Plasma-wakefield accelerator simultaneously boosts electron beam energy and brightness

Domain: physics
Published: 2025-11-28
Editorial outcome: minor_revision

Abstract
High-energy particle colliders and X-ray free-electron lasers demand electron beams with qualities currently achieved only in kilometer-scale radio-frequency accelerators. Plasma accelerators promise a compact alternative but have faced challenges in delivering the needed beam quality at relevant energies. Here, we demonstrate that a plasma-wakefield accelerator operating in the nonlinear regime acts as a transformer to simultaneously boost the energy and brightness of an electron bunch injected from the plasma. Using a 10-GeV drive bunch and a three-stage meter-scale plasma source, we generated electron bunches exceeding 20 GeV with sub-percent energy spread, 2 mm·mrad normalized emittance, and multi-kA peak current. A significant number of drive-bunch electrons lost over 90% of their energy, a prerequisite for high energy-conversion efficiency. This demonstration of an energy transformer ratio exceeding two and a brightness enhancement over an order of magnitude opens a path towards cost-effective accelerators for future colliders and light sources.

Introduction
Advances in conventional radio-frequency (RF) particle accelerators have driven the frontiers of scientific discovery, from probing the subnuclear structure of matter and forces with high-energy colliders1,2, to enabling femto- and atto-science with ultrabright X-ray free-electron lasers (XFELs)3,4. However, these powerful discovery tools require extremely large and expensive facilities, due to the effective electric field breakdown limits (currently at ~100 MV/m) in RF cavities5. This limitation has prompted the development of plasma-based accelerators (PBAs)6, which can support acceleration gradients orders of magnitude larger than conventional approaches7.

Plasma accelerators use either relativistic charged particle beams (plasma wakefield accelerators, PWFAs8) or intense laser pulses (laser wakefield accelerators, LWFAs9) to drive large-amplitude plasma waves. In the nonlinear ‘blowout’ regime10 of the PWFA, the driver completely expels plasma electrons from its path, forming a nearly spherical ion cavity enclosed by a thin plasma electron sheath moving at nearly the speed of light11. This cavity, with radially uniform accelerating fields and linear focusing forces, creates ideal acceleration conditions for electrons11,12—essential for preserving beam quality during acceleration.

The plasma acceleration concept has advanced significantly over the past two decades, demonstrating energy gain of ~10s of GeV in a meter-scale plasma13–15, a few percent energy spread and high-efficiency energy transfer to a second distinct trailing bunch16, initial demonstration of energy spread, emittance and charge preservation17–19, energy reproducibility20, proof-of-principle staging21, and PWFA as a beam quality transformer22. These continuous advancements have recently enabled demonstration of PBA-driven free electron lasing in the extreme ultraviolet (EUV) to optical wavelengths23–25. Despite this remarkable progress, plasma accelerators have yet to simultaneously deliver the combination of high energy (multi-GeV), narrow energy spread, and high beam brightness required for applications in hard X-ray FELs26. Achieving these beam parameters may also enable a near term demonstration of PWFA technology in a hybrid plasma/RF linear collider27.

Here we demonstrate that a plasma wakefield accelerator can be used as a transformer to simultaneously boost the energy and brightness of a self-injected electron bunch. Using the 10 GeV electron bunch (Methods), delivered by the recently commissioned FACET-II National User Facility28 at SLAC National Accelerator Laboratory, and a meter-scale three-stage beam-ionized hydrogen plasma source29,30, we have generated electron bunches that have more than twice the energy of the drive bunch, a sub-percent energy spread, an order of magnitude smaller emittance, and kA-level peak currents. These parameters yield an energy transformer ratio exceeding two and a brightness enhancement of more than an order of magnitude in comparison to the drive bunch.

Results
Experimental setup
Our plasma wakefield transformer consists of a three-stage plasma source (Fig. 1a) that integrates drive bunch focusing, injection of the trailing bunch, and acceleration of the trailing bunch to beyond 20 GeV (Methods). The drive bunch contains variable current spikes (15-100 kA) which induce ionization of hydrogen gas while a longer, lower current base produces the plasma wake30,31.

The first stage comprises a 1.25-meter-long low-density hydrogen gas region upstream of the gas jet. A 10 GeV electron bunch (1.6 nC charge, 22.6±1.9 mm·mrad emittance, ~20 µm r.m.s. bunch length) from the FACET-II linac operating at 5 Hz was focused at variable positions with respect to the gas jet using quadrupole magnets with a nominal β* of 50 cm. The high-current spike(s) of the drive bunch31 partially ionize the hydrogen gas before the drive bunch reaches the gas jet, creating a variable density plasma that acts as a thick, passive lens32. This plasma lens further focuses the drive bunch to a few microns (much smaller than its vacuum waist spot size of ~25 µm), increasing the beam density well above the plasma density—essential for exciting a reproducible nonlinear wake33 even before the drive bunch reaches the gas jet. While this plasma lens section improves the reproducibility of the wake at the gas jet, the position of the of plasma/wake formation with respect to the gas jet varies from shot to shot because of the shot-to-shot variation of the magnitude of the current spike(s) in the drive bunch caused by the amplitude and phase jitter of the RF30. As a result, the drive bunch enters the gas jet having lost 1-3 GeV energy to the wake. The second stage is the sharp density downramp with a scale length of a few hundred micrometers, created by a movable blade that intercepts the gas flow at the jet exit (see Fig. 1a), which enables injection of plasma electrons as the phase velocity of the wake’s trailing edge suddenly becomes subluminal34,35. The third stage consists of the 2.85-meter-long gas region downstream of the gas jet, where the injected electrons are further accelerated until energy of the drive bunch is nearly fully depleted and wake is terminated. The gradual density transition from the higher-density jet to the lower-density gas region self-matches the injected bunch into the acceleration stage35, as evidenced by the lack of characteristic betatron oscillation features in the bunch’s energy spectrum, which will be discussed later. This design eliminates the need for additional plasma-channel guiding36 or external magnetic elements, as both the unmatched drive and self-matched injected bunches are self-guided by the wakefields throughout the entire meter-scale plasma.

Drive bunch depletion and 26 GeV injected bunch gain
The energy loss of the drive bunch and energy gain of the injected electrons (Methods) are evident in the energy spectra shown in Fig. 1b–d. These three spectra were measured in different shots while using different spectrometer settings to accommodate the large energy difference between the highest energy gain (>20 GeV) and energy loss (≤10 GeV). Figure 1b shows an example of the drive bunch energy loss in the ~1–4 GeV range, where electrons at the peak of the positive electric field of the wake reach the 1 GeV limit of the spectrometer—indicating that some drive bunch electrons have lost 90% of their energy. Charge measurements using beam position monitors (BPMs) immediately downstream of the plasma show that ~200 pC of drive bunch charge was lost, providing additional evidence of energy depletion of the drive bunch, as electrons must lose nearly all their energy before they are overtaken by the wake37.

Figure 1c displays the energy spectrum in the 4–12 GeV range. While some charge remains at 10 GeV, consisting of electrons ahead of the beam-induced ionization front (previously quantified to be up to 30% of the total charge30), the majority of the bunch’s interacting electrons experience significant deceleration. The energy loss spectrum exhibits pronounced beam spot size modulations (blue curve), arising from varying divergence angles at different betatron oscillation phases upon exiting the plasma. Applying the analysis method from ref. 12 to these modulations revealed that the 10 GeV electrons undergo ~57 betatron oscillations, while decelerated electrons (9–5 GeV) experience an additional 3-16 oscillations. This corresponds to an effective plasma length of 1.7±0.3 m and a maximum decelerating gradient of 5-7 GeV/m. As we shall see later not all of this plasma length is useful for accelerating the injected particles which are always produced at the downramp.

When the gas jet was activated, a distinct spectral peak appeared (in the case of shot shown in Fig. 1d) at 26 GeV with smaller divergence than the drive bunch. The injected bunch was only observed when the gas jet was turned on and the relative positions of the gas jet and the blade were optimized (to give approximately a factor of two density change in a few hundred µm distance), confirming its origin from the downramp injection process. The bunch in Fig. 1d exhibited an r.m.s. energy spread of only 0.7% and a total charge of 2.3 pC.

High transformer-ratio acceleration
To change the acceleration length sampled by the injected electrons we positioned the drive bunch vacuum waist at variable distances downstream of the gas jet, effectively shifting the whole plasma, while keeping the injection point fixed at the gas jet downramp. By maximizing the acceleration length (drive bunch vacuum waist 75–100 cm downstream of the gas jet), we achieved electron beam energies exceeding 20 GeV. Figure 2a presents background-subtracted, linearized energy spectra (Methods) of 20 shots, arranged in ascending order of energy, each displaying a well-defined, narrow peak above 20 GeV. Several shots show spectral charge density levels high enough to cause signal saturation on the camera. When we shifted the drive bunch vacuum waist by one meter in four equal 25 cm steps beyond the gas jet, the final energy of the injected bunch increased linearly from ~13 GeV to ~26 GeV. While the wakefield strength may have varied with this change, the linear trend of energy gain with acceleration length indicates that the interaction length was the primary factor determining the final energy, corresponding to an effective average accelerating gradient of 13 GeV/m. Even higher energy but low charge peaks were occasionally seen with a maximum energy up to 29 GeV as shown in Fig. 2a.

We have estimated the energy transformer ratio (E-TR)—defined here as the energy gained by the accelerating bunch divided by energy lost by the drive bunch. The E-TR versus charge contained in the injected bunch plotted in Fig. 2b shows two branches: the first has less than 5 pC of charge but energy higher than 20 GeV, while the second has higher charge (> 5 pC) with lower energy. For the low-charge branch, E-TR rapidly increases as the charge decreases due to injection nearer the bubble’s high-field region combined with negligible beam loading, whereas for > 5 pC charge the E-TR decreases slowly with charge as onset of beam loading occurs. We note that for injected charge > 5 pC, approximately half of the shots achieved E-TR exceeding 2, with maximum measured charge of 40 pC. Since linear wakes produced by a longitudinally symmetric drive bunch cannot achieve a transformer ratio greater than two38,39, our results show that we are in the nonlinear regime. Previous high-gradient nonlinear plasma wakefield experiments with unshaped drive bunches showed E-TRs of only 1-1.540,41. While higher ratios have been demonstrated using shaped drive bunches, those proof-of-principle experiments were limited to ~MeV energy gains using low-gradient acceleration42,43. Simulations show that ~3 GeV of the 10 GeV drive bunch energy is lost before it encounters the downramp. Thus, for a bunch accelerated to 20 GeV energy, the E-TR is likely to be up to 3, an estimate that accounts for the ~3 GeV of drive bunch energy lost prior to the injection point. In other words, the E-TR estimates are likely to be an underestimate.

A bunch charge of 10s pC may be adequate for an XFEL, but a future plasma collider will need hundreds of pC charge per bunch for a high drive-to-trailing-bunch energy transfer efficiency and to get the required luminosity at a practical repetition rate27. While our current experiments show a maximum injected charge of tens of pC, theoretical beam loading studies using shaped bunches indicate the potential to load several hundred pC with preservation of beam quality44. Such a shaped bunch can, in principle, be produced via downramp injection by tailoring the density profile of the ramp35,45.

Simultaneous brightness enhancement
We now demonstrate that our plasma wakefield energy transformer also acts as a brightness transformer. Beam brightness is defined as Bn = 2Ipeak / (ϵn)^2, where Ipeak and ϵn are the peak current and normalized transverse emittance. Clearly, the brightness can be increased by either raising peak current or reducing emittance or both. Here we show that the injected bunch inherently possesses much lower emittance, giving it higher brightness despite lower current than the drive bunch.

Figure 3a presents a high-resolution energy spectrum of an injected bunch captured by Camera 1 (Fig. 1a). The bunch has the smallest waist size at the spectrometer focusing energy of 16.5 GeV in the non-dispersed direction, and the size σx increases as we move away from this value, as also shown by the blue curve in Fig. 3b. The best fit using the transport matrix of the spectrometer gives a normalized emittance of 2.4 mm·mrad for this shot (Methods). Unlike the drive bunch spectrum (Fig. 1c), the injected bunch shows weak or no betatron envelope oscillations, indicating it is matched. Its emittance is an order of magnitude smaller than the drive bunch, and it remains matched to the plasma by gradually decreasing its transverse spot size σx as it gains energy46.

To determine the current profile generating the measured energy spectrum, we developed a physics-informed machine learning framework (Methods) to solve the inverse problem. In this framework, we employed a multi-sheath model47 that accurately describes the plasma wakefield to map an arbitrary injected bunch current profile to a final energy spectrum and iteratively optimized the trial current profile until the calculated spectrum matched experimental measurements (charge is therefore implicitly conserved). The multi-sheath model parameters were adjusted as a function of propagation distance based on PIC simulations to account for wake evolution and dynamic beam loading to improve accuracy. The method was benchmarked using energy spectrum and current profile of downramp injected bunches obtained from PIC simulations, showing good agreement (Methods).

When applied to the experimentally measured energy spectrum (Fig. 3a), this approach revealed the current profile shown in Fig. 3c, which has an approximately trapezoidal shape with ~2 µm (FWHM) bunch length and ~3.5 kA peak current, with a total charge of 25 pC matching the measurement. The corresponding longitudinal phase space (LPS) of the injected bunch is shown in Fig. 3d. The LPS exhibits a nearly linear positive energy chirp with reduced slope at higher energies—a signature of the onset of beam loading. Given that the contained charge is modest and the reconstructed LPS indicates an underloaded wake, the peak current obtained here represents a lower bound of the actual peak current. More than 100 optimizations with different initial current profiles having peak magnitudes ranging from 0.1 to 5 kA converged to similar current profiles as shown in Fig. 3c, indicating that this is a robust solution.

When comparing the energy spectrum derived from this reconstruction (Fig. 3e), assuming a 0.1% slice energy spread reproduces the measured spectrum more accurately than the measured 0.5% r.m.s. projected energy spread, which gives a broader spectral peak with a lower charge density. Using the 0.1% slice energy spread, the longitudinal emittance of the injected bunch is calculated to be ~74 keV·ps, comparable to LCLS-II (13.6 GeV, ~0.01% slice energy spread, emittances of 14–73 keV·ps)48. The linear energy chirp can be removed by using either a magnetic chicane to compress the beam to much higher peak current49, or RF/plasma-based dechirpers20,50.

The brightness of the injected bunch is calculated using the measured emittance and retrieved peak current, reaching approximately 1.2×10^15 A/m²/rad² for the shot in Fig. 3a. Similar analysis performed for multiple shots is shown in Fig. 3f, with average brightness reaching approximately 0.5×10^15 A/m²/rad². Compared to the beam brightness (blue dot in Fig. 3f) of the drive bunch with 8 kA peak current and 22.6±1.9 mm·mrad emittance, the injected bunch is up to 38 times brighter. The experimental brightness values reported here should be considered conservative estimates, as they combine potentially underestimated peak currents with overestimated emittance measurements that likely include growth due to beam transport mismatch outside the plasma. We note that the ~20 GeV peak energy, ~kA peak current, µm-level emittance and 5×10^14 A/m²/rad² (see Fig. 3f and Supplementary Fig. 1) were all reproduced in particle-in-cell simulations (Methods) that model the experiment. Recent simulation studies have shown that leveraging dynamic beam loading effects during pump depletion can accelerate self-injected bunches to above 20 GeV with <1% energy spread and brightness as high as 10^19 A/m²/rad², indicating that an improved version of our approach has potential to further boost beam brightness far beyond that of conventional accelerators51.

Methods
Drive electron bunch
The upgraded FACET-II National User Facility delivered 10 GeV electron bunches to the interaction point28. A photocathode gun generated low-emittance bunches, which were subsequently accelerated through four stages to 10 GeV and compressed using three magnetic chicane compressors installed between acceleration stages. The bunch charge was 1.6 nC with ~2% (r.m.s.) shot-to-shot fluctuation. The normalized emittance was measured to be 22.6±1.9 mm·mrad using the quadrupole scan method. Bunch length was measured to be ~20 µm using an X-band Transverse Deflecting Cavity (XTCAV); however, the temporal resolution was insufficient to resolve femtosecond-scale current spikes suggested by beamline simulations30,31. These 15-100 kA spikes, containing ≲20% of the total charge, were responsible for ionizing the hydrogen gas but were not the primary driver of the plasma wake. Consequently, charge contained in the current spike (e.g., 0.25 nC) was neglected when calculating the peak current and brightness of the drive bunch (Fig. 3f).

Plasma source
The plasma was produced by the drive bunch self-ionizing a continuous flow of hydrogen gas. A differential pumping system isolated the 4.1-meter-long gas region from the high-vacuum region of the linac29. The gas region was bounded by two 75-µm thick beryllium windows with sub-mm holes that limited gas flow into the high-vacuum region. These holes were self-drilled by the intense drive bunch and were large enough to allow both drive and injected bunches to propagate through.

Hydrogen gas was delivered using a combination of a pulsed gas jet and an adjustable continuous-flow needle valve to maintain the desired background pressure. The gas jet was created by a custom nozzle that internally transitions from a 3-mm diameter circular input to a slot-shaped throat (2.0 mm by 0.5 mm), and then expands to a 2-cm-long by 2-mm-wide slit exit. The nozzle was positioned ~1.25 m from the upstream beryllium window. For the pump depletion measurements (Fig. 1b, c), the gas jet was turned off and the background pressure was maintained using the adjustable needle valve only. For the injection experiments, the adjustable needle valve was closed, and the pulsed gas jet was operated with a backing pressure of 100 psi at 5 Hz, which maintained the background pressure at 4 Torr, corresponding to a plasma density of 1.3×10^17 cm^-3 assuming singly ionized hydrogen molecules. A custom-shaped stainless steel blade, with a 10 mm by 4 mm active section and a leading edge machined to 100 µm thickness, covered ~4 mm of the gas jet on the downstream side to create a density downramp. The drive bunch was positioned 2 mm above the nozzle exit. The gas jet operated with 1 ms opening time, carefully timed to maximize injection signal detection probability (~15%). Fluid simulations indicated the downramp had a density ratio of ~2 over a length of several hundred micrometers. The plasma position was controlled by tuning the final focusing quadrupoles to shift the drive bunch vacuum waist (-0.5 to 1.25 m relative to the gas jet), effectively changing the acceleration length since the injection point remained fixed at the downramp location.

Electron imaging spectrometer
The imaging spectrometer consisted of a quadrupole triplet to capture and refocus electrons exiting the plasma, followed by a dipole magnet to disperse electrons vertically. A high-resolution in-vacuum profile monitor used a cerium-doped yttrium aluminum garnet (Ce:YAG) crystal to convert electron flux into visible light, which was imaged by two cameras with different magnifications: Camera 1 (Fig. 1a) with 3.6 µm effective pixel size and a second camera (not shown) with 30.5 µm pixel size. Additionally, a gadolinium oxysulfide (GOS) scintillator screen viewed by a large field-of-view camera (Camera 2, Fig. 1a) covered the multi-GeV spectral range with 89.1 µm pixel size. These spatial resolutions provided energy resolutions of ~0.01% (Camera 1) and 0.15% (Camera 2). The spectrometer’s dispersion curve was calibrated by varying the dipole magnet strength, with an uncertainty of <1% in determining absolute electron energy.

Injected bunch analysis
Spectrometer images were first background-subtracted using reference images taken without plasma interaction. A region-of-interest analysis isolated the injection signal from the drive bunch contribution using image segmentation. Signal regions were identified by binarizing the image with a threshold of 500 counts for most datasets, with 100 counts used for weaker signals to ensure detection. Among identified regions, the region containing the highest-energy electrons was selected as the injection signal based on energy-weighted pixel intensities. The original pixel intensities within the selected region were preserved for charge calculations. The background-subtracted images were then linearized to account for the nonlinear energy dispersion of the spectrometer (Fig. 2a). The integrated energy spectrum was obtained by summing the signal in the non-dispersive (horizontal) direction.

Charge calibration was performed by comparing the integrated signal from the drive bunch (without plasma) with its known charge measured by upstream beam position monitors. This calibration factor was then applied to the injected bunch signal to determine the injected bunch charge.

The energy spread of the injected bunch was calculated from the linearized energy spectrum using the full width at half maximum (FWHM) divided by 2.355 to convert to an effective r.m.s. spread, which provides a robust measure for non-Gaussian spectral distributions.

Emittance measurement
The drive bunch emittance was measured using a multi-shot quadrupole scan by varying the spectrometer quadrupole focusing strength to scan the M12 element of the transport matrix while keeping the detector plane physically fixed. Electron spot size in the non-dispersive (horizontal) direction was measured by scanning M12 from -5 to 5 meters in 11 steps, and the emittance was fitted using: σx(E)^2 = ϵn / γ * (M11^2 * β0 - 2 * M11 * M12 * α0 + M12^2 * (1 + α0^2) / β0), where all transport matrix elements are functions of beam energy. The drive bunch emittance was measured to be 22.6±1.9 mm·mrad without plasma.

For the injected electron bunch, which exhibited larger shot-to-shot jitter, a single-shot emittance measurement was performed using the natural energy spread of the bunch and the highest resolution camera (Camera 1 in Fig. 1a). Since transport matrix elements are energy-dependent, electrons with different energies within the same bunch focus to different spot sizes. By analyzing the correlation between energy and horizontal spot size, the emittance can be extracted from a single shot. Analysis of multiple shots showed injected bunch emittances ranging from 1.9 to 5 mm·mrad with an average of 3.2±2.0 mm·mrad.

Injected bunch LPS reconstruction
We developed a physics-informed machine learning framework to reconstruct the longitudinal phase space of the injected bunch from measured energy spectra. This inverse problem approach allowed inference of critical bunch properties that could not be directly measured with the available experimental setup.

Our method employed a multi-sheath model47 that accurately described the plasma wakefield, with parameters fitted to match the wakefield structure from our QPAD simulation without injected bunch (see Methods). To account for wake evolution and dynamic beam loading effects, we divided the plasma into 10 longitudinal sections, each with independently fitted multi-sheath parameters, effectively implementing a piecewise-linear approximation of the wake dynamics. This segmentation focused on the first meter of acceleration following injection, where the multi-sheath model remains valid and the injected bunch parameters (energy, energy spread, charge) stabilize (Supplementary Fig. 1c).

The reconstruction followed an iterative optimization process. Beginning with an initial hypothesis for the injected bunch current profile, we calculated the loaded wakefield across all 10 plasma sections using each section’s multi-sheath parameters extracted from the QPAD simulation. For each section, we solved the ordinary differential equation governing the bubble shape (with beam loading from the injected bunch), then integrated the resulting accelerating field over that section’s length. Energy gains from all 10 sections were summed to obtain the final energy spectrum, which was then compared with the measured spectrum. The current profile was then iteratively adjusted using stochastic gradient descent until convergence between calculated and measured spectra was achieved.

To validate this technique, we benchmarked it against PIC simulations by reconstructing current profiles from simulated energy spectra, finding good agreement between reconstructed and directly simulated profiles (Supplementary Fig. 2). When applied to experimental data, our analysis revealed injected bunches with peak currents ranging from 0.3 to 3.9 kA, scaling roughly linearly with bunch charge.

PIC simulation
We performed particle-in-cell simulations using two complementary codes: QPAD52, which employs quasi-static approximation with azimuthal mode decomposition for efficient modeling of meter-scale plasma interactions, and quasi-3D OSIRIS53 for modeling the downramp injection process. Our simulation approach consisted of three sequential stages.

First, using QPAD, we simulated plasma generation through beam ionization and drive bunch dynamics. The simulation employed a moving window of 12×10 c/ωp divided into 1152×960 cells with a time step of 20 ωp^-1. Based on previous results30, the drive bunch was modeled as a superposition of two Gaussian distributions: a current spike (0.25 nC, 0.5 µm bunch length) superimposed onto a base structure (1.35 nC, 20 µm bunch length). The base structure center was positioned 3 c/ωp from the window boundary, with the current spike 15 µm ahead. Both components had 10 GeV energy, 20 µm vacuum beam spot sizes, and 50 cm beta functions (corresponding to 16 mm·mrad normalized emittance). A 2.5-meter hydrogen gas region was simulated with the gas jet at 0.6 m and drive bunch focused at 1.0 m. The gas jet region featured a realistic density profile: a 5 mm sin²-shaped upramp from background density (1.3×10^17 cm^-3) to peak density (2×10^17 cm^-3), a 1.5 cm uniform region, and a 500 µm sin²-shaped downramp back to background density. The longitudinal neutral gas density profile and the resulting plasma distribution are shown in Supplementary Fig. 1a and b, respectively.

Second, we extracted the 6D phase space of the drive bunch prior to injection and imported it into an OSIRIS simulation to model downramp injection. We used pre-ionized plasma with the radial distribution extracted from the first QPAD simulation to avoid computationally expensive field convergence calculations and suppress unphysical ionization injection not observed experimentally (no injection signal was observed with gas jet off). This approach improved consistency between the codes’ different treatments of field and particle-pushing algorithms. The simulation captured plasma electron trapping as the drive bunch traversed the downramp and initial acceleration over 2.3 mm to tens of MeV energy.

Finally, we imported both injected and drive bunch 6D phase spaces into a second QPAD simulation to model subsequent meter-scale acceleration. The injected bunch charge was adjusted by rescaling charge-per-macroparticle to match experimental measurements while preserving all other beam quality parameters.

Simulations showed that at the exit of the plasma (see Supplementary Fig. 1), the injected bunch was accelerated to ~18 GeV, with 1% projected energy spread (~0.2% slice energy spread), 2.5 mm·mrad normalized transverse emittance, and a ~1.6 kA peak current, giving a brightness of 5×10^14 A/m²/rad² (green diamond in Fig. 3f).

Data availability
Source data required to reproduce the figures in this study are freely available in the Zenodo repository54 under the dataset identifier (https://doi.org/10.5281/zenodo.17260117).

Code availability
The MATLAB and Python scripts used to generate the figures from the deposited data are available in the Zenodo repository under the dataset identifier (https://doi.org/10.5281/zenodo.17260117). The OSIRIS and QPAD simulation codes are available from the OSIRIS Consortium upon signing a license agreement.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "The authors of this article present and experimentally demonstrate that a plasma wakefield accelerator can simultaneously\nboost the energy and brightness of an electron beam.\nIn my opinion, this study is very interesting and shows promising results that can certainly be useful to the scientific\ncommunity.\nOverall, I find the article to be well written and the results to be well presented, with all measurement and analysis methods\nalso well described in the appropriate sections.\nHere are some observations, mainly related to the plasma source and its characteristics.\nPage 4: When the authors say, \"The high current peaks of the propulsion unit partially ionise the hydrogen gas before the\npropulsion unit reaches the gas jet, creating a variable-density plasma that acts as a thick, passive lens,\" is there a\nsimulation of this effect available, or a direct or indirect measurement of plasma density due to ionisation peaks? I believe\nthis would certainly add to this deduction.\nPage 4: \"The position of the onset of plasma/wake formation varies from shot to shot because of the shot-to-shot variation of\nthe longitudinal phase space profile of the drive bunch\", is there an estimate of this variation? How was it calculated?\nPage 4: \"The second stage is the sharp density downramp at the gas jet exit\", how long is the second stage? How is the\nsharp density downramp achieved? With the peak of the driver beam after the modulations? Or because of the blade shown\nin Figure 1? The latter is not mentioned here in the text.\nPage 4: \"This design eliminates the need for additional plasma-channel guiding or external magnetic elements as both the\nunmatched drive and self-matched injected bunches are self-guided throughout the plasma\", I believe this depends on the\nlength of the second stage, otherwise we cannot evaluate the effect of self-guiding...\nPage 5: \"The analysis revealed that 10 GeV electrons undergo approximately 57 betatron oscillations, while decelerated\nelectrons (9-5 GeV) undergo an additional 3-16 oscillations\", what analysis are we talking about? It might be appropriate to\nreport it or add a link.\nPage 7: \"We note that for injected charges >5 pC, about half of the shots reached an E-TR greater than 2, with a maximum\nmeasured charge of 40 pC. Since the linear trails produced by a longitudinally symmetric pulse group cannot achieve a\ntransformation ratio greater than two, our results show that we are in a non-linear regime\", for the benefit of completeness, I\nsuggest reporting or linking this concept to the application of a model/scaling laws/simulation. The same applies to the end of\nthe same paragraph: \"Thus, for a bunch accelerated to 20 GeV energy, the E-TR is likely to be up to 3. In other words, the\nE-TR estimates are likely to be an underestimate.\"\nPage 11 (section b), plasma source): what are the dimensions and cross-sectional geometry of the section through which the\ngas is sent via the valve? From the text, we only know its length.\nPage 11: \"For the injection experiments, the gas jet operated with 100 psi backing pressure at 5 Hz (with the valve closed) to\nmaintain 4 Torr background pressure\", does “valve” here refer to the \"adjustable needle valve\"? Was a fluid dynamics\nsimulation of this condition performed to confirm the result of 100 psi backing pressure?\nPage 11: What material and shape does the blade have?\nOnce revised, I believe this work is suitable for publication, appropriate for the journal, and very useful for the plasma\naccelerator community.", "reviewer_2": "The manuscript by Chaojie Zhang et al. reports experimental results on beam-driven plasma wakefield acceleration. The\ndriver beam has an energy of 10 GeV, while the accelerated electron beam reaches a maximum energy of 26 GeV; its\nbrightness exceeds that of the drive bunch by more than an order of magnitude. Previously, such results could only be\nachieved using low-gradient acceleration methods. As the authors note, these findings are significant for future x-ray free-\nelectron laser (FEL) sources and particle colliders based on plasma wakefield acceleration (PWFA), where both high\nacceleration energy and superior beam quality are critical requirements. The current study is highly timely, and the\nexperimental descriptions are generally well-written. While the manuscript merits publication, several conclusions lack\nclarity and require further refinement.\n1. A key factor contributing to the high transformer ratio and brightness of the final accelerated electron beam is downramp\ninjection. I note that the particle-in-cell (PIC) results (see Extended Data Fig. 1) derive from a reduced simulation with a 2.5\nm plasma length. However, the downramp injection process is not clearly depicted in this simulation; instead, electrons\nappear to be injected at the initial stage. If this observation is accurate, the horizontal axis is misaligned and should start\nfrom 0.6 m.\n2. It would be beneficial to include a clearer visualization of the injection process here. In particular, the gradient of the\ndensity downramp in the simulation should be explicitly provided.\n3. I am curious as to why the on-axis ion density is lower in Extended Data Fig. 1b.\n4. In the first paragraph of Page 4, the authors state: “The gradual density transition from the higher-density jet to the lower-\ndensity gas region self-matches the injected bunch into the acceleration stage. This design eliminates the need for\nadditional plasma-channel guiding or external magnetic elements as both the unmatched drive and self-matched injected\nbunches are self-guided throughout the plasma.” However, the claim of self-matching is not clearly substantiated. Significant\nelectron loss may occur in this region, with only the matched electrons undergoing acceleration in the third stage.\n5. In the first paragraph of Page 5, the authors assert that “most electrons experience significant deceleration,” which is also\nnot clearly demonstrated. Examining Fig. 1c, most electrons appear to remain around 10 GeV (notably, while the gas jet is\noff and no electrons are injected here, this does not impact the depletion of the drive bunch). The authors should provide a\nclear energy spectrum of the drive bunch spanning up to 10 GeV, rather than the limited energy range presented in Fig. 1b.\n6. The acceleration length is varied by adjusting the drive bunch’s vacuum waist, while the downramp injection position\nremains fixed. As is known, the drive bunch waist affects plasma ionization throughout the entire plasma. This adjustment\nchanges not only the acceleration length but also the injection charge and the wake’s acceleration gradient. Attributing the\nenergy tuning of the accelerated electrons solely to the acceleration length is therefore inaccurate.\n7. To maintain high beam quality while increasing the final accelerated charge, the authors state that the injected bunch is\nshaped. However, the underlying mechanism for this shaping is not described.\nIf the above issues can be reasonably addressed and supplemented, I agree to the publication of the article.", "reviewer_3": "I co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature Communications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career Researchers who co-review manuscripts."}, "author_response": "Response to Reviewers’ Comments\nNCOMMS-25-51241A, C. Zhang et al., “Plasma-Wakefield Accelerator Simultaneously\nBoosts Electron Beam Energy and Brightness”.\nWe thank all the reviewers for their valuable feedback. In the following, we provide a\ndetailed response to their comments.\nThe reviewers’ comments are in black and our responses are in blue.\nReviewer #1\nReviewer Comments: The authors of this article present and experimentally demonstrate that\na plasma wakefield accelerator can simultaneously boost the energy and brightness of an\nelectron beam. In my opinion, this study is very interesting and shows promising results that\ncan certainly be useful to the scientific community.\nOverall, I find the article to be well written and the results to be well presented, with all\nmeasurement and analysis methods also well described in the appropriate sections.\nHere are some observations, mainly related to the plasma source and its characteristics.\nOur response: We thank the reviewer for their positive assessment of the quality of our\npaper and thoughtful comments on the plasma source. We have addressed each point\nbelow.\nReviewer Comment: Page 4: When the authors say, \"The high current peaks of the propulsion\nunit partially ionise the hydrogen gas before the propulsion unit reaches the gas jet, creating a\nvariable-density plasma that acts as a thick, passive lens,\" is there a simulation of this effect\navailable, or a direct or indirect measurement of plasma density due to ionisation peaks? I\nbelieve this would certainly add to this deduction.\nOur Response: We thank the reviewer for this question. Our statement is supported by\nPIC simulation shown in the Extended Data Fig. 1b, which shows that high-current spikes\nin the drive bunch start ionizing the hydrogen gas before the bunch reaches the gas jet.\nThis section of plasma acts as a thick passive lens (length much greater than plasma skin\ndepth), providing additional focusing to the drive bunch.\nTo provide a clear, quantitative illustration of this effect, we have modified Extended\nFigure 1b. In the updated figure, we have superimposed the spot size of the drive bunch\nin plasma (solid blue line) for comparison against its calculated vacuum spot size (dashed\nblack line). This comparison visually confirms the strong focusing effect of the plasma\nprior to the gas jet, validating its function as a plasma lens.\nIn addition, the text in the figure caption has been modified as follows:\n“The beam size curves clearly show that the best focus position of the electron beam (black-\ndashed) moves upstream (blue solid) and the beam is more tightly focused by the partially\nionized plasma (see color bar of the ion density). Consequently, the gas jet and the subsequent\nmeter-scale hydrogen gas region are fully ionized by the tightly focused electron beam.”\nExtended Data Fig. 1b is shown below for your convenience:\nb\nbeam propaga*on direc*on\ngas jet\nReviewer Comment: Page 4: \"The position of the onset of plasma/wake formation varies from\nshot to shot because of the shot-to-shot variation of the longitudinal phase space profile of the\ndrive bunch\", is there an estimate of this variation? How was it calculated?\nOur Response: We thank the reviewer for pointing out this possible confusion. The\nreviewer is correct that the phrase \"variation of the longitudinal phase space profile\" was\nnot clear.\nThe variation we refer to is caused by shot-to-shot amplitude and phase jitter of the RF.\nThis jitter alters the peak current of the fs-scale spikes in the drive bunch exiting the final\nbeam compression stage due to the coherent synchrotron radiation (CSR) effect. A shot\nwith a higher peak current will begin to ionize the hydrogen gas further upstream of the\ngas jet, while a shot with a lower peak current will begin the ionization closer to the jet.\nThis effect thus causes a variation in the onset position of the plasma. We note that this\nmechanism and its effects on plasma formation were also observed and documented in\nour previous work. (see Fig. 2 of Ref. 30).\nTo clarify this for the reader, we have rephrased the sentence in the manuscript to read:\n\"The position of the onset of plasma/wake formation with respect to the gas jet varies from\nshot to shot because of the shot-to-shot variation of the magnitude of the current spike(s) in\nthe drive bunch caused by the amplitude and phase jitter of the RF30.\"\nReviewer Comment: Page 4: \"The second stage is the sharp density downramp at the gas jet\nexit\", how long is the second stage? How is the sharp density downramp achieved? With the\npeak of the driver beam after the modulations? Or because of the blade shown in Figure 1?\nThe latter is not mentioned here in the text.\nOur response: The reviewer is correct that while the blade is shown in Figure 1a, its\nfunction was not adequately described in the main text where the plasma source stages\nwere introduced.\nThe sharp density downramp is created by a movable blade that partially intercepts the\nsupersonic gas flow from the 2-cm slit nozzle. This creates a density transition with a\nscale length of a few hundred micrometers, which constitutes the second stage of the\nplasma source that enables electron injection.\nTo ensure this is clear for readers, we have revised the manuscript to explicitly include\nthis information on page 4. The sentence now reads:\n\"The second stage is a sharp density downramp, with a scale length of a few hundred\nmicrometers, created by a movable blade that intercepts the gas flow at the jet exit (see Fig.\n1a).\"\nReviewer Comment: Page 4: \"This design eliminates the need for additional plasma-channel\nguiding or external magnetic elements as both the unmatched drive and self-matched injected\nbunches are self-guided throughout the plasma\", I believe this depends on the length of the\nsecond stage, otherwise we cannot evaluate the effect of self-guiding...\nOur Response: We thank the reviewer for this question. There seems to be a\nmisunderstanding, which we are happy to clarify.\nThe self-guiding mechanism and the \"second stage\" downramp serve two different\nfunctions and occur on different length scales.\n• Self-Guiding: This effect occurs throughout the entire meter-scale plasma. The\nhigh-current spikes of the drive bunch ionize the hydrogen gas, and the resulting\nwakefield provides a continuous focusing force that guides both the rest of the\ndrive bunch and the injected trailing bunch. This is what eliminates the need for\nexternal guiding elements over the full acceleration length.\n• Second Stage (Downramp): This is a very short region, only a few hundred\nmicrometers long, located at the exit of the 2-cm gas jet. Its role is to inject\nplasma electrons into the wake.\nThe self-guiding is therefore not dependent on the length of the second stage. As long as\nthe drive beam has sufficient energy to excite the wake, the focusing field of the plasma\nions can focus both the drive and the trailing bunch without the need for external/\nadditional focusing. To prevent this confusion for readers, we have revised the sentence\nin the manuscript to be more precise:\n\"This design eliminates the need for additional plasma-channel guiding or external magnetic\nelements, as both the unmatched drive and self-matched injected bunches are self-guided by\nthe wakefields throughout the entire meter-scale plasma.\"\nReviewer Comment: Page 5: \"The analysis revealed that 10 GeV electrons undergo\napproximately 57 betatron oscillations, while decelerated electrons (9-5 GeV) undergo an\nadditional 3-16 oscillations\", what analysis are we talking about? It might be appropriate to\nreport it or add a link.\nOur Response: The analysis, detailed in Ref. [12], deduces the number of betatron\noscillations from the energy-dependent modulations of the beam spot size visible on the\nspectrometer. The principle is that bright spots in the spectrum correspond to electrons\nexiting the plasma with minimal divergence. The condition that adjacent bright spots are\nseparated by a betatron phase of 𝜋 allows us to accurately calculate the total number of\noscillations.\nTo make this clearer in the manuscript, we have rephrased this part and now it reads:\n\"The energy loss spectrum exhibits pronounced beam spot size modulations (blue curve),\narising from varying divergence angles at different betatron oscillation phases upon exiting the\nplasma. Applying the analysis method from Ref. [12] to these modulations revealed that the\n(9-5 GeV) experience an additional 3-16 oscillations.\"\nReviewer Comment: Page 7: \"We note that for injected charges >5 pC, about half of the shots\nreached an E-TR greater than 2, with a maximum measured charge of 40 pC. Since the linear\ntrails produced by a longitudinally symmetric pulse group cannot achieve a transformation\nratio greater than two, our results show that we are in a non-linear regime\", for the benefit of\ncompleteness, I suggest reporting or linking this concept to the application of a model/scaling\nlaws/simulation. The same applies to the end of the same paragraph: \"Thus, for a bunch\naccelerated to 20 GeV energy, the E-TR is likely to be up to 3. In other words, the E-TR\nestimates are likely to be an underestimate.\"\nOur Response: We thank the reviewer for the suggestion to add a more explicit link to\nthis concept. The principle that a finite length, symmetric drive bunch in a linear wake is\nlimited to a transformer ratio of TR≤2 is a foundational result in plasma accelerator\ntheory. Our manuscript already cited a relevant discussion in Ref. [38]. However, to\nimprove completeness, we have now also added a citation to the original work that\nestablished this theorem: K. L. F. Bane et al., IEEE Trans. Nucl. Sci. 32, 3524 (1985), ref.\n39.\nRegarding the second point, our statement that the E-TR is an underestimate is based on\nthe ~3 GeV energy loss of the drive bunch before the witness bunch is injected. The\nprojection of E-TR of ~3 is a direct calculation accounting for this pre-injection energy\nloss (i.e., 20 GeV / [10-3] GeV). To make this clear, we have revised the sentence in the\nmanuscript to read:\n\"Thus, for a bunch accelerated to 20 GeV energy, the E-TR is likely to be up to 3, an estimate\nthat accounts for the ~3 GeV of drive bunch energy lost prior to the injection point.\"\nReviewer Comment: Page 11 (section b), plasma source): what are the dimensions and cross-\nsectional geometry of the section through which the gas is sent via the valve? From the text,\nwe only know its length.\nOur Response: We thank the reviewer for this question. The manuscript already specifies\nthe 2 cm by 2 mm slit exit of the nozzle. To provide further detail, the nozzle is fed by a\n3-mm diameter circular input orifice. This circular geometry transitions internally to a\nslot-shaped throat (2.0 mm by 0.5 mm) which then expands through a diverging section\nto form the final supersonic jet at the slit exit. We have added these details to the\nMethods section to improve clarity, which reads:\n\"The gas jet was created by a custom nozzle that internally transitions from a 3-mm\ndiameter circular input to a slot-shaped throat (2.0 mm by 0.5 mm), and then expands to\na 2-cm-long by 2-mm-wide slit exit.\"\nReviewer Comment: Page 11: \"For the injection experiments, the gas jet operated with 100 psi\nbacking pressure at 5 Hz (with the valve closed) to maintain 4 Torr background pressure\", does\n“valve” here refer to the \"adjustable needle valve\"? Was a fluid dynamics simulation of this\ncondition performed to confirm the result of 100 psi backing pressure?\nOur Response: The \"valve\" mentioned refers to the continuous-flow needle valve (which\nwas closed), not the separate solenoid valve for the pulsed gas jet. The 100 psi is the\nmeasured backing pressure for the gas jet, not a simulated value.\nWe have clarified this in the revised manuscript (method section), which now reads:\n\"For the injection experiments, the adjustable needle valve was closed, and the pulsed gas jet\nwas operated with a backing pressure of 100 psi at 5 Hz, which maintained the background\npressure at 4 Torr.\"\nReviewer Comment: Page 11: What material and shape does the blade have?\nOur Comment: The blade is made of stainless steel and has a \"Γ\" shape to facilitate\nmounting (see Fig. 1a). The active section that intersects the gas jet is approximately 10\nmm by 4 mm with a general thickness of 1 mm. The leading edge that intercepts the gas\nflow is machined to a minimal thickness of 100 µm. We have revised the Methods\nsection to include these key details, which now reads:\n\"A custom-shaped stainless steel blade, with a 10 mm x 4 mm active section and a leading\nedge machined to 100 µm thickness, covered approximately 4 mm of the gas jet on the\ndownstream side to create a density downramp.\"\nReviewer Comment: Once revised, I believe this work is suitable for publication, appropriate\nfor the journal, and very useful for the plasma accelerator community.\nOur Response: We thank the reviewer for their valuable feedback and encouraging\nassessment. We have addressed all comments point-by-point and hope the revised\nmanuscript is now suitable for publication in Nature Communications.\nReviewer #2:\nReviewer Comment: The manuscript by Chaojie Zhang et al. reports experimental results on\nbeam-driven plasma wakefield acceleration. The driver beam has an energy of 10 GeV, while\nthe accelerated electron beam reaches a maximum energy of 26 GeV; its brightness exceeds\nthat of the drive bunch by more than an order of magnitude. Previously, such results could only\nbe achieved using low-gradient acceleration methods. As the authors note, these findings are\nsignificant for future x-ray free-electron laser (FEL) sources and particle colliders based on\nplasma wakefield acceleration (PWFA), where both high acceleration energy and superior\nbeam quality are critical requirements. The current study is highly timely, and the\nexperimental descriptions are generally well-written. While the manuscript merits publication,\nseveral conclusions lack clarity and require further refinement.\nOur Response: We thank the reviewer for their positive assessment of our work's\nsignificance and timeliness. In the following responses, we provide additional details and\nclarifications to address each of the points raised.\nReviewer Comment: 1. A key factor contributing to the high transformer ratio and brightness\nof the final accelerated electron beam is downramp injection. I note that the particle-in-cell\n(PIC) results (see Extended Data Fig. 1) derive from a reduced simulation with a 2.5 m plasma\nlength. However, the downramp injection process is not clearly depicted in this simulation;\ninstead, electrons appear to be injected at the initial stage. If this observation is accurate, the\nhorizontal axis is misaligned and should start from 0.6 m.\nOur Response: We thank the reviewer for identifying that the downramp injection\nprocess was not sufficiently illustrated in the original manuscript. This may have led to a\nmisunderstanding about the simulation, which we are happy to clarify.\nThe results in Extended Data Fig. 1 are from a complete, start-to-end simulation of the\nentire 2.5-meter beam-ionized plasma, not a \"reduced\" one. As detailed in the Methods\n(section g), our simulation is a self-consistent, three-stage process that uses two codes to\naccurately model the distinct physics of each stage (drive bunch focusing (QPAD),\ninjection (OSIRIS), and acceleration (QPAD)), including the plasma lens effect (z<0.6 m)\nthat precedes injection. The horizontal axis in the figure is therefore correct, as it\nrepresents the full interaction distance.\nTo provide greater clarity and to resolve any ambiguity about the injection location, we\nhave now added a new panel (e) to Extended Data Fig. 1. This new panel, shown below\nfor your convenience, explicitly illustrates the downramp injection process in stage two\n(the gas jet region). Then the injected electrons are imported into a second QPAD\nsimulation to model the subsequent meter-scale acceleration, which is why in Extended\nData Fig. 1c we label the horizontal axis as acceleration length (after injection) instead of\nthe absolute position.\ne\ne, Snapshots from the OSIRIS simulation showing the charge density of plasma electrons during\nthe downramp injection process. The frames illustrate the trapping of plasma electrons into a\ndistinct bunch at the back of the wake as the driver traverses the 500-µm-long sin2-shape\ndensity downramp, which starts at 𝑧 ≈ 0.62 m and drops from 1.5 to 1.0 𝑛 , where 𝑛 ≈\n! !\n1.3×10\"# cm-3.\nWe believe this explanation, combined with the new visualization in panel (e), now clarify\nthe simulation method and results.\nReviewer Comment: 2. It would be beneficial to include a clearer visualization of the injection\nprocess here. In particular, the gradient of the density downramp in the simulation should be\nexplicitly provided.\nOur Response: As requested by the reviewer, we have added a clear visualization of the\ninjection process (a new panel (e) in Extended Data Fig. 1). The figure caption has been\nupdated to state that the injection occurs over a 500-µm-long sin²-shaped density\ndownramp that drops from 1.5 to 1.0 𝑛 , where 𝑛 ≈ 1.3×10\"# cm-3 is the density of the\n! !\nacceleration stage.\nReviewer Comment: 3. I am curious as to why the on-axis ion density is lower in Extended\nData Fig. 1b.\nOur Response: The on-axis ion density is lower because the simulation models the drive\nbunch with a Gaussian transverse profile, which has zero transverse electric field on-axis\nto cause ionization. We have added this to the caption of Extended Data Fig. 1b to\nclarify.\nReviewer Comment: 4. In the first paragraph of Page 4, the authors state: “The gradual density\ntransition from the higher-density jet to the lower-density gas region self-matches the injected\nbunch into the acceleration stage³⁵. This design eliminates the need for additional plasma-\nchannel guiding or external magnetic elements as both the unmatched drive and self-matched\ninjected bunches are self-guided throughout the plasma.” However, the claim of self-matching\nis not clearly substantiated. Significant electron loss may occur in this region, with only the\nmatched electrons undergoing acceleration in the third stage.\nOur Response: We thank the reviewer for this insightful question, which allows us to\nclarify the evidence supporting our self-matching claim.\nOur primary evidence is the lack of betatron oscillations in the injected bunch's dispersed\nenergy spectrum. Unlike the drive bunch (Fig. 1c), which shows strong modulations\ncharacteristic of a mismatched beam, the injected bunch's spectrum is smooth (Fig. 2a,\n)1−pωc(r\nz=0.62 m - 118 µm z=0.62 m (injection starts) z=0.62 m + 118 µm z=0.62 m + 236 µm z=0.62 m + 354 µm (injection ends)\n3\n2\n1\n0\n2 4 6 8 10 12 2 4 6 8 10 12 2 4 6 8 10 12 2 4 6 8 10 12 2 4 6 8 10 12\nξ(cωp−1) ξ(cωp−1) ξ(cωp−1) ξ(cωp−1) ξ(cωp−1)\nytisned\negrahC\n)2−c2pωe(\n0 0\ninjected bunch driver -1 -5\n-2 -10\n-3\n-4 -15\n-5 -20\nFig. 3a), indicating that it is matched to the wake. This is further supported by the final\nemittance, which was measured to be as low as 2 µm. This result is consistent with our\nsimulations (Extended Data Fig. 1c), and the absence of catastrophic emittance growth\nconfirms that the injected bunch is matched.\nRegarding the concern about electron loss, our new visualization of the injection process\n(Extended Data Fig. 1e) shows that once electrons are trapped, they stay phase-locked to\nthe drive bunch and do not get lost during the transition from the injection to the\nacceleration stage because of the seamless transition.\nTo make this clearer for the reader, we have added a sentence to the manuscript on Page\n4 to clarify this point. It now reads:\n\"The gradual density transition from the higher-density jet to the lower-density gas region self-\nmatches the injected bunch into the acceleration stage³⁵, as evidenced by the lack of\ncharacteristic betatron oscillation features in the bunch's energy spectrum, which will be\ndiscussed later.\"\nReviewer Comment: 5. In the first paragraph of Page 5, the authors assert that “most\nelectrons experience significant deceleration,” which is also not clearly demonstrated.\nExamining Fig. 1c, most electrons appear to remain around 10 GeV (notably, while the gas jet\nis off and no electrons are injected here, this does not impact the depletion of the drive bunch).\nThe authors should provide a clear energy spectrum of the drive bunch spanning up to 10 GeV,\nrather than the limited energy range presented in Fig. 1b.\nOur Response: The two figures, 1b and 1c, show measurements from separate shots with\ndifferent spectrometer settings, which were necessary to capture the broad energy range\nof the decelerated beam. The electrons that remain at 10 GeV are part of the drive bunch\nbut stay ahead of the beam-induced ionization front and thus propagate in neutral gas\nwithout interacting with the plasma. As we have shown in previous work, this non-\nparticipating charge can be up to 30% of the total [Ref. 30]. Therefore, our statement\nthat \"most electrons experience significant deceleration\" refers specifically to the\ninteracting portion of the bunch, which is decelerated to energies below 2 GeV. To\nprevent this confusion for readers, we have revised the relevant sentence in the\nmanuscript to clarify this point. It now reads:\n\"While some charge remains at 10 GeV, consisting of electrons ahead of the beam-induced\nionization front (previously quantified to be up to 30% of the total charge [Ref. 30]), the\nmajority of the bunch's interacting electrons experience significant deceleration.\"\nReviewer Comment: 6. The acceleration length is varied by adjusting the drive bunch’s vacuum\nwaist, while the downramp injection position remains fixed. As is known, the drive bunch waist\naffects plasma ionization throughout the entire plasma. This adjustment changes not only the\nacceleration length but also the injection charge and the wake’s acceleration gradient.\nAttributing the energy tuning of the accelerated electrons solely to the acceleration length is\ntherefore inaccurate.\nOur Response: We thank the reviewer for this excellent point. The method we used to\nvary the acceleration length was to tune the final focusing quadrupoles while maintaining\nthe drive bunch's beta function. This is analogous to shifting the focus of a laser by\nmoving an optical lens, which effectively shifts the entire plasma interaction region\nlongitudinally without altering the plasma conditions.\nWhile we agree that small variations in the wakefield could still occur, our analysis shows\nthese were secondary effects. We found that the injected charge remained relatively\nstable as we varied the waist position, and the measured energy gain exhibits a linear\ntrend with the acceleration length. The plot below summarizes data from several datasets\nto show the energy gain as a function of various drive bunch waist locations (acceleration\nlength); the blue dots show the energy gain for each individual shot, the orange points\nshow the mean and standard deviation for each waist location, and the green line is a\nlinear fit to the data.\n35\n30\n25\n20\n15\n10\n100 120 140 160 180 200\nAcceleration length (cm)\nDespite of the shot-to-shot variations, the linear correlation confirms that the change in\ninteraction length was the primary contribution to the energy tunability. We agree with\nthe reviewer that our original wording was probably too strong and have revised the\nmanuscript to improve the clarity. The relevant sentence now reads:\n\"...When we shifted the drive bunch vacuum waist by one meter in four equal 25 cm steps\nbeyond the gas jet, the final energy of the injected bunch increased linearly from ~13 GeV to\n~26 GeV. While the wakefield strength may have varied with this change, the linear trend of\nenergy gain with acceleration length indicates that the interaction length was the primary\nfactor determining the final energy, corresponding to an effective average accelerating\ngradient of 13 GeV/m.\"\nReviewer Comment: 7. To maintain high beam quality while increasing the final\naccelerated charge, the authors state that the injected bunch is shaped. However, the\nunderlying mechanism for this shaping is not described.\nOur Response: We thank the reviewer for their question. The reference to \"shaped\nbunches\" [43] was intended as a forward-look to future high-charge applications and not\na description of our current experiment.\nOur downramp injection method does, however, offer a promising path to creating such\nshaped bunches. As shown in prior work [35], a mapping exists between the initial\npositions of the plasma electrons in the downramp and their final locations within the\n)VeG(\nniag\nygrenE\nData\nMean standard deviation\n'\nLinear fit with < interval\n'\nGradient: 12.9±1.4 GeV/m\ninjected bunch once they are trapped. Consequently, the injected bunch's current profile\ncan be controlled by tailoring the downramp's density profile, as demonstrated in our\nown previous simulation work [Zhang et al., PRAB 22, 111301 (2019), now included as\nref. 45]. While we did not actively pursue this in the current experiment, it is a promising\ndirection for future research.\nTo clarify this for the reader, we have added a sentence to the second last paragraph on\npage 8, which now reads:\n\"...While our current experiments show a maximum injected charge of tens of pC,\ntheoretical beam loading studies using shaped bunches indicate the potential to load\nseveral hundred pC with preservation of beam quality44. Such a shaped bunch can, in\nprinciple, be produced via downramp injection by tailoring the density profile of the\nramp35, 45.\"\nReviewer Comment: If the above issues can be reasonably addressed and supplemented,\nI agree to the publication of the article.\nOur Response: We thank the reviewer again for their constructive feedback and positive\nassessment. We have addressed all of the points raised and hope that the revised\nmanuscript is now suitable for publication.\nReviewer #3:\nI co-reviewed this manuscript with one of the reviewers who provided the listed reports.\nThis is part of the Nature Communications initiative to facilitate training in peer review\nand to provide appropriate recognition for Early Career Researchers who co-review\nmanuscripts.\nOur Response: We thank the reviewer for their contribution and appreciate this co-\nreview initiative."}, {"round": 2, "reviewer_comments": {"reviewer_1": "The authors present and experimentally demonstrate that a plasma wakefield accelerator can simultaneously enhance both\nthe energy and the brightness of an electron beam. The study is, in my view, of significant interest and provides promising\nresults that are of clear relevance to the scientific community.\nThe manuscript is generally well written, with the results presented in a clear and structured manner. The experimental\nmethods and data analysis procedures are adequately described in the appropriate sections, allowing the reader to properly\nassess the robustness of the conclusions. Importantly, the authors have taken into account the reviewers’ comments and\nimplemented the requested revisions, which have further strengthened the manuscript and increased its overall value.\nIn conclusion, I consider this work to be suitable for publication, appropriate for the scope of the journal, and of notable utility\nfor the plasma accelerator community.", "reviewer_2": "I am very pleased to see that the authors have substantially improved their manuscript in response to the\nreferees’comments. The current results represent an important step forward for PWFA-based accelerators and their potential\napplications, including FELs. I fully support its publication in Nature Communications.", "reviewer_3": "I co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature\nCommunications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career\nResearchers who co-review manuscripts."}, "author_response": ""}]

Decision letter