High e+/e− Ratio Dense Pair Creation with 1021W.cm−2 Laser Irradiating Solid Targets

We report results of new pair creation experiments using ~100 Joule pulses of the Texas Petawatt Laser to irradiate solid gold and platinum targets, with intensities up to ~1.9 × 1021 W.cm−2 and pulse durations as short as ~130 fs. Positron to electron (e+/e−) ratios >15% were observed for many thick disk and rod targets, with the highest e+/e− ratio reaching ~50% for a Pt rod. The inferred pair yield was ~ few ×1010 with emerging pair density reaching ~1015/cm3 so that the pair skin depth becomes < pair jet transverse size. These results represent major milestones towards the goal of creating a significant quantity of dense pair-dominated plasmas with e+/e− approaching 100% and pair skin depth ≪ pair plasma size, which will have wide-ranging applications to astrophysics and fundamental physics.

in a gas jet (~10 9 ) 20 than in laser-solid interactions (~10 12 -10 13 ) 6,7 , the total number of pairs created using the "2-step" process is lower than the "1-step" process, but the emergent e+ e− beam can reach higher energy (>100 MeV), lower divergence and higher density [20][21][22] . Hence the applications of laser pair creation using solid targets (1-step) versus gas jets (2-step) are different and complementary (see Discussion). Here we focus on the "1-step" approach as we are more interested in high yield applications. For a given laser energy irradiating solid targets, higher intensity is expected to create more energetic pairs which escape more easily from a thicker target, while a shorter pulse can create pairs at higher density and produce stronger internal and sheath fields to assist the positron escape. This motivates the pursuit of pair creation using more intense laser with shorter pulse to irradiate thicker targets.
The Texas Petawatt laser (TPW) in Austin, Texas 5 was upgraded in 2012 with a new f/3 dielectric off-axis parabolic mirror donated by Los Alamos National Laboratory, allowing it to focus > 100 J of energy from pulses as short as 130 fs to peak intensities > 10 21 W.cm −2 . We performed ~130 shots on Au, Pt targets. 15% of shots reached peak intensities ≥10 21 W.cm −2 . Hot electrons were heated to kT ≥ 15 MeV, and copious gamma-rays and pairs were observed. Our most important new findings include: (1) The observed e+ /e− ratio exceeds 15% in 20 shots using thick disk and rod targets, reaching ~50%+ /− 10% for one Pt rod. (2) We infer a maximum emerging pair density ~10 15 /cm 3 , so that the effective pair skin depth = (mc 2 /8π e 2 n + ) 1/2 becomes smaller than the plasma size. (3) Long narrow rod targets produce higher observed e+ /e− ratios than disk targets. (4) For thick disk and rod targets, Pt produces higher observed e+ /e− ratio than Au. Hence Pt rod may be the favorite target for creating pair-dominated plasmas 1,11 in future laser-solid experiments.

Results
The experiments were carried out in the 2m-diameter solid-target chamber TC1 of TPW with heavy radiation shielding. Figure 1 shows schematically the experimental setup, sample laser focal spot size and pulse profile. Laser and target parameters for all shots are summarized in Table 1. Charged particle signals are recorded on Fuji imaging plates (IP) attached onto NdFeB magnetic spectrometers (Fig. 1c, see Methods). Figure 2a shows sample IP images of electron, positron and proton (e+ e − p) spectra after conversion to PSL units 23,24 . The positron signals are clearly visible in both the low-energy (0.5-45 MeV) and high-energy (1.5-130 MeV) IP images. Proton signals from target surface contaminants are also seen in many shots, with energies ~1-2 MeV. Figure 2b highlights the positron signal compared to the background level (mostly secondary x-rays produced inside the spectrometer), which is highly nonuniform along and across the magnet gap. Background subtraction is performed using detailed polynomial fits (Fig. 2d,e), and the procedure is certified using shots with no positrons (Al targets and e-beams, see Methods). The spectrometer response curves (Figs 1d and 2c) are generated using GEANT4 simulations 25 based on detailed magnetic field measurements, and then calibrated using clinical e-beams of known energies at the LSU Mary Bird Perkins Cancer Center (MBPCC) at Baton Rouge, Louisana 26 . Figure 3a compares the TPW e+ /e− ratio vs. disk target thickness with published Titan Au data 2 and with GEANT4 simulations 25 . For targets thinner than 3 mm, TPW and Titan data basically agree, but the TPW ratio rises steeply from 3 mm to 4 mm thickness and clearly deviates from the linear trend extrapolated from the Titan results, which had no published data above 3 mm. TPW intensity was higher than Titan and produced higher energy electrons, which in turn create higher energy bremsstrahlung photons and pairs that can escape more easily from thick targets, while the primary electrons are more attenuated by thicker targets. Our data agree qualitatively with the trend predicted by GEANT4 ( Fig. 3a blue diamonds), which also shows that the decline above 4 mm is due to the small disk diameter (4.5 mm) used in our experiment. Figure 3b shows that, if we had used much bigger diameter disks (»4.5 mm), the e+ /e− ratio should continue to rise beyond 4 mm thickness (red dots). Quantitatively, GEANT4 underpredicts the e+ /e− ratio for thicknesses ≤ 1 mm, and overpredicts the ratio for thickness ≥ 3 mm (Fig. 3a). The underprediction for thin targets is likely caused by GEANT4 not including the Trident process 10 or sheath electric fields 27 , both of which should increase the e+ yield for thin targets. This may also partially explain why the Titan data trend appears linear. However the GEANT4 overprediction for thick targets (≥3 mm) remains to be understood since the Trident process and sheath field should play little role for thick targets. We note that the predicted absolute positron yield actually tops out at ~1-2 mm thickness 25 . Thus the monotonic rise of the emergent e+ /e− ratio with thickness ( Fig. 3b red dots) is mainly caused by the increasing absorption of primary electrons with increasing thickness. Figure 3c compares the e+ /e− ratio of Au versus Pt disk targets. We see that the observed e+ /e− ratio for Pt jumps to more than twice that of Au for thicknesses ≥ 4 mm. This is caused by the reduction of hot electrons emerging from thick Pt targets, while the absolute positron yield stays roughly the same for Au and Pt. Pt has five times the electrical resistivity of Au, which likely reduces the return current of ambient electrons in the target and inhibits the propagation of the hot electrons 7 .
Our most important result comes from the rod targets (Fig. 4). The idea is to irradiate the end of a long narrow rod so that the primary hot electrons and their bremsstrahlung photons propagate mainly along the rod axis (Fig. 3a). Away from the rod axis, we should detect a higher e+ /e− ratio by avoiding most of the primary electrons. Moreover, a long narrow rod provides more optical depth for the bremsstrahlung emission and pair production along the rod axis, while it minimizes the absorption of pairs emitted sideways. This idea is largely confirmed by our rod target data: most of our rod targets produce maximum e+ /e− ratios > 10% when observed at angles away from the rod axis towards target Scientific RepoRts | 5:13968 | DOi: 10.1038/srep13968 normal (TN) direction (Fig. 4b,c). Shots using 3 mm diameter rods (Fig. 4c) produced higher e+ /e− ratios than 2 mm diameter rods (Fig. 4b), raising the hope that using rods with diameter > 3 mm may produce even higher ratios. Again Pt rods work better than Au rods, with the e+ /e− ratio of one 3 mm diameter Pt rod reaching 52%+ /− 10%. These results suggest that Pt rods may be the preferred target to create pair-dominated plasmas with e+ /e− > 50% at birth, independent of any energy selection or magnetic focussing schemes to further increase the e+ /e− ratio downstream 28 .
The highest inferred emerging pair density comes from our 0.35 mm thick Au disks. For these targets the observed positron yields were ~3 × 10 10 /str. Integrating over an emission cone of 25 o (~laser incident angle, see also 3,25,29 ), we conservatively estimate a total positron yield of N +~1 .8 × 10 10 for 100 J of laser energy. Detailed GEANT4 simulations 25 show that in this case the emerging positrons are concentrated in a pill box of diameter D ~ 0.4 mm and thickness cΔ t ~ 90 μ m, where Δ t = 3 00 fs is the pulse duration of the emerging positrons. Hence the inferred positron density in this case is n + ~ 1.8 × 10 10 /π (0.02) 2 (0.009) = 1.6 × 10 15 cm −3 . At this density the "pair skin depth" c/ω pair = c/(8π n + e 2 /m) 1/2 is ~ 0.1 mm. Hence Dω pair /c ~ 4, qualifying the pair jet as a "pair plasma" using a common definition of "plasma 30 " (see Discussion). However, for many relativistic kinetic processes the more relevant length scale to compare with D is the "relativistic pair skin depth" = cγ 1/2 /ω pair where γ is the average Lorentz factor of the pairs 20 (see Discussion). In this case our 1 mm thick Au target data actually lead to a smaller "relativistic pair skin depth" relative to the plasma size D, because their positron Lorentz factor is much lower than those for 0.35 mm thick targets (see below). The average positron Lorentz factor of our 1 mm thick Au targets with the highest e+ yield (N + ~ 2 × 10 10 ) was γ ~ 14. Hence γ 1/2 = 3.7, and the ratio Dω pair /cγ 1/2 = 1.1, marginally > 1. As Sarri et al. 20 point out, this ratio is independent of D, and scales as (N + /γ Δ t) 1/2 . For laser-solid interactions, N + scales with laser energy 15 . Hence our results demonstrate that future ultraintense lasers with Δ t < 100 fs and energy  100 J irradiating mm-thick Au or Pt targets should easily create a pair plasma with Dω pair /cγ 1/2  1. Figure 5 shows sample deconvolved positron and electron spectra for Au targets. While the positron peak energy varies widely (6-23 MeV), the electron peak energy is remarkably stable (10-16 MeV) independent of target geometry, thickness and material. Positron kT is typically ~1/2 of the electron kT except for the rod target, for which the positron slope is almost as hard as the electron slope. This is likely due to the convolution of positrons emitted by different parts of the rod. All of our electron spectra show a strong deficit of electrons below a few MeV. This spectral behavior differs from those reported for other PW laser experiments 3,7,16,31 , and suggests that TPW electrons below a few MeV are more strongly attenuated and/or refluxed back into the target. This new regime of hot electron transport requires further investigation. Figure 6a compares the positron spectra of various target thickness and detector angle for Au disks. The positron peak energy ranges from ~6 MeV up to 23 MeV. Figure 6b compares the thickness dependence of the positron peak energy E + and proton peak energy E p . While E p decreases monotonically with thickness, E + has a minimum around 2 mm. The decrease of E p and E + (below 2 mm) with increasing target thickness is consistent with sheath field acceleration 27,32 since the sheath field is stronger for thinner targets. However, the reversal of E + from 2 mm to 4 mm is likely caused by increasing attenuation of low-energy positrons by the thicker targets. Since E p is much smaller than E + , the protons must experience only a small fraction of the sheath potential seen by the positrons. To help understand these results we have performed particle-in-cell (PIC) simulations 30 to explore the plasma physics of positron and proton acceleration. Figure 7 shows the results of a 2-dimensional PIC simulation using the EPOCH code (see Methods). A 1 μ m wavelength laser with intensity = 10 2 1 W.cm −2 , pulse duration = 160 fs and Gaussian focal spot diameter = 2 μ m irradiates from left a "solid gold" plasma (electron density = 4200 × critical density and ion mass = 197 × proton mass), at an incident angle of 15 o and electric field parallel to target surface (s-polarized). The simulation box has physical dimensions of 34 μ m × 7 μ m, with cell size = c/ω e = 2.5 × 10 −3 μ m (see Methods for details). The Au target has thickness of 1 μ m, located between × = 3 μ m and 4 μ m. An exponential density ramp is provided in front of the target to simulate the preplasma (TPW laser contrast ~ 10 −7 5 ). Even though such a thin target is unrealistic compared to the mm thick targets of our experiment, it should allow the hot electrons accelerated at the target front to penetrate the target, exit the back surface, and propagate for sufficient distance (30 μ m) to create a meaningful sheath potential. Passive tracer particles are used to model the positrons (initialized throughout the target) and protons (initialized only at the target back surface). The idea is to model some aspects of the sheath acceleration of positron and proton from first principles. Figure 7a-d show spatial profiles of E x , B z , N e (electron density) and N p (proton density) at 110 fs, just before the hot electrons reach the right boundary. Figure 7e shows the lineout at y= 3.5 μ m of E x and the sheath potential (S E x dx) which reaches ~5 MeV at this stage. Figure 7f shows the energy distribution of positrons reaching the upper right boundary near the laser forward direction. The positrons form two distinct peaks separated by ~5 MeV. The low energy peak corresponds to positrons directly accelerated by the laser prior to the formation of the sheath potential, which cannot occur in a real experiment since the pairs are created deep inside the thick target and cannot experience any laser acceleration. The high energy peak at ~7.5 MeV corresponds to positrons accelerated by both the laser and the sheath field. Even though real positrons created inside our thick targets are not subject to direct laser acceleration, it turns out they are in fact born with energies peaking at ~1.5-2 MeV 25 due to the convolution of the pair production cross section 10 with the TPW bremsstrahlung spectrum 29 . Hence the prediction of the ~7.5 MeV high energy peak in Fig. 7f is semi-realistic. In the real experiment, space is 3D and a fraction of the hot electrons is attenuated by the mm thick target, both of which reduce the sheath potential. On the other hand, the focal spot size (Fig. 1e) and target y-dimension are larger, both of which increase the sheath potential. Hence it is satisfying that the prediction of Fig. 7f lies within the range of the observed positron energies (Fig. 6). At the same time, Fig. 7d shows that the protons have travelled only 1-3 μ m from the target at 110 fs. From the red curve of Fig. 7e this distance translates into a sheath potential of ~1 MeV, thus qualitatively explaining the large difference between the proton and positron energies (Fig. 6b). The PIC simulation also shows that positrons along the target normal direction reach lower energies than those along the laser forward direction, in agreement with observations (Fig. 6), since more electrons are emitted towards laser forward than target normal. In summary, even though our PIC simulation can only model a very thin Au target in a small 2D box, it seems to capture some of the essential physics of positron and proton acceleration, and qualitatively explain the observed positron and proton energies from first principles.

Discussion
The most important results of our experiments are: (a) Pt targets can lead to higher emergent e+ /e− ratio than Au targets, and (b) long narrow rods allow pairs to escape off-axis with higher e+ /e− ratio than disks. Since one of our 3 mm diameter Pt rods produced the highest e+ /e− ratio observed so far (52%+ /− 10%) for laser-solid experiments, we will explore using even bigger Pt rods to reach higher e+ /e− ratios. We infer a "pair skin depth" ~4 times smaller than the transverse pair jet size, and a "relativistic pair skin depth" marginally smaller than the transverse pair jet size 20 . Since our pairs are imbedded in a nonneutral electron plasma of higher density, it is debatable what the best definition of a "pair plasma" should be. Different plasma instabilities also have different dependences on the Lorentz factor 7,30 . Hence it may be too simplistic to use a single kinetic length scale to characterize a relativistic "pair plasma". Despite this, there is little doubt that future laser pulses with intensity > 10 21 W.cm −2 , pulse showing the variation with thickness (a-e) and geometry (f). All spectra are recorded by detectors near laser forward (LF) direction (+ 3 o to − 10 o ). All electron spectra peak at ~10-16 MeV while the positron peak ranges from ~6 MeV to 23 MeV. The positron high energy slope is softer than the electron slope for all disk targets (a-e), but is almost as hard as the electron slope for the rod target (f). All electron spectra show a deficit of low energy electrons. Some electron spectra show a second harder component beyond ~ 40 MeV  (a,b). The deep troughs seen in some spectra are due to IP or scanner defects.
duration < 100 fs and energy 100 J irradiating solid Au and Pt targets, should create more pairs with higher density that will easily satisfy any "pair plasma" definition. A sufficiently large quantity of dense pair-dominated plasma will have wide ranging applications to laboratory astrophysics (simulating pulsar winds and gamma-ray bursts) and fundamental physics (Bose-Einstein condensate of positronium 33 and gamma-ray amplification via stimulated annihilation radiation or GRASAR 1,33 ). It is useful to highlight here the key differences and complementarity between the 1-step (laser-solid 2-4 ) and 2-step (laser-gas jet-converter 19,20 ) approaches to laser pair creation, since both are actively pursued. The 1-step approach creates ~ MeV pairs with a broad beam and hence lower pair density. The 2-step approach creates ≥ 0.1 GeV pairs with a narrow beam and hence higher pair density 20 . The 1-step approach produces higher pair yield (observed N + ~ fewx10 10 -10 11 3 ), and N + scales with laser energy. The 2-step approach produces lower yield (N +~f ewx10 7 observed and ~10 9 simulated 20 ), and it is unclear how to increase N + with laser energy. The advantage of the 2-step approach is that the LWFA electron beam can readily reach GeV energies and their bremsstrahlung photons can penetrate cm-thick converters to produce quasi-neutral pairs with e+ /e− ratio ~100% 20 , whereas the 1-step approach will have to wait for much higher laser intensities to reach GeV electron energies. But our rod targets may provide an alternative approach to achieving high e+ /e− ratio. Interestingly, the results reported here and in Sarri et al. 20 both give similar Dω pair /c< γ > 1/2 values of ~1, despite their very different N + , Lorentz factors and pulse durations. Thus both approaches are at the "threshold" of achieving a "pair plasma" however it is defined, but of very different dimensions and properties. Looking ahead, we believe that the 1-step approach will be more useful for applications requiring large amount of pairs at low energies such as the creation of a BEC of positronium, since it is easier to slow MeV pairs than GeV pairs, while the 2-step approach will be more useful for applications requiring narrow e+ e− beams at high energies, such as particle accelerators and advanced light sources. Both approaches can produce pair plasmas relevant to astrophysics 1 .

Methods
Magnetic Spectrometers. Three positron-electron-proton (e+ e − p) spectrometers made with NdFeB magnets of 0.4T to 0.6T and 3 mm diameter pinholes were used to measure the e+ e − p spectra at distances of 18-40 cm from the target (Fig. 1). The spectrometers cover the energy ranges 0.5-45 MeV,  We show spatial profiles of (a) electric field E x , (b) magnetic field B z , (c) electron density N e , (d) proton density N p , at 110 fs. (e) Lineout of sheath electric field E x (blue curve) and sheath potential (red curve) along y = 3.5 μ m. The total sheath potential reaches ~5 MeV in this run. (f) Positron energy distribution near the upper right boundary at 110 fs shows two distinct peaks at ~2.5 MeV and ~7.5 MeV respectively, separated by the 5 MeV sheath potential. At this time the protons have travelled only 1-3 μ m (Fig. 7d) and gained ~1 MeV of sheath potential (Fig. 7e). Pb-Cu-Al-plastic stack collimators with 3 mm pinholes were attached to the front of the spectrometers to provide shielding and collimation. Spectra were recorded using Fuji imaging plates (#BAS-IP-MS) and FLA7000 scanner 23,24 . Positron data. Even though the positron signal is weak compared to the internal x-ray background, it is concentrated in a ~4 mm wide strip along the center of the magnet gap (Fig. 2). Hence we developed a background subtraction procedure based on polynominal fits to the two dimensional background, using the optimization of R 2 as a function of central pixels removed. This method produced robust background-subtracted signal for which the 1 − σ uncertainty is well-quantified. We tested this algorithm using Al target and clinical e-beam data, whose e+ IP backgrounds contain no real positrons, while their e-IP backgrounds are similar to those of Au and Pt shots. All such e+ IP images gave null (< 1 − σ ) positron signal after background subtraction. All Au and Pt data reported in this paper come from positron signals >3 − σ . To facilitate comparison of e+ /e− ratios from all spectrometers, we include only positrons and electrons between 2 MeV and 50 MeV. GEANT4 simulations. We used GEANT4 to simulate bremsstrahlung and pair production by laser-driven hot electrons in Au and Pt targets. GEANT4 is a widely used object-oriented Monte Carlo code developed at CERN for nuclear and particle physics. We inject hot electrons starting with a trial spectrum, 160 fs pulse duration and beam opening angle of 15 o into the Au target, and then iterate the incident spectrum until the output spectrum agrees with the observed electron spectrum. The positron output from the final iteration is then collected at a hemispherical detector surrounding the target, as a function of energy, angle and time. To generate the magnetic spectrometer response curve E(x) (Fig. 2c) we input detailed 3-dimensional magnetic field data measured inside the gap and inject normal-incident electrons and positrons into the 3-mm diameter pinhole at 0.5 MeV energy intervals. The positions of electrons and positrons hitting the imaging plates are then recorded. The red curve of Fig. 2c represents the centroid position of the Monte Carlo electron distributions. The proton energy E p can be determined using the positron E(x) curve by substituting the positron momentum with the proton momentum = (2E p m p ) 1/2 where m p is the proton mass. PIC simulation. We carried out two-dimensional particle-in-cell (PIC) simulation using the EPOCH code which has been widely used to model high energy density physics and laser target interactions. The core algorithm of this code is the same as the PSC code 34 . Our simulation domain spans 34 microns in x and 7 microns in y. A solid-density gold plasma of kT = 2.5 keV and 1 micron thickness is located between x = 3 micron and x = 4 micron. A laser beam comes in from the lower left boundary, and hits the center of the target at 15 o from target normal. The laser has a peak intensity of 10 21 W.cm −2 , duration of 160 fs, wavelength of 1 micron and focal spot diameter of 2 microns. Behind the target (x > 4 micron) is 30 microns of vacuum. In front of the target (x < 3 micron) is a gold plasma whose density falls off exponentially (e-folding distance = 0.12 microns) from the target surface to model the preplasma created by the laser prepulse. We included two passive tracer particle species in the simulation. The first one represents positrons, which follow the initial electron distribution. The second one represents protons which are located in a thin layer at the target back surface. We used cell size equal to electron skin depth so that the grid measures (13804 × 2842), with 20 particles per cell in the target region. The time step is half of the inverse electron plasma frequency in the target. We ran the simulation up to t = 200 fs.