Ultra-short, MeV-scale laser-plasma positron source for positron annihilation lifetime spectroscopy
Thomas L. Audet, Aaron Alejo, Luke Calvin, Mark Hugh Cunningham, Glenn Ross Frazer, Nasr A. M. Hafz, Christos Kamperidis, Song Li, Gagik Nersisyan, Daniel Papp, Michael Phipps, Jonathan Richard Warwick, Gianluca Sarri
UUltra-short, MeV-scale laser-plasma positron source for positronannihilation lifetime spectroscopy
Thomas L. Audet, ∗ Aaron Alejo, Mark Hugh Cunningham, Glenn Ross Frazer, Nasr A. M. Hafz,
2, 3, 4
Christos Kamperidis, Song Li, Gagik Nersisyan, DanielPapp, Michael Phipps, Jonathan Richard Warwick, and Gianluca Sarri Centre for Plasma Physics, School of Mathematics and Physics,Queen’s University Belfast , BT7 1NN, Belfast United Kingdom ELI-ALPS. ELI-HU Non-profit Ltd., H-6728 Szeged, Hungary National Laboratory on High Power Laser and Physics,SIOM, CAS, Shanghai 201800, China Dept. of Plasma and Nuclear Fusion, Nuclear Research Center,Atomic Energy Authority, Abu-Zabal 13759, Egypt
Abstract
Sub-micron defects represent a well-known fundamental problem in manufacturing since they signifi-cantly affect performance and lifetime of virtually any high-value component. Positron annihilation lifetimespectroscopy is arguably the only established method able to detect defects down to the sub-nanometer scalebut, to date, it only works for surface studies, and with limited resolution. Here, we experimentally showthat laser-driven positrons, once aptly collimated and energy-selected, can overcome these well-known lim-itations, by providing ps-scale beams with a kinetic energy tuneable from 500 keV up to 2 MeV and anumber of positrons per shot in a 50 keV bandwidth of the order of 10 . Numerical simulations of the ex-pected performance of a typical mJ-scale kHz laser demonstrate the possibility of generating narrow-bandand ultra-short positron beams with a flux exceeding 10 positrons/s, of interest for fast volumetric scanningof materials at high resolution. ∗ [email protected] a r X i v : . [ phy s i c s . acc - ph ] S e p . INTRODUCTION Positron Annihilation Lifetime Spectroscopy (PALS) [1] is arguably one of the most successfultechniques for the non-invasive inspection of materials and identification of small-scale defects.PALS presents several unique advantages compared to other inspection techniques: it works vir-tually with any type of material (crystalline and amorphous, organic and inorganic, biotic andabiotic), it can identify even sub-nanometer defects with concentrations as low as less than a partper million, and it can provide information on the type of defect and its characteristic size. PALShas found applications in testing systems as diverse as turbines, polymers, semiconducting devices,biomimetic systems, zeolites, and solar cells.Even small-scale defects can have a dramatic effect on the performance and lifetime of high-performance and high-value components, especially when made in, and required to perform under,hostile environments. Heat and pressure treatments, new welding methods, radiation exposure,impact damage, are all examples of scenarios that can leave sub-micron defects in materials duringadvanced manufacturing or extreme performance use.In a nutshell, PALS relies on the temporally resolved detection of gamma-rays resulting fromthe annihilation of positrons as they interact with the material [2]. In a perfect crystal lattice, animplanted positron would rapidly thermalize and subsequently annihilate from a delocalised state.However, a positron is likely to be trapped in the potential induced by a vacancy, such as a missingatomic core [3]. A trapped positron will thus have a more localised state and, therefore, a longerlifetime. The temporal evolution of the gamma-ray emission from the material will thus containseveral exponential decays, each with a typical timescale characteristic of the bulk material and ofany defects in it. Normally, positron lifetimes in materials are of the order of 200 ps, with longerlifetimes if defects are present (see, for instance, Ref. [2]).Typical machines designed for PALS routinely operate at a positron energy in the keV rangeand bunch durations of the order of hundreds of picosecond [4–7]. Despite the high performanceof these machines and their wide use for industrial applications and fundamental science, theymainly suffer of two well-known limitations. First, the available positron energy restricts materialscanning only to sub-mm depths. Second, the positron bunch duration is relatively long and thusaffects the resolution of the technique. For higher resolution, it is preferable to have positron bunchdurations that are significantly smaller than the timescales of interest, i.e., at least in the range ofa few to tens of ps. In that case, the resolution of the system will be only limited by the detector2esponse.These limitations can be overcome if laser-driven positrons are used. Commercially availablehigh power lasers with short pulse durations (fs to ps), can routinely generate high-charge relativis-tic electron beams of similar duration [8]. The interaction of these electrons with high-Z convertertargets can thus produce multi-MeV positron beams with durations in the range of a few to fewtens of ps [9–19]. Two main approaches have been identified, based on whether the electrons aregenerated during direct laser irradiation of the converter target or if they are first generated in agaseous medium following, for instance, the laser-wakefield acceleration (LWFA) mechanism [8].Independently of their source, the propagation of high energy electrons through a high Z con-verter results in the generation of a positron beam. For sufficiently thick converters, two mecha-nisms are mainly involved: the emission of a high energy photon through bremsstrahlung and thesubsequent decay of the photon in electron-positron pairs, with both processes mediated by thenuclear field. Subsequent cascading is also possible, but it is unlikely for sub- radiation lengththicknesses [9].In this article, we show, numerically and experimentally, that positron beams with characteris-tics appealing to PALS can be produced in a fully-laser driven scenario. First, we experimentallyshow, using the TARANIS laser hosted by the Centre for Plasma Physics at Queen’s UniversityBelfast [20], that MeV-scale positron beams with a yield of up to ∼ × positrons / shot canbe obtained. Numerical simulations indicated a positron beam duration at source of the order of afew picoseconds. Implementing a quadrupole doublet system and a dogleg configuration providessufficient capture and energy-selection of the positron beam so that, at the sample, a positron beamcontaining a sizeable amount of positrons in a selected energy bandwidth and with a duration ofthe order of tens of picoseconds can be obtained. Numerical simulations indicate that the sameconfiguration can then be used in conjunction with currently available multi-tens mJ laser systemsoperating at kHz-scale repetition rates, providing up to 10 positrons/s in a 50 keV bandwidth,with an energy tuneable from sub-MeV up to a few MeV. Numerical simulations indicate a dura-tion of the beam at the sample plane of the order of 100 ps, thus confirming the feasibility of thissystem for novel practical applications.The structure of the article is as follows : Sec. II will describe the main experimental andnumerical results concerning positron beam generation and transport using the direct laser-solidinteraction scheme. In Sec III we will show numerical results of extending this work to highrepetition rate low-energy laser systems. A final discussion of the results presented in this article3nd concluding remarks will then be provided in Sec. IV. II. POSITRON GENERATION BY DIRECT LASER SOLID IRRADIATIONA. Experimental setup
The experiments reported in this section were performed using the TARANIS laser facility atthe Queen’s University Belfast [20]. A sketch of the experimental setup is shown in Fig. 1.TARANIS is a chirped pulse amplification (CPA) laser system based on a Ti:Sapphire front-end and a Nd:Glass amplification section. In our experiment, the system delivered laser pulseswith an energy of E l = ( . ± . ) J in a τ l = ( . ± . ) ps full width at half maximum (FWHM)pulse duration. The typical intensity contrast of the laser is ∼ − at 1.5 ns before the mainpulse. The laser was focused using an F/3 off-axis parabolic mirror (OAP) to a FWHM spotsize of w x = ( . ± . ) µ m and w y = ( . ± . ) µ m in the horizontal and vertical directionsrespectively, leading to a peak intensity on target of I L = ( . ± . ) × W / cm . Inset of Fig 1shows the measured intensity distribution of the laser focal spot in-vacuum. The angle of incidence FIG. 1. Sketch of the experimental setup. Three different configurations have been adopted: full system (including the quadrupole doublet and the second dipole), collimation only (with quadrupole doublet but nosecond dipole), generation only (no quadrupole doublet and no second dipole). Additionally, some shotshave been taken with a thin gold target (50 µ m) to measure and characterize the initial electron spectrumstarting the positron generation inside the converter.
4f the laser beam on the target was 30 ◦ .When focused on a thin target, the pedestal of the laser pulse generates an overdense plasma witha characteristic keV-scale electron temperature. The interaction of the high-intensity peak of thelaser with this cold plasma generates a super-thermal population of electrons, with a characteristictemperature of T hot (cid:39) µ m . Fig. 2(a) shows an example of the spectrumof these electrons. The electrons follow a Maxwell-Boltzmann distribution with a temperature of k B T e (cid:39) . (cid:126) J × (cid:126) B heating mechanism [21].Here, the total number of detected electrons is N e − detected (cid:39) . × , in a 6 ×
30 mrad collectionangle. In the full emission cone, the estimated total number of electrons escaping the rear of the Autarget is of the order of N e − emitted (cid:39) × . This electron population will be considered hereafter asa good approximation for the electron population starting the cascade within the thicker convertertarget. For the rest of the article, we will focus on one specific converter, i.e., a l Ta = T CH = .
25 mm thicklayer of plastic (polyethylene) followed by a T Al = T Pb =
25 mm thick layer of lead (Pb). The second collimator consists of a T CH = .
25 mmthick layer of plastic followed by a T Al = T Pb =
50 mm thicklayer of Pb. Each collimator has a centered circular aperture with a diameter of (cid:31) =
11 mm and (cid:31) =
19 mm, respectively. In the generation only configuration, the collimators are followed by asingle dipole magnet with an average field of B =
50 mT and length of 30 mm.In the collimation only configuration, a doublet of quadrupole magnets in the Hallbach configura-tion (similar to those described in Ref. [22]) was added in between the target and the collimatorsto increase the collection and collimation of the positrons. Both quadrupoles are 10 mm long andthey are separated by 10 mm. Their inner diameters are 44 mm and 88 mm and their magneticfield gradients are 17.8 T/m and 8.95 T/m, respectively.In the full system configuration, a second identical magnetic dipole was added between the firstdipole and the detector. This second dipole was placed off-axis, on the positron side to form whatis commonly known as a dogleg. 5 a) (b)
FIG. 2. (a) : Measured electron spectrum (black solid line) and Maxwellian fit (dashed red line) after theinteraction of the TARANIS laser (details in the text) with a 50 µ m gold target. The collection angle was ∼ ∼
30) mrad in the horizontal (vertical) direction, implying a total generated number of electrons of ∼ × . The Maxwellian fit corresponds to an electron temperature of 0.9 MeV. (b) : Experimentalpositron spectra obtained using the full system (red dotted line), the quadrupole doublet but no seconddipole (blue dashed line), and using no quadrupole and no second dipole (black solid line). The meanelectron spectra escaping the solid target in that last configuration is also shown for comparison (dasheddotted magenta line). Error bars are representative of the shot-to-shot standard deviation. Additional lead shielding (not shown on Fig 1) was used on each side of the collimators to reducenoise at the detector location. In all configurations, electrons, positrons and photons were detectedusing and imaging plate (IP). The IP used was a BAS-SR2025 (Fuji Film).
B. Experimental results
During the experiments, several shots in each configurations were taken and the distances be-tween the target, the collimators and the IP were changed. In order to allow for a quantitativecomparison between the different configurations, the positron spectra are hereafter normalized bythe limiting angle defined by the circular aperture of the collimators in mrad. The angle definedby the diameter of the aperture was varied between 74 and 102 mrad.6ig. 2(b) shows positron spectra averaged over several shots in the three different configurations,with error bars representative of the shot-to-shot standard deviation; as it can be seen, the positrongeneration was fairly stable throughout the experiment. To allow for a better comparison, inall cases the averaged spectra are limited to the energy range common to the different realiza-tions. The spectra all exhibit an exponentially decreasing shape and the total number of detectedpositrons in the different configurations were N e + generation (cid:39) . × , N e + collimation (cid:39) . × and N e + f ull (cid:39) . × respectively. Electrons obtained during the same shots as the positrons withno quadrupoles and without the second dipole are also shown as a dashed-dotted magenta line inFig. 2(b). The electron yield is approximately two orders of magnitude higher than the positronyield in the same configuration.The performance of the quadrupoles and dogleg is exemplified in Fig. 3(a) as a function of en-ergy, limited to the common energy range; as expected, the addition of the quadrupole doubletleads to an increase of the detected positrons by more than a factor 2. However, the full system,i.e., including the quadrupole doublet and the second dipole to form a dogleg, showed a reductionof the number of positrons detected. The dogleg efficiency varied between 11% and 22%, andit is shown as a function of energy in Fig. 3(b). This relatively low efficiency can be partiallyexplained by the vertical (perpendicular to dispersion plane) limiting angle of the second dipole,which was 5% smaller than the pinholes limiting angle. Another contribution might be the notperfectly dipolar nature of the magnetic field in both of the magnets, as suggested by simulations (a) (b) (c) FIG. 3. (a) Ratio between the positron spectrum after collimation (blue dashed line in Fig. 2(b)) and thepositron spectrum at source (black solid line in Fig. 2(b)). (b) Ratio between the positron spectrum after thequadrupoles and the dogleg (red dotted line in Fig. 2(b)) and the positron spectrum after the quadrupoles(blue dashed line in Fig. 2(b)). (c) Ratio between the positron spectrum after the quadrupoles and the dogleg(red dotted line in Fig. 2(b)) and the positron spectrum at source (black solid line in Fig. 2(b)). ∼
52 % to ∼
23 % capture when comparing the full system to the generation only configuration asshown in Fig. 3(c).
C. Numerical Modelling
In order to validate the experimental results discussed in the previous section, numerical mod-elling of the experiment was performed using the Monte-Carlo code FLUKA [23, 24]. An electronpopulation with a Maxwellian distribution having an electron temperature of 1 MeV was chosen asan input for the simulation (Fig. 4(a)), in agreement with the experimental results using a thin gold(Au) target with a thickness of 50 µ m (Fig. 2). The simulations were performed with 2 to 4 × primary electrons and will be scaled up to 5 × primaries for comparison with experimentalresults. Due to computational constraints, a pencil-like electron beam with zero temporal durationand a point-like source was assumed.All previously described configurations were simulated for comparison with the experiment. Inall cases, the magnetic dipoles are modelled by an ideal dipolar magnetic field of 50 mT amplitudeinside the magnet gap and no magnetic field outside the gap. The quadrupoles are also simulatedas ideal quadrupole fields inside the magnets gaps with the gradients corresponding to the experi-mental values.Fig. 4(b-d) shows the positron spectra obtained with FLUKA in the three different configurations.In the generation only configuration (i.e., no quadrupole doublet and no second dipole), the simu-lations show the same order of magnitude of positrons as in the experiment (compare Fig. 4(b) andthe black solid line in Fig. 2(b)). Similar results are also obtained in the collimation only config-uration (compare Fig. 4(c) and the blue dashed line in Fig. 2(b)). However, simulation of the fullsystem (red dotted line) shows a higher number of positrons after the dogleg than experimentalresults. The FLUKA simulations would indicate a dogleg efficiency ranging from 53% at 0 . / e time duration of τ target / e (cid:39) τ dogleg / e (cid:39)
340 ps after8 a) (b)(c) (d)
FIG. 4. (a) : Normalized electron energy distribution used as input for FLUKA simulations. (b) : Positronspectra obtained with FLUKA in the generation only configuration without quadrupoles or second dipole;(c) in the collimation only with quadrupoles but no second dipole and (d) using the full system. (b-d) areusing a 2mm thick Ta target. the dogleg. The broad spectrum of the positrons at source induces different times of flight betweenthe target and the detection plane after the dogleg, as well as different trajectories through the dog-leg: these are responsible for the temporal lengthening of the positron beam. It must be notedthat these results do not take into account the duration of the primary electron beam at source,which can be estimated as τ e (cid:39) . τ l (cid:39) FIG. 5. Positron temporal distributions obtained with FLUKA at the target back surface (blue solid line)and after the dogleg (dashed black line).
III. EXTENSION TO DIFFERENT LASER SYSTEM : LASER WAKEFIELD ELECTRONSCONVERSION
While the results in Sec. II B & II C demonstrate interesting positron properties, their imple-mentation to practical applications is limited by the typically low repetition rate of Nd:glass high-energy laser systems (approximately a shot every 15 minutes for the TARANIS laser). In thefollowing, these results will be applied to a different approach. This is motivated by the recentavailability of TW-scale laser systems with ultra-short (of the order of few fs) pulse duration, andkHz repetition rate. The ultra-short pulse duration of these systems allows them to drive a laser-wakefield accelerator (LWFA) stage able to generate fs electron bunches [8, 26]. As a matter offact, LWFA electron beams have already been utilized for positron generation experiments [9, 19].While LWFA electron beams have been limited to electron bunch charges of the order of tens tofew hundreds of pC ( ∼ to few 10 electrons), the increase of repetition rate to the kHz level10nd the higher electron energy accessible ( (cid:38) A. Simulations of LWFA electron beam
Numerical simulation of the acceleration was carried out using the EPOCH3D Particle-in-Cellcode [29]. The simulation domain was a 24 µ m × µ m × µ m moving window with freeboundaries, and a mesh resolution on 50 nm ×
200 nm ×
200 nm, with 2 particles per cell. Thelaser pulse parameters - as expected on-target from the SYLOS2 laser system - were 28 mJ, 7fs, at 900 nm wavelength, focused to a 2 . µ m FWHM focal spot size for the maximum vacuumintensity of 3 × W cm − and a = .
3, propagating in the x direction. The simulated targetwas pure N gas with a supergaussian profile of order 2 .
8, with a density "plateau" of 100 µ m between 90% density values and 100 µ m ramps (between 10% −
90% density values). The laserfocused at the start of the plateau (at the first 90% density value). The background electrons fromthe Nitrogen L-shell were assumed to be pre-ionized, while the two K-shell electrons were non-ionized. Ionization injection was modelled using the EPOCH built-in routines for field, barriersuppression and multiphoton ionization processes. The background electron density of the targetwas 6 × cm − corresponding to a plasma wavelength of 4.3 µ m.Fig. 6(a) shows the plasma bubble at the end of the density plateau. At this stage the laser beamis depleted, with a ∼ . ∼ µ m long electron bunch lengthfrom the continuous injection. Fig. 6(b) shows the longitudinal phase-space of the acceleratedelectron beam after exiting the plasma (180 µ m after the plateau end). The high-energy (above18 MeV) tail of the spectrum is entirely from the leading edge of the electron beam. It extends to60 MeV and has an average energy of 37 MeV and 27 pC of total charge (1 . × electrons).The low-energy spectrum, with a peak at 3.5 MeV, is from the continuous injection following the11eading bunch, with a total charge of 137 pC (8 . × electrons). The angular divergence of theelectron beam is shown in Fig. 6(d), the low-energy fraction has a FWHM divergence of 115 mradin the y (laser polarization) direction and 78 mrad in the z direction. The high-energy fraction hasa smaller divergence, 41 mrad (14 mrad) FWHM in the y ( z ) direction. A n g u l a r d i s t r i b . ( a r b . u . ) FIG. 6. Plasma density profile snapshot, after transition to beam driven wake, with orange arrow showing theposition of the driving electron bunch, and white one showing the position of the laser pulse (a); longitudinalphase-space plot of the injected electrons 90 µ m after the plasma (b) and their spectrum (c); and the angulardistribution of the high- and low-energy electron population (d) in both transverse directions. B. Conversion of LWFA electron beam to positrons
A suitable fitting of the electron spectrum predicted by PIC simulations (see Fig. 7(a)) was usedas an input for a FLUKA simulation of the full system , i.e., including the 2mm tantalum convertertarget, the quadrupole magnets, the collimators, and the dogleg. The simulated configuration ofthe system was identical to the one discussed in Sections II and III, with the only difference thatthe collection angle was reduced by a factor 2, from 95 mrad to 47.5 mrad.In order to account for the different divergence angles of the low-energy (below ∼
18 MeV) andhigh-energy (above ∼
18 MeV) components of the electron spectrum, two different simulationswere performed and combined together. The input of the first simulation was an electron beam12 a) (b)
FIG. 7. (a) Normalized electron spectra : expected energy distribution (black dotted line), low energyelectron distribution for FLUKA input (blue dashed line), high energy electron distribution for FLUKAinput (green solid line), sum of both high and low energy distribution for FLUKA (red dotted dashed line).(b) Positron spectrum after the dogleg, obtained by combination of two FLUKA simulations. with a low energy distribution exhibiting a gaussian angular distribution with a 100 mrad FWHMwidth, displayed as a blue dashed line on Fig. 7(a). In a second simulation, the electron beam input,shown on Fig. 7(a) as a solid green line, consisted in a Gaussian energy distribution centered on35 MeV with a 20 MeV FWHM energy spread and a gaussian divergence of 25 mrad FWHM.Combining and scaling these two simulations resulted in the initial electron distribution shown inFig. 7(a) as a red dotted dashed line.The interaction of such an electron beam with a 2mm thick Ta target generated a positron beamwhich, after collimation and propagation through the magnetic system, resulted in the distributionshown in Fig. 7(b) recorded at the exit of the dogleg. Similarly to what was seen in Sec. II C, thepositron distribution after the dogleg is peaked around 500 keV as a consequence of the higherefficiency of the system for this energy.Fig. 8 shows the temporal distribution of the positron beam after the dogleg for different energybandwidths. The total positron population has a temporal distribution with a / e value of ∼ ±
50 keV reduces the temporal durationdown to a / e value of ∼ −
100 ps (see Fig. 8 and Table I). Even in such a small bandwidth,13 a) (b)(c) (d)
FIG. 8. Temporal distribution of the positrons after the dogleg, for the whole spectrum displayed on 7(a),for positrons with an energy of 1 ± .
05 MeV (b), for positrons with an energy of 700 ±
50 keV (c), forpositrons with an energy of 500 ±
50 keV (d). the number of positrons escaping the whole system is of the order of 1 −
10 per pC of the primaryelectron beam per shot. The results, summarised in Table I, would then indicate, for a realisticprimary electron beam containing 10 pC of charge, approximately 100 positrons per shot in a 50keV bandwidth. Operating at 1 kHz repetition rate, this would then translate into more than 10 positrons per second in a 50 keV bandwidth, well within the requirements for PALS.Due to the transverse spatial chirp induced by the dogleg on the positron beam, on-shot en-ergy selection can be easily achieved by introducing a moveable slit after the dogleg. This isdemonstrated in Fig. 9, which shows the positron energy distribution in different points along the14 nergy τ dogleg / e N e + Currentrange (ps) 1 pC e −
10 pC e −
150 pC e − ( e + / s )Whole distribution 230 ∼ . ∼ ∼ . × ∼ . × ± .
05 MeV 90 ∼ . ∼ ∼ . × ∼ . × ±
50 keV 100 ∼ . ∼ ∼ . × ∼ . × ±
50 keV 90 ∼ . ∼ ∼ . × ∼ . × TABLE I. Temporal duration and number of positrons after the dogleg for different energies and differentcharge of the primary electron beam. The current is given assuming a 10 pC primary electron bunch at a 1kHz repetition rate.
FIG. 9. Example of energy selection after the dogleg. All distributions correspond to a 4.9 mm wide positionselection centered on ∼ . ∼ . ∼ . transverse axis after the dogleg. The position-energy correlation introduced by the dogleg thusallows for energy selection by selecting the position of the slit. In practice, a slit would be placedjust after the dogleg to select the required part of the positron spectrum and shield the rest of thebeam. In the example shown in Fig. 9, the virtual slit is 4.9 mm wide and select positrons withenergies (peak ± FWHM) of ∼ ±
130 keV (black solid line), ∼ ±
200 keV (blue dashedline) and ∼ ±
630 keV (red dotted line). 15ith this setup, the energy selection can be adjusted with the position of the slit and the energyspread can be adjusted with the width of the slit at the expense of the number of positrons reachingthe sample. Furthermore, the quadrupoles and dipoles fields could be adjusted to allow a differentenergy band to go through the dogleg and be selected in the same fashion.
IV. DISCUSSION AND CONCLUSIONS
In summary, we report on experimental and numerical studies demonstrating the suitability oflaser-driven positron beams as probes for high-resolution and volumetric scanning of materials.Preliminary experiments using the TARANIS laser and a rudimentary beam-line already indicategood efficiency in collection and energy-selection of positrons generated during the interaction ofa laser-driven electron beam with a thick tantalum target. Numerically extending these results tothe next generation of high repetition rate low-energy laser systems indicates that more than 10 positrons per second can reach the sample to be probed, with an energy tuneable virtually fromzero up to a few MeV, a 50 keV bandwidth, and a duration of the order of 90 - 100 ps. Thesevalues are well within the requirements for positron annihilation lifetime spectroscopy studiesand provide, for the first time, the possibility of performing volumetric scanning with improvedresolution.It must be noted that the results presented in this paper only used a 2 mm thick Ta target. How-ever, the target thickness can be adjusted with an impact on the positron yield and its duration. Forexample, preliminary simulations with the same electron input as presented in Fig. 4(a) resultedin a ∼
20 % increase in the positron yield if a 1 mm thick tantalum converter is used. As a con-sequence, further optimization of the positron characteristics could be achieved with a scan of thetarget thickness and a more refined beam-line, which will be the subject of further studies.
V. ACKNOWLEDGEMENTS
We acknowledge support from the Engineering and Physical Sciences Research Council (grantnumbers: EP/N027175/1, EP/P010059/1, and EP/T021659/1).Four of the authors (D.P., S.L., C.K., N.A.M.H.) are supported by the European Union throughthe ELI-ALPS Project under Grant GINOP-2.3.6-15-2015-00001 and in part by Horizon 2020,the EU Framework Programme for Research and Innovation under Grant Agreement No. 65414816nd No. 871124 Laserlab-Europe. N. A. M. H. acknowledges the President International Fellow-ship Initiative (PIFI) of the Chinese Academy of Sciences; the International Partnership Program(181231KYSB20170022) of CAS; the Inter-Governmental Science and Technology Cooperationof MOST. [1] R. Krause-Rehberg and H. Leipner,
Positron Annihilation in Solids. Defect Studies (1999).[2] D. J. Keeble, S. Wicklein, R. Dittmann, L. Ravelli, R. A. Mackie, and W. Egger, Physical ReviewLetters , 226102 (2010).[3] M. J. Puska, C. Corbel, and R. M. Nieminen, Phys. Rev. B , 9980 (1990).[4] “ ,”.[5] “ ,”.[6] “ ,”.[7] “ ,”.[8] E. Esarey, C. B. Schroeder, and W. P. Leemans, Rev. Mod. Phys. , 1229 (2009).[9] G. Sarri, W. Schumaker, A. Di Piazza, M. Vargas, B. Dromey, M. E. Dieckmann, V. Chvykov, A. Mak-simchuk, V. Yanovsky, Z. H. He, B. X. Hou, J. A. Nees, A. G. R. Thomas, C. H. Keitel, M. Zepf, andK. Krushelnick, Physical Review Letters , 255002 (2013).[10] G. Sarri, W. Schumaker, A. D. Piazza, K. Poder, J. M. Cole, M. Vargas, D. Doria, S. Kushel,B. Dromey, G. Grittani, L. Gizzi, M. E. Dieckmann, A. Green, V. Chvykov, A. Maksimchuk,V. Yanovsky, Z. H. He, B. X. Hou, J. A. Nees, S. Kar, Z. Najmudin, A. G. R. Thomas, C. H. Kei-tel, K. Krushelnick, and M. Zepf, Plasma Physics and Controlled Fusion , 124017 (2013).[11] G. Sarri, K. Poder, J. M. Cole, W. Schumaker, A. Di Piazza, B. Reville, T. Dzelzainis, D. Doria, L. A.Gizzi, G. Grittani, S. Kar, C. H. Keitel, K. Krushelnick, S. Kuschel, S. P. D. Mangles, Z. Najmudin,N. Shukla, L. O. Silva, D. Symes, A. G. R. Thomas, M. Vargas, J. Vieira, and M. Zepf, NatureCommunications , 6747 (2015).[12] H. Chen, S. C. Wilks, J. D. Bonlie, E. P. Liang, J. Myatt, D. F. Price, D. D. Meyerhofer, and P. Beiers-dorfer, Phys. Rev. Lett. , 105001 (2009).[13] G. Sarri, J. Warwick, W. Schumaker, K. Poder, J. Cole, D. Doria, T. Dzelzainis, K. Krushelnick,S. Kuschel, S. P. D. Mangles, Z. Najmudin, L. Romagnani, G. M. Samarin, D. Symes, A. G. R.Thomas, M. Yeung, and M. Zepf, Plasma Physics and Controlled Fusion , 014015 (2016).
14] H. Chen, S. C. Wilks, J. D. Bonlie, S. N. Chen, K. V. Cone, L. N. Elberson, G. Gregori, D. D.Meyerhofer, J. Myatt, D. F. Price, M. B. Schneider, R. Shepherd, D. C. Stafford, R. Tommasini,R. Van Maren, and P. Beiersdorfer,
Physics of Plasmas , Physics of Plasmas , 122702 (2009).[15] H. Chen, S. C. Wilks, D. D. Meyerhofer, J. Bonlie, C. D. Chen, S. N. Chen, C. Courtois, L. Elberson,G. Gregori, W. Kruer, O. Landoas, J. Mithen, J. Myatt, C. D. Murphy, P. Nilson, D. Price, M. Schnei-der, R. Shepherd, C. Stoeckl, M. Tabak, R. Tommasini, and P. Beiersdorfer, Phys. Rev. Lett. ,015003 (2010).[16] H. Chen, F. Fiuza, A. Link, A. Hazi, M. Hill, D. Hoarty, S. James, S. Kerr, D. D. Meyerhofer, J. Myatt,J. Park, Y. Sentoku, and G. J. Williams, Phys. Rev. Lett. , 215001 (2015).[17] T. S. Pedersen, J. R. Danielson, C. Hugenschmidt, G. Marx, X. Sarasola, F. Schauer, L. Schweikhard,C. M. Surko, and E. Winkler, New Journal of Physics , 035010 (2012).[18] E. Liang, T. Clarke, A. Henderson, W. Fu, W. Lo, D. Taylor, P. Chaguine, S. Zhou, Y. Hua, X. Cen,X. Wang, J. Kao, H. Hasson, G. Dyer, K. Serratto, N. Riley, M. Donovan, and T. Ditmire, ScientificReports , 13968 (2015).[19] S. Li, G. Li, Q. Ain, M. S. Hur, A. C. Ting, V. V. Kulagin, C. Kam-peridis, and N. A. M. Hafz, Science Advances (2019), 10.1126/sciadv.aav7940,https://advances.sciencemag.org/content/5/11/eaav7940.full.pdf.[20] T. Dzelzainis, G. Nersisyan, D. Riley, L. Romagnani, H. Ahmed, A. Bigongiari, M. Borghesi, D. Do-ria, B. Dromey, M. Makita, S. White, S. Kar, D. Marlow, B. Ramakrishna, G. Sarri, M. Zaka-Ul-Islam,M. Zepf, and C. L. S. Lewis, Laser and Particle Beams , , 451 (2010).[21] W. L. Kruer and K. Estabrook, The Physics of Fluids , The Physics of Fluids , 430 (1985).[22] T. Eichner, F. Grüner, S. Becker, M. Fuchs, D. Habs, R. Weingartner, U. Schramm, H. Backe, P. Kunz,and W. Lauth, Phys. Rev. ST Accel. Beams , 082401 (2007).[23] A. Fasso, A. Ferrari, J. Ranft, and P. R. Sala, FLUKA: a multi-particle transport code , Tech. Rep.(CERN-2005-10, 2005).[24] T. Böhlen, F. Cerutti, M. Chin, A. Fassò, A. Ferrari, P. Ortega, A. Mairani, P. Sala, G. Smirnov, andV. Vlachoudis, Nuclear Data Sheets , 211 (2014).[25] J. Fuchs, P. Antici, E. d’Humières, E. Lefebvre, M. Borghesi, E. Brambrink, C. A. Cecchetti,M. Kaluza, V. Malka, M. Manclossi, S. Meyroneinc, P. Mora, J. Schreiber, T. Toncian, H. Pépin,and P. Audebert, Nature Physics , 48 (2006).[26] T. Tajima and J. M. Dawson, Physical Review Letters , 267 (1979).
27] D. Guénot, D. Gustas, A. Vernier, B. Beaurepaire, F. Böhle, M. Bocoum, M. Lozano, A. Jullien,R. Lopez-Martens, A. Lifschitz, and J. Faure, Nature Photonics , 293 (2017).[28] S. Toth, T. Stanislauskas, I. Balciunas, R. Budriunas, J. Adamonis, R. Danilevicius, K. Viskontas,D. Lengvinas, G. Veitas, D. Gadonas, A. Varanaviˇcius, J. Csontos, T. Somoskoi, L. Toth, A. Borzsonyi,and K. Osvay, Journal of Physics: Photonics , , 045003 (2020).[29] T. D. Arber, K. Bennett, C. S. Brady, A. Lawrence-Douglas, M. G. Ramsay, N. J. Sircombe, P. Gillies,R. G. Evans, H. Schmitz, A. R. Bell, and C. P. Ridgers, Plasma Physics and Controlled Fusion , ,113001 (2015).,113001 (2015).