Validation of a Compact and Tunable Continuous Gas-Flow Laser-Plasma Target for Electron Beam Production Above 150 MeV

Abstract

The present article reports on the generation of stable 50 pC low-divergence electron beams above 150 MeV from laser-driven wakefield acceleration using a continuous-flow gas target prototype tested at the 60 TW Salle Jaune facility at LOA. The gas target design is meant to be easily transported and integrated as an element of the beamline with a differential pumping system offering some 10⁻⁴ mbar pressure in the rest of the line. A dedicated gas injection system allows for the control of the gas mixture concentration and gas pressure in two different regions of the target within the frame of controlled ionisation injection schemes. The measured electron beam parameters show the importance of gas density profiles and longitudinal gas mixture confinement.

1. Introduction

Theorised in the second half of the twentieth century [1,2,3], plasma acceleration nowadays aims to compete with radio-frequency (RF) technology. Due to its ionised state, plasma can achieve fields which exceed the usual 100 MV/m breakdown limit in RF and can sustain accelerating gradients that are many orders of magnitude higher. In 2007, Blumenfeld et al. [4] demonstrated at SLAC the energy doubling of an incoming 42 GeVelectron beam in 85 cm of plasma.

In addition to acceleration, plasma may also be used as an electron source or so-called “injector”. In comparison with conventional photocathodes, laser-plasma injectors can produce electron bunches with much shorter bunch lengths (down to the sub-micron) [5,6,7,8] and typical currents in the kA regime [9,10]. These features enable a wide range of applications, e.g., as an X-ray source for free-electron lasers (FELs) [11,12,13] or as a direct tool in medicine, such as Very High Energy Electrons (VHEE) therapy [14,15,16,17], potentially in combination with the FLASH effect [18], for localised selective dose deposition. Due to the strong focusing fields within the plasma-accelerating structure, electron beams from plasma injectors usually have a relatively small size (of the order of micrometers), which is counterbalanced by a large divergence at the exit. Combined with a broad energy spread, this makes them hard to transport. One solution is to have a smooth downramp of decreasing density, which slowly reduces the focusing field of the wake, as discussed in [19,20,21,22,23,24]. In the perfect-case scenario, the focusing force in the outramp remains linear and decreases slowly enough to act adiabatically on the beam, i.e., to preserve the transverse emittance. This slowly increases the beam size and decreases the divergence, making the free drift in vacuum after the source less critical for later capture.

As part of the European EuPRAXIA project [25], the PALLAS project at IJCLab [26] focuses on the design and testing of technological components for a laser-plasma injector, using the LASERIX facility [27] as the laser source. The objective is to demonstrate the operation of a stable and reliable electron beam with the following characteristics: 30 pC of charge, 150 MeV to 200 MeV of energy, a spread of less than 3%, emittance below 1 mm.mrad, and divergence below 1 mrad.

Since the PALLAS facility was not yet operational at the time of the experiment, the target design was tested at the Salle Jaune laser facility at LOA. It delivers high-stability laser pulses at 800 nm, with a typical pulse duration of 30 fs and peak powers reaching up to 60 TW after compression. The Salle Jaune facility is a highly versatile platform dedicated to laser-plasma acceleration and ultrafast radiation science. It supports the production of electron beams spanning a wide range of parameters, from multi-nanocoulomb bunches at a few MeV [28] to a few pC at energies exceeding 1 GeV [29]. The facility is also used to generate ultrabright X-ray sources through Compton scattering [30,31] and betatron radiation [32,33]. These sources enable a wide range of applications, including the investigation of warm dense matter [34,35] and studies in radiobiology [36,37].

We propose here a design that operates in continuous gas flow and which is meant to be easily transportable, as a part of the beamline. Such an approach brings novelty to the community, approaching an easy integration of laser-plasma electron sources.

We begin by introducing the laser-plasma electron source design in Section 2, along with the setup used to test it. The experimental results of electron beam production are presented in Section 3, with an emphasis on stability and divergence (Section 3.1). We then improve their spectra through gas mixture and pressure control in Section 3.2. Finally, we conclude on the results presented and propose future developments for the target design.

2. Materials and Methods

2.1. Target Design

To fulfil the laser-plasma electron source parameters, we choose the self-truncated ionisation injection technique [38,39]. The target has a first region where a dopant (high-Z gas, like N₂) is mixed with a background gas (typically He). A laser pulse ionises the region and creates a plasma wake. When the laser becomes intense enough, the inner-shell electrons of the high-Z gas may be trapped inside the wake and accelerated. The target’s second region only contains a background gas, preventing dopant injection and serving as an accelerating stage for the injector.

The gas cell we use as a laser-plasma electron source is presented in Figure 1. It is inspired by the design used by the LUX team at DESY [10] mixed with the design from Kim et al. [40].

It consists of three plates glued together. The two quartz outer plates have optical quality to allow for diagnostics. The central one is made of ceramic (Al₂O₃) and has inner features that, once mounted with the two outer plates, correspond to channels for a gas inlet, an outlet, and a central longitudinal plasma channel with a $500\times 500 \mathsf{\mu }\mathrm{m}$ cross-section. Transverse optical diagnostics can be performed for the plasma density profile at low laser energy.

Our objective is to have two distinct regions: the first (region 1) fed through inlet 1 (at $z=-0.800$ mm) with He doped with N₂ for electron injection and the second (region 2) fed through inlet 2 (at $z=+1.00$ mm) with pure He for electron acceleration. The gas flows and dopant concentration can be varied with a $0.5$ s response time through a dedicated gas injection system monitored and controlled by pressure gauges and mass flow controllers, allowing continuous concentration tuning from 1.5% to 100% and pressure ranging from 10 ± 0.12 mbar to 150 ± 0.45 mbar (RMS evaluated over a 3 min continuous operation), evaluated on an axis using fluid simulation. A central outlet outlet 2 ($z=0$ mm) between the two regions allows for better control of the mixing interface.

Relativistic self-focusing in a plasma (decrease in laser waist, increase in intensity) is triggered when the laser power exceeds the critical power $P_c\left[\mathrm{GW}\right]\approx 17.4{({\lambda }_p/{\lambda }_L)}^2$ [41], with ${\lambda }_p$ and ${\lambda }_L$ denoting the plasma and laser wavelength, respectively. For a typical 50 TW pulse, this happens for a fully ionised He pressure above 12 mbar. In order to avoid early self-focusing, which could lead to a long and uncontrolled electron injection, we decided to have a sharp opening at the cell entrance to keep the gas upramp as short as possible. On the contrary, the exit has a long, low-gas-density tail which slowly decreases the focusing strength on the beam and controls its divergence.

The target lifetime depends on hazardous alignment errors. The current data were collected using a single target with over 3800 laser shots, and the target remained functional.

2.2. Integration in the Beamline

The cell holder from Figure 1 is inserted inside a $14\times 14$ cm vacuum cube, as presented in Figure 2, with two apertures (3 mm diameter) that allow the laser to pass through and provide differential pumping between the cube and the rest of the beamline.

A vacuum pumping system connected to the cube enables continuous-gas-injection-mode operation at around 100 mbar. The pressure in the differential pumping cube rises up to 1.2 mbar, and the rest of the beam line remains at a relatively low level, rising from 3 × 10⁻⁵ mbar (no gas injection) to 3 × 10⁻⁴ mbar (gas injection) with the standard secondary pumps. Optical quality windows allow for in-air optical transverse diagnostics.

This cube can be easily transported and integrated as a direct element of the beamline with bellows connections, as for the PALLAS project (Figure 2, left). For the specific experiment at LOA, the design had to be inserted inside a large vacuum chamber (1.5 m diameter, 1 m height). It was then modified, with a main structure that maintains the cube upside down and a hexapod with a vacuum motion feedthrough, allowing the independent motion of the cell holder (Figure 2, right).

2.3. Set-Up Used at LOA

A schematic of the set-up used at LOA is presented in Figure 3.

The P-polarised (along x) laser was tuned to deliver pulses with a duration of $T_{FWHM}^{\left(exp\right)}=32\pm 2$ fs at wavelength ${\lambda }_L=810$ nm, with $1.5\pm 0.2$ J energy (50 TW) at 1 Hz, focused with a $1.5$ m focal length spherical mirror. The pulse is estimated to be a 5th-order Flattened Gaussian Beam (FGB) [42], with a waist in vacuum of $w_{0,vac}^{\left(exp\right)}=17\pm 2 \mathsf{\mu }\mathrm{m}$ inside the cell, which corresponds to a Rayleigh length ${\lambda }_R^{\left(exp\right)}\approx 1$ mm.

We estimate the normalised vector potential, $a_0$, in vacuum to be around $a_{0,vac}^{\left(exp\right)}=1.7$. Such a value is not enough to reach the barrier suppression ionisation (BSI) threshold of N⁵⁺ and N⁶⁺, respectively, of 2.21 and 2.77 at 800 nm [43]. However, if the plasma wavelength ${\lambda }_p$ is short enough (i.e., if the density is high enough), the laser power can exceed the so-called “critical power” for self-focusing (given in Section 2.1), which is the case for our injector once the pulse starts entering region 1.

An ISP deformable mirror composed of 33 piezo motors for wavefront correction is located 10.6 m upstream of the spherical mirror and allows the focal plane to be shifted along the optical axis within a $[-2.5,+4.5]$ mm range, with 0 corresponding to the centre of outlet 2. The laser-pointing stability is evaluated to be $\pm 15 \mathsf{\mu }$rad. This corresponds to a variation of roughly a spot size in all transverse directions at the cell entrance. The laser is removed after the electron spectrometer, approximately 75 cm from the cell exit, using a mirror with a hole (10 mm in diameter), followed by a 25 $\mathsf{\mu }\mathrm{m}$-thick grazing incidence aluminium foil.

As presented in Figure 3, several cameras are used for laser and plasma diagnostics: a camera with a movable mirror for focal spot analysis at the cube entrance, a camera (ALIGN) with a movable mirror for the alignment of the cell, and a camera (PLASMA) for the live visualisation of the target.

The electron beams are monitored in:

• Energy with an electron spectrometer consisting of a 1.5 T, a 10 cm movable dipole magnet with two YAG:Ce screens, imaged on an Allied vision PROSILICA GT 1290 camera (Allied Visions GmH, Stadtroda, Germany), positioned, respectively, at 14 cm, 30 cm and 40 cm downstream of the target, enabling electron energy measurements above 140 MeV with an error increasing from 5 to 80 MeV (per mm of entrance jitter in dispersive direction) at energies from 140 to 500 MeV;
• A charge with an integrating current transformer (ICT) for charge measurement above 60 MeV (we estimate from PIC simulations the energies below 60 MeV to be too divergent to pass through the mirror with a hole) with a [0.5–300] pC range and a typical signal-to-noise ratio (SNR) above 50, placed at $148\pm 5$ cm from the source;
• Divergence and pointing stability with a beam screen, composed of a LANEX scintillator screen (Kodak GmbH, Stuttgart, Germany) mounted on a thin aluminium frame, imaged onto a Basler acA640-120gm CCD camera (Basler AG, Ahrensburg, Germany), positioned at 167 ± 1 cm from the source at the end of the beamline.

Those diagnostics cannot be used simultaneously and, therefore, require repeating the shot series. For some series, however, data were recorded only on the spectrometer screen. In that case, the screen intensity, cross-calibrated with ICT measurements, can be used to estimate the charge. The spectrometer-screen data also provide the divergence component transverse to the beam-dispersion direction of the dipole.

3. Results

3.1. Stable and Low-Divergence Beams

We present a series of 10 consecutive shots in Figure 4, obtained with a dopant concentration of $c_{N_2}=14.6\%$ and pressures of $P_1=125$ mbar and $P_2=121$ mbar, corresponding to a pressure gradient on axis $\Delta P=-4$ mbar. The laser is focused around the centre of inlet 2. Since the Rayleigh length is approximately 1 mm, the laser intensity is high enough to trigger self-focusing in the density upramp so that $a_0$ in the plasma actually becomes high enough to ionise N⁵⁺ and N⁶⁺ and inject their electrons in the plasma wake.

This series shows a typical spectrum stability with 10% fluctuation. The estimated charge is $50\pm 25$ pC (RMS). All spectra displayed in Figure 4, however, exhibit both a high and a low energy feature, characterised by two distinct energy populations: one long tail centred at approximately 200 MeV and a peak at approximately 360 MeV.

We performed PIC simulations to find the origin of those two energy populations. The code used is SMILEI [44], with an envelope approximation and cylindrical symmetry with one azimuthal mode. Species are initialised as ionised up to He²⁺ and N⁵⁺, ionisation is modelled from the envelope model coupled with tunnel ionisation rates [45], and we use 1 particle per cell to track the species (such an approximation was already discussed in [46]). The laser is modelled as a 5th-order FGB, with a duration of $T_{FWHM}^{\left(sim\right)}=35$ fs, a waist in vacuum of $w_{0,vac}^{\left(sim\right)}=15 \mathsf{\mu }\mathrm{m}$, and energy of $1.5$ J, resulting in an $a_0$ in vacuum of $a_{0,vac}^{\left(sim\right)}=1.7$.

The density profiles and mixing are assessed with OpenFOAM [47] simulations. Since we did not find a solver that combines both compressibility and diffusion, we proceeded in two steps, with two different solvers, as already proposed in [48]. First, rhoPimpleFoam [49] (compressible, non-miscible) assesses the main density profile, accounting for the compressibility effect, which is especially necessary in the up-/down-ramps. Its output is then used as input for interMixingFoam [50] (incompressible, miscible), which models dopant mixing at the interface between regions 1 and 2. Our simulation data are left open and available on a Git repository [51].

We set the simulation settings to: $P_1=125.57$ mbar, $P_2=121.57$ mbar, $x_{\mathrm{off}}=+1294 \mathsf{\mu }\mathrm{m}$ ($x_{\mathrm{off}}=0$ corresponds to the centre of outlet 2), and $c_{{\mathrm{N}}_2}=14\%$, which are similar to the experimental ones in Figure 4. In order to investigate the importance of the dopant mixing interface, we also simulated the case with $\Delta P=0$ for comparison. The simulation results are displayed in Figure 5.

Simulations reveal that the laser undergoes strong self-focusing, which is not optimal for a controlled injection. Its normalised intensity goes from below 2 in vacuum to approximately 4 in region 1 and then 6 inside region 2. This originates from a high density in the cell.

In both cases, the bunch is accelerated to approximately $z=1$ mm. The energy then decreases, first due to dephasing within the laser-driven bubble, and then transitions to a beam-driven decelerating regime (the laser is not intense enough to drive a wakefield). From $z=0$, the energy spread already begins to increase due to the non-optimally loaded bubble, yielding a gradient in the accelerating field, $E_z$, as is visible at $z=0.27$ mm. For the $\Delta P=-4$ mbar case, the energy spread increase is even more pronounced. This originates from a higher plasma density inside region 2 from dopant leakage (N₂ not confined inside region 1), shortening the bubble and creating a steeper gradient in $E_z$. The origin of the splitting into two energy populations for the $\Delta P=-4$ mbar case very likely comes from an original spatial splitting which then translates into two distinct energy populations when accelerated with a gradient in $E_z$, as is visible in the positively chirped longitudinal phase space at $z=4$ mm (Figure 5c).

The experimental beam pointing stability measured on the beam screen from a consecutive series of 18 shots with the same target parameters is evaluated to be $(0.78,0.60)$ mrad RMS in $(x,y)$, which is the state of the art [10,52,53,54,55]. Electron beam pointing variation may originate from the laser wavefront and pulse front tilt stability, which may change the laser propagation together with the injection condition and bubble shape from shot to shot [56,57]. The slight asymmetry can be explained by the laser polarisation along x.

The experimental RMS divergence evaluated over 18 consecutive shots from the same conditions is $({\sigma }_{x^{\prime }},{\sigma }_{y^{\prime }})=(1.23\pm 0.21,0.60\pm 0.09)$ mrad in $(x,y)$ (higher value in the laser polarisation direction, explained by an additional initial transverse momentum imparted to the electrons at the moment of their ionisation from the laser field, as already observed in [10,54,58]). This competes with other experimental results using a similar injector and presenting a typical divergence in the [0.5–1.0] mrad range [10].

The evolution of the divergence in the outramp is extracted from the PIC simulation for $\Delta P=-4$ mbar and presented in Figure 6.

While the bubble was laser-driven and accelerating in region 2, it transitions after $z=1$ mm into a transitional regime where both the dephased laser and the accelerated beam contribute to the wakefield formation (Figure 6b). The regime then fully becomes beam-driven after $z=3$ mm (Figure 6c). In both cases, the wakefield is decelerating and focusing. The divergence is progressively reduced below 1 mrad, with a slightly higher value in the laser polarisation direction x. The particular case of beam-driven divergence control is explained by a passive plasma lensing effect, as already presented in [19,20,21,22,23,24].

The emittance is evaluated using PIC simulation (no quadrupole scans possible or additional screens available in the experiment), and filters out particles below 150 MeV. The values are $({ϵ}_x,{ϵ}_y)=(2.86,1.77)$ mm.mrad and $({ϵ}_x,{ϵ}_y)=(1.29,0.62)$ mm.mrad, for $z=1.58$ mm and $z=4.63$ mm, respectively. For the same reasons as for the divergence, the emittance is higher in x than y.

3.2. Spectrum Improvement Through Dopant Control

Although the beams presented in Section 3.1 have interesting features, such as low RMS values for pointing stability and divergence, their spectra, shown in Figure 4, have a large low-energy tail, which is not desirable for beam transport since chromatic effects will eventually result in charge loss [19]. We, therefore, experimentally scan the helium gas pressure $P_2$ between 80 and 105 mbar while keeping $P_1$ constant at around 100 mbar, with a slightly reduced dopant concentration, $c_{N_2}=6.67\%$, in order to see the effect of $\Delta P$ on dopant confinement and subsequently on the electron density inside region 2. The resulting spectra are presented in Figure 7.

All spectra displayed in Figure 7 have a plateau shape ending with a local maximum, followed by a sharp cut-off. We attribute this broad shape to a non-optimally loaded bubble. In addition, a high-energy population appears between 430 and 470 MeV. This series of spectra, however, shows a regular and remarkable behaviour with $P_2$.

When increasing $P_2$, the energy shifts towards lower values, from a local maximum of around 350 MeV down to 220 MeV, but with a higher spectral density. The high-energy population also shifts towards slightly lower energies and increases in spectral density, similarly to the local maximum. We attribute this effect to the increasing dopant confinement inside region 1 with an increasing $P_2$. This corresponds to a lower electron density inside region 2 and, thus, a reduced accelerating field.

The charge is about 50 pC for all cases, which is comparable to the results from Figure 5. The RMS divergence evaluated on the spectrometer screen evolves from $1.57\pm 0.1$ mrad ($\Delta P=-25$ mbar) to $2.05\pm 0.15$ mrad (for $\Delta P=0$ mbar), which is greater than in Section 3.1. The reduction in the dopant concentration, together with its progressive confinement inside region 1, decreases the length of the downramp, thus acting more shortly on the divergence and resulting in larger values than for Figure 5.

4. Conclusions

A continuous-flow gas target was designed and tested for ionisation injection in a laser-driven wakefield. The design allows for easy transport and integration as a direct element of the beamline or in a large interaction vacuum chamber. Fluid simulations have highlighted the capabilities of our design to control both the pressure over a large range and the dopant location inside the target.

The initial results demonstrate electron beams with sub-mrad pointing and divergence above 150 MeV, reflecting the stable gas species distribution in the target. However, under non-fully optimised injection conditions, the beams exhibit two distinct energy populations. The mechanism behind this splitting is explained using PIC simulations. Their low final divergence is achieved through a long, low-density tail, which eventually acts as a passive plasma lens.

Using a dedicated gas injection system, the pressure differences between the gas mixture and the background gas (He), as well as the dopant (N₂) concentration in the mixture, were varied. Increasing the pressure difference up to $\Delta P=0$ mbar results in a dopant confined inside region 1, which lowers the density inside region 2, yielding well-defined and more peaked spectra. The gas target operates in a high-vacuum environment across a wide pressure range in continuous flow, making it a viable integration option for high-repetition-rate laser wakefield accelerator setups.

Investigating lower pressures would have allowed for a reduction in the observed strong self-focusing, resulting in a more localised injection, as proposed from PIC simulations in [46], and very likely well-defined lower energy spread bunches. A deeper investigation into the laser control could even improve the longitudinal focal spot positioning and the relatively good pointing stability. The divergence can be reduced by testing other output geometries. Further experiments on the now-operational PALLAS test facility will allow for more dedicated beam time, providing an opportunity to obtain additional data for optimisation.