Enhancing positron production using front surface target structures

Producing a high-density, relativistic electron-positron pair plasma in the laboratory could significantly deepen the understanding of exotic astrophysical objects such as pulsars and quasars, but is extremely challenging.^1–5 With the advances in high intensity laser technology, several methods for pair production have been either demonstrated or proposed, with different mechanisms dominating the physics in different regimes of laser intensity. For example, the Schwinger mechanism⁶ requires an extremely high intensity, above ∼10²⁹ W/cm², for spontaneous pair creation from vacuum, whereas the Breit-Wheeler (BW) mechanism⁷ requires about 10²⁴ W/cm² for avalanche-type discharge.^8,9 These intensities are far beyond the capability of state-of-the-art lasers (up to 10²² W/cm²).

An alternative method is to inject laser produced high-energy electrons into high-Z target materials,^4,10–16 with the electrostatic field of the nucleus involved in the pair production process releasing the constraint on the laser electric field intensity. If a thick converter target is used, positrons are mainly produced through the 3-step Bethe-Heitler (BH) process.¹⁷ First, relativistic electrons are generated through a laser plasma interaction (LPI) at the front side of the target. These electrons then transport through the high-Z material and produce high-energy photons via Bremsstrahlung radiation. Propagation of the high-energy photons in the field of nucleus then creates electron-positron pairs. The key step is to transfer laser energy into enough high-energy (tens of MeV) electrons, for which, only a moderate intensity laser (∼10²⁰ W/cm²) is needed. Experiments using this type of setup have produced up to 10¹² pairs/shot, which is the highest yield reported to date by use of lasers.

A key to higher positron yield is the production of hotter electrons. Substantial enhancement in electron energies can be obtained by manipulating the laser-plasma interaction using a structured target.^18,19 Specifically, highly ordered silicon microwire arrays facing the laser pulse enable guiding the relativistic electron beam along the structured surface and moreover facilitate a direct laser acceleration mechanism. Such an electron beam can then create a substantial enhancement in the Bremstrahlung radiation produced by a high-Z convertor target.²⁰ The Bremsstrahlung x-rays further interact with atomic nuclei and create more electron-positron pairs.

We demonstrate herein experimentally a substantial enhancement in both the yield and the energy of generated positrons using target structures, which suggests an efficient and inexpensive approach to improvement of positron sources. Particle-in-cell (PIC) simulations with the code Chicago²¹ have been used to explain the experimental results and have allowed a direct simulation of the LPI effects on the positron yield. Moreover, the simulation is in good qualitative agreement with the experimental data.

A schematic diagram of the experimental setup is shown in Fig. 1(a). The structured target was irradiated with the OMEGA EP laser pulse, with a wavelength of 1.053 μm, an energy of 500 J, and a pulse length of approximately 700 fs. Eighty percent of the laser energy was enclosed in a 35 μm diameter focal spot as is derived from an on-shot wavefront and far-field measurement. The peak intensity was estimated to be 4.5 × 10²⁰ W/cm² according to the measured fluence map. Prior to the experiment, the structure geometry (spacing and length) was optimized through PIC simulations of the hot electron temperature. This geometry, which we call structure 1, is an array of silicon microwires with 3 μm diameter, 13 μm length, and 15 μm center-to-center transverse distance. For reference, we have also shot flat targets as well as another type of unoptimized structure (structure 2) that showed detrimental effects on electron energies in simulations. Structure 2 had 3 μm diameter, 100 μm length, and 7 μm center-to-center distance. The microwires in the latter target had much longer lengths than the laser depth-of-focus, and much smaller space in between them than the laser focal spot size, so they tend to break the laser pulse during its propagation, resulting in a poor laser intensity at the critical density surface. Consequently, they led to a low-energy electron spectrum.

Figures 1(b) and 1(c) show scanning electron microscope images of both target structures used in the experiment. The Si microwire arrays 100 μm in height (structure 2) were first grown on a Si ⟨111⟩ wafer by the vapor-liquid-solid growth method,²² whereas the shorter microwire arrays (structure 1) were etched from Si ⟨100⟩ wafers via Deep Reactive Ion Etching.²³ The microwires were then embeded in a ∼30 μm thick polydimethylsiloxane layer and peeled off of the substrate. This thin polydimethylsiloxane layer was then glued to a 1 mm thick Au backing layer. In this case, the high-energy electrons generated and guided by the surface structures would transport through a thick high-Z material (Au) and induce pair production. The transverse size of the Au block used in the experiment was also 1 mm. The laser was directed at normal incidence onto the target and the microwire arrays were oriented along the laser direction. This configuration has been shown in the previous work to yield the highest enhancement of electron energy.^18,19 The positron spectra were measured by an electron/positron spectrometer on the back side of the target along the laser direction (which was also the target normal direction).

The experimental positron and electron spectra for three different types of targets are shown in Figs. 2(a) and 2(b). Target structure 1 generated about 50% more positrons than the regular flat target, and its laser to positron conversion efficiency increased by ∼97% compared to the flat substrate. The spectrum peak also shifted from ∼50 MeV for the flat target to ∼60 MeV for structure 1. Structure 2 showed fewer as well as much lower-energy positrons, in accord with expectations as the length and spacing of the microwires encumber the laser focusing. The electron spectrum from structure 2 also showed the same trend, in agreement with the positron measurements. However, the electron spectra from flat and from structure 1 were mutually similar, with both having an electron temperature of about 21 MeV.

Multiple simulations to model the entire process were performed to elucidate why the measured positron spectrum from structure 1 is obviously superior, while its electron spectrum is similar to that from flat target. The simulations used the same laser conditions and target geometries as the experiment. We fitted the measured laser fluence map with two Gaussian functions to maintain the intensity distribution of the experiment. The OMEGA EP laser had a substantial prepulse that could affect the conversion efficiency from the laser to fast electrons and would therefore affect the yield and energy of positrons. The facility has an on-shot prepulse measurement from 3 ns to 1 ns prior to the main laser pulse. For the prepulse within 1 ns, we assumed a similar profile to that measured by Dorrer et al. on OMEGA EP.²⁴ The total energy of the prepulse was about 3.5 mJ. Hydrodynamic simulations with the code HYDRA²⁵ were used to calculate the preplasma profile, as shown in Fig. 3(a). The preplasma scale length between relativistic critical density and critical density is about 2 μm, and the scale length below critical density is 10 μm.

Full 3D PIC simulations to model all physics processes are impractical with current supercomputers. We instead adopted a two-stage approach that has been demonstrated on other targets^26,27 to simulate LPI and transport processes separately. Both stages were performed with the code Chicago.²¹ The overall simulation process is illustrated in Fig. 3(b). First, a 2D Cartesian geometry was used to simulate the LPI process, with only x and z dimensions modeled in space. However, the velocity was 3D as all three components v_x, v_y, and v_z were updated at each time step. We could not use a cylindrical geometry, because the laser was linearly polarized in the x direction. The electrons were measured at a plane that was 5 μm inside the target. The energy, direction, position, and time of each electron macroparticle have all been recorded. We then processed the laser-generated electrons to get their distribution as a function of energy, angle, transverse distance, and time. At this point, we assumed a rotational symmetry along the laser propagation axis for both space and velocity, and converted the distribution to cylindrical coordinates. The transport simulation was performed in a 2D cylindrical geometry. When hot electrons leave the target, they would create a strong sheath field on the back side. It is critical to model the sheath field properly to obtain the correct yield and spectrum. The cylindrical geometry is required to accurately model the $1/r2$ falloff of the E field, whereas the 2D Cartesian geometry would result in a $1/r$ falloff. The hot electrons were then re-sampled according to its distribution and injected into a 1 mm thick, 1 mm diameter Au target in a 2D cylindrical geometry. Positron generation and transport was then simulated both inside and behind the Au target. To compare with the experimental results, statistics of escaped electrons and positrons were performed at another extraction plane that was 2 mm from the backside of the target.

The electron spectra generated from the LPI simulations are shown in Fig. 3(c). The dashed curves are the raw distributions derived in Cartesian coordinates, and the solid curves are converted distributions in cylindrical coordinates. Note that the 2D Cartesian simulation has a virtual dimension in y axis so the electron spectrum has a different unit, corresponding to the right y axis in Fig. 3(c). The electron temperatures Te for different portions of the spectra are also labeled in the plot. After conversion, the temperature for higher-energy-range electrons is maintained at around 20 MeV, which is quite close to the experimentally measured temperature of 21 MeV. Lower energy electrons have a wider angular distribution and thus tend to be more easily affected by the conversion. Te decreased by about 3 MeV for electrons within 25–70 MeV. Comparing structure 1 (red) to flat (black), the main difference appears at energies above 25 MeV, as structure 1 tends to produce about an order of magnitude more electrons within this energy range.

To evaluate the positron yield by different electron spectra, in Fig. 3(d), we have plotted $f(E)·Pe+(E)$⁠, where f(E) is the spectrum of injected electrons [solid curves in Fig. 3(c)], and $Pe+(E)$ is the probability that one positron could be generated and exit from the 1 mm thick, 1 mm diameter Au target as one incident electron with energy E is normally injected. $Pe+(E)$ (blue curve) was obtained using a Monte Carlo code MCNP,²⁸ and the field effects have been ignored. Note that we cannot directly compare the positron yield from MCNP to the experimental result as the escaped positron yield and spectra are also largely affected by the self-generated field. MCNP only provides an estimation of the positron production capability of different energy electrons. The positron production probability grows sharply with energy for incident electrons below ∼30 MeV and gradually saturates at high energies. The black and red solid curves indicate the calculated $f(E)·Pe+(E)$ for flat and structured targets, respectively. Both curves peak at about 15 MeV. However, electrons within 25–150 MeV from structure 1 contributed to a great extent to the positron yield, whereas for the flat target most of the positrons are generated by lower energy electrons. Overall, the injection spectrum from structure 1 produced about 30% more positrons than the flat target. Note that this estimation does not consider any field or electron reflux effects that in reality play an important role.

The Monte Carlo simulation only provides an intuitive view of the pair production capability of LPI electrons. Understanding the energy difference in the measured positron spectra requires closer evaluation of the transport PIC simulations that involve the sheath field. The comparison of modeled and experimentally measured positron spectra at target normal (laser direction) is shown in Fig. 4(a). The simulated spectra agree qualitatively with the experimental data. In Fig. 4(b), the dark solid curves show the simulated spectra of escaped electrons at 0°, whereas for comparison the light solid curves in the background show the corresponding experimental spectra. Both spectra have a relatively good overlap within the energy range between 40 and 110 MeV. At lower energy, the mismatch is expected, because the experimentally measured spectra include electrons that are generated at much later times than those covered by the simulation. The simulated spectra showed less particles at high energies. However, according to Fig. 3(d), electrons above 110 MeV would make a negligible contribution to the positron yield. These high energy electrons have a small impact on the sheath field as well because their total charge is low. Therefore, the simulated positron and electron spectra indicate that the injected electron source from LPI simulation models the experimental condition reasonably well. For both the flat and the structure 1 target, the electron spectra measured at the target normal direction are mutually quite similar, whereas the positron spectra are obviously different, in accord with experimental observations. In Fig. 4(b), we have also plotted the total electron spectrum (in MeV^–1) as the dashed black and red curves. Unlike the spectra at 0°, the total spectrum from structure 1 clearly shows more high energy electrons, which explains the large discrepancy in the positron spectra, as forward going positrons are generated by all electrons, not just by the forward going ones.

There are two acceleration mechanisms that are responsible for the highest energy electrons, including the loop-injected direct acceleration²⁹ which is associated with any targets having moderate scale length preplasma, and the structure-guided direct laser acceleration which occurs only with the structured target.^18,19 We have also found strong Weibel instabilities³⁰ near the critical density surface for both target types, which largely widens the electron divergence. This effect was dominating so that the usual collimating effect associated with the front surface micro-wires described in previous work^18,19 did not show up in the electron spectrum measured at 0°.

The energy of positrons is largely determined by the sheath field on the back side of the target. Figure 5 shows the evolution of the sheath field E_z as a function of the longitudinal position z and time t. Column (a) are the results from the flat target, and column (b) are from structure 1. Images (a1),(b1) and (a3),(b3) show the E_z field at r = 0 and average E_z field over the 1 mm diameter disk, respectively, whereas (a2), (b2) and (a4), (b4) are the corresponding voltages V calculated by integrating E_z over the longitudinal distance z. $V=∫zozEzdz$⁠, where z₀ = 1 mm indicates the back surface of the target. These plots allow for an estimate of the accelerating capability of the sheath field. The images at r = 0 indicate that passes of electrons gradually build up the sheath field on the target backside. Comparing the integrated voltage for flat and structured targets, both the voltage at r = 0 and the average voltage for the structured target are about 10 MV higher than that for flat target, which is consistent with the measured energy difference between their positron peaks.

The two-stage PIC simulation reproduced the experimental results, suggesting its potential for further target structure optimization to control the yield and energy of positrons and other secondary particles, such as ions that are also greatly influenced by the sheath field. Optimal target parameters will vary substantially with laser pulse length, intensity, focal spot size, and the amount of prepulse. As we have shown, for a given laser condition, the structures can be optimized by performing 2D Cartesian LPI simulations and converting the electron distributions to cylindrical coordinates. After the conversion, the hot electron temperature and the laser-to-electron conversion efficiency can both be realistic metrics for estimating the positron yield. We plan to probe a broader parameter space in future work.

In summary, front surface target structures have been shown experimentally to substantially enhance the positron yield and energy, constituting a cost-effective approach to use laser-generated positron sources for laboratory astrophysics applications. The follow-up simulations explain the entire process of how the laser-plasma interaction that is manipulated by the target structure affects the yield and energy of positrons. The agreement between the simulated and experimental spectra indicates the possibility of further target optimization using two-stage PIC simulations.

We thank the OMEGA EP team for laser operation and technical support. This work was performed under the auspices of the U.S. DOE by LLNL under Contract No. DEAC5207NA27344, and funded by LDRD (No. 17ERD010). The fabrication of Si microwire arrays was supported through the Office of Science of the U.S. Department of Energy under Award No. DE- SC0004993. Additional support for this work was provided by the Lockheed Martin Corporation (Award No. 4103810021). We thank the staff at the Kavli Nanoscience Institute at Caltech for their technical assistance with fabrication.