Microcoulomb (0.7 ± 0.40.2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\frac{0.4}{0.2}$$\end{document} μC) laser plasma accelerator on OMEGA EP

Laser-plasma accelerators (LPAs) driven by picosecond-scale, kilojoule-class lasers can generate particle beams and x-ray sources that could be utilized in experiments driven by multi-kilojoule, high-energy-density science (HEDS) drivers such as the OMEGA laser at the Laboratory for Laser Energetics (LLE) or the National Ignition Facility at Lawrence Livermore National Laboratory. This paper reports on the development of the first LPA driven by a short-pulse, kilojoule-class laser (OMEGA EP) connected to a multi-kilojoule HEDS driver (OMEGA). In experiments, electron beams were produced with electron energies greater than 200 MeV, divergences as low as 32 mrad, charge greater than 700 nC, and conversion efficiencies from laser energy to electron energy up to 11%. The electron beam charge scales with both the normalized vector potential and plasma density. These electron beams show promise as a method to generate MeV-class radiography sources and improved-flux broadband x-ray sources at HEDS drivers.

www.nature.com/scientificreports/ divergences as low as 32 mrad, record-setting bunch charges exceeding 700 nC, and laser-to-electron conversion efficiencies up to 11%. The bunch charge is comparable to high-bunch-charge radio-frequency (rf) accelerators (~ 1 μC), but with sub-picosecond durations versus the millisecond durations characteristic of rf sources. These electron beams are, to our knowledge, the highest-charge and highest-conversion-efficiency electron beams produced from an LPA.

Experimental setup
Experiments were performed on the OMEGA EP Laser System 29 at LLE. The laser was run with a central wavelength λ of 1054 nm at best compression (pulse duration of 700 ± 100 fs). To improve the quality of the focal spot and increase the Rayleigh length, the focusing geometry of the short-pulse laser beams was converted from its nominal f/2 geometry by using spatially filtered apodizers 30 located at the injection plane before amplification in the Nd:glass beamline to control the beam diameter and generate an f/5, f/6, f/8, or f/10 geometry. The properties of these configurations are summarized in Table 1, and nominal focal spots at the target plane for the standard f/2 focus and the f/6 apodizer are shown in Fig. 2a,b, respectively. Note that no electrons with energies exceeding 14 MeV were produced in shots where the f/2 configuration was fielded. At focus, the R80 spot size of the laser (i.e., radius that contains 80% of the total energy) was between 11.5 and 19.9 μm. The apodized laser energy varied from 10 to 115 J, which produced on-target peak normalized vector potentials (a 0 ∼ = 8.6 × 10 −10 I 0 W/cm 2 [µm] , where I 0 is the vacuum intensity) between 1.8 and 6.7. The apodized laser pulse was focused 500 μm inside a Mach 5 gas jet with nozzle diameters varying between 2 and 10 mm as shown in Fig. 2c. The gas was 100% He, and the resultant plasma densities in the plateau ranged from 1.5 × 10 18 to 4.5 × 10 19 cm −3 depending on nozzle diameter and backing pressure. The gas jet was an ultrafast (opens and closes in ~ 100 μs) system specifically designed to limit the total gas release in the event of failure in order to protect the sensitive electronics in the compressor 31 . Figure 3a shows the transverse profile of the lowest-divergence electron beam produced in this experiment. The charge in this beam was 148 nC and was produced by an a 0 = 4.4 laser shot propagating through a plasma density of 1.1 × 10 19 cm −3 generated by a 10-mm-diameter nozzle. The divergence of this beam was 32 × 39 mrad, and it was pointed 8 mrad from the axis of the electron-positron-proton spectrometer (EPPS). The divergence was calculated by fitting the lineout of the transverse profile through the peak of the electron beam with a Lorentzian and taking the full width at half maximum (FWHM). The total charge in the FWHM was 19 nC. This divergence demonstrates a major step forward in the possible quality of electron beams from SML-WFA since it is significantly reduced from the next best divergence reported from other SMLWFA experiments (64 × 100 mrad ± 10 mrad 6 ) and is on the order of the divergences (< 10 mrad) of the electron beams produced by LWFA being driven by ultrashort-pulse lasers (τ < λ p ). The possibility of lower-divergence electron beams Figure 1. Plot of the maximum charge of the electron beams produced by laser-plasma accelerators at different facilities [41][42][43][44][45][46][47] . The yellow star is the result reported in this work. Table 1. Properties of injection-plane apodizers used for this work. The maximum energy is given for operation at best compression, i.e. duration of 700 ± 100 fs. The maximum a 0 value given in column four and the peak intensity given in column five are the maximum values calculated from the laser energy, spot size, and pulse duration measured during this course of experiments. www.nature.com/scientificreports/ from SMLWFA-based LPAs increases their utility when using the produced electron beams to generate compact sources of high-energy electrons for conversion to photons and positrons. The increased directionality of these electron beams makes them easier to transport and to point either to converter targets or to the interaction being probed. Lower-divergence electron beams will mean a lower source size, and therefore a higher spatial resolution, for bremsstrahlung or inverse Compton scattering x-ray sources generated using these electron beams. For the lowest-divergence electron beam reported here, that source size would be approximately half of  www.nature.com/scientificreports/ that produced by the electron beam from Ref. 6 . Lower-divergence electron beams also reduce the background noise in these applications. The nature of SMLWFA means that there is variation in the reproducibility of the electron beam quality. The divergence of the electron beams will be affected by the plasma density profile and uniformity, the laser focal spot quality and size, the phase front of the laser, and the interaction between the laser and the plasma, including the coupling of the laser into the plasma and the subsequent laser evolution (modulation and self-focusing). For all but three of the 23 high-plasma-density (n e > 1.9 × 10 19 cm −3 ) shots in this experiment, the produced electrons did not form a defined beam, and instead, the transverse charge profile was distributed across the entire solid angle collected by the EPPS. For those three shots, all were produced in 10-mm nozzles, which suggests that having longer plasmas, and therefore longer distances for laser evolution, may help maintain the transverse beam profile. For the remainder of the 49 shots with charge ≥ 50 nC, the shots were either single-peaked with higher divergence than the shot shown in Fig. 3a or had multiple peaks. Figure 3b shows the electron-beam profile for the highest-total-charge (707 nC) electron beam, which has a much larger divergence than the lowest-divergence shot shown in Fig. 3a and two distinct charge peaks. This electron beam was produced by an a 0 = 6.6 laser shot propagating in a plasma density of 7.5 × 10 18 cm −3 created by a 6-mm-diameter nozzle. Although this highest-charge electron beam shows that there was variability in the transverse beam quality in the LPA platform being developed here, it is still on the order of the best divergences reported in other SMLWFA experiments, while still having at least a factor of 10 more charge. 50% of the total charge is encompassed in a 53.9 mrad and 59.4 mrad radius for the beam profiles shown in Fig. 3a,b, respectively. Figure 4 shows that the total charge in the electron beams scales approximately linearly with a 0 . The data shown is for a 6-mm-diameter nozzle operating at a plasma density of 5 × 10 18 cm −3 , but plasma densities of 1, 2, and 3 × 10 19 cm −3 showed the same trend. This trend was also seen for 4-mm-diameter nozzles operating at 1 × 10 19 cm −3 and 10-mm-diameter nozzles at densities of 0.2, 0.5, 1, and 3.5 × 10 19 cm −3 . There are several potential factors affecting this observed scaling. Quasi-3D 34 OSIRIS simulations of one of the shots from this experiment (a 0 = 6, n e = 7.5 × 10 18 cm −3 , nozzle diameter = 6 mm) show that for this parameter regime, the laser begins to pump deplete as early as 1 mm into the constant-plasma-density region. In this experiment, because the spot size is approximately constant, a higher a 0 is correlated to higher laser energy, and therefore the pump depletion may be mitigated. A higher a 0 is also correlated to a higher laser power, which means that a larger percentage of the 700 fs pulse duration will have a power higher than the critical power for self-focusing 35 . This means that a larger percentage of the laser pulse will not be diffracted, which also mitigates pump depletion, and can contribute to the series of laser micropulses driving the wake, and thus produce more plasma periods accelerating charge. Higher a 0 values are also associated with longer plasma periods in the wakefield 36,37 , which can hold more charge. The charge in the electron beams was calculated using the method described in "Methods". Figure 5a shows that the charge in the electron beam scales approximately linearly with plasma density until a density of 1 × 10 19 cm −3 . The two data sets shown each have a different a 0 value; the rate of increase of charge with plasma density is steeper for the higher a 0 value. The highest-charge electron beam measured in this experiment, which had a charge of 707 ± 429/224 nC, was produced at an a 0 of 6.6 and a plasma density of 7.5 × 10 18 cm −3 .

Results and discussion
Using an electron energy of 17.9 MeV, which is the weighted average electron energy of the representative electron spectrum from this experiment (Fig. 2d), this charge corresponds to a conversion efficiency from laser energy to electron energy of 11%. The details of this calculation are included in "Methods". 30%, 50%, and 90% of that total energy is contained in electrons with energies below 18.5 MeV, 25.6 MeV, and 85.1 MeV, respectively.
In this experiment, trapping was observed to begin at a plasma density of 1.5 × 10 18 cm −3 . About 30% of the shots taken at this density produced measurable charge. Above a plasma density of 2.4 × 10 18 cm −3 , charge was trapped on every shot. Measurable charge was first observed for P/P crit values of 3.4, where P is the laser power and P crit is the critical power required for relativistic self-focusing. This value is in reasonable agreement with the P/P crit ~ 3 threshold measured for LWFA in the blowout regime 38 . Measurable charge was seen in 1/3 of shots at this P/P crit value. Charge was consistently trapped once P/P crit exceeded 5.2. Figure 5b shows that when the charge scaling is extended to higher plasma densities, the maximum charge produced plateaus with density. A similar trend was seen for data taken on a 6-mm-diameter nozzle for both a 0 values of 5 and 6. www.nature.com/scientificreports/

Conclusions
A microcoulomb-class, high-conversion-efficiency laser-plasma accelerator was demonstrated, providing the first laser-plasma accelerator driven by a short-pulse, kJ-class laser (OMEGA EP) connected to a multi-kJ HEDS driver (OMEGA). The produced electron beams have maximum energies that exceed 200 MeV, divergences as low as 32 mrad, record-setting charges that exceed 700 nC, and laser-to-electron conversion efficiencies up to 11%. Total charge in the electron beam is found to scale with both a 0 and plasma density. Based on these empirical scalings, higher-charge electron beams may be possible using laser systems that can deliver a 0 values larger than the maximum a 0 of 6.7 produced in this configuration while still maintaining longer f/#s and near-Gaussian, single-moded laser spots on target. These electron beams are, to our knowledge, the highest-charge electron beams produced from a laser-plasma accelerator and are well poised as a path to MeV-class radiography sources and improved flux for broadband sources of interest at HEDS facilities.

Methods
Experimental setup. In the OMEGA EP experimental chamber, the produced electron beam propagated 47.63 or 56.52 cm downstream where it was intercepted by an Electron Positron Proton Spectrometer (EPPS), which was mounted using a ten-inch-manipulator, with a modified blast shield on the front. This modified blast shield held an image-plate (IP) stack orthogonal to the electron beam for measurements of the transverse electron beam profile, the divergence, the electron-beam pointing, and charge. The image plate stack on the front of the EPPS consisted of 12.5 μm or 25 μm of aluminum, to block transmitted laser light, followed by two FujiFilm BAS-MS image plates. These image plates will be referred to as the first and second "front" image plates for the remainder of this paper. The first front image plate acted as a filter for electrons with energies < 400 keV. Any x-rays produced either on the foil or in the wakefield itself were negligible compared to the signal produced by the electrons on the IPs. The second front image plate recorded the transverse profile, the divergence, the pointing, and the charge of those electrons that were energetic enough to pass through the first front image plate.
No charge was recorded on the second front image plate when the laser was fired with no gas target. The front image plates were run with or without a hole at the center; the hole was used to allow the electrons to propagate unaffected into the pinhole of the spectrometer portion of the EPPS and be dispersed. The spectrometer portion of EPPS was operated with the high-energy/low-dispersion magnet pack and therefore has a maximum energy resolution of 200 ± 20 MeV, so any electrons with energies exceeding 200 MeV were not resolved. In this experiment, electron beams with energies up to this maximum resolvable energy were measured.
Charge measurement. The photostimulated luminescence (PSL) signal from the second front image plate of the image plate stack on the front of the EPPS was used to measure the charge of the incident electron beam. When an electron of a known energy is incident on an image plate, the response of that image plate in photostimulated luminescence (PSL) is known 39,40 as shown in Figure 7 of Ref. 39 . Thus, for a monoenergetic electron beam, it is straightforward to scan an image plate, integrate the total number of PSL from that image plate, and then convert that PSL to charge using the known response (PSL/electron). In this experiment, this process was used except that a weighted PSL/electron conversion factor, calculated based on the measured electron spectrum, was used to account for the fact that the incident electron beams are not monoenergetic. We calculate this weighted PSL/electron conversion factor by taking a representative electron spectrum from the experiment (Fig. 2d), integrating along energy from 0.9 to 200 MeV (the range resolvable by the EPPS) to find the total number of particles/sr in that spectrum, and then calculating what percentage of the total number of particles/ sr are at each energy. The percentage at a given electron energy is then multiplied by the PSL/electron response at that energy, and the products of each multiplication are summed to produce a single conversion factor for the electron spectrum. For this case, that weighted conversion factor was 0.026 PSL/electron. Note that this method of calculating the weighted conversion factor assumes that the electron spectrum is constant over the entire divergence. Once this weighted conversion factor was determined, we could simply sum the total PSL measured on the second front image plate and convert the total PSL to charge. In this calculation, the total measured charge reported was determined within the solid angle of the front image plates. Note that for the highest-charge shot www.nature.com/scientificreports/ only, the EPPS detector was located at a distance of 47.63 cm from target chamber center, and so the reported charge is over a solid angle of 26 msr, unlike the remainder of the shots, where the EPPS sat at 56.52 cm from target chamber center, and so the reported charge is over a solid angle of 18 msr. The charge in the highest-charge shot contained in the 18 msr aperture is 600 ± 185/162 nC. For those image plates where a hole was present, a Gaussian fit to the data was used to estimate the charge that passed through the hole. The error introduced by making this correction is included in the error bars. Due to the significant amount of charge generated in this experiment, part or all of the readout of the second front image plate was saturated. Because the PSL signal decreases by a prescribed amount each time an image plate is scanned, the front image plates were scanned repeatedly until no saturation in the readout existed. The measurement was recorded for seven locations shown in Fig. 6a distributed diagonally across the second front image plate after each scan. As seen in Fig. 6b, the decay of the PSL signal with scan number for each of the seven points takes the form of a power distribution PSL = αN β , where PSL is the signal and N is the number of scans of the image plate. The decay of the PSL signal for each of the seven points was fitted with the power distribution to recover the fit parameters α and β for each point. Those fit parameters from the seven points were averaged to produce an average decay of the signal on the image plate for each scan. The total signal from image plates that have a saturated readout on the first scan can then be recovered via the ratio PSL scan1 /PSL scanN = α(1) β /αN unsat β = 1/ N unsat β , where N unsat is the number of scans required to unsaturate the image plate readout. The fit parameter α cancels in this ratio, and the signal is strictly a function of N unsat and the fit parameter β. Once the total signal was determined from the fit parameter β, the signal was adjusted for any fade that occurred between when the shot was fired and when the image plate was scanned by using the known fade rate formulas given by Boutoux et al. 39 . To convert from PSL to electrons, a conversion factor of 0.026 PSL/electron was used. The calculation of this factor was described in the previous paragraph.
Error analysis. The largest contribution to the uncertainty in the reported charge is from the variation in β when fitting the decay curves as described in the above paragraph. As stated above, the average β was used to calculate the reported charge. The charge was also calculated using the highest and lowest β value from across the seven fit points. This difference due to the variation in β is included in the error bars for the reported charge. The percent difference in charge by comparing shots taken using different f/#s (f/5, f/6, f/8, and f/10) is ± 16%, and this difference was also included in the error bars in plots when comparing data taken on different f/#s. The error bars also include the small differences in charge due to the uncertainty in the PSL/electron conversion factor itself as reported by Boutoux et al. 39 .
The charge calculation method described has one additional systemic source of uncertainty, which could reduce the overall reported charge by up to a factor of 0.65. As described above, the constant factor used to convert from PSL to electrons was calculated by convolving a representative measured electron spectrum (over the range of 0.9-200 MeV as measured with the EPPS) with the PSL/electron response at each electron energy. The PSL/electron response varies significantly for electron energies below 2 MeV, so uncertainties in the electron spectrum below the lowest measured value of 0.9 MeV could alter the weighted PSL conversion factor and thus the reported charge. To investigate this possibility, the transmission of electrons with energies below 0.9 MeV through the front image plate stack was modelled in Geant4 and convolved with the PSL/electron response in that energy range. The result shows that even if every PSL recorded on the front image plates was due to electrons with energies below 0.9 MeV, which would be the extreme lower bound on the reported charge, the reported charge would only be reduced by a factor of 0.65. www.nature.com/scientificreports/ Conversion efficiency. In order to calculate the conversion efficiency from laser energy to the energy contained in the electron beam, a weighted average electron energy need to be calculated. In the work shown here, this weighted average electron energy was calculated using the representative electron spectrum from this experiment (Fig. 2d). The total charge in the electron beam was integrated by multiplying the signal at each energy by the width of the step in the electron energy in MeV. This integration gives a total number of particles/ sr. The electron signal at each electron energy was then divided by the total charge/sr to calculate the fraction of the total charge at each electron energy. The fraction of the total charge at each electron energy can then be multiplied by that energy and summed to get the weighted energy of a typical electron in that spectrum. Once the energy of a typical electron is known, the total charge in that beam can be converted to energy, and from there, the efficiency can be calculated.

Data availability
The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.