrupoles into an approximately 4 m-long continuous flow gas region, achieving a root mean square spot size of ${\geq }20\,\mathrm {\mu }{\rm m}$. This region is confined by two $50\,\mathrm {\mu }{\rm m}$ thick beryllium windows with approximately $200\,\mathrm {\mu }{\rm m}$ diameter holes drilled in situ by the electron bunch itself. The pressure of the hydrogen gas flow is adjustable from a few mTorr up to 5 Torr and can be maintained within 0.5 % precision on the time scale of a day. A four-stage differential pumping system on the upstream side has been implemented to isolate the high-pressure gas region from the high vacuum conditions upstream (e.g. better than $10^{-9}$ Torr at the X-band deflecting cavity). Similarly, a two-stage differential pumping system on the downstream side has been implemented to get better than $10^{-6}$ Torr pressure to reduce beam scattering as the beam propagates to the end of the beamline.

In the experiment, the vacuum focus of the beam was placed at the position of the topview camera and the vacuum beta of the beam was approximately 50 cm. The spot size of the beam is related to the beta function $\beta$ through $\sigma =\sqrt {\varepsilon \beta }$, where $\varepsilon$ is the geometric emittance of the bunch. As the electron bunch approaches the vacuum focus region, it initiates ionization induced by the transverse electric field of the beam within the hydrogen gas (field-induced ionization) even before the beam has reached the vacuum focus position which is close to the centre of the field of view of the topview camera, one of three cameras that look at the plasma light emission. For bunches with peak current above $\sim$30 kA (exceeding the ionization threshold of hydrogen molecules for a $\sigma _r=30\,\mathrm {\mu }{\rm m}$ Gaussian bunch) the hydrogen gas is ionized earlier in the risetime of the beam current over a length of several metres, far greater than the vacuum beta of the beam, suggesting that the beam is both focused and guided by the plasma that it has created. Plasma formation is immediately followed by wake formation. In transversely displacing the plasma electrons, the beam electrons lose kinetic energy, which mostly appears as the wake potential. The majority of the bunch loses energy to the wake; however, the very back of the bunch can gain energy if the plasma density is high enough.

After interaction with the plasma, the electron bunch is analysed by downstream diagnostics that measure its charge, energy spectrum and emittance, as well as the total X-ray signal. Surrounding the gas region, there are two additional cameras to the already mentioned topview camera – sideview 1 and sideview 2 in figure 2 – that also capture the time- and spectral-integrated plasma light emission (within the visible range, i.e. 400–700 nm). All these diagnostics are capable of operating on a single-shot basis (Gessner Reference Gessner and Kim2021) and can in principle be operated at up to 30 Hz.

In figure 3, we present examples of data acquired by the energy spectrometer, the integrated betatron emission screen and visible emission recorded by the sideview1 camera. Figure 3(a) displays the linearized energy spectra of the drive bunch for a dataset of 200 consecutive shots, taken with hydrogen gas at 1.0 Torr. Since the data were taken during the commissioning phase of the facility, with not-yet optimized beam shot-to-shot stability, this resulted in a fluctuating beam–plasma interaction strengths within the same dataset. The LFOV recorded the dispersed energy spectrum of the electron bunch after it has both produced and interacted with the plasma for each shot. The raw spectrum was first integrated along the undispersed direction and subsequently linearized along the dispersed direction, using the pre-calibrated dispersion curve of the dipole magnet. The dataset is sorted in ascending order according to the X-ray signal. In all shots, the prominent peak at 10 GeV represents the charge that either did not interact with the plasma (e.g. electrons preceding the ionization front) or did not undergo significant energy change (e.g. electrons at the zero-field phase of the wakefield). A prior publication has established that this ‘non-participating’ charge comprises up to 30 % of the total charge for all gas pressures used, indicating >30 kA peak current at the front of the drive bunch (Zhang et al. Reference Zhang, Storey, San Miguel Claveria, Nie, Marsh, Hogan, Mori, Adli, An and Ariniello2024). The red line in figure 3(a) marks the minimum energy ($E_{\rm min}$), corresponding to the maximum energy loss ($E_{\text {max loss}}=10-E_{\rm min}$) by the drive bunch, except for the last 25 shots, where the energy loss exceeded the spectrometer's measurement limit ($\gtrsim$5 GeV) in this configuration.

Figure 3. Representative data samples. (a) Linearized electron energy spectra of a set of 200 shots, sorted by increasing integrated X-ray signal on the screen shown in (b). The red line marks the minimum energy ($E_{\rm min}$) detected by the spectrometer (corresponding to the maximum energy loss $E_{\text {max loss}}$). (b) A typical X-ray signal as recorded by the GAMMA1 detector. Note that the hole in the middle and the other smaller hole underneath are not features of the betatron radiation, but are due to regions of decreased light output of the detector due to radiation related damage, and persist unchanged shot to shot. The defects cause the local apparent yield to be $\sim$15 % smaller. (c) An illustrative image of the plasma light emission captured by the sideview1 camera with an exposure time of $50\,\mathrm {\mu }{\rm s}$. The adjacent plot displays the integrated signal along the beam direction (solid blue line), along with a Lorentzian fit (dashed red line). The Lorentzian fit has a full width at half maximum of 2.75 mm and 80 % of it is within the transverse field of view of the camera.

Figure 3(b) presents a representative image of the betatron X-ray signal captured by the ‘GAMMA1’ detector, which records the spatial profile of the X-ray signal without resolving the spectrum. The set-up and calibration details of this detector are provided in Claveria et al. (Reference Claveria, Storey, Cao, Di Piazza, Ekerfelt, Gessner, Gerstmayr, Grismayer, Hogan and Joshi2023). In the particular shot displayed, the drive bunch experienced a maximum energy loss of approximately 5 GeV. Although the left and top edges of this screen are partially shadowed and approximately 15 % of the data are missing, the X-ray intensity profile appears round with a full width at half maximum (FWHM) of approximately 3 mrad. The betatron emission aperture angle is $\theta \approx (1+K)/\gamma$, where $K=K_pr_\beta \sqrt {\gamma /2}$ is the equivalent of the undulator strength parameter in synchrotrons, $r_\beta$ is the betatron oscillation magnitude and $\gamma$ is the Lorentz factor of the electrons. The upper estimated limit of the aperture angle is estimated to be $\sim$1 mrad by using an energy of 5 GeV (average energy loss of 5 GeV), an emittance of $30\,\mathrm {\mu }{\rm m}$ and $r_\beta$ approximated by the matched spot size of $3.5\,\mathrm {\mu }{\rm m}$ (corresponding to $K\sim 8.3$). The observed X-ray emission angle, being three times larger, suggests that the bunch is not matched, which is further supported by the significant (more than an order of magnitude) increase in its emittance (Storey et al. Reference Storey, Zhang, San Miguel Claveria, Cao, Adli, Alsberg, Ariniello, Clarke, Corde and Dalichaouch2024). This emittance growth would increase the average matched size of the bunch, increasing $r_\beta$ and thereby the angle.

In figure 3(c), a representative image of the plasma light captured by the sideview1 camera is shown. For this run, no colour filter was used, allowing the camera to record plasma emissions across the complete wavelength range of approximately 400–700 nm. The camera's exposure time was set to $50\,\mathrm {\mu }{\rm s}$, far longer than the lifetime of the wakes (San Miguel Claveria et al. Reference San Miguel Claveria, Adli, Amorim, An, Clayton, Corde, Gessner, Hogan, Joshi and Kononenko2019; Zgadzaj et al. Reference Zgadzaj, Silva, Khudyakov, Sosedkin, Allen, Gessner, Li, Litos, Vieira and Lotov2020; D'Arcy et al. Reference D'Arcy, Chappell, Beinortaite, Diederichs, Boyle, Foster, Garland, Caminal, Lindstrøm and Loisch2022). The image shows a stripe a few millimetres wide that indicates the plasma width as the beam travels from left to right across the field of view. The line plot adjacent to the image shows the integrated signal over a 2.5 mm region (within the two dashed white lines) along the beam direction, which is well fitted by a Lorentzian function with a background. The Lorentzian part of the signal is likely due to the direct imaging of the plasma emission, while the background may be explained due to multiple reflections of the plasma emission light within the chamber. The plasma light emission has a FWHM core of approximately 2.75 mm. The transverse field of view of the camera collects approximately 80 % of the Lorentzian part of the signal. That is to say, the light coming from the expanding plasma core is likely to be the main factor responsible for correlations observed with X-ray emission that will be described later.

3. Correlations identified in PWFA experiments

In this section, we discuss the correlations identified between these observables, which have proven to be useful in enhancing our understanding of the nonlinear beam–plasma interactions. We note that for these correlations we do not model the details of the betatron X-ray emission nor of the visible light emission by the plasma. The reason is that both the betatron and the integrated visible light data are likely to be experiment specific (namely, they depend on beam and diagnostics configurations).

During the experiment for a given setting of the beam parameters one or more sets of 200 shots are recorded. The correlation plots such as those shown below can be produced within minutes of the end of the certain beam configuration setting and can be recorded as a measure of likely usefulness of the data that need further analysis.

For example, one objective of the E300 experiment at FACET-II is to demonstrate high energy transfer efficiency from the drive to the trailing bunch. This efficiency is the product of the drive bunch to the wake energy transfer $\eta _{D\text {-}W}$ and the energy transfer from the wake to the trailing bunch $\eta _{W\text {-}T}$. In the case of a non-evolving wake the product of the two efficiencies can be estimated from a measurement of partial energy loss of the drive bunch and energy gain by the trailing bunch (Litos et al. Reference Litos, Adli, An, Clarke, Clayton, Corde, Delahaye, England, Fisher and Frederico2014; Corde et al. Reference Corde, Adli, Allen, An, Clarke, Clayton, Delahaye, Frederico, Gessner and Green2015). For an experimental demonstration of a single stage of a multi-stage PWFA-based linear collider, the energy of the drive bunch must be fully depleted in producing the wake. Ideally, energy depletion happens when all the particles in the beam are decelerated by the wake at the same rate and therefore the minimum energy recorded by the spectrometer approaches zero for all the particles in the beam, or alternatively, when the maximum energy loss ($E_{\text {max loss}}$) approximates the drive bunch's initial energy. However, this situation requires a specially shaped current profile of the electron beam (Chen et al. Reference Chen, Su, Dawson, Bane and Wilson1986; Loisch et al. Reference Loisch, Asova, Boonpornprasert, Brinkmann, Chen, Engel, Good, Gross, Grüner and Huck2018; Roussel et al. Reference Roussel, Andonian, Lynn, Sanwalka, Robles, Hansel, Deng, Lawler, Rosenzweig and Ha2020). Since in the present work the current profile of the bunch is not optimized, different longitudinal slices of the bunch loose energy at a different rate. This means that, while electrons in a portion of the beam may very well be pump depleted, those in other longitudinal slices will not be fully depleted. Indeed, if the beam has a long tail, then the electrons in the tail may well be in the accelerating phase of the wake and therefore gain energy. There is also a practical problem to making the ideal measurement. The post-interaction beamline (from the exit of the plasma to the energy spectrometer screen) may only be optimized to focus and transport electrons only within a specific energy range. This is less problematic for lower-energy electron drive beams; for example, recent studies have demonstrated near-total energy loss of a 500 MeV drive bunch to the wake in discharge plasmas inside a 15 cm-long capillary (Peña et al. Reference Peña, Lindstrøm, Beinortaitė, Svensson, Boulton, Diederichs, Foster, Garland, Caminal and Loisch2023). For higher-energy drive bunches, like the 10 GeV used at FACET-II, this method is not feasible because it would require transporting electrons that have an excessively broad energy range. For instance, a two-bunch experiment aimed at doubling the trailing bunch's energy while depleting the drive bunch would require a beamline capable of handling electrons with energies ranging from 0 to 20 GeV, which is not possible within a single optics configuration. In addition to maximum energy loss, the total energy deposited into the plasma by the drive bunch is also important, as it relates to the efficiency of energy transfer from the drive to the trailing bunch. Assuming that energy dissipation through other mechanisms such as betatron X-ray emission and ionization of the neutral gas by the drive bunch is negligible, we calculate the energy deposited into the plasma as the difference between the initial and post-interaction energies of the drive bunch. However, due to some low-energy electrons not being captured and transported to the spectrometer imaging screens as previously explained, this method can encounter significant uncertainties. Consequently, both scenarios necessitate the development of alternative methods that can be calibrated to rapidly give the maximum energy loss and the energy deposited into the plasma. This is particularly crucial when the imaging energy of the spectrometer optics is set to a few GeV to ascertain the emittance of decelerated electrons within a narrow energy range around the imaging energy, employing the butterfly technique where the width of beam in the undispersed direction reaches the minimum at the focusing energy and increases at non-focusing energies (Storey et al. Reference Storey, Zhang, San Miguel Claveria, Cao, Adli, Alsberg, Ariniello, Clarke, Corde and Dalichaouch2024).

3.1. Correlation between betatron X-ray signal and maximum energy loss and total energy lost by the beam

We have discovered that the total incoherent but directional (betatron) X-ray emission is an effective indicator of the initially 10 GeV beam's maximum energy loss ($E_{\text {max loss}}$) within the spectrometer setting limit (up to 5 GeV in this case). The maximum energy loss is determined by the product of the maximum decelerating field experienced by a slice of the beam and the plasma length at a given density. Conversely, the betatron X-ray signal not only depends on these parameters (wakefield strength, and length over which the wake exists) but also on the beam's energy and the particles’ displacement from the propagation axis within the beam. The longitudinal phase space of the beam is continuously evolving as the beam slices lose energy by different amount to the wake. In principle, a three-dimensional moving window particle-in-cell (PIC) simulation allows one to model the electron trajectories and these can be coupled to a radiation code to determine the X-ray yield (Albert et al. Reference Albert, Lemos, Shaw, Pollock, Goyon, Schumaker, Saunders, Marsh, Pak and Ralph2017; Lemos et al. Reference Lemos, Albert, Shaw, Papp, Polanek, King, Milder, Marsh, Pak and Pollock2018).

In our experiment, despite the complex dependencies of the X-ray yield on beam, wake and plasma parameters, we observed linear correlations between the maximum energy loss and the X-ray signal, as well as the total beam energy deposited into the plasma and the X-ray signal, as shown in figures 4(a) and 4(b), respectively, for shots such that the entire bunch charge remains visible on the profile monitor. Since the beam electrons are relativistic, beam–plasma electron collisions are a not significant mechanism of energy transfer. The energy is transferred in a collisionless process mediated by the transverse space charge field of the highly relativistic beam. In this process the plasma electrons are pushed outward by the repulsive force of the drive-beam electrons. While most of them are eventually captured in a thin sheath by the attractive force of the plasma ions, some may escape. Here, we assume that this is a small effect and all the energy lost by the beam electrons is transferred to the wake. The dataset analysed here is the same as that shown in figure 3(a) and was acquired at a static hydrogen pressure of 1.0 Torr. The spectrally and spatially integrated X-ray signal is calculated by summing the total counts for each shot.

Figure 4. Correlations between the maximum energy loss of the drive bunch. (a) The energy lost by the beam while traversing the plasma and (b) the integrated betatron X-ray signal. In both (a,b), the data (green dots) exhibit a strong correlation, as demonstrated by the linear fit (red line), with the two dashed lines indicating the 95 % prediction interval of the fit. Note that, in (a), data points with a maximum energy loss remaining at $\sim$5 GeV, as the X-ray signal increases beyond $8\times 10^8$, are due to the spectrometer's setting limit for this dataset and have been excluded from the linear fit.

In figure 4(a), there are data points for which the X-ray signal continues to increase (up to $10^9$ counts) even though the maximum energy loss is capped at 5 GeV due to the spectrometer setting limit in this configuration. If projected onto the established linear correlation, these points would suggest a maximum energy loss of 8 GeV and a deposited energy of around 5 J. However, it should be noted that extrapolating the linear correlation must be verified with spectrometer settings that can measure the spectrum over an extended range to confirm its validity. We also note that the correlation almost certainly breaks down as a large fraction of the beam electrons are pump depleted since they can no longer emit betatron X-rays, so eventually the X-ray emission must also begin to show saturation. What is clear is that these correlation plots are experiment specific and over the range of measurement of both the variables, provide a playbook for rapid scanning of beam parameters during the experiment.

3.2. Correlation among three different visible light cameras

In addition to the X-ray diagnostic, we also used cameras to measure the visible light emitted by the plasma transversely at multiple locations around the interaction point area (see the topview and sideview cameras depicted in figure 2). Modelling light emission from a plasma with a set initial density and temperature is already a complex problem. In our experiments, this complexity is compounded as the plasma's peculiar initial state must take into account plasma formation by beam field ionization, energy deposition by the beam into the wake and dissipation processes including transverse shock wave generation (Singh et al. Reference Singh, Pathak, Shin, Choi, Nakajima, Lee, Sung, Lee, Rhee and Aniculaesei2020) and is largely unknown (not diagnosed directly). Therefore, here, we do not intend to establish a quantitative model to describe it but to show that, despite the involved physics, the spectral- and time-integrated but spatially localized plasma light provides useful information about the beam–plasma interaction.

We first present correlations among the plasma light recorded by three cameras situated at different locations, which provide information on the plasma length over which the wake is excited. Then, we examine the correlation between the plasma light and the X-ray signal in the next section. Figure 5(a) displays plasma light collected by these cameras, with each column representing an individual shot summed over the beam propagation direction, and the dataset is presented in the order in which the data were acquired. The dataset was taken at 1.0 Torr. The top panel (labelled with TopView) illustrates the light captured by the topview camera at the vacuum beam waist location, while the other two panels show the light collected by the sideview cameras, located 0.56 and 1.82 m downstream, respectively. Correlations between these measurements are shown in figure 5(b,c), with the red lines showing the best fit using a power function and a logistic function, respectively, to indicate the nonlinear trend of the correlations.

Figure 5. Correlations among different visible light diagnostics for 200 consecutive shots obtained at 10 Hz. (a) Displays plasma light captured by the topview, sideview1 and sideview2 cameras, with each column corresponding to an individual shot and summed along the beam propagation direction. (b) Illustrates the plasma light signal recorded by the sideview1 camera plotted against the signal from the topview camera. (c) Shows the correlation between the signals from the two sideview cameras. The red lines in (b,c) are the best fit to the data using a power function and a logistic function, respectively, to show the nonlinear trend of the data.

In figure 5(b), the plasma light signal from the sideview1 camera is plotted as a function of the topview camera signal. Notably, the topview camera signal starts at approximately $5\times 10^7$ counts, coinciding with the onset of the sideview1 camera signal, indicating that certain shots, likely with a beam peak current just above the ionization threshold of hydrogen molecules, only generate plasma and excite wakes near the vacuum waist. However, this density is not large enough to guide the beam up to the sideview1 camera, where it could also produce ionization to the same degree, thereby producing light. It is not surprising that this translates to a large spread in the correlation plot shown in figure 5(b). Despite this spread, it is clear that the sideview1 camera signal increases with the topview camera signal but then begins to saturate. The correlation implies that, as the drive beam's peak current rises, it creates a larger wake that eventually dumps more energy per unit length along its path, resulting in stronger visible light emissions detected by both cameras. The saturation of the sideview1 signal, despite continued increases in the topview camera signal, suggests that the energy deposition at the sideview1 location has plateaued, possibly because the plasma and wake originated further upstream for beams with higher peak currents.

Figure 5(c) illustrates the correlation between the signals from the sideview2 camera, positioned further downstream, and the sideview1 camera signal. For the shots yielding the lowest sideview1 signals, the sideview2 signal is nearly zero, indicating that the plasma and wake are present at the sideview1 location but do not extend to the more distant sideview2 location. As the drive-beam intensity increases, signals from both sideview1 and sideview2 cameras increase, and a linear correlation emerges. However, for the shots with the highest sideview1 signals, the sideview2 camera's plasma light collection tends to saturate, corresponding to a shift of the entire plasma upstream, as discussed earlier. These inter-camera correlations suggest that, in most cases, the plasma and wake extend across the entire 1.8 m span from the topview camera to the downstream sideview2 camera. These are the longest (1.8 m) beam-driven plasma wakes in a relatively high density ($3.5\times 10^{16}\,{\rm cm}^{-3}$) plasma that the authors are aware of. We note that the datasets obtained at other pressures (e.g. 1.5 and 2.0 Torr) show similar results.

3.3. Visible plasma light vs X-ray signal

Despite the facts that the X-ray diagnostic measures the longitudinally integrated betatron emission, whereas the topview and sideview cameras record the plasma light locally, we show in this section that these two observables are correlated and therefore, could provide additional information about the beam–plasma interaction.

In figure 6, the plasma light captured by the sideview1 camera is presented as a function of X-ray signal for three different gas pressures. For the 1.0 Torr dataset in figure 6(a), a notable linear correlation emerges initially between the visible plasma light and betatron X-ray signals. This correlation is particularly significant given the localized collection of plasma light (covering roughly 1.5 cm), in contrast to the metre-scale plasma length over which the X-ray radiation is generated. This linear correlation is notable considering that the plasma light is collected locally (spanning approximately 1.5 cm, much shorter than the metre-scale plasma length along the longitudinal direction). In the 1.5 Torr dataset depicted in figure 6(b), a similar pattern of correlation is observed, but the slope of the linear part is larger, indicating that the electrons are losing more energy at the turning points of their betatron orbits due to a larger acceleration in higher plasma density wakes. Also, at the highest values of the X-ray signal there is some indication of saturation.

Figure 6. Correlation between plasma light and X-ray signal. The plasma light detected by the sideview1 camera is plotted as a function of the X-ray signal for three datasets acquired at different pressures. The red lines are polynomial fits (with orders one (linear) for (a) and three (cubic) for b,c) to illustrate the trend of the data.

As the gas pressure further increases to 2.0 Torr, figure 6(c) reveals a distinct behaviour: the visible plasma light initially increases linearly with the X-ray signal for shots with smaller X-ray signals, as anticipated. However, after peaking at an X-ray signal of $8\times 10^8$, it declines almost linearly with a slope similar to the increase phase, despite the continued rise in X-ray signal. This trend could be attributed to a shift of the plasma upstream for shots with higher peak currents, resulting in plasma formation further upstream, as explained earlier. Consequently, by the time the beam reaches the sideview1 camera location, it has been partially depleted and is less efficient in exciting wakes and depositing energy into the plasma. Alternatively, this pattern might indicate that the rear of the drive bunch enters the accelerating phase, extracting energy from the wake and thereby reducing the energy deposited into the plasma, which in turn lowers the plasma light yield. Notably, for datasets at pressures of 1.5 Torr and above, we observed using the imaging spectrometer that electrons had gained multiple GeV of energy (Zhang et al. Reference Zhang, Storey, San Miguel Claveria, Nie, Marsh, Hogan, Mori, Adli, An and Ariniello2024).

These results indicate that, upon appropriate calibration, plasma light can be utilized as a non-invasive diagnostic tool. It is noteworthy that similar linear correlations between plasma light and energy deposition have recently been reported in other PWFA experiments (Oz Reference Oz and Yakimenko2004; Boulton et al. Reference Boulton, Lindstrøm, Beinortaite, Svensson, Garland, Caminal, Hidding, Loisch, Peña and Põder2022).