Bright electron bunches from a plasma-wakefield accelerator with a steep density down-ramp

Domain: neuroscience
Published: 2026-02-11
Editorial outcome: minor_revision

Abstract
High-brightness electron bunches drive fundamental research in particle physics and photon science. Key to achieving a high brightness is to have a low transverse emittance, which ensures that the bunch can be tightly focussed. In radio frequency accelerators a low initial emittance can be rapidly degraded due to space charge forces, which are greatly diminished once the electron bunch attains a relativistic velocity. A plasma accelerator can maintain orders-of-magnitude higher accelerating fields than radio frequency accelerators, while multiple techniques exist to create a low emittance electron bunch directly inside the plasma accelerator structure. Plasma accelerators therefore offer a possibility to create high-brightness bunches in wakefields driven even by low-quality drive bunches. Here we demonstrate the injection and gigavolt-per-metre acceleration of electron bunches with mm-mrad normalised emittance, O(10 pC/MeV) spectral density and per-cent-level energy spread, all with excellent reproducibility.

Introduction
Radio frequency particle accelerators based on metallic cavities drive fundamental research in particle physics and photon science, but the rate at which they can accelerate particles is limited to ~100 MeV m−1 by the onset of electrical breakdown inside the accelerating structure. As a result, the accelerators for free-electron lasers (FELs) are several hundreds of metres long, and particle colliders reach tens of kilometres in length. An emerging and significantly more compact alternative is the plasma-based accelerator (PBA), which has no such limit as it is already made of broken-down material. In a PBA, an intense laser pulse or charged particle beam driver propagates through a plasma and expels electrons from its vicinity via its ponderomotive force or space-charge field, respectively1,2. The charge density wave left in its wake, the plasma wakefield, is used to rapidly accelerate a trailing bunch at rates of order (1–100 GV m−1) in most experiments to date. Major results in beam-driven plasma acceleration (termed plasma wakefield acceleration or PWFA) include multi-GeV energy gains with few-per-cent energy spreads3,4 and energy-spread preservation with >40% energy-transfer-efficiency5. The energy doubling of high-energy electrons has also been demonstrated, where the rear of a bunch was accelerated in the wakefield driven by the front of the bunch6. The wakefield has linear transverse focusing fields, enabling the rapid acceleration of an electron bunch without increasing its normalised emittance ϵn7. Low ϵn bunches are desirable since the property is inversely proportional to the 6D beam brightness B6D=I/(ϵn,x ϵn,y σE) where I is the beam current and σE the energy spread. A high B6D is required to drive brilliant FELs, while a large B4D=Q/(ϵn,x ϵn,y), where Q is the beam charge, is a key ingredient in the luminosity of colliders.

The large accelerating field of a plasma wakefield can also be exploited to create a plasma injector, in which electrons are rapidly accelerated from rest to relativistic energies. This greatly reduces the effects of space-charge-driven emittance growth, which is a major limiting factor for the injectors for high-current RF accelerators. A PWFA could, therefore, provide lower emittance electron bunches than is possible with radio frequency injectors. The generation of high brightness bunches in plasma accelerators is also central to schemes to drive compact hard-x-ray FELs with saturation lengths of order 10 m8. Several schemes have been proposed to inject ultra-low-emittance, short-pulse, high-brightness electron bunches into a PWFA, either from ionisation processes within the wakefield9–14, or via density-downramp injection (DDRI)15–24. In both sets of schemes above, there are advantages to electron beam rather than laser drivers, since radiofrequency electron linacs are already capable of accelerating tens of thousands of bunches per second with high efficiency25, and extremely intense laser drivers preclude the possibility of controlled ionisation within the wakefield13 or the production of truly customisable plasma density profiles.

Here, we focus on the DDRI scheme. In DDRI, a downramp is created in the longitudinal plasma density profile. Downramps can be generated simply and flexibly in a PWFA, for example, by using a moderate-intensity laser pulse orthogonal to the driver bunch to ionise additional gas species22,23,26. Since the wake wavelength increases as the density ne decreases, similar to the plasma wavelength λp ∝ 1/\sqrt{ne}, the rear of the wakefield is found progressively further behind the driver as a driver bunch travels through a downramp. Therefore its velocity drops significantly below that of the driver (~c), allowing background plasma electrons with high longitudinal velocities to be trapped in the wakefield and subsequently accelerated. Although the injected electrons initially receive a large transverse impulse from the drive beam, as they approach the back of the wake they experience a magnetic field from the radial current of the plasma electrons that form the wake structure. This generates a defocussing force, significantly reducing the transverse momentum and emittance of the injected electrons27,28. It has been shown in simulations that DDRI can produce bunches with ϵn < 100 nm21,27–29, which is comparable to the very best conventional FEL driver linacs today30.

To date, experimental work on injection in PWFAs (e.g. by DDRI) has either shown high spectral density (dQ/dE) bunches with relatively high ϵn ~ 10 mm-mrad23, or few-mm-mrad emittance bunches with dQ/dE < 1 pC MeV−114. In this work, we experimentally demonstrate the injection into a PWFA of 1.2 mm-mrad normalised emittance, 1.3% energy spread (σE) bunches with 14 pC MeV−1 spectral density. The average 3D brightness B3D=⟨dQ/dE⟩/ϵn,x was 11.3 pC/MeV/mm-mrad. This represents a significant step forwards in the quality of plasma-generated electron bunches. We achieved this using the DDRI mechanism with an especially high-density injection region with steep density gradients, far beyond what has been considered previously. We describe the physics of this scheme with particle-in-cell (PIC) simulations. Full 3D PIC simulations recreating the experimental conditions as faithfully as possible suggest the normalised emittance of the injected beam in our setup could become as low as 0.14 × 0.55 mm-mrad.

Results
Experimental description
The experiment, depicted in Fig. 1a, was performed at the FLASH Forward facility31. A ~50 mm long plasma, consisting mostly of Ar+ and Ar neutrals, was created by the long-focal-length longitudinal laser pulse (see ‘Methods’ section). A transverse laser pulse was used to ionise additional gas at z = 20 mm after the capillary. As a result, the plasma density profile shown in Fig. 1c exhibited a large density spike, the edge of which was used for DDRI22,23,26. The longitudinal laser underwent significant ionisation defocusing while producing the plasma32, leading to the decaying density as a function of propagation distance. Only a small fraction of atoms were ionised for much of the accelerator length, although ne(z > zh) ≈ 2 × 1016 cm−3 was sufficiently high to accelerate injected bunches to relativistic energies. The transverse laser pulse did not undergo significant ionisation defocussing.

The driving electron bunch was produced by the FLASH linac33. Its charge was (304 ± 2) pC and its mean energy was 689 MeV, with a root-mean-square (rms) energy spread of 5 MeV and a peak spectral density dQ/dE = 47 pC MeV−1. Its current profile was measured using an X-band transverse deflecting structure (TDS) downstream of the setup34,35. The current profile that maximised injected charge is shown in Fig. 1b with a peak current Ipk = (1.9 ± 0.2) kA and a (96 ± 6) fs rms duration. All uncertainties here are the standard deviation. It was focused into the plasma using the final-focusing quadrupoles (FFQs) to drive the plasma wakefield. Both drive and injected bunches were characterised with one of two imaging spectrometers: a broadband electron spectrometer (ESPEC) used for energy and divergence measurements, and a high-resolution spectrometer (HRSPEC) used for emittance measurements. The imaging was performed using a quadrupole triplet downstream of the capillary as shown in Fig. 1a. An example object-plane (zobj) scan of the non-interacted driver performed with the downstream quadrupoles on the HRSPEC, done to measure its emittance, is shown in Fig. 1d (see ‘Methods’). The normalised emittance ϵn,x = \sqrt{⟨x2⟩⟨px2⟩ − ⟨xpx⟩2}, where x and px are the position and transverse momentum, was (21.7 ± 0.4) mm-mrad. ϵn,y could not be measured because this was the dipole dispersion direction.

Optimisation of the injected bunch
After performing the spatio-temporal overlap procedure detailed in the ‘Methods’ section, the injected bunch was first characterised on the ESPEC with the imaging energy set to 30 MeV. Electrons were only injected when the transverse laser was present, as also found previously23. The input parameters were optimised to maximise the injected charge Qi and the spectral density dQi/dE, which were strongly correlated throughout parameter scans. The four main controls over Qi and their effects are detailed in Fig. 2, where each variable was changed independently from an approximate global optimum.

In Fig. 2a, the final-focusing-quadrupole (FFQ) field strengths in the x and y directions were varied. Due to the large β-functions in these quadrupoles changes in their strength mostly varied the driver waist position, while changing the β-functions at focus only at the 5% level. Strength changes Δk of 0.2–0.5% significantly altered Qi, demonstrating that precise control over the bunch focusing was necessary to optimise the interaction. Simple calculations suggest that a 1% change in kx, ky corresponded to focal position shifts of approximately 1 cm and 2 cm, respectively (c.f. the density profile in Fig. 1c).

Figure 2b shows the dependence of Qi on the y offset of the transverse laser. Qi was strongly reduced for offsets larger than ~25 μm, around half a spot width, falling to almost zero for 50 μm offsets, close to the plasma skin depth 1/kp = 42 μm around the density spike. Hence, this injection technique is relatively insensitive to the pointing jitter of most modern laser systems. The pointing jitter of the injection laser spot was typically 5 μm rms in each axis. While the centroid jitter of the longitudinal laser was 30–40 μm, its large spot size minimised the impact of these fluctuations.

Plotted in Fig. 2c is Qi as a function of the rms driver duration τrms, which was varied by altering the linac compression settings. We plot τrms rather than the peak current since it was monitored non-invasively on every shot by a calibrated bunch compression monitor. Qi drops to very low levels by τrms = 140 fs. While bunches of such long length were not characterised with the TDS, we can simply estimate that this corresponds to Ipk = 1.3 kA assuming driver charge Qd ∝ Ipk τrms. Electrons can only be trapped in the wakefield if their forwards velocity, which they obtain from their interaction with the high-current driver, exceeds the velocity of the back of the wakefield in the downramp. Given the extremely steep density ramps used, it is likely that 1.3 kA is close to the minimum driver current required in practice for DDRI. Furthermore, by fitting a power-law of the form y = A(x − b)n to the data with y = Qi and x = 1/τrms we retrieved n = 0.81 ± 0.05. The suggested close-to-linear scaling of injected charge with drive current is promising for the extension of this scheme to higher drive currents, as the increased driver current will be compensated almost one-to-one by increased injected bunch charge.

A final, powerful control over the injected bunch properties was the delay Δt between the arrival of the ionising laser beams and the driver bunch, since the timing determines the height and shape of the density spike, as discussed in the next section. This was adjusted by changing the laser trigger timing in steps of 18.46 ns. Qi(Δt), shown in Fig. 2d, increased from a few pC at Δt = 10–20 ps to a peak of 27 pC at Δt = 18.46 ns before dropping to approximately zero over the following 37 ns. This strongly suggests that the temporal evolution of the plasma density spike affected injection, and that this process can be optimised to produce significantly higher-charge bunches.

Optimal ramp height and length for DDRI
To understand how the laser-to-electron-bunch delay affected injection, we first consider that a plasma generated by a Gaussian laser beam is hottest in the centre, and the resulting pressure gradient drives hot plasma outwards. Initially, this decreases the height of a plasma spike. As the flow of hot plasma is supersonic, eventually a Sedov-Taylor-like shock wave with a steep, short downramp will form36,37, which can also trigger DDRI38,39. Since the shock wave is unsupported its amplitude will decrease over time and eventually injection will be impossible. Imprecise knowledge of the initial conditions in this experiment precluded the use of magneto-hydrodynamics simulations, but insight into how this general scenario affects injection was gained from a set of lab-frame quasi-3D FBPIC simulations. The purpose of this simulation set was to determine the effects of the plasma spike’s height and ramp length on the injected bunch charge. The simulations were intentionally simplified to isolate the injection physics from the experimental complexities and to provide a basic physical understanding of the behaviour recorded in Fig. 2d.

The resolution of the simulations was dz = 0.25 μm, dr = 0.4 μm with 2 azimuthal modes. There were 2, 2 and 8 particles per cell in the r, z and θ directions, except in a small longitudinal region around the injection spike, where 4, 4 and 8 particles per cell were used. The box radius was 106.3 μm and its length was 354 μm. A bi-Gaussian driver bunch was used with 304 pC charge, Ipk = 1.9 kA, ϵn = 20 mm-mrad and σr = 16 μm. It consisted of 300,000 macroparticles. The plasma was a 9 mm flat-top of density n0 = 2 × 1016 cm−3, with 0.5 mm linear ramps either side. At the centre, a density spike was added with a flat-top length of 40 μm, peak density hr n0, and with linear ramps of length Lr either side (sketched in Fig. 3). The density varied only longitudinally, and not with radius or angle. A 2D scan of Lr and hr was performed. The experimental Δt = 0 plasma spike [Fig. 1c] is well approximated by hr = 60, Lr = 30 μm (case I). Similar results were obtained for smaller scans with flat-top lengths of 25, 10 and 2.5 μm (1/kp = 4.8 μm for hr = 60).

Figure 3a shows that the most charge was injected for hr = 8–12, confounding the naive expectation that steeper ramps inject more charge via a slower wakefield phase velocity in the downramp. The explanation lies in Fig. 3c, which shows, at a time shortly before the arrival of the drive bunch, the longitudinal locations of the electrons that get injected, along with the density downramps in case I, and at optimal parameters Lr = 45 μm, hr = 12 (case II). For lower hr (case II) electrons are trapped at a moderate rate throughout the downramp. For large hr (case I), a strong wakefield cannot be driven for most of the downramp because ne > nb, the bunch density, so trapping only happens close to the end of the ramp, although the higher density gradient results in rapid charge injection. In both cases, longer ramps increase the distance over which charge is trapped, increasing the injected charge. This is an unusual parameter regime, with previous works using hr = 1–222,26 or with Lr > 1/kp, for which injected charge decreases with Lr21. However, it is clearly advantageous for charge injection to have plasma-spike densities up to the drive-bunch density.

Density downramps with peak densities n0 ~ nb maximise both the injected charge and B3D, as shown in Fig. 3b, since the emittance varied little across this scan (ϵn,x = 0.4–0.5 mm-mrad for Qi > 20 pC). This is a surprising result, since in radio frequency linac injectors the emittance of the bunch increases with charge, or at least current, due to space charge forces after its creation.

The hydrodynamically expanding density spike in the experiment samples a space like that in Fig. 3a. As the initially high-density peak decreases in amplitude [moving downwards from point I in Fig. 3a], the injected charge increases. At later times, as a shock front forms, the ramp length decreases (moving left or left and up) and the injected charge drops. The high charge per MeV injection resulting from these optimised density transitions, with high peak downramp densities equal to the bunch density, was a key factor in producing bright injected bunches in this experiment.

Stability, emittance and brightness of the injected bunch
After the experimental optimisation, at the Δt = 18.46 ns data-point from Fig. 2d, a 1000-shot dataset was acquired in nominally identical conditions at 2 Hz. The injected bunch spectra, shown in Fig. 4a, were highly reproducible with a low mean σE = 1.3 ± 0.1% FWHM, where the uncertainty is the error on the mean. The peak energies (where dQi/dE is maximal) were tightly clustered at (30 ± 2) MeV and the mean Qi = (19 ± 7) pC (errors are standard deviations). The mean peak spectral density was ⟨dQi/dE⟩ = (14 ± 6) pC MeV−1, and a histogram of all shots is shown in Fig. 4b. Its maximum value was 36 pC MeV−1, close to that of the driver. The combination of this injection mechanism and a stable driver created a notably stable and low-energy-spread plasma-based injector.

To measure the emittance of a bunch one must obtain its width over a range of object planes, as was done for the driver. This was performed for the injected bunch on the ESPEC, shown in Fig. 4c. While providing a good divergence measurement σx0 = (0.32 ± 0.01) mrad, it was found that low resolution combined with chromatic imaging led to a significant overestimation of the minimum bunch width σx,min and therefore ϵn,x. Instead σx,min was measured on the HRSPEC, and ϵn was calculated in the absence of the correlation term i.e. ⟨ϵn,x⟩ = γβ⟨σx,min⟩⟨σx0⟩. Bunch jitters over the long distance to the HRSPEC combined with the small field-of-view of the diagnostic made it impractical to perform an object-plane scan. Nevertheless, 106 measurements of σx,min were made. An example image is shown in Fig. 4d. Both the bunch tilt and defocussing from chromatic effects (e.g. beyond 29.5 MeV) meant that an energy slicer rather than the projection gave a fair measurement of σx,min. Details of the σx,min calculation from the HRSPEC images are given in the ‘Methods’ section. A histogram of measured σx,min is shown in Fig. 4d. The mean value with its standard error was ⟨σx,min⟩ = (66 ± 3) µm, which was significantly above the resolution limit of 2.5 μm. Combining this with the divergence ⟨ϵn,x⟩ = (1.2 ± 0.1) mm-mrad was found. Using the mode σx,min = 43 µm, ϵn,x = 0.8 mm-mrad. The 3D brightness B3D = ⟨dQ i/dE⟩/⟨ϵn,x⟩ = 11.3 pC/MeV/mm-mrad. Note that this value is constructed only from averaged values, with the exception of the injected bunch divergence, which was determined from a fit to a scan including ~600 data points. In this experiment the driver B3D,d = 2.4 pC/MeV/mm-mrad.

6D brightness estimate from particle-in-cell simulations
In the experiment, it was not possible to measure ϵn,y or the current profile of the injected bunch, so to estimate 6D brightness (B6D) PIC simulations were required. Figure 5 shows the longitudinal phase space, current profile and slice emittances of the injected bunch from the end of a lab-frame, fully 3D WarpX simulation40, which used cell sizes dx = dy = 0.39 μm, dz = 0.14 μm, a box size of 200 × 200 × 400 μm and 1 and 4 particles per cell in the background plasma and plasma spike regions, respectively. The longitudinal plasma density was that from Fig. 1c, which was our best estimate of the plasma density from the experiment, as described in the Methods section. In y the spike density profile was that from Fig. 1c inset (i.e. at Δt ≈ 0), and in x, the transverse laser propagation direction, it extended infinitely. The driver current profile from Fig. 1b) was used along with a transverse emittance and bunch width in both directions of 20 mm-mrad and 16.5 μm (σ for a Gaussian bunch with the measured emittance and beta function). Figure 5a shows that the injected bunch, consisting of 1.3 × 105 macroparticles, was accelerated to a peak E = 28.6 MeV, consistent with the experiment. The injected charge was 19.3 pC and the peak dQi/dE = 5.7 pC/MeV. The slice emittances are asymmetric, as are the projected ϵn,x = 0.14 mm-mrad and ϵn,y = 0.55 mm-mrad, suggesting that the curvature of the plasma spike profile in y caused a larger emittance. This could be partially mitigated by using a larger transverse laser spot or an astigmatic focus41. The simulated B3D = 42 pC/MeV/mm-mrad, calculated using the projected emittances, was 3.7 times the experimental value, which used a conservative measurement of ϵn,x. The injected bunch peak current was 0.19 kA, resulting in B6D = 1.3 kA MeV−1 mm−2 mrad−2.

Methods
Plasma profile
The plasma was created in a 50 mm long, 1.5 mm diameter open-ended capillary, which was continuously filled from a 46 mbar buffer containing 97% Ar and 3% H2 by volume. The H2 dopant was used as part of an off-line line-broadening-based density diagnostic. The gas density profile (Fig. 1c) was estimated using a benchmarked ANSYS Fluent model. The plasma was laser-ionised with (32.6 ± 0.2) fs full-width-half-maximum (FWHM) duration pulses from a Ti:Sapph system. The longitudinal laser pulse, which ionised the bulk of the plasma, had a FWHM spot size of (430 ± 10) μm × (350 ± 10) μm and a peak intensity of (3.0 ± 0.1) × 1014 W cm−2. The transverse laser was focussed to a spot size of (48 ± 1) μm × (43 ± 1) μm FWHM and intensity of (5.2 ± 0.1) × 1015 W cm-2 (all uncertainties here are the standard deviation). The plasma electron density (ne) profile in Fig. 1c was produced by an FBPIC simulation45,46 employing an ADK ionisation model47, using the simulated gas profile and measured laser parameters.

Drive bunch emittance measurement
The emittance of the drive bunch was found by measuring its rms width σx throughout a scan of the downstream quadrupole triplet’s object plane zobj. The emittance was retrieved from the fit to σx(zobj) = ϵn/γβ \sqrt{β* + (zobj − z0)2/β*}, where β and γ take their usual definitions from special relativity, z0 is the virtual source point and β* is the beta-function at z0. An example of this method is shown in Fig. 1d.

Electron and laser beam spatio-temporal overlap
The longitudinal laser was overlapped spatially with the electron bunch using two optical-transmission-radiation screens up- and downstream of the capillary, imaged onto CMOS cameras. The upstream camera also imaged the focal spot of the transverse (injection) laser, which was translated to the same height as the electron beam. The laser and electron beam temporal overlap was found to within 0.5 ps using the plasma afterglow light technique48, whereby the interaction of an electron bunch with a pre-formed plasma produces strong light emission. Both laser beams were derived from the same pulse, and their synchronisation with the electron bunch was maintained with <0.1 ps jitter using the system described in ref. 49. Changes in the amplitude of the plasma glow signal with position of both laser beams provided an additional check on the spatial overlap.

Calculation of the minimum bunch width from the HRSPEC images of the injected bunch
The chief difficulties in determining σx,min from these images were the presence of hot pixels (i.e. single or small clusters of pixels with high counts, which can be formed via the detection of a high-energy bremsstrahlung photon, for example) and the low signal-to-noise ratio. To stop the fitting algorithm from erroneously identifying a hot pixel as a narrow beam slice, the hot pixels were removed with a 3 × 3 median filter. It could then be the case that the remaining low-level noise, or part of it, could be identified by the algorithm as part of the bunch. To remove this possibility, the image was first binned into 11-pixel-wide slices along the energy axis to increase the signal-to-noise ratio. Then, a region of the binned image far from the signal was used to find the maximum per-pixel noise counts Cn, and bins with maximum values < Nmin Cn were rejected from the analysis. This ensured a high level of confidence that the remaining image slices contained a high signal level attributable to the injected electron bunch. In practice Nmin = 2.5 provided a good balance between a low level of image rejection and eliminating erroneous fitting to noise. Gaussians were fitted to the remaining slices, and the smallest width was selected as the best estimate of the true bunch width. A manual check was performed to ensure that the fit was to a slice containing part of the injected electron bunch, giving further confidence in the image processing and fitting algorithm. While the median filter kernel size, bin width and Nmin were free parameters, varying each of them by a factor of two changed the mean measured emittance by < 10%. The median filter, binning and the elimination of low-signal slices all act to increase the retrieved electron bunch width, meaning that our stated brightness represents a conservative measurement.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "Referee report on Brightness-Boosted Electron Bunches froma a Plasma Accelerator, by. J.C. Wood et al.\nThe manuscript deals with experimental results, about the generation of high brightness electron beams via PWFA driven by\na LINAC, with “witness” (accelerated) electron beams obtained by density downramp injections. The results reported in the\nmanuscript are interesting for the plasma acceleration community, the discussed physical processes are generally sound\nand the manuscript is well written. As there are, however, some specific points to be clarified or where the manuscript can be\nimproved, the Referee suggests Authors to revise their manuscript accordingly to the items below.\nQuestion1: Pg4, left column, after “...the plasma was a 9 mm flat-top ..’.\nWhy Authors used a flat-top density profile for their simulations although the plasma profile (by their simulations) is\ndecreasing [see Fig 1c] ? The same question can be raised for the WarpX simulation shown after. Can Authors comment on\nthis?\nQuestion2: As the energy of the accelerated beam is quite low, is the value of measured emittance mostly getting\ncontributions from the injection/acceleration or from the downramp?\nAuthors did q3D and 3D simulations but they didn’t report on the evolution of the phase longitudinal and transverse space\ncuts along the beams propagation. This would definitely help in understanding how the energy spread compression is made\n(the superposition with the longitudinal on-axis gradient will help) and how the x,y emittances vary with the longitudinal\nposition. It’s also important to distinguish between the B_3D at the end of the acceleration and that after the downramp, in\norder to have a view on the room they have for minimizing the emittance growth in the downramp. The Referee suggests to\nadd all or at least some of the relevant information reported above.\nMinor changes:\nThe title looks somewhat misleading. The world “boosted” recalls a (large) increase of a quantity which is already existing.\nFor example, we can safely name ‘brightness-boosted bunches’ any bunch having a certain brightness before the\nacceleration stage and having higher brightness at its end. In the case of the present manuscript title, Authors claim they\ncreated ‘brightness-boosted’ bunches as the final brightness of those bunches exceeds that of the wakefield driver. My\nsuggestion is to change the title by referring to high brightness electron beams. The last-last sentence of the Abstract should\nbe changed accordingly.\n1. Pg3, left column. “.In Fig. 2(a) the final-focussing-quadrupole (FFQ) field strengths k in the x and y directions, which almost\nexclusively determined the driver waist position in z while preserving its spot size, were varied”\nAuthors should add information about the longitudinal variation of the driver beam focus once the field strength is changed.\nThis, along with the information of the beam beta function, will give direct information on how sensitive is the PWFA process\non the drive final focus positions, with the optimized parameters of this experiment. It would be helpful to give these spatial\ninformation together with the density map profile, which also plays a relevant role.\n2. Pg3, right column after “Given the extremely steep density ramps used in this work we suggest this as being close to the\nminimum peak current required to trigger DDRI in PWFAs”. The referee definitively agrees with the analysis, but the\nsentence should be made more clear. It may help the introduction of the concept of minimum wakefield amplitude for sharp\ndensity downramps.\n3. Pg3, right column after “This was adjusted by changing the laser trigger timing in steps of 18.46 ns. Qi(∆t), shown in Fig.\n2(d), increased from a few pC at ∆t = 10–20 ps to a peak of 27 pC at ∆t = 18.46 ns before dropping to approximately zero\nover the following 37 ns”.\nAs this is one of the key points of the density downramp scheme, the reader expects a sentence here about the time\nevolution of the electron density spike generated by the ionization laser pulse. At least Authors can add “(...as the timing is\nlinked to the electron density spike profile, as shortly discussed in the next paragraph)”\n4. Pg4, left column, after “The resolution was dz = 0.25 µm, dr = 0.4 µm with 2 azimuthal modes”. Authors should also\ninclude information about the box (cylinder) radius, length, the number of ppc (Nr x Nt x Nz) of the plasma and how they\nsimulated the driver (as a distribution, with given macroparticles) and, most importantly, if they used a Lorentz boosted frame\ntechnique (in the case, as that technique also squeezes the plasma, they should also add information about the total number\nof macroparticles describing the accelerated beam, information which is relevant to understand the quality of the phase-\nspace analysis)\n5. Pg5, right column. Related to the WarpX simulation, Authors should state the number of macroparticles which result in the\naccelerated beam (as for FB-PIC: did the use a Lorentz boosted technique?). Did Authors use impact ionization for the\nplasma?", "reviewer_2": "The manuscript by J. C. Wood et al., titled “Brightness-boosted electron bunches from a plasma accelerator” describes the\nfirst experimental demonstration that achieved both low emittance and energy spread. As described in the manuscript,\nprevious experimental demonstrations only achieved a large emittance (10 micron) and a few micron emittance with a large\nenergy spread respectively. However, this demonstration achieved a 1 micron emittance with ~30 pC charge. Also, the\nspectral density has improved by almost a factor of 10 compared to the previous researches. While these numbers are still\nmuch worse than what we can generate using conventional linacs, it is remarkable progress in this new scheme, which has\nbig potential to overcome the limitations that conventional methods have. Furthremore, authors provided experimental study\non system parameters that turned out to be critical for the total charge generated and explained the principle behind it using\nsimulations. Such observations would significantly help subsequent researches on plasma-based electron sources.\nI believe the demonstrated results and analysis in this manuscript are indeed an important step towards the realization of\nplasma-based high-brightness electron sources, which are critical for future accelerators. Its impact would naturally be\nbroad. Therefore, I believe this manuscript satisfies Nature Communications’ publication criteria. However, there are two\nmajor issues and several minor items that must be addressed by authors.\nMajor issue:\n[1] The authors claim that the scheme they presented made a significant boost in brightness. However, this claim is not\naccurate. The drive beam used in the experiment had a charge of ~300 pC, and its emittance was 20 micron. This emittance\nis almost 40 times larger than what I would expect from a 300 pC charge. If a nicely generated drive beam of the same\ncharge has been prepared, the brightness of the drive beam could be improved by a factor of 1600. It is unfair to claim\nenhancement in brightness using such low-quality drive beam. Additionally, to claim that the scheme is really improving the\nbrightness, such transverse emittance improvement on the drive beam must improve the main beam’s up to some level.\nHowever, based on the description in this manuscript, I don’t expect such improvements. Furthermore, the achievable\nbrightness usually improves as the charge decreases. Thus, directly comparing the driver and injected bunches, having\ndifferent charge level, is inappropriate. If we call such scheme as brightness boost, almost any schemes using two beams\nwith difference charges can be considered as brightness boost. The wording “brightness boost” is incorrect and\ninappropriate. It must be eliminated for publication. The results of this manuscript are solid. I suggest that authors focus on\ntheir great demonstration of high-brightness plasma-based electron source.\n[2] It was not clear to me what changes were made from other researches and what led to the improvements presented by\nauthors. The authors need to provide more explanations regarding the changes they made compared to previous researches\nand how those changes contributed to achieving the enhancements.\nMinor items:\n1. The introduction doesn’t seem nicely organized. For example, the first two paragraphs almost repeat the same argument.\nThe third one focuses on emittance and what can be possibly achieved, which is ok. However, the fourth paragraph goes\nback to why you need DDRI and beam-driven. Also, the fourth paragraph explains too much low level details without any\nother explanations. It was hard to read and hard to catch what authors wanted to say. I think such difficulty was coming from\nthe paragraph and sentence structures. It would be great if the authors can improve this section.\n2. “as they approach the back of the wake they experience a magnetic field from the radial current of sheath electron which\nact as a defocusing force”. Is it defocusing force not focusing force?\n3. It would be good to have more explanation of DDRI in the introduction. Currently it is forcing readers to find references to\nunderstand what that is, and it seems inappropriate for Nature Communications’ readers. It doesn’t have to be long but\nwould be nice if you have what it is and why you do it (or what advantages are expected).\n4. “the drive waist position in z while preserving its spot size”. If you change the focusing point in z direction, it changes the\nspot size. Do you mean by the change is ignorable? Or you actually made other compensation upstream? It would be better\nto describe it more precisely.", "reviewer_3": "The article \" Brightness- Boosted Electron Bunches from a Plasma Accelerator\" describes an electron driven Plasma\nwakefield acceleration experiment using internal injection of the witness bunch. In injection mechanism is a density\ndownramp injection.\nThe main result is a 3D brightness measurement of the accelerated witness bunch which the authors claim is 4.8 times\nhigher then the originally driving electron bunch.\nThe paper is well written, rather clear and definitely original. The results presented are new and certainly important for the\nfield of plasma acceleration. The paper describes a complicated experiment combined with a challenging data analysis.\nI therefore recommend the paper to be published. I would like the authors to consider nevertheless the following comments:\nIntroduction:\nTo my opinion the authors describe somewhat inaccurate the limitation of conventional accelerators. For example a state of\nthe art FEL is only a few 100 m long not several kilometers (for example Swiss FEL). Furthermore those conventional FEL's\nproduce beams with an emittance of 100 nm for 100 pC charge. Therefore actually superior of what has been achieved in\nthis paper. See for example:\nE. Prat, P. Dijkstal, M. Aiba, S. Bettoni, P. Craievich, E. Ferrari, R. Ischebeck, F. Löhl, A. Malyzhenkov, G. L. Orlandi, S.\nReiche, and T. Schietinger Phys. Rev. Lett. 123, 234801, 2019. DOI:\nThis facts should be mentioned which does not diminish the achievements of the publication.\nI find the term brightness-boost extremely misleading because there are two different beams, one looses energy and the\nother gains energy and is actually generated within the plasma. What is actually the brightness of the witness beam at its\nsource if this can be simulated/determined.\nResults:\nIn this section I am missing the detailed data of the result.\nWhich bunch charge, which emittance and energy spread was achieved. An image of both beams would be nice as well. It\ncomes later but those are major results.\nOptimal Ramp Height &Length for DDRI:\nThis chapter is somewhat confusing. It seems to be a simulation study but it is not so clear how it is related to the\nexperiment.\nDid the experiment had clear control on the ramp profile, do we know which profile gave the best result in the experiment. ?\nPlease clarify this points.\n6D brightness estimate from PIC simulations:\nThe authors like to suggest that the brightness boost in 6D could be more impressive then the measured one in 3D.\nThe simulations seem to show quite asymmetric emittance values, wouldn't this suggest that the 3D measurement presented\nbefore might be optimistic because likely measured in the lucky plane?\nStability, Emittance and brightness of the injected bunch:\nIt would be nice to make clearer what results are averaged over the data set and which are best shots results in this chapter.\nIs the 4.8 times boost a best shot result ? What is the average of the data sample ?", "reviewer_4": "The paper presents an experimental investigation of high-brightness electron bunches generation from a plasma\naccelerator, achieved through injection control of improved density transition using an additional injection laser to generate a\nhigher density plasma spike. The injected electron bunch exhibits an improved brightness, with a 3D brightness 4.8 times\ngreater compared to the driver electron bunch. The experimental results are elaborately discussed alongside particle-in-cell\nsimulations. However, it is noted that a brightness-boosting scheme was previously proposed in [Phys. Rev. STAB. 7.\n011301 (2004)] (Ref. [16] in the paper), and the experimental setup is almost identical to their previous work (Phys. Rev.\nAccel. Beams. 24. 101302 (2021)). As such, this paper appears to be more of an experimental verification work rather than\none that extends the boundaries of knowledge. Therefore, it may not be suitable for publication in Nature Communications.\nThere are several additional issues that need further discussion and revise:\n1. In the scan simulations using the quasi-3D FBPIC code, which employs a cylindrical coordinate model, the simulated\nsystem needs to exhibit cylindrical symmetry. However, the spike plasma density created by the tightly focused injection\nlaser deviates from cylindrical symmetry, which could impact the accuracy of the simulations.\n2. The authors mention that, for the experimental results, although the emittance of the injected electron bunch is 17 times\nlower than that of the driver, the 3D brightness (B3D) only shows an increase of 4.8 times. This discrepancy is attributed to\nthe deduced dQi/dE, which decreases as the energy spread increases. This challenge highlights the need to control the\nenergy spread and phase space rotation of the injected electron bunch.\n3. The authors suggest that their simulations indicate a potential >1000-fold increase in the 6D brightness (B6D) in their\nexperimental configuration. However, it is noted that the emittance values used in the simulations are slice-normalized\nemittances, whereas the experimental results provide normalized transverse emittance values. This discrepancy could be\nmisleading, as slice emittance is typically much lower than normalized transverse emittance. Furthermore, the simulations\ndo not include the parameters of the driver, and it would be beneficial to compare the phase space distribution between the\ndriver and the injected electron bunch.\n4. In Figure 6(b), the emittance appears different from that in Figure 5. It would be beneficial to include the brightness\nevolution in this figure for a more comprehensive analysis.\n5. The format of the references should be revised. For example, in reference [10], \"Plasma Physics and Controlled Fusion\"\nshould be formatted as \"...Plasma Phys. Control. Fusion...\""}, "author_response": "DeutschesElektronen-SynchrotronDESY\nAResearchCentreattheHelmholtz-Association\nDESY|JonathanWood,Notkestraße85,22607Hamburg\nJonathanWood\nTeamleaderforBeamDrivenPlasma\nAccelerators\njonathan.wood@desy.de\nNotkestraße85\n22607Hamburg\nTel.+4940-8998-5297\n6thOctober2025\nResponsetotheReviewers\nDearEditor,\nOnbehalfofalloftheco-authors,Iwouldliketothankyouforthecontinuedconsiderationofthismanu-\nscriptandtothankthereviewersfortakingtheirtimetoengagewithandprovidetheirvaluablefeedback\nonthiswork. Weapologiseforthedelayintheproductionofthisresponse,althoughwenowbelievethat\nwehavemanagedtoengagewithandanswereveryoneoftheconcernsraisedbyeachofthereviewers.\nIntherestofthisletteraresponsetothereviewer’scommentsisprovided,withtheiroriginalcommentsin\nbluetext,ourresponseinblack,andchangesmadetothemanuscriptingreen. Unlessstatedotherwise,\nlinenumbersrefertolocationsintheupdatedratherthantheoriginalmanuscript.\nReviewer 1\nThemanuscriptdealswithexperimentalresults,aboutthegenerationofhighbrightnesselectronbeams\nviaPWFAdrivenbyaLINAC,with“witness”(accelerated)electronbeamsobtainedbydensitydownramp\ninjections. Theresultsreportedinthemanuscriptareinterestingfortheplasmaaccelerationcommunity,\nthediscussedphysicalprocessesaregenerallysoundandthemanuscriptiswellwritten. Asthereare,\nhowever,somespecificpointstobeclarifiedorwherethemanuscriptcanbeimproved,theReferee\nsuggestsAuthorstorevisetheirmanuscriptaccordinglytotheitemsbelow.\nWethankthereviewerfortheircomplimentaryremarksandtheirinterestinthiswork. Individualresponses\ntotheirsuggestionsaremadebelow.\nQuestion1: Pg4,leftcolumn,after“...theplasmawasa9mmflat-top..’. WhyAuthorsusedaflat-top\ndensityprofilefortheirsimulationsalthoughtheplasmaprofile(bytheirsimulations)isdecreasing[seeFig\n1c]? ThesamequestioncanberaisedfortheWarpXsimulationshownafter. CanAuthorscommenton\nthis?\nDeutschesElektronen-SynchrotronDESY BoardofDirectors Prof.Dr.BrittaRedlich\nNotkestraße85,22607Hamburg,Germany\nProf.Dr.Dr.h.c.BeateHeinemann Prof.Dr.ChristianStegmann\nLocationZeuthen (Chairperson)\nIrisWilhelm\nPlatanenalle6,15738Zeuthen,Germany\nDr.TiesBehnke(interim) (DeputyChairperson)\nwww.desy.de\nProf.Dr.WimLeemanns Dr.ArikWilner(CTO)\nPage2of13\nFigure2(d)ofthemanuscriptstronglysuggeststhattheevolutionofthedownrampovertimedramatically\nchangestheamountofinjectedcharge,andwepostulatebasedonknownphysicsthatthisislikelytobea\nresultoftheevolvingheightandlengthofthedensitydownramp. ThepurposeoftheFBPICsimulations\nwastoexplorehowdifferentrampheightsandlengthsaffectedthecharge,andincidentallythebrightness,\noftheinjectedbunch. Forthisstudywefounditbeneficialtosimplifytheproblembytakingasimplified\nplasmadensityprofile. Whilethisdidnotaccuratelyrepresenttheexperiment,itprovidedgreatinsightinto\nwhytheinjectedchargewaslowforasmalllaser-to-electron-beamdelay,andsuggestedanexplanation\nfortheobservedbehaviourinFigure2(d). Furthermore,thesesimulationsshowedthatitcanbebeneficial\ntouselargerampheights,withmuchhigherrelativedensitiesthanhavebeenusedinliteraturebefore,\nandweexplainedthisbehaviour. Inordertoclarifythepurposeofthesesimulationsinthemanuscript,we\nhaveaddedthefollowingtexttolines261-267:\n“Thepurposeofthissimulationsetwastodeterminetheeffectsoftheplasmaspike’sheightandramp\nlengthontheinjectedbunchcharge. Thesimulationswereintentionallysimplifiedtoisolatetheinjec-\ntionphysicsfromtheexperimentalcomplexities,andtoprovideabasicphysicalunderstandingofthe\nbehaviourrecordedinFig.2(d).”\nThefull-3DWarpXsimulationwasverycomputationallyexpensive,anditwasnotpossibletoperform\nparameterscansatsufficientlyhighresolution. TheWarpXsimulationdidnotuseaflat-topplasmadensity\nprofile,itusedtheplasmaprofileshowninfigure1(c)ofthemanuscript,whichwasourbestestimateof\ntheexperimentalplasmadensityprofile. Thiswasoriginallystatedinthesection“6DBrightnessEstimate\nfromParticle-in-CellSimulations”withtheline“n (z)fromFig. 1(c)wasused”. Thiswastoobriefand\ne\nmadeittooeasytomissthisimportantpoint. Thislinewasreplacedwiththefollowingtextonlines\n390-394ofthemanuscript:\n“ThelongitudinalplasmadensitywasthatfromFig.1(c),whichwasourbestestimateoftheexperimental\nplasmadensityfromtheexperiment,asdescribedintheMethodssection.”\nQuestion2: Astheenergyoftheacceleratedbeamisquitelow,isthevalueofmeasuredemittancemostly\ngettingcontributionsfromtheinjection/accelerationorfromthedownramp?\nItwasunfortunatelynotpossibletodeterminethisintheexperiment,sincewecanonlymeasurewhat\nmakesittoourdetectors,andhadlittlecontrolovertheoveralllongitudinalplasmadensityprofile,par-\nticularlythelongdownrampintothevacuumsection. Inthefigurebelow,weplottheevolutionofthe\nemittanceoftheinjectedbunchintheWarpXsimulationinbothxandy,aswellasthesimulatedplasma\ndensityprofile.\nEvolutionofthenormalisedemittanceoftheinjectedbeamintheWarpXsimulationdetailedinthe\nmanuscript. Theshadedblueregionistheplasmadensityprofile(notethelogarithmicscale).\nTheemittanceofthebunchdoesnotchangeduringthetransitionfromplasmatovacuum. Attheinjection\npoint(z = 20mm)theemittanceofeachbunchissurprisinglysimilar,andatthe100nmlevel. While\ntheemittancerapidlysaturatesinthexdirection,inthey directionitcontinuestogrow. Typicallythis\nisduetobetatrondecoherence,withbadlymatchedbunchesexperiencinggreateremittancegrowth\nduringaccelerationintheplasma. Itis,thus,stronglyindicatedbythesimulationsthattheemittanceafter\nPage3of13\ntheplasma,whichiswhatwasquotedinthemanuscript,hasitsvalueasaresultoftheinjectionand\naccelerationprocess,ratherthanbeinganeffectoftheplasma-to-vacuumtransition.\nAuthorsdidq3Dand3Dsimulationsbuttheydidn’treportontheevolutionofthephaselongitudinaland\ntransversespacecutsalongthebeamspropagation. Thiswoulddefinitelyhelpinunderstandinghowthe\nenergyspreadcompressionismade(thesuperpositionwiththelongitudinalon-axisgradientwillhelp)and\nhowthex,yemittancesvarywiththelongitudinalposition. It’salsoimportanttodistinguishbetweenthe\nB attheendoftheaccelerationandthatafterthedownramp,inordertohaveaviewontheroomthey\n3D\nhaveforminimizingtheemittancegrowthinthedownramp. TheRefereesuggeststoaddalloratleast\nsomeoftherelevantinformationreportedabove.\nFirstregardingthetransversephasespace. Intheq3D(FBPIC)simulations,theemittanceinbothplanes\nwasapproximatelyconstantinbothplanesafterinjection. ThiscanbeseeninFig.6ofthemanuscript,\nwhichisarepeatofthecase-IIsimulationfromFig.3(a)&(b)butwithalongerplasmaaftertheinjection\npoint. Inthefull3D(WarpX)simulation,wehopethattheanswertothepreviousquestionassuagesthe\nreviewer’sconcerns.\nRegardingthelongitudinalphasespace,belowweplottheevolutionoftheabsoluteandrelativeenergy\nspreadsinthefull3Dsimulation. Whilethesimulationshowsthatabunchwithlowemittanceinboth\nplanescanbeinjectedviaourmethod,thesimulationsignificantlyoverestimatestheenergyspreadwith\nrespecttotheexperiment. Theagreementinthetotalenergygainbetweenthesimulationandexperiment\nsuggeststhatourunderstandingoftheplasmaprofilepost-injectionisgood,soweattributethisdisagree-\nmenttoalackofknowledgeofthepreciseshapeofthedensityspike. Thiscouldnotbemeasuredinthe\nexperiment-itwouldhaverequireddiagnosisofaveryunderdenseplasmawithmicrometreresolution,\nwhichisnotpossibleinouracceleratorenvironment. TheWarpXsimulationwasabest-effortattemptto\nrecreatethe∆t=0datapointfromtheexperiment. Webelievethatitaddsvaluetothepaperbyshowing\nthatinprinciplebunchescanbeinjectedwithsignificantlysub-micrometrenormalisedemittancesinboth\nplanes. Howeverwewouldprefernottoaddthelongitudinalanalysisofthesimulationtothemanuscript\nsinceitagreespoorlywiththedata. Welackanunderstandingofhowtheenergyspreadcompression\nhappensintheexperiment,andalteringthe3Dshapeofthedensityspiketoreducetheenergyspread\ntowardstheexperimentvaluewouldbebothspeculativeandanill-posedproblem,sinceseveralfeatures\ncouldbechangedwithonlyasingleresulttocompareto. Forthelongerq3Dsimulationinfigure6we\nhaveaddedthe(unoptimised)energyspreadtotheplot. Thisshowsthat,inprinciple,bunchesinjectedvia\nourtechniquecanmaintainasmallabsoluteenergyspreadandapproximatelyconstantrelativeenergy\nspreadwhileexperiencingalargeenergygain. Assuchitisnotalwaysthecasethatalargecompression\noftheenergyspreadisrequired.\n1019\n1018\n1017\n1016\n1015\n1014\n10 20 30 40 50\ns (mm)\n)3\nmc(\nen\n4.0\n3.5\n3.0\n2.5\n2.0\n1.5\n1.0\n0.5\n0.0\n)VeM(\nsmr,E\n8\n7\n6\n5\n4\n3\n2\n1\n0\n)%(\nE\nEvolutionofabsoluteandrelativeenergyspreadsintheWarpXsimulation.\nMinorchanges:\nThetitlelookssomewhatmisleading. Theworld“boosted”recallsa(large)increaseofaquantitywhich\nisalreadyexisting. Forexample,wecansafelyname‘brightness-boostedbunches’anybunchhavinga\ncertainbrightnessbeforetheaccelerationstageandhavinghigherbrightnessatitsend. Inthecaseofthe\nPage4of13\npresentmanuscripttitle,Authorsclaimtheycreated‘brightness-boosted’bunchesasthefinalbrightnessof\nthosebunchesexceedsthatofthewakefielddriver. Mysuggestionistochangethetitlebyreferringto\nhighbrightnesselectronbeams. Thelast-lastsentenceoftheAbstractshouldbechangedaccordingly.\nWeacceptthiscommentfromthereviewer. Theconceptofproducingahigh-brightnesselectronbeam\ninaplasmaacceleratordrivenbyalow-brightnesselectronbeamhasbeencoineda‘brightnessbooster’\nwithintheplasmawakefieldacceleratorcommunity,althoughaspointedoutthisnamecanbemisleading.\nWehavechangedthetitleto: ‘BrightElectronBunchesfromaPlasma-WakefieldAcceleratorwitha\nSteepDensityDown-Ramp’. Wealsoremovedthephrasebrightnessboosterfromtheabstract,andthe\nfinalsentencesofitnowread‘Plasmaacceleratorsthereforeofferapossibilitytocreatehigh-brightness\nbunchesinwakefieldsdrivenevenbylow-qualitydrivebunches. Herewedemonstratetheinjectionand\ngigavolt-per-metreaccelerationofelectronbuncheswithmm-mradnormalisedemittance,O(10pC/MeV)\nspectraldensityandper-cent-levelenergyspread,allwithexcellentreproducibility.’\n1. Pg3,leftcolumn. “.InFig. 2(a)thefinal-focussing-quadrupole(FFQ)fieldstrengthsk inthexandy\ndirections,whichalmostexclusivelydeterminedthedriverwaistpositioninzwhilepreservingitsspot\nsize,werevaried”Authorsshouldaddinformationaboutthelongitudinalvariationofthedriverbeam\nfocusoncethefieldstrengthischanged. This,alongwiththeinformationofthebeambetafunction,will\ngivedirectinformationonhowsensitiveisthePWFAprocessonthedrivefinalfocuspositions,withthe\noptimizedparametersofthisexperiment. Itwouldbehelpfultogivethesespatialinformationtogetherwith\nthedensitymapprofile,whichalsoplaysarelevantrole.\nDuetoexperimentaltimeconstraintsitwasnotpossibletoperformanaccuratemeasurementofthewaist\nlocationforeachk −k pair,anditisnotpossibletocalculatetheabsolutewaistlocationwithsufficient\nx y\naccuracyfromtheread-backvalueofthequadrupolecurrents. Weagreewiththereviewerthat,were\nsuchmeasurementsavailable,thiswouldbeavaluableresource. Neverthelessonecanmakeasimple\nestimateofthemagnitudeofthiseffect. Changingthefocussingstrengthby1%changesthefocallength\nbyapproximately1%. Thefinalfocussingquadrupoleinxhadafocallengthofapprox.1.1m,soa1%\nchangeink correspondedtoa∼1.1cmchangeinfocalposition. Thefinalfocussingquadrupoleiny had\nx\nafocallengthofapprox.2.1m,soa1%changeink correspondedtoa∼2.1cmchangeinfocalposition.\ny\nThefollowingtextwasaddedtolines196-199ofthemanuscript: ‘Simplecalculationssuggestthata1%\nchangeink ,k correspondedtofocalpositionshiftsofapproximately1and2cmrespectively[c.f.the\nx y\ndensityprofileinFig.1(c)].’ Regardingchangesinthebetafunction,pleaseseeourresponsetoReviewer\n2minoritem4.\n2. Pg3,rightcolumnafter“Giventheextremelysteepdensityrampsusedinthisworkwesuggestthis\nasbeingclosetotheminimumpeakcurrentrequiredtotriggerDDRIinPWFAs”. Therefereedefinitively\nagreeswiththeanalysis,butthesentenceshouldbemademoreclear. Itmayhelptheintroductionofthe\nconceptofminimumwakefieldamplitudeforsharpdensitydownramps.\nWeandtherevieweragreethatthereisaclearminimumwakefieldamplitudeforinjectionintosharp\ndensitydownramps,whichnaturallyappearsinthedataasaminimumcurrentforinjectionofcharge. The\nsentencereferredtobythereviewerhasbeenremovedandreplacedonlines219-226with: “Electrons\ncanonlybetrappedinthewakefieldiftheirforwardsvelocity,whichtheyobtainfromtheirinteraction\nwiththehigh-currentdriver,exceedsthevelocityofthebackofthewakefieldinthedownramp. Giventhe\nextremelysteepdensityrampsused,itislikelythat1.3kAisclosetotheminimumdrivercurrentrequired\ninpracticeforDDRI”.\n3. Pg3,rightcolumnafter“Thiswasadjustedbychangingthelasertriggertiminginstepsof18.46ns.\nQ (∆t),showninFig. 2(d),increasedfromafewpCat∆t=10–20pstoapeakof27pCat∆t=18.46ns\ni\nbeforedroppingtoapproximatelyzerooverthefollowing37ns”. Asthisisoneofthekeypointsofthe\ndensitydownrampscheme,thereaderexpectsasentencehereaboutthetimeevolutionoftheelectron\ndensityspikegeneratedbytheionizationlaserpulse. AtleastAuthorscanadd“(...asthetimingislinkedto\ntheelectrondensityspikeprofile,asshortlydiscussedinthenextparagraph)”\nPage5of13\nWethankthereviewerforhelpingtoclarifythispoint. Theprecedingsentencewasupdatedtoread‘A\nfinal,powerfulcontrolovertheinjectedbunchpropertieswasthedelay∆tbetweenthearrivalofthe\nionisinglaserbeamsandthedriverbunch,sincethetimingdeterminestheheightandshapeofthedensity\nspike,asdiscussedinthenextsection.’ onlines233-237.\n4. Pg4,leftcolumn,after“Theresolutionwasdz =0.25µm,dr =0.4µmwith2azimuthalmodes”. Authors\nshouldalsoincludeinformationaboutthebox(cylinder)radius,length,thenumberofppc(Nr×Nt×Nz)\noftheplasmaandhowtheysimulatedthedriver(asadistribution,withgivenmacroparticles)and,most\nimportantly,iftheyusedaLorentzboostedframetechnique(inthecase,asthattechniquealsosqueezes\ntheplasma,theyshouldalsoaddinformationaboutthetotalnumberofmacroparticlesdescribingthe\nacceleratedbeam,informationwhichisrelevanttounderstandthequalityofthephase-spaceanalysis)\nThedescriptionofthesimulationswasupdatedonlines268-276toread:\n“Theresolutionofthesimulationswasdz = 0.25µm,dr = 0.4µmwith2azimuthalmodes. Therewere\n2,2and8particlespercellinther,z andθ directions,exceptinasmalllongitudinalregionaroundthe\ninjectionspike,where4,4and8particlespercellwereused. Theboxradiuswas106.3µmanditslength\nwas354µm. Abi-Gaussiandriverbunchwasusedwith304pCcharge,I = 1.9kA,(cid:15) = 20mm-mrad\npk n\nandσ =16µm. Itconsistedof300,000macroparticles.”\nr\nTheLorentzboostedframetechniquewasnotused. Itisuncommontouseitinelectron-beam-driven\nsimulations,sincethesmallestlongitudinallengthscaleofinterest,thebunchlength,issimilartothe\nplasmawavelength,ratherunlikethecomparisonbetweenthelaserandplasmawavelengthswhen\nconsideringlaser-plasmaaccelerators. Furthermore,thesmallestlengthscaleofinterestinthesesim-\nulationswastheinjectionspikeintheplasmadensityprofile,makingthetechniqueofLorentzboosting\nthesimulationparticularlypoorlysuitedtoourcase. Lines257-261werechangedtosimplyreflectthis.\nTheynowread‘Impreciseknowledgeoftheinitialconditionsinthisexperimentprecludedtheuseof\nmagneto-hydrodynamicssimulations,butinsightintohowthisgeneralscenarioaffectsinjectionwas\ngainedfromasetoflab-framequasi-3DFBPICsimulations.’\n5. Pg5,rightcolumn. RelatedtotheWarpXsimulation,Authorsshouldstatethenumberofmacroparticles\nwhichresultintheacceleratedbeam(asforFB-PIC:didtheuseaLorentzboostedtechnique?). Did\nAuthorsuseimpactionizationfortheplasma?\nAtotalof134,049macroparticleswereintheacceleratedbeamandconvergencetestsfocussedon\nthepropertiesoftheacceleratedbeamwereperformed. Lines401-404wereupdatedtoread‘Figure\n5(a)showsthattheinjectedbunch,consistingof1.3×105 macroparticles,wasacceleratedtoapeak\nE =28.6MeV,consistentwiththeexperiment.’\nForthereasonsoutlinedintheanswertoreviewer1minorchange4,theLorentzboostedtechniquewas\nnotused. Lines383-390wereupdatedtoread: Figure5showsthelongitudinalphasespace,current\nprofileandsliceemittancesoftheinjectedbunchfromtheendofalab-frame,fully3DWarpXsimulation,\nwhichusedcellsizesdx = dy = 0.39µm,dz = 0.14µm,aboxsizeof200×200×400µmand1and4\nparticlespercellinthebackgroundplasmaandplasmaspikeregionsrespectively.\nImpactionisationwasnotused. Wedidcheckiftheelectricfieldofthedriverbeamwaslargeenoughto\ncausesignificantionisation,andfoundthatthiswasunlikelytobethecaseduetothelargeemittanceof\nthedriverbunch(L.BoultonPhDThesis,UniversityofStrathclyde,DOI10.48730/w6y5-9q35). Wecan\nexcludethisasapossibleinjectionmechanismsinceinjectedelectronswereonlyobservedwhenthe\ntransverse(plasma-spike-creating)laserwasturnedon. Furthermore,page169-170ofthesamethesis\ncontainscalculationsofneutralgasscattering,whichhasalargereffectthanelectron-ionscatteringfor\nourparameters. Thecalculationsshowedthatthenormalisedemittancegrowthfromelectron-neutral\nscatteringwasatthe30-40nmlevel.\nReviewer 2\nThemanuscriptbyJ.C.Woodetal.,titled“Brightness-boostedelectronbunchesfromaplasmaacceler-\nator”describesthefirstexperimentaldemonstrationthatachievedbothlowemittanceandenergyspread.\nPage6of13\nAsdescribedinthemanuscript,previousexperimentaldemonstrationsonlyachievedalargeemittance(10\nmicron)andafewmicronemittancewithalargeenergyspreadrespectively. However,thisdemonstration\nachieveda1micronemittancewith 30pCcharge. Also,thespectraldensityhasimprovedbyalmosta\nfactorof10comparedtothepreviousresearches. Whilethesenumbersarestillmuchworsethanwhat\nwecangenerateusingconventionallinacs,itisremarkableprogressinthisnewscheme,whichhasbig\npotentialtoovercomethelimitationsthatconventionalmethodshave. Furthremore,authorsprovided\nexperimentalstudyonsystemparametersthatturnedouttobecriticalforthetotalchargegeneratedand\nexplainedtheprinciplebehinditusingsimulations. Suchobservationswouldsignificantlyhelpsubsequent\nresearchesonplasma-basedelectronsources. Ibelievethedemonstratedresultsandanalysisinthis\nmanuscriptareindeedanimportantsteptowardstherealizationofplasma-basedhigh-brightnesselectron\nsources,whicharecriticalforfutureaccelerators. Itsimpactwouldnaturallybebroad. Therefore,Ibelieve\nthismanuscriptsatisfiesNatureCommunications’publicationcriteria. However,therearetwomajorissues\nandseveralminoritemsthatmustbeaddressedbyauthors.\nWethankthereviewerfortheirpositivecommentsandfortheirappreciationoftheadvancesmadeinthis\nwork. Weengagewiththeissuestheyraisedbelow.\nMajorissue:\n[1]Theauthorsclaimthattheschemetheypresentedmadeasignificantboostinbrightness. However,\nthisclaimisnotaccurate. Thedrivebeamusedintheexperimenthadachargeof 300pC,andits\nemittancewas20micron. Thisemittanceisalmost40timeslargerthanwhatIwouldexpectfroma300\npCcharge. Ifanicelygenerateddrivebeamofthesamechargehasbeenprepared,thebrightnessofthe\ndrivebeamcouldbeimprovedbyafactorof1600. Itisunfairtoclaimenhancementinbrightnessusing\nsuchlow-qualitydrivebeam. Additionally,toclaimthattheschemeisreallyimprovingthebrightness,such\ntransverseemittanceimprovementonthedrivebeammustimprovethemainbeam’suptosomelevel.\nHowever,basedonthedescriptioninthismanuscript,Idon’texpectsuchimprovements. Furthermore,\ntheachievablebrightnessusuallyimprovesasthechargedecreases. Thus,directlycomparingthedriver\nandinjectedbunches,havingdifferentchargelevel,isinappropriate. Ifwecallsuchschemeasbrightness\nboost,almostanyschemesusingtwobeamswithdifferencechargescanbeconsideredasbrightness\nboost. Thewording“brightnessboost”isincorrectandinappropriate. Itmustbeeliminatedforpublication.\nTheresultsofthismanuscriptaresolid. Isuggestthatauthorsfocusontheirgreatdemonstrationof\nhigh-brightnessplasma-basedelectronsource.\nWeacceptthecommentsaboutthephrase“brightnessbooster”andagreewiththereviewerthatwe\nshouldconcentrateontheexplanationandimplicationsofourresults. Otherreviewershadsimilar\ncommentsandwehavepartiallydealtwiththiscommentinourresponsestothem. Wehavechangedthe\ntitleandabstractofthemanuscripttoremovementionsofthebrightnessboosterconceptasdiscussed\ninourfirstminorresponsetoreviewer1. Whilereorganisingtheintroductionasrequestedintheminor\ncommentsfromreviewer2wesimilarlyeliminatedbrightnessboosterreferences.\nAnisolatedreferencetothe“brightnessboosterscheme”wasfoundonlines215-216(oftheoriginalrather\nthantheupdatedmanuscript)andreplacedby“thisscheme”,simplyreferringtoDDRI.\nReferencestobrightnessboostingweredroppedinthemainresultssectionsentitled“Stability,Emittance\nandBrightnessoftheInjectedBunch”. Thebrightnessofthedriverissimplystatedas“Inthisexperiment\nthedriverB = 2.4pC/MeV/mm-mrad”onlines377-378. Sincethebrightnessboosternarrative\n3D,d\nwasdroppeditnolongermadesensetocomparethebrightnessesofthedriverandinjectedbunches.\nThereforefigures4(e),and5(b)&(c)wereremoved. Therestofthefigureswereexpandedtoprovide\ntheirdetailsmoreclearly,andthefigurecaptionswereadjustedaccordingly.\nInthe“6DBrightnessEstimatefromParticle-in-CellSimulations”sectioncomparisonstothedriver\nbrightnesswereremoved.\nInthe“Discussion”sectionweremovedthefirsthalfsentencethatdidread“Havingprovidedthefirst\nexperimentaldemonstrationofthebrightnessboosterconcept”. Theremainderofthissectionuntilthe\nfinalparagraphonlyfocussesonimprovingtheinjectedbeampropertiesandfutureoutlook. Thefinal\nparagraphoftheDiscussionsectionhasbeenmostlychangedtosimplyrestatethemainresultsof\nPage7of13\nthepaper,andnowreads“Insummary,wehavepresentedexperimentalresultsfromabeam-driven\nplasmaacceleratorinwhichahigh-qualityelectronbunchwasinjectedviadensity-downrampinjection.\nThe1.3%energyspread,14pCMeV−1 buncheswereacceleratedatapproximately1GVm−1 withhigh\nreproducibility. Themeannormalisedemittanceoftheinjectedbunchwasmeasuredtobe(1.2±0.1)mm-\nmrad. ThecombinationofhighchargeperMeVandlowemittancewasaresultofusingashort‘spike’\nintheplasmadensityprofile,withapeakdensityanorderofmagnitudegreaterthanthesurrounding\nplasmadensity. Particle-in-cellsimulationsshowedthatpeakspikedensitiesuptothedrivebeamdensity\nincreasedboththechargeandbrightnessoftheinjectedbunches.”.\n[2]Itwasnotcleartomewhatchangesweremadefromotherresearchesandwhatledtotheimprove-\nmentspresentedbyauthors. Theauthorsneedtoprovidemoreexplanationsregardingthechangesthey\nmadecomparedtopreviousresearchesandhowthosechangescontributedtoachievingtheenhance-\nments.\nThemostimportantchangewastheuseofdensitydownrampswithratiosofthepeakplasmadensity\ntothefollowingplasmadensityfargreaterthanhavebeenconsideredbefore. Thisisnowstatedin\nthefinalparagraphoftheintroduction(lines113-118)as“Thisrepresentsasignificantstepforwards\ninthequalityofplasma-generatedelectronbunches. WeachievedthisusingtheDDRImechanism\nwithanespeciallyhigh-densityinjectionregionwithsteepdensitygradients,farbeyondwhathasbeen\nconsideredpreviously.” Themechanismbehindthisisexplainedinthesection“OptimalRampHeight\n&LengthforDDRI”.Foraslongasthedrivebunchdensityisgreaterthantheplasmadensityinthe\ndownramp,injectioncanoccur. Thelargestamountofchargeisinjectedinthesimulations(manuscript\nfigure3)whenthepeakdownrampplasmadensityequalsthebeamdensity. Thisisalsothemechanism\nbehindthevariationininjectedchargewithlaser-to-electron-beamdelayshowninfigure2(d)inthe\nmanuscript. Thishasbeenfurthersummarisedattheendofthissection. Lines324-328havebeenaltered\nto“ThehighchargeperMeVinjectionresultingfromtheseoptimiseddensitytransitions,withhighpeak\ndownrampdensitiesequaltothebunchdensity,wasakeyfactorinproducingbrightinjectedbunchesin\nthisexperiment.”. Furthermore,wechangedthefinalsummaryparagraphtomoreclearlystatethemain\nresults,asdetailedintheanswertoyourfirstmajorissue.\nWhatisparticularlyunusualandinterestingaboutthescanoframpheightandlengthshowninfigure3\nisthattheelectronbeamchargecanbeincreasedwithnodetrimenttotheemittance,whichisshown\nviatheclosecorrelationbetweeninjectedchargeandbrightness(comparefigure3(a)and(b)). Thisis\nincontrasttoRFlinacswherechargeandemittanceareintrinsicallylinkedduetospacechargeforces\nintheinjector,whicharerapidlyeliminatedbymulti-GV/mfieldsinaplasmawakefield. Tofurtherclarify\nourresults,andtotakeintoaccountthisnewinsightwhichcameaboutthankstothereviewer’squestion,\nthefollowingsentenceswereaddedonlines311-317: “Densitydownrampswithpeakdensitiesn ∼n\n0 b\nmaximiseboththeinjectedchargeandB ,asshowninFig.3(b),sincetheemittancevariedlittleacross\n3D\nthisscan((cid:15) = 0.4−0.5mm-mradforQ > 20pC). Thisisasurprisingresult,sinceinradiofrequency\nn,x i\nlinacinjectorstheemittanceofthebunchincreaseswithcharge,oratleastcurrent,duetospacecharge\nforcesafteritscreation”.\nMinoritems:\n1. Theintroductiondoesn’tseemnicelyorganized. Forexample,thefirsttwoparagraphsalmostrepeat\nthesameargument. Thethirdonefocusesonemittanceandwhatcanbepossiblyachieved,whichis\nok. However,thefourthparagraphgoesbacktowhyyouneedDDRIandbeam-driven. Also,thefourth\nparagraphexplainstoomuchlowleveldetailswithoutanyotherexplanations. Itwashardtoreadandhard\ntocatchwhatauthorswantedtosay. Ithinksuchdifficultywascomingfromtheparagraphandsentence\nstructures. Itwouldbegreatiftheauthorscanimprovethissection.\nThestructureoftheintroductionhasbeenchanged. Referencestopreviousplasmaaccelerationworkhas\nbeenmovedtothefirstparagraphtoavoidrepetition. Explicitdiscussionofdriver-witnesspairshasbeen\nomittedtohelpclarifywhatitiswestudiedinthiswork. Thesecondparagraphdiscusseshowthelarge\nacceleratingfieldsofaplasmaacceleratorenablelow-emittancebunchcreation. Thethirdexplainsdensity\ndownrampinjection,whichwasthechoseninjectionmethodinthiswork. Moreexplanationwasaddedin\nPage8of13\nthissectionassuggestedinthethirdminorcommentbythisreviewer. Thefourthparagraphprovidesa\nsummaryofthestateofthefieldandthemajorresultsofthispaper. Wehopethisstructureimprovesthe\nreadingexperience,andthankthereviewerforthesuggestions. Duetothelargechangesmadetothe\nintroduction,wedidnothighlightthemindividuallythistime.\n2. “astheyapproachthebackofthewaketheyexperienceamagneticfieldfromtheradialcurrentof\nsheathelectronwhichactasadefocusingforce”. Isitdefocusingforcenotfocusingforce?\nTheforceisdefocussing,asexplainedinRef.23ofthemanuscript(Xuetal.,inparticulartheirfigure3a).\nInthatpaper,followingLuetal. (references33and34fromXu’spaper),thetransverseforceonaplasma\nelectronisdescribedasconsistingof3components: adefocussingforcefromthedriver,afocussingforce\nfromtheionsandadefocussingforceproportionaltothecurvatureofthewakefieldpotential(whichLu\ndescribesasbeingduetothemagneticfieldproducedbytheradialplasmaelectroncurrent). Attheback\nofthebubblethecurvatureofthewakefieldpotentialbecomesverylarge(commonlyplottedasarapidly\nvaryinglongitudinalelectricfield),andonlyaroundthislocationdoesthedefocussingforceduetothe\nradialplasmacurrentexceedthefocussingforceoftheions. Inaconstantdensityplasmathiscauses\nmostbubblesheathelectronsto”bounce”fromtheaxisratherthancrossingit,whichisobservedinPIC\nsimulationsofplasmaacceleratorsoverawiderangeofconditions,includingwithlaserdrivers. However\ninadensitydownramp,electronsthatreturntotheaxiswithalargeforwardsvelocitycanbetrappedin\nthewakefieldwhiletheyareexperiencingthisdefocussingforce,whichcanleadtotheinjectionofalow\ntransversemomentumandthuslowemittancebunch. AmathematicaldescriptionisgivenbyXuwhich\ncannotbeimproveduponhere.\n3. ItwouldbegoodtohavemoreexplanationofDDRIintheintroduction. Currentlyitisforcingreadersto\nfindreferencestounderstandwhatthatis,anditseemsinappropriateforNatureCommunications’readers.\nItdoesn’thavetobelongbutwouldbeniceifyouhavewhatitisandwhyyoudoit(orwhatadvantages\nareexpected).\nPleaseseeourresponsetominorquestion1andtheupdatedthirdparagraphofthemanuscript,which\nnowprovidesabasicoverviewoftheDDRIprocess.\n4. “thedrivewaistpositioninzwhilepreservingitsspotsize”. Ifyouchangethefocusingpointinz\ndirection,itchangesthespotsize. Doyoumeanbythechangeisignorable? Oryouactuallymadeother\ncompensationupstream? Itwouldbebettertodescribeitmoreprecisely.\nThisistrue,wewantedtoimplythatthechangewassmall. Thiswasachievedbyhavingalargebeta\nfunctioninthefinalfocussingquadrupoles,suchthatchangingtheirfocallength(strength)madea\nsignificantchangetothefocalplanepositionbutonlyasmallchangetothebetafunction/spotsize\natfocus. BunchtrackingcalculationsinOCELOTshowthatalargechange(intermsoftheeffecton\ninjection)of0.5%ink or1%ink changethebetafunctionatfocusontheorderof1mm,comparedtoa\nx y\nnominalbetafunctionof20mm. Lines188-193ofthemanuscriptwerechangedtoread: ‘InFig.2(a)the\nfinal-focussing-quadrupole(FFQ)fieldstrengthsk inthexandy directionswerevaried. Duetothelarge\nβ-functionsinthesequadrupoleschangesintheirstrengthmostlyvariedthedriverwaistposition,while\nchangingtheβ-functionsatfocusonlyatthe5%level.’\nReviewer 3\nThearticle”Brightness-BoostedElectronBunchesfromaPlasmaAccelerator”describesanelectron\ndrivenPlasmawakefieldaccelerationexperimentusinginternalinjectionofthewitnessbunch. Ininjection\nmechanismisadensitydownrampinjection. Themainresultisa3Dbrightnessmeasurementofthe\nacceleratedwitnessbunchwhichtheauthorsclaimis4.8timeshigherthentheoriginallydrivingelectron\nbunch. Thepaperiswellwritten,ratherclearanddefinitelyoriginal. Theresultspresentedarenewand\ncertainlyimportantforthefieldofplasmaacceleration. Thepaperdescribesacomplicatedexperiment\ncombinedwithachallengingdataanalysis. Ithereforerecommendthepapertobepublished. Iwouldlike\ntheauthorstoconsiderneverthelessthefollowingcomments:\nPage9of13\nWethankthereviewerfortheirpositivecommentsandtheirappreciationofthechallengesinvolvedinthis\nexperiment.\nIntroduction: Tomyopiniontheauthorsdescribesomewhatinaccuratethelimitationofconventional\naccelerators. ForexampleastateoftheartFELisonlyafew100mlongnotseveralkilometers(for\nexampleSwissFEL).FurthermorethoseconventionalFEL’sproducebeamswithanemittanceof100nm\nfor100pCcharge. Thereforeactuallysuperiorofwhathasbeenachievedinthispaper. Seeforexample:\nE.Prat,P.Dijkstal,M.Aiba,S.Bettoni,P.Craievich,E.Ferrari,R.Ischebeck,F.Löhl,A.Malyzhenkov,\nG.L.Orlandi,S.Reiche,andT.SchietingerPhys.Rev.Lett.123,234801,2019. DOI:Thisfactsshouldbe\nmentionedwhichdoesnotdiminishtheachievementsofthepublication. Ifindthetermbrightness-boost\nextremelymisleadingbecausetherearetwodifferentbeams,oneloosesenergyandtheothergains\nenergyandisactuallygeneratedwithintheplasma. Whatisactuallythebrightnessofthewitnessbeamat\nitssourceifthiscanbesimulated/determined.\nWeacceptthereviewer’sremarksaboutstate-of-the-artFELfacilitiesandhavemadeseveralchangesto\nthemanuscript. Wehaveupdatedlines28-30toread‘Asaresult,theacceleratorsforfree-electronlasers\n(FELs)areseveralhundredsofmetreslong,andparticlecollidersreachtensofkilometresinlength.’\nRegardingtheemittanceofSwissFEL,wehaveupdatedthesentencenowonlines100-103toread‘Ithas\nbeenshowninsimulationsthatDDRIcanproducebuncheswith(cid:15) <100nm[refs],whichiscomparable\nn\ntotheverybestconventionalFELdriverlinacstoday[ref]’,wherethefinalreferenceistheonesuggested\nbythereviewerabove. Finally,wehavemadesignificantchangestothemanuscripttomostlyremovethe\ntermbrightnessbooster-pleaseseeourresponsestothefirstmajorissuefromreviewer2. Regardingthe\nbrightnessofthewitnessbeamatitssource,pleaserefertoouranalysisoftheevolutionoftheinjected\nbunch’semittanceandenergyspreadinsimulationsinourresponsetoreviewer1majorquestion2.\nResults: InthissectionIammissingthedetaileddataoftheresult. Whichbunchcharge,whichemittance\nandenergyspreadwasachieved. Animageofbothbeamswouldbeniceaswell. Itcomeslaterbutthose\naremajorresults.\nWethankthereviewerforthiscomment-weofcoursewantourresultstobeasclearaspossible. A\nsummaryoftheresultsincludingtheemittance,energyspreadandspectraldensityoftheinjected\nbuncheshasnowbeenincludedattheendofparagraph4oftheintroduction(ithasnotbeenhighlighted\nduetothelargechangesthatweremadetotheintroduction). Unfortunatelyitisdifficulttoshowimagesof\nthedriveandinjectedbeamsthatprovideafair,orsimple-to-understand,comparison,sinceallimages\nweretakenwithanimagingspectrometer,whichimageddifferentenergiesinthetwocases. Additionally,\nthedispersionchangesasafunctionofenergy. So,wefinditbesttorelyonderivedquantitiesratherthan\ntheimages.\nOptimalRampHeight&LengthforDDRI:Thischapterissomewhatconfusing. Itseemstobeasimulation\nstudybutitisnotsoclearhowitisrelatedtotheexperiment. Didtheexperimenthadclearcontrolonthe\nrampprofile,doweknowwhichprofilegavethebestresultintheexperiment. ? Pleaseclarifythispoints.\nThisisanimportantpointsincewebelievethatthesimulationsinthissectionprovideastrongscientific\nbasisforunderstandingourexperimentalresults. Similarcommentstothisoneweremadebytheother\nreviewers,andwebelievewehavedealtwiththisreviewer’scommentinourresponsestotheother\nreviewers. Pleaseseeourresponsestoreviewer1question1,reviewer1minorquestion4andreviewer4\nquestion1.\nTheexperimentonlyhadcontrolovertherampshapeviathedelaybetweenthearrivaloftheionising\nlaserbeamsandthearrivaloftheelectronbeam. PleaseseetheupdatedfirstparagraphoftheOptimal\nRampHeight&LengthforDDRIwhichnowcontainsadescriptionofhowthesesimulationsrelatetothe\nexperiment. Wealsoreferbacktoourresponsetoreviewer1minorquestion3.\n6DbrightnessestimatefromPICsimulations: Theauthorsliketosuggestthatthebrightnessboostin6D\ncouldbemoreimpressivethenthemeasuredonein3D.Thesimulationsseemtoshowquiteasymmetric\nemittancevalues,wouldn’tthissuggestthatthe3Dmeasurementpresentedbeforemightbeoptimistic\nbecauselikelymeasuredintheluckyplane?\nPage10of13\nWecouldonlymeasuretheemittanceintheplanewheresimulationsshowthesmallestemittance. This\ncouldbeconsideredserendipitous,butitisalsofairtosaythatimprovementscouldbemadetoreducethe\nemittanceintheotherplane. Itisalsonoteworthythatwehavealotoffreedomtochangeparametersin\ntheexperiment,butwecannotoptimisewhatwecannotmeasure.\nThefirstfigureinourresponsetoreviewer1showsthatthebunchesareinjectedwithsimilaremittance\nbutinthey planetheemittancegrowsasitispoorlymatchedtotheplasma,albeitwiththecaveatthat\nwehadnowaytoexperimentallyverifythis. Withmorelaserenergyandadaptiveopticstheplasmaspike\nitselfcouldlikelybeshapedtoreducetheemittancegrowth. Wesuspectthatthereasonforthemismatch\nisthattheplasmaspikeiscurvedmorestronglyiny,whereitswidthisoforderthelaserspotwidth,than\ninx,whereitswidthisoforderthelaserRayleighrange. Soevenusingalargerfocalspotsizemay\ndecreasetheemittanceinthey plane.\nStability,Emittanceandbrightnessoftheinjectedbunch: Itwouldbenicetomakeclearerwhatresultsare\naveragedoverthedatasetandwhicharebestshotsresultsinthischapter. Isthe4.8timesboostabest\nshotresult? Whatistheaverageofthedatasample?\nThe4.8timesboost(whichisnolongerreported,seeourresponsetoreviewer2,althoughthebrightness\noftheinjectedbunchisstillreported)representsanaveragequantity,wedonotreportonbestshot\nresultsunlessweveryexplicitlystatethatwearedoingso. The3Dbrightnessisbuiltupfromthespectral\ndensityoftheinjectedbunchdQ /dE,theinjectedbeamsizeaftertheplasmaσ anditsdivergence\ni x\nσ . WeusedthemeanvalueofdQ /dE from1000measurements,themeanσ from106successful\nx(cid:48) i x\nbeamsizemeasurementsandthedivergenceinferredfromanobjectplanescanconsistingof608\nsuccessfulmeasurements. Wefeelthatitwouldbeunfairtoestimateabestshotresult,sincenotall\nofthesequantitiescouldbemeasuredatthesametime(althoughtheyweremeasuredinthesame\nconditions). Itmaynothavebeenclearthatthiswasthemethodweusedinthemanuscript,sincewe\nattemptedtoindicatethatanaveraginghadbeendoneusingabracketnotation. Additionaltexthasbeen\naddedtotheendofthe”Stability,EmittanceandBrightnessoftheInjectedBunch”sectiontoconveythis\nmoreclearly. Inreferencetothe3Dbrightnessoftheinjectedbunch,itreads: ”Notethatthisvalueis\nconstructedonlyfromaveragedvalues,withtheexceptionoftheinjectedbunchdivergence,whichwas\ndeterminedfromafittoascanincluding∼600datapoints.”\nReviewer 4\nThepaperpresentsanexperimentalinvestigationofhigh-brightnesselectronbunchesgenerationfrom\naplasmaaccelerator,achievedthroughinjectioncontrolofimproveddensitytransitionusinganaddi-\ntionalinjectionlasertogenerateahigherdensityplasmaspike. Theinjectedelectronbunchexhibitsan\nimprovedbrightness,witha3Dbrightness4.8timesgreatercomparedtothedriverelectronbunch. The\nexperimentalresultsareelaboratelydiscussedalongsideparticle-in-cellsimulations. However,itisnoted\nthatabrightness-boostingschemewaspreviouslyproposedin[Phys. Rev. STAB.7. 011301(2004)](Ref.\n[16]inthepaper),andtheexperimentalsetupisalmostidenticaltotheirpreviouswork(Phys. Rev. Accel.\nBeams. 24. 101302(2021)). Assuch,thispaperappearstobemoreofanexperimentalverificationwork\nratherthanonethatextendstheboundariesofknowledge. Therefore,itmaynotbesuitableforpublication\ninNatureCommunications.\nWethankthereviewerforengagingwiththeunderlyingphysicsoftheexperiment. Itistruethatprevious\npublicationshaveproposedusingdensity-downrampinjection,orotherschemessuchasTrojanHorse\ninjection(Phys. Rev. Lett. 108,035001,(2012)),toproduceverybrightelectronbunches. Wenote\nthatweprovidedthisreference,plustheonessuggestedbythereviewerhere,aswellasfurthersimilar\nreferencesintheoriginalmanuscript. Whiletheconcepthasbeenshownintheoryandsimulation,\nexperimentalconfirmationwaslackingthathighspectraldensity(dQ/dE)buncheswithlowemittancecan\nbeinternallyinjectedwithinPWFAs. Asinallphysicsfields,experimentalproofiscritical. Furthermore,\nthefieldofplasmaacceleratorsoftendrawscriticismduetothelargeshot-to-shotjittersintheaccelerated\nbeamparameters,whichwouldlimittheirproposedapplications. Therefore,itisnotimmediatelyclearfrom\nPage11of13\natheoreticalpaperthattheschemecanproducebuncheswithstableparametersinthepresenceofjitters.\nInadditiontomeasuringbrightbunchesfromthisscheme,wealsoshowthatwecanproducethemvery\nrepeatably,whichwethinkaddsgreatvaluetotheheadlineresults.\nWhilethesetupissimilartopreviousworkfromtheFLASHForwardexperimentbyKnetschetal. (Phys.\nRev. Accel. Beams. 24. 101302(2021))thekeyinnovationwemadetocreatethesebrightinjected\nbuncheswastouseextremelysteep,highpeakdensitydownrampstoinjectthem,whichweexplained\nwithparticle-in-cellsimulationsinthesectiontitled‘OptimalRampHeight&LengthforDDRI’.Wedidnot\nfindthisregimeusedorproposedelsewhereinliterature. Furthermore,diagnosticupgradesweremade\nsincetheexperimentationofKnetschetal.: thehighresolutionimagingspectrometerstation(referred\ntoastheHRSPECinthemanuscript)wasinstalledtoenablethemeasurementofsmallemittances. In\nFigure2ofthemanuscriptandthesurroundingtextwestudiedhowthesystemparametersaffected\ninjection. Threeofthese: drivebunchfocalposition,driverdurationandthedelaybetweentheionising\nlaserandthearrivalofthedriverwerenotconsideredbyKnetsch. WealsohighlightthatReviewer2\npositivelycommentedonthisaspectofthestudyanditsimplicationsforfutureworkinthisarea.\nThereareseveraladditionalissuesthatneedfurtherdiscussionandrevise:\n1. Inthescansimulationsusingthequasi-3DFBPICcode,whichemploysacylindricalcoordinatemodel,\nthesimulatedsystemneedstoexhibitcylindricalsymmetry. However,thespikeplasmadensitycreatedby\nthetightlyfocusedinjectionlaserdeviatesfromcylindricalsymmetry,whichcouldimpacttheaccuracyof\nthesimulations.\nSimilartoourresponsetoQuestion1fromReviewer1,thegoaloftheq3DFBPICsimulationswasnot\ntosimulatetheexperimentasaccuratelyasreasonablypossible. Thatwasthegoalofthefull-3DWarpX\nsimulation,theresultsofwhichwerepresentedinFig.5. Insteadweaimedtoprovideanexplanationfor\nthetemporalvariationoftheinjectedcharge,withthejustifiedassumptionthatthisvariationaffectsthe\ninjectionprocessbyachangingdownrampheightandlength. Itwasnecessarytoperforma2Dscanof\ntheseparameterssincetherampheightsweusedhavenotbeenreportedinliteraturebeforeandboth\nrampheightandlengthimpactthephysicsofinjection,asdetailedinthediscussionofFig.3c. Itwasnot\npossibletoperforma2DparameterscanofthemorerealisticWarpXsimulationsduetotheirprohibitive\ncost-thesinglesimulationinFig.5usedapproximately1monthofourgroup’sGPUtimeontheJUWELS\nBooster. Thusthereduced-dimensionalitycodewasused. ThedensityrampintheFBPICsimulations\nwasalinearrampinz only,itdidnotvaryasafunctionofr orangle. Thishasbeenclarifiedonlines\n281-282withthetext: “Thedensityvariedonlylongitudinally,andnotwithradiusorangle.” Webelieve\nthatthesimplifiedFBPICsimulationsalsoprovideinsighttootherexperimentsandthewiderfielddueto\ntheirconceptualsimplicity. Wehopethattheadditionaltextinthemanuscript,detailedinourresponseto\nQuestion1fromReviewer1,adequatelydescribesourintentionsforthissimulationset.\n2. Theauthorsmentionthat,fortheexperimentalresults,althoughtheemittanceoftheinjectedelectron\nbunchis17timeslowerthanthatofthedriver,the3Dbrightness(B3D)onlyshowsanincreaseof4.8\ntimes. ThisdiscrepancyisattributedtothededuceddQi/dE,whichdecreasesastheenergyspread\nincreases. Thischallengehighlightstheneedtocontroltheenergyspreadandphasespacerotationofthe\ninjectedelectronbunch.\nWeagreewiththeviewerthatcontroloftheenergyspreadisimportant. PWFAsgenerallydonotfeature\nphasespacerotation. Sincethedriverandthewitnesspropagateatverysimilarspeeds,intheabsenceof\nsignificantdriverevolutioneachsliceofthewitnessstayslockedatthesamephaseinthewakefield. In\ntheabsenceofproperbeamloading(Tzoufrasetal.,Phys. Rev. Lett. 101,145002(2008))thiscauses\nthewitnessbunchtobecomechirped,althoughthesliceenergyspreadremainsconstant. Ithasbeen\nfoundthatanoptimallengthforlow(projected)energyspreadbunchesfromdensitydownrampinjection\nexists,whichwascalculatedinpublicationssuchasHueetal.,MatterRadiat. Extremes8,024401(2023).\nOverthislengththeenergyspreadisreducedastheinitialchirpfromtheinjectioniscancelledoutduring\nacceleration,providingapotentialsolutiontoovercometheproblemofimproperbeamloading. Onemay\nalsospeculatethatgoodbeamloadingconditionsmaybefoundbytailoringtheshapeofthedownrampto\nvarythecurrentoftheinjectedbunchalongitslength,althoughastudyofthisisunderstandablybeyond\nPage12of13\nthescopeofthismanuscript. Therefore,schemesexisttoproducealowprojectedenergyspreadbunch\nfromdensitydownrampinjectionaftersignificantacceleration,inadditiontoalowsliceenergyspread. We\nalsonotethattheenergyspreadoftheacceleratedbunchinthesimplifiedsimulationinfigure6inthe\nmanuscriptremainsbelow1%afteraccelerationto635MeV,overtwentytimesmoreenergygainthanthe\nmeasuredbunches.\n3. Theauthorssuggestthattheirsimulationsindicateapotential>1000-foldincreaseinthe6Dbrightness\n(B6D)intheirexperimentalconfiguration. However,itisnotedthattheemittancevaluesusedinthe\nsimulationsareslice-normalizedemittances,whereastheexperimentalresultsprovidenormalized\ntransverseemittancevalues. Thisdiscrepancycouldbemisleading,assliceemittanceistypicallymuch\nlowerthannormalizedtransverseemittance. Furthermore,thesimulationsdonotincludetheparameters\nofthedriver,anditwouldbebeneficialtocomparethephasespacedistributionbetweenthedriverandthe\ninjectedelectronbunch.\nFigure5(a)plotstheslicenormalisedemittanceoftheacceleratedbunch. Theprojectedemittancesare\nalsosmallasstatedonlines406-407. The6Dbrightnessfromthesimulationwascalculatedwiththese\nprojectedvaluesalthoughthiswasnotstatedinthemanuscript. Themanuscriptwasupdatedonlines\n410-413toread;‘ThesimulatedB =42pC/MeV/mm-mrad,calculatedusingtheprojectedemittances,\n3D\nwas3.7timestheexperimentalvalue,whichusedaconservativemeasurementof(cid:15) .’ Theinitialdriver\nn,x\nparametersarealreadystatedonlines397-401.\n4. InFigure6(b),theemittanceappearsdifferentfromthatinFigure5. Itwouldbebeneficialtoincludethe\nbrightnessevolutioninthisfigureforamorecomprehensiveanalysis.\nFigure6showsresultsfromanidealisedFBPIC(quasi-3D)simulationwhileFigure5showsresultsfrom\nafull3DWarpXsimulationthatrecreatedtheexperimentasfaithfullyaspossible. Tomakethismore\nclear,lines438-440wereupdatedtoread‘ThecaseIIsimulationfromFig.3wasextendedinFBPICtoa\n195mmlongplasmausingthesamedrivebunch.’ Togiveabetterpictureoftheevolutionoftheinjected\nbunchbrightnessinthissimulationweaddedtheevolutionoftherelativeenergyspreadtofigure6(b).\nLines448-452wereupdatedtoreadTheFWHMenergyspreadofthebunchatz = 195mmremains\nlowat0.6%,butisincreasedinabsolutetermsfromaminimumvalueof0.1MeVshortlyafterinjection\nto3.7MeVattheendoftheplasmaduetoimproperbeamloading. Giventheapproximatelyconstant\nemittancethisgivesafullpictureofthebrightnessevolutionanditscausei.etheincreasingenergyspread.\nPleasenotethatinthissimulationnoeffortwasmadetooptimisetheenergyspreadoftheinjectedbunch.\nItslowvaluedemonstratesthepotentialofthisschemetoproducehighbrightnessbunchesathigher\nenergies.\n5. Theformatofthereferencesshouldberevised. Forexample,inreference[10],”PlasmaPhysicsand\nControlledFusion”shouldbeformattedas”...PlasmaPhys. Control. Fusion...”\nThereferencesweusedwereproducedbydownloadingthebibtexfilefromthepaperURLwherever\npossible. WhenthiswasnotpossibleourintentionwastoconformtothehousestyleofNatureCommunic-\nations. Ifinconsistencieswithotherjournalsarefound,suchastheonehelpfullyhighlightedbythereferee,\nthenwewouldbehappytodefertothewishesoftheeditors.\nAdditional changes to the manuscript\nWefoundtwosmallmistakesintheanalysisoffigure6,regardingtheenergygainandenergyspread.\nTheelectronenergyreportedinfigure6andthesurroundingtextwastoosmallbyafactorofm c =\ne\n0.511MeV/c,whichwehavenowcorrected,andtheenergyspreadoftheinjectedbunchwasoverstated\nforbothitsminimumandmaximumvalues. Specificallyfigure6(a)wasupdatedandthetextonlines445-\n452waschangedto‘Thepeakelectronenergyincreaseslinearlywithpropagationdistanceto635MeV\natz =195mmatarateof3.3GeVm−1. TheFWHMenergyspreadofthebunchatz =195mmremains\nlowat0.6%,butisincreasedinabsolutetermsfromaminimumvalueof0.1MeVshortlyafterinjectionto\n3.7MeVattheendoftheplasmaduetoimproperbeamcloading.’\nFurthermore,amistakewasfoundonline370ofthemanuscript. Previouslywestatedthattheresolution\noftheHRSPECwas7µmbutthisdidnotaccountforthemagnificationof∼ 2.8. Theresolutionisnow\ncorrectlystatedas2.5µm. Themagnificationwasalreadycorrectlyaccountedforintheanalysisofthe\nbunchwidths,however,andthesehavenotchanged. Thisdoesnotchangeanyconclusion,sincethe\nbeamwidthsweremuchlargerthantheresolutionsotheywereandarewellresolved.\nYoursfaithfully,andonbehalfofalloftheauthors\nJonathanWood"}, {"round": 2, "reviewer_comments": {"reviewer_2": "As already commented in earlier report, I believe this manuscript satisfies Nature Communications’ publication criteria.\nThe previous report provided two major issues and a few minor issues that must be addressed. Authors provided\nappropriate replies to each issue and updated the manuscript accordingly.\nI recommend the publication of this manuscript.", "reviewer_3": "Revision of the paper \" Bright Electron Bunches from a Plasma-Wakefield Accelerator with a Step Density Down-Ramp\" by\nJ.C. Wood et al.\nThe authors prepared a very detailed and rigorous response to the reviewers questions and concerns.\nThey made a number of changes in the manuscript in order to address the issues raised by the reviewers.\nI am happy with the revised paper and feel my concerns have been taken into account appropriately.\nI recommend to publish the paper in this version."}, "author_response": ""}]

Decision letter