Gas-dynamic density downramp injection in a beam-driven plasma wakeﬁeld accelerator

present the experimental demonstration of density downramp injection at a gas-dynamic shock in a beam-driven plasma accelerator. The ultrashort driver electron beam with a peak-current exceeding 10 kA allows operation in the blowout regime and enables injection of electron witness bunches at gentle density ramps, i.e., longer than the plasma wavelength, which nurtures prospects for ultralow bunch emittance. By precision control over the position of injection we show that these bunches can be energy-tuned in acceleration gradients of near 120 GV m − 1 .

We present the experimental demonstration of density downramp injection at a gas-dynamic shock in a beamdriven plasma accelerator. The ultrashort driver electron beam with a peak-current exceeding 10 kA allows operation in the blowout regime and enables injection of electron witness bunches at gentle density ramps, i.e., longer than the plasma wavelength, which nurtures prospects for ultralow bunch emittance. By precision control over the position of injection we show that these bunches can be energy-tuned in acceleration gradients of near 120 GV m −1 . Beam-driven Plasma Wakefield Accelerators (PWFAs) enable dephasing-free acceleration of electron bunches at gradients >100 GV m −1 when a plasma wakefield is excited by a relativistic particle beam of high peak-current [1,2]. Operation of a PWFA in the blowout regime [3,4] results in stable wakefield formation with linear uniform focusing fields, a prerequisite to enable emittance preservation during acceleration. Rapid progress was made in recent years with the demonstration of energy doubling of 42 GeV electrons [5], of high energy-transfer efficiency from driver to witness beam [6], and with the proof-of-concept addition of plasma photocathodes for witness beam injection [7]. Development of internal injection methods in PWFAs is a crucial task toward high-quality low-emittance bunch generation and improved control over bunch parameters for quality-demanding applications like free-electron lasers [8] or high energy colliders [9].
Equally vital as bunch quality for applications is the ability to control and adjust bunch parameters. The injection mechanism plays a pivotal role in both aspects, as it determines the initial properties a witness bunch acquires in the wakefield, including its emittance. Additionally, if able to control and adjust the point of injection within a PWFA, independent of * j.couperus@hzdr.de other accelerator parameters, one achieves on-demand tunability of the final energy. In recent years, several injection methods directly inside a PWFA have been proposed aiming for the generation of ultralow bunch emittance [10][11][12][13][14][15][16]. Injection triggered by a plasma density downramp [10,17] is especially appealing for its adjustability and its potential for witness injection with only few tens of nanometer emittance [18,19].
In this letter, we present the first experimental implementation of such a density downramp injection (DDI) scheme induced by a hydrodynamic shock-front in a PWFA. We show energy tuning capability by means of tuning the downramp location in a high-density, high accelerating gradient PWFA. Downramp injection can only occur when the longitudinal velocity of plasma electrons β z temporally exceeds the wake's phase velocity β φ , i.e., β z > β φ ≈ (1 + χ 2k p n p dn p dz ) −1 , which reduces while the driver traverses a negative density gradient. Here n p (z) is the local plasma density, χ = k p (z − β b ct ) the electron's phase relative to the driver and β b the driver speed relative to the speed of light. For this condition to be fulfilled, the density gradient has to be sufficiently steep and the driver has to excite a strong enough blowout to generate sufficiently fast wake electrons, which typically only occurs when the drive beam peak-current exceeds a few kilo-amperes. Generally, stronger drivers lead to a higher longitudinal velocity of plasma electrons when returning to the propagation axis (β z ) and thus allow for injection to occur at more gradual density ramps [17]. Despite being a common injection scheme in laser-driven wakefield accelerators (LWFAs) [20][21][22][23][24][25], fulfilling both requirements simultaneously in linac-driven PWFA . From left to right, a high-intensity laser pulse drives the LWFA, where the PWFA drive beam is generated. A kapton foil reflects the spent LWFA drive laser, while the electron beam propagates into the PWFA as a drive beam. A low-intensity counterpropagating laser preionizes the PWFA medium. Optionally, a position-adjustable 20-μm wire can be inserted inside the PWFA stage to invoke a hydrodynamic shock-front. The density downramp of this shock allows for injection of a witness bunch at a predetermined position. The inset shows a shadowgram of the beam-driven plasma wave at the second shock-front captured by a few-fs probe beam. Panels (b)-(d) each display 10 consecutive electron distributions [all using the color-scale shown in (d)] used for determining the statistical parameters. Panel (b) shows the drive beams before interaction with the PWFA stage. They are transmitted through the blocker foil while the PWFA is still disabled. Panel (c) shows the remaining drive beams after interaction with the PWFA stage enabled but no shock-wire present. Panel (d) shows the spectra with wire for DDI at the PWFA center. Accelerated witnesses are visible at low energies, highlighted in (e) as a zoom view of (d).
facilities [26,27] is especially challenging at shallow ramps [10] linked to the relatively low β z attainable with currently available PWFA drive beams [17]. At steep ramps (downramp length l shorter than c/ω p ) DDI has recently been demonstrated [7,28,29] using a laser-generated cold plasma torch [11], which offers particularly steep density gradients. In contrast, the gas-dynamic shock injection regime produces gentle density downramps (i.e., l > c/ω p [19]), which promises a more adiabatic injection process with particularly low emittance for the injected witness bunch [18].
In our experiment, shown in Fig. 1(a), we generate the PWFA drive beam in a preceding laser-driven LWFA. This staged LWFA-driven PWFA (LPWFA) [30][31][32] exploits the high peak-currents from the LWFA beam, which exceed 10 kiloamperes [33,34], to drive the PWFA such that the injection requirements are met even on gentle gas density downramps. Meanwhile, the inherent ultrashort electron beam duration of around 10 fs [35] allows operation at plasma densities above 10 18 cm −3 . These high plasma densities lead to high amplitude wakefields and the potential for high-brightness witness generation [36].
Our setup consists of two consecutive gas jets forming the two separate laser-and beam-driven accelerators. The 3-mm-long LWFA is driven by the 150 TW DRACO laser [37] and is operated in a tailored self-truncated ionization-induced injection (STII) scheme detailed in Ref. [38] and employs beam loading to limit energy spread [33]. The generated beam exhibits a broad energy spectrum with a distinguishable quasimonoenergetic fraction which contains a mean high-charge Q of 335 ± 24 pC within its FHWM and 39 ± 2 MeV FWHM energy spread at a mean energy within the FWHM, E, of 323 ± 9 MeV (S.E.M.). This corresponds to a spectral charge density S = Q/( E /E ) of 28 ± 2 pC % −1 . The beam duration (FWHM) was reconstructed at an equivalent configuration from the spectral intensity of transition radiation measurements [39,40] to 14.8 ± 1.6 fs at an envelope peak-current of 12.4 ± 1.1 kA [41], sufficient to drive the subsequent PWFA in the strong blowout regime. A 25 μm kapton foil placed in vacuum, 0.5 mm behind the LWFA, acts as a plasma mirror to fully reflect the spent drive laser. Before entering the PWFA as a drive beam, the beam divergence was measured to be 3.1 ± 0.2 mrad (rms). This comparably high divergence results from current filamentation instability created by high-intensity laser-foil interaction before foil transition [42]. The spectral distributions of a set of consecutive drive beams is shown in Fig. 1(b). Throughout this letter the operational conditions of the LWFA are kept constant at the aforementioned conditions.
The PWFA consists of a 3-mm hydrogen jet, placed 0.5 mm behind the blocker foil. Using a counterpropagating low-power (∼20 mJ with a FWHM focal spot size of ∼120 μm) laser pulse, which leaves the gas jet through the left edge about 1 ps before the drive electron beam enters the gas jet through the left edge, a preformed plasma channel defines the PWFA medium. The PWFA is first operated without density downramp, i.e., no shock wire inserted. At a plasma density of 4.0 × 10 18 cm −3 , a strong beam-plasma interaction is observed in the remaining driver spectra, as shown in Fig. 1(c). The driver's peak FWHM-integrated charge is reduced to an average of 50 ± 4 pC. The energy spread broadens to 69 ± 9 MeV, while the associated mean peak energy reduces to 302 ± 10 MeV. The spectral charge density is reduced to 2.3 ± 0.2 pC % −1 . These effects are signatures of energy transfer from the drive beam into the plasma for the excitation of a plasma wakefield. However, as confirmed in simulations, a fraction of the driver beam is decelerated to energies significantly below the FWHM lower bound, thus these values do not contain the entire driver beam and do not allow us to determine exact charge loss and energy transfer values from experimental measurements. Shadowgraphy probe images show wakefield formation by revealing a distinct plasma wave captured by a synchronized few-cycle laser pulse [43]. The presence of these wakefields together with a reduction by a factor of more than two in divergence, i.e., down to 1.4 ± 0.1 mrad, demonstrates that a substantial fraction of the drive beam originating from the LWFA is successfully transported and refocused by utilizing the initial part of the hydrogen jet as a passive plasma lens [44][45][46][47]. Due to the lack of an injection mechanism at this configuration, no witness bunch is observed in the spectra shown in Fig. 1(c).
To prompt injection of a witness, we introduce a density downramp by placing a 20-μm wire 2 mm below the propagation axis of the driver, down from the center of the PWFA. This induces a hydrodynamic shock and creates two distinct density downramp regions [ Fig. 2(c)]. The gas-flow disruption is highly localized to prevent significant influencing the PWFA gas jet upramp required to recapture the drive beam. As we will show in more detail later, electrons injected at the first shock are fully decelerated while passing through the second shock. Therefore, despite two shocks, a single witness bunch is expected in this arrangement. Exiting the PWFA, the remaining driver shows similar beam parameters as in the case without wire; a reduced mean divergence at 1.5 ± 0.1 mrad, a likewise reduced peak charge at 55 ± 4 pC, a mean peak energy of 301 ± 7 MeV with 71 ± 5 MeV energy spread, and a spectral charge density of 2.4 ± 0.1 pC % −1 . Since a similar response is found as in the case without shock wire, we deduce that the drive beam is sufficiently rigid not to be disturbed by the induced plasma density steps. With the introduction of a DDI region, the emergence of witness bunches accelerated up to a mean maximum energy of 57 ± 2 MeV is observed as shown in Fig. 1(d). This value is determined at the most energetic witness signature, prominently distinguished from the reference average without shock, and averaged over all events showing injection. Furthermore, the large energy spread down to few-MeV energies indicates that witness electrons are injected at different phases of the wakefield. This can be attributed to a large density step from the shock-peak down to the plateau region leading to the injection of long witness bunches [17]. Here, the bunch experiences a high accelerating gradient difference between the head, closer to the accelerating field's zero crossing point, and the tail, at the rear-side of the wakefield.
To assure the origin of the injection, a 3D particle-in-cell (PIC) simulation is performed using PIConGPU [48] implementing a LWFA-PWFA digital twin of the experiment. We achieve start-to-end simulation capability by integrating all stages of the experiment into a single, large-scale, GPUaccelerated simulation on 192 K80 GPUs, mimicking the experiment as closely as possible while ensuring numerical stability for more than 3.6 × 10 5 PIC cycles.
The simulation models the LWFA drive laser using a Gauss-Laguerre mode, up to order 12, fitted to the measured laser profile within one Rayleigh length around the focus. The gas profile is based on measurements using tomographic interferometry [49] which was further refined by plasma-wave shadowgrams. The latter provides higher spatial resolution for the determination of the exact position of the highly localized shock-fronts. However, the simulated shock density profile is still an approximation, which may result in deviations in witness quality compared to experiment. Inserting a wire perturbs the gas, creating two shock regions to the left (shock I) and right (shock II) of the wire with reduced density in its shadow [ Fig. 2(c)].
The simulation box consists of 768 × 4608 × 768 cells with a transversal resolution of 177.2 nm and a longitudinal resolution of 22.15 nm. This resolution ensures numerical stability throughout this start-to-end LPWFA. A combined BSI [50] and ADK [51] ionisation model was used with the Lehe [52] field solver, the Boris pusher [53], and the Esirekepov current deposition scheme [54]. A full setup of the simulation can be found under [55]. The beam's transition through the foil is simplified, due to including this being prohibitively expensive computationally, thus neglecting the complex dynamics resulting from the interaction between the magnetic instabilities at the surface of the foil and the electron bunch and its influence on the divergence during transition [42].
With a charge of 226 pC, a divergence of 3.4 mrad (rms), and an FWHM energy spread of 30 MeV around a mean peak energy of 366 MeV after passing through the foil, the simulated driver approximates the parameters of the experiment. After expansion in the intermediate vacuum, the drive beam is effectively recaptured as it enters the PWFA stage. Most of the beam is focused down to a FWHM beam diameter of 2.4 μm [ Fig. 2(a)] while a substantial portion, mostly consisting of its higher divergence fraction, is lost and does not contribute to the wakefield formation. A high driver density, much larger than the ambient plasma density (n b n e ), with a peak-current I peak > 10 kA is achieved and sustained during propagation while the short beam duration condition remains fulfilled. This enables the driver to excite a strong enough blowout, providing fast electrons required to trigger shockfront injection and subsequently accelerate witness electrons, as illustrated in Fig. 2(b).
The simulation further reveals that the density downramps at both shock-fronts lead to injection, i.e., green and red shades illustrate electrons from shocks I and II, respectively [ Fig. 2(c)]. However, only the witness electrons from the second shock stay in phase with the accelerating field and continuously gain energy. After injection at z i , the relative phase χ (z) of an electron within the wake changes with the density n p (z) as χ (z) = χ (z i ) n p (z i )/n p (z). Electrons only experience acceleration in the back half of the cavity at −2π χ −π [17]. The witness injected at shock I is generated in the low-density shadow region of the wire and rephases to a decelerating region of the second cavity (χ −2π ) during the transition through shock II, where it decelerates quickly. In contrast, the witness bunch generated at shock II is injected spatially separated and does not undergo further density steps and is accelerated over the remaining length of the accelerator with an average accelerating gradient of 96 GVm −1 reaching 74 MeV shown in Fig. 2(d).
Experimentally, taking advantage of the localized injection, we achieve energy tuning capability by adjusting the position of injection and thus changing the effective acceleration length of the injected witness. Figure 3 presents the witness energy as a function of shock II position. The energy gain is directly related to the change of the acceleration length, which allows us to determine the effective accelerating gradient to 85 GV m −1 as seen in Fig. 3(b). Shifting shock II toward the end of the PWFA reduces the acceleration length such that, just before the start of the gas jet density downramp, the maximum witness energy reduces to 17 ± 1 MeV, barely above the low energy background. This confirms shock II as the source of witness injection. In the absence of other injection mechanisms and unique for the scenario with the shock wire in place, the injection of the witness is solely attributed to density downramp injection.
Additionally, tuning the accelerating gradient, autonomous from the acceleration length, is possible by adjusting the plasma density and expected to scale as E z ∝ √ n p [40,56]. To investigate this, the wire is placed at the jet center, fixing the point of injection and thus acceleration length. Scaling plasma density from 3.0 × 10 18 cm −3 up to 8.2 × 10 18 cm −3 , we tune the acceleration gradient manifesting in higher witness energies following the expected scaling, as is shown in Fig. 4. At a plasma density of 8.2 × 10 18 cm −3 a maximum acceleration gradient of 121 GV m −1 is achieved.
In summary, making use of a high peak-current driver originating from a preceding LWFA, we have demonstrated the possibility of DDI in PWFAs at gradual ramps, as advised for high quality beam injection. These results provide a promising outlook for oncoming commissioning experiments at conventional sources, e.g., FACET-II and the intention to utilize their upgraded driver peak current to inject at gradual downramps where the wavelength of the wake adiabatically increases [26]. This concept can then be scaled at conventional accelerators to much higher energies and repetition rates, connecting a broad community striving toward the generation of energetic, ultrashort, and ultralow emittance beams. Meanwhile, compact LPWFAs' short beam durations of ∼15 fs allows operation of PWFAs in a high-density regime that is hardly accessible for conventional electron sources, yielding increased accelerating gradients while opening a pathway toward ultrahigh-brightness beam production [36]. The next step for bunch quality improvement is to tune properties of the density transition, which our setup lacks at this point. Properly finetuning the density step promises to reduce energy spread and emittance [17]. Witness bunch creation with only few tens nm emittance is considered feasible [18,19]. The presented DDI at a previously inaccessible regime of plasma densities above 10 18 cm −3 , utilizing drivers with peak-currents beyond 10kA, represents an essential step toward exploring PWFAs, both conventional or LWFA driven, as compact sources for high brightness [36] and ultrafast [57,58] science.   our experiment was explicitly designed not to significantly influence the up-ramp region of the gas-jet, where the beam capturing and refocusing occurs, on which we will detail in the next section. This is achieved by using a wire, which creates only a very localized disruption in the gas-flow, without significantly influencing the remainder of the gas-jet. This is contrary to e.g. a razor blade, which would completely remove the front section of the gas jet, which is required for beam capturing.
A simulation of the plasma lensing in absence of a wire, with a direct comparison to the simulation with shocks created by the wire (as included in the manuscript), is given in Fig. 5. The synthetic spectrometer data [Figs. 5(b) and 5(d)] show very similar bunch structures. In agreement with experimental measurements, the driver's FWHM charge are Q FWHM = 44 pC for the double-shock case and Q FWHM = 47pC for the unperturbed scenario.

Details on beam recapture
Mentioned in the main manuscript, the initial part of the hydrogen jet acts as a passive plasma lens to refocus a substantial part of the driver beam. A part of the driver beam is not refocused and thus excluded from the measured FWHM divergence value in the experiment.
In order to illustrate the effect of this selection in the experiment, we analyzed the bunch divergence as the bunch propagates through the PWFA stage using a PIC simulation (Fig. 6).
The strength of the focusing effect via plasma lensing depends on the radial (and longitudinal) position of electrons in the bunch.
Before plasma lensing occurs, 80% of the bunch charge is located within the FWHM divergence region (enclosed by the solid black line in Fig. 6) which amounts to ∼12 mrad. After plasma lensing at the end of the PWFA stage, only 40% of the total bunch charge is within the FWHM. But the FWHM divergence has reduced by a factor two to ∼6 mrad. To depict the individual contributions to the final electron energy distribution more clearly, the separated contributions zoomed in to energies below 200 MeV and the PWFA jet range only, are given in Fig. 7.
The driver beam [black in Fig. 2(c) in the main text] has a sizeable contribution to lower energies. This can partially be attributed to a secondary downramp injection at the LWFA gas jet exit, and partially due to deceleration of the main, higher energy fraction of the driver beam.
Electrons originating from the first shock [green in Fig. 2(c) in the manuscript] are initially accelerated at the low density region between both shocks. During the increase of plasma density toward the second shock, its main fraction is rephased to the dephasing region (χ −2π ) and thus decelerated. The dephasing means these electrons are spatially separated from the electrons injected into the first cavity at the second shock.
FIG. 6. Divergence evolution of the bunch while propagating through the PWFA stage. In black, the FWHM of the divergence is marked. When the bunch enters the PWFA stage and is being focused, the FWHM divergence θ FWHM reduces.