Scaling of 3D printed microstructured targets in the multi-ps, quasi-relativistic regime for high-flux laser-driven ion acceleration

Laser-driven ion acceleration has emerged as a promising technique for producing high-flux, energetic proton beams for applications in high-energy-density science, radiography, and inertial fusion energy concepts like ion fast ignition. Recent advances in target fabrication, notably the use of 3D-printed microstructured arrays with graded density profiles, have demonstrated significant improvements in proton energy and conversion efficiency compared to conventional flat foils, particularly in the highly relativistic laser regime. In this work, we present a detailed experimental scaling study of laser-driven ion acceleration using log-pile microstructured targets in the quasi-relativistic, multi-picosecond regime. Experiments were conducted at the OMEGA-EP facility, utilizing short-pulse laser beams with energies up to 1250 J, pulse durations ranging from 0.6 to 10 ps, and focal spot sizes from 14 to 50 μ m, corresponding to normalized vector potentials a 0 from approximately 0.7–9.2. Target parameters, including micro-wire diameter (0.5-1 μ m) and total thickness (10-50 μ m), were systematically varied. Proton spectra and beam profiles were characterized using radiochromic film stacks, while electron spectra were measured with a magnetic spectrometer. Our results show that ion performance metrics such as the maximum proton energy and conversion efficiency scale strongly with target parameters including the target average density. These findings provide important scaling relationships for optimizing target design and laser parameters in future high-flux, laser-driven ion acceleration experiments.

Twenty years ago, scientists at Lawrence Livermore National Laboratory’s (LLNL) Nova petawatt laser discovered that directing Nova’s high intensity beams onto thin solid targets produced a beam-like source of high energy protons (∼ MeV energies) [1]. Since their discovery, the field of laser-driven proton acceleration has grown substantially and experiments on this topic have demonstrated the production of many different particle species, including protons, light and heavy ions, electrons/positrons and even neutrons. In particular, these sources have been critical in the field of high-energy-density science since these MeV-energy proton sources enable applications to proton radiography of dense materials [2], proton heating by laser-driven sources to access warm dense matter regimes [3] and fusion energy schemes such as proton fast ignition [4]. Many of these applications, including isochoric heating and radiography, require both energetic (> 50 MeV) and high-flux ion sources (> 10 kilo-Joules of protons).

The most widely studied mechanism for laser-driven proton acceleration is the Target Normal Sheath Acceleration (TNSA) process, where high-intensity lasers incident on thin foils generate an underdense plasma and electrons within this plasma are accelerated to MeV energies by the laser field via the ponderomotive force and establish a strong electrostatic field that can pull ions off the surface of the foil thus creating a beam-like source of protons. While this mechanism has been widely researched since its original discovery at Lawrence Livermore National Laboratory in 2000 [5], the highest maximum proton energy achieved via TNSA has plateaued at ∼ 70 MeV, and typical conversion efficiencies, that is, the ratio of the total produced ion energy to the short-pulse laser driver energy, do not typically exceed a few percent [6].

In a departure from the flat foil targets typically used in TNSA experiments, recent work has been conducted with the use of novel targets, such as nanowires [7], foams [8], thin substrates [9], and microtubes [10], in an effort to increase the conversion efficiency and/or flux of laser-driven ion acceleration. In this work, we consider 3D-printed microstructure array targets with a graded density profile. Microstructured arrays considered here are composed of micron-scale wires made of a CHO-based polymer that are 3D-printed in a close-pack structure. The diameter of each wire is typically 0.5–1 microns, and the wire arrays are printed using the state-of-the-art two-photon-polymerization (2 PP) technique [11]. The microwire spacing and patterning of the wire-structure can be carefully controlled during manufacturing to achieve a specified density profile. In particular, two 2 PP-printed target types developed at General Atomics consist of (a) log-pile microstructured arrays (LPA), in which micron-scale wires are arranged in an ordered grid, and (b) stochastic microstructured arrays (SMA), which are randomized wire arrays. Both SMA and LPA targets achieve a defined density gradient by gradually increasing the wire spacing along the target’s depth.

Recent experiments at the OMEGA-Extended Performance (EP) facility using these microstructured arrays in laser-driven ion acceleration experiments have shown impressive results, demonstrating maximum proton energies > 100 MeV and ion conversion efficiencies 6 − 8 × that of conventional flat foil targets depending on the microstructured array type [12]. However, these targets have largely been considered in the highly relativistic laser intensity regime, in which the laser’s peak electric field amplitude is intense enough to oscillate electrons in laser-plasma interactions to highly relativistic velocities. The laser is often parametrized using the normalized vector potential, a 0 = e E 0 / (ω m e c), with speed of light c, electron mass m e, electron charge e, laser frequency ω, and laser electric field magnitude E 0. This vector potential can be represented in a practical form as a 0 ≈ I Laser [ W / c m 2 ] λ 0 2 [ μ m 2 ] / 1.37 × 1 0 18, with laser intensity I Laser and wavelength λ 0. The normalized vector potential separates the relativistic (a 0 > 1), highly relativistic (a 0 ≫ 1), and quasi-relativistic (0.1 < a 0 ≤ 1) regimes, suitably named to describe the velocities of electrons oscillating in the laser’s electric field.

In this work, we present a detailed scaling of laser-driven ion acceleration using 3D microstructured targets in the quasi-relativistic laser regime. Several multi-kilojoule, multi-picosecond short-pulse lasers have been constructed over the last 2 decades, such as the National Ignition Facility-Advanced Radiographic Capability (NIF-ARC) laser, the PETAL laser at the Laser MegaJoule (LMJ) Facility, and the LFEX (Laser for Fast Ignition Experiment) laser at the Institute for Laser Engineering (ILE). The tremendous energy of these laser systems enables exciting opportunities to produce high-brightness, high-energy laser-driven proton sources which will be crucial for developing and investigating proton fast ignition platforms for inertial fusion energy [13] as well as high-flux radiography and probing sources for high-energy-density science [14].

These lasers operate in a unique parameter space compared to other terawatt- and petawatt-class lasers, as they often have larger focal spots (≫ 10 μ m), multi-kJ energies, and longer (1–30 ps) pulse durations, resulting in quasi-relativistic laser intensities. Laser-plasma experiments using solid-density flat foils on these laser platforms have demonstrated enhanced accelerated proton energies and electron temperatures when compared to established scaling laws based on relativistic sub-ps laser systems [15]. The work presented here aims to investigate whether this phenomenon extends to microstructured targets. In particular, the boosted proton energies observed with solid targets on multi-ps, multi-kJ lasers are attributed to the longer pulse creating a larger scale-length underdense plasma at the foil’s front surface, enhancing laser-electron coupling over extended time-scales and generating a stronger sheath field for acceleration. In addition, the large focal spot size has been thought to trap electrons in the laser field, thereby increasing the probability of coupling of the laser energy to the electrons [16].

While these microstructured targets have demonstrated impressive performance in the highly relativistic regime, their behavior in the quasi-relativistic, multi-ps regime remains largely unexplored. To address this, we present a detailed scaling study of microstructured targets in the multi-ps, quasi-relativistic regime, where we vary the laser pulse duration, laser energy, and laser focal spot size as well as target characteristics like microwire diameter and total target thickness. One benefit of additively manufactured targets is that the target characteristics, including the wire size, target thickness, wire pattern, and density profile, can all be accurately controlled, which in principle would allow precise tailoring of the target for particular laser parameter regimes to maximize laser-driven ion characteristics, such as conversion efficiency and ion energy. This scaling study presented here is intended to provide additional experimental data toward this long-term objective.

This work was conducted over two experiments at the OMEGA-EP laser facility at the Laboratory for Laser Energetics (LLE) at the University of Rochester. OMEGA-EP is a kilojoule-class neodymium-doped glass laser system composed of four laser beams, two of which can be compressed to short pulse durations, providing 1053 nm laser light in pulse durations of 0.6–100ps and providing up to 500J at 0.6ps and 1250J at 10ps. The short pulse capability has a reported intensity contrast, which is defined as the ratio of the main pulse intensity to the pre-pulse intensity, of approximately 1 0 10 [17]. Only these two short pulse beams, which will be referred to as Beam 1 and Beam 2 throughout this work, were utilized in these experiments. The laser characteristics of Beam 1 and Beam 2 are nearly identical with a few exceptions. Beam 2 can operate at slightly higher energies (e.g., up to 500J at best compression for Beam 2 vs. 300J at best compression for Beam 1), and the focal spot size at best focus for Beam 1 is 20% larger. Beams 1 and 2 can be used independently and propagate orthogonally to each other in the OMEGA-EP target chamber, allowing diagnostics to be placed along both laser axes. Since each laser beam has an independent cool-down time between shots, the shot rate was doubled in these experiments by alternating between Beam 1 and Beam 2. For both Beam 1 and Beam 2 shots the laser incidence angle on the target was parallel to target normal.

The experimental configuration used in this series of experiments (see Figure 1) was used to perform scans of both laser and target parameters. Only log-pile microstructured arrays, in which micron-scale wires are arranged in an ordered grid, are considered in this work. The target thickness (l target) was varied from 10 to 50 μ m, and two different micro-wire diameters (d wire) of the log pile targets were tested: 0.5 ± 0.3 μ m and 1 ± 0.2 μ m. In addition, three laser intensity regimes were investigated by varying laser parameters to achieve a nominal a 0 value of 1, 2, and 10. Within each a 0 scan, the laser pulse duration (τ Laser) was varied throughout the experiment to nominal pulse durations of 0.6, 2, 5, 10, and 30ps to study the effect of pulse duration on ion acceleration with microstructured targets. To study laser acceleration in the quasi-relativistic, large focal spot, multi-ps regime, the a 0 = 1 scan used a laser focal spot (r 80), which we define as the radius that contains 80% of the laser intensity, of 44 ± 4 μ m. For scans at the relativistic and highly relativistic regimes, that is the a 0 = 2 and a 0 = 10 scans, the laser focal spot size was at best focus which was 16 ± 2 μ m. Nominal pulse durations and a 0 values are used throughout discussion in this paper but measured target and laser characteristics of each shot in this scaling study are listed in Table 1.

As shown in Figure 1, a radiochromic film (RCF) stack is placed along both the Beam 1 and Beam 2 laser-axis, i.e., the target normal axis, at a distance of 8 cm away from the laser-target interaction point. RCF is a common diagnostic in laser-ion acceleration experiments used to measure the ion source’s spectrum and divergence. It is composed of single or double layer microcrystal monomers and upon irradiation by ionizing radiation, the film turns blue, and the darkness of the pigment is proportional to the absorbed dose. In this experiment, the RCF stack was composed of 40 individual layers of RCF separated by tin or aluminum filters. All the layers in the stack except the last six were HD-V2 RCF and the last layers were EBT-3 RCF. EBT-3 is more sensitive than HD-V2 enabling measurement of highest energy protons produced which are typically fewer in number [18]. Protons deposit their energy in each layer of the RCF stack in a well-defined Bragg curve, which can be calculated using standard stopping power models [19] and used together with the proton dose deposited in each layer to determine a discrete proton spectrum. For Beam 2 experiments only, an Electron Positron Proton Spectrometer (EPPS) [20], which uses a magnet to disperse electrons via their momentum to measure the electron spectrum, was fielded 37 cm from the laser-target interaction point and 27 degrees off the target normal axis.

As previously mentioned, all microstructured targets considered in this work are of the log-pile variety and were printed via the two-photon-polymerization (2 PP) method by General Atomics. Two photon polymerization is an additive manufacturing technique that uses a liquid resin, which in this work has the chemical formula of C 14 H 18 O 7. A high numerical aperture laser beam is directed on the liquid resin in a pre-defined printing pattern. When molecules in this resin absorb two photons from the laser light, the resin is polymerized, resulting in a hardened polymer. This process enables printing of micron-scale features with high precision. The log pile array targets tested during these experiments were printed onto a CHO washer with a thickness of 50 μ m and outer diameter of 250–300 μ m to provide structural stability. Following prior work using microstructured targets for ion acceleration in the highly relativistic regime, the targets used here were all printed with a density gradient shown in Figure 1 to create continuity with that prior work [12]. This density gradient is achieved by printing the wires with increasing wire spacing along the target depth to gradually lower the average density through the target. The microwires were also printed such that each layer in the structure is offset one wire diameter from each preceding layer, since this same prior work has found increased performance with this type of printing structure. Scanning electron microscope (SEM) images were taken to metrologize each target type in a batch. This is a destructive metrology technique, since SEM images require coating the target with a conductive material such as gold; therefore, only a subset of targets were measured in this manner.

The proton beam profile and spectra were measured using RCF stacks on all shots. Figure 2a shows RCF images at four energies (∼ 11–14 MeV) for four representative shots in units of optical density (OD) which is defined as − log (I / I 0), where I is the transmitted intensity and I 0 is the unexposed film transmission. Optical density is converted to dose using a known calibration [18] that enables conversion of the scanned optical density of the film to dose. Using these measured dose values as a function of energy and the calculated proton energy deposition for the RCF stack, a forward fit routine [21] is then used, assuming a single-temperature Boltzmann-like function of the form d N d E = N ⁡ exp − E T p to unfold the corresponding proton spectra, where N is the proton number, E is the proton energy, and T p is the slope temperature. Figure 2b shows the unfolded proton spectra corresponding to the four shots shown in Figure 2a. These four shots had log-pile target thicknesses of l target = [ 20,20,50,50 ] μ m and wire thicknesses of d wire = [ 1.0, 0.5, 1.0, 0.5 ] μ m and were all taken with a laser pulse duration (τ laser) of 2ps and a 0 ∼ 1. The uncertainty band on all curves takes into account both the uncertainty of the fit and the uncertainty on the measured dose which is driven by the RCF calibration used to convert the signal on the RCF to dose [18] and properly identifying the background contribution on the RCF from electrons and x-rays. Several background regions are measured on each RCF film to constrain this uncertainty. In Figure 2b, the orange curves correspond to a log-pile thickness (l target) of 20 μ m, and the green curves correspond to a log-pile thickness of 50 μ m. The dashed lines correspond to a wire thickness of 0.5 μ m, and the solid lines correspond to a wire thickness of 1.0 μ m. Comparing the dashed and solid orange curves, we observe that reducing the wire thickness and thus the target density, increases the maximum proton energy from 17 MeV to 31.5 MeV for a fixed log-pile thickness of 20 μ m. This pattern is also observed for the 50 μ m log-pile case, where the 0.5 μ m wire thickness case also yields a higher maximum proton energy of 22.4 MeV compared to 17 MeV. Similarly, the conversion efficiency for the case where l target = 20 μ m and d wire = 0.5 μ m is 6.45 ± 3.8%, which was the highest performing shot in this a 0 ∼ 1 series. In comparison, for the same target thickness and laser parameters but increased wire diameter of 1 μ m (SN: 41884), the conversion efficiency is 0.75 ± 0.4%. Figure 3 provides a summary of key proton measurement metrics for experiments with a nominal a 0 ∼ 1 and includes the measured maximum proton energy in (a), the measured proton slope temperature in (b) and the conversion efficiency into protons greater than 10 MeV up to the maximum proton energy for that shot in (c), where the conversion efficiency is defined as 1 E laser ∫ 10 E max d N d E E d E. The conversion efficiency is reported between the ranges of 10 MeV to E max and this range was chosen to compare to prior work by Tochitsky et al. which used LPA targets but in the relativistic laser regime and observed conversion efficiencies of ∼ 10% between 10 and 55 MeV. All metrics are plotted in terms of the product of the wire diameter and target thickness d wire × l target. As mentioned previously, the average density of the target is varied using the wire diameter and thus d wire × l target serves as a proxy for the density-length product (ρ L). Here we see that for all three metrics, the maximum proton energy, slope temperature and conversion efficiency increase with decreasing ρ L, but also within this trend all of the lower average density targets, meaning those with a d wire = 0.5, perform better on all metrics than the thicker wire targets.

Analysis of the radiochromic film also allows measurement of the ion beam divergence. This was obtained by analysis of the background-subtracted dose on each RCF. For both the horizontal and vertical axes, a 1-D Gaussian fit was used to determine the radius within which 99 % of the dose was contained on each film. Taken together with each RCF’s distance from TCC, this radius provided a half-angle describing the divergence of the ion source for each film, or each proton energy. The divergence as a function of proton energy was then normalized according to the proton cutoff energy for each shot and plotted in Figure 4. For both the 10 μ m and 50 μ m thick targets with 1 μ m microwire diameter, the beam divergence angle for lower normalized proton energies increases with pulse length. A previous scaling study at OMEGA-EP using solid density targets investigated the relationship between pulse duration and beam quality and found that longer pulse durations result in poorer beam quality and emittance which is related to angular divergence. This is attributed to large pulse durations resulting in a pre-expansion of the rear side surface which in turn creates strong filaments in the sheath field and less uniform ion beam quality [22].

As noted, for all Beam 2 experiments, an electron spectrometer was placed 27° above target normal which enables collection of the escaping electron spectra from the target. Figures 5a,b shows the measured electron spectra for four different shots at two different pulse durations, 5ps and 10ps. Figure 5c shows the electron temperature as a function of wire thickness which is obtained by fitting the electron spectra in (a) and (b) with a Boltzmann-like function of the form ∼ exp − E / T e. The ponderomotive temperature as defined by 0.511 × a 0 MeV is overlaid on this figure. All points exceed the ponderomotive temperature, but as shown in Figure 5c, lower density targets with d wire = 0.5 μ m have higher electron temperatures.

In addition to target density, a 0 is also a key parameter for optimizing proton source performance. Figure 6 shows the effect of a 0 on target performance, where three different spectra are extracted from radiochromic film data from three shots with laser parameters with a nominal a 0 of 1, 2, and 10. Here, both maximum proton energy E max and slope temperature T p increase with a 0. For shots at a 0 ∼ 1, 2, and 10, the maximum proton energy increases from 17 MeV to 50 MeV–61 MeV, and the slope temperature increases from 2.5 ± 0.2 keV to 7.3 ± 0.15 keV to 13.3 ± 0.3 keV, respectively.

We observe experimentally that in this laser-parameter regime, lowering the average density of the target, which was achieved in this experiment by decreasing the wire diameter, results in increased proton acceleration performance including the proton maximum energy, slope temperature and conversion efficiency. The highest performing shot in the series studying a nominal a 0 ∼ 1 had a target thickness of 20 μ m and target wire diameter of 0.5 μ m leading to a conversion efficiency of 6.45 ± 3.8% which is nearly 9 × that of a similar shot that had the same target thickness and laser parameters but a thicker wire diameter (d wire = 1 μ m). Similarly, a 0 also strongly affects proton performance in terms of slope temperature, maximum energy and conversion efficiency as shown in Figure 6, suggesting that a 0 and target ρ L may allow for a combined optimization of performance.

To better understand these experimental results, we investigate the observed drop of the measured MeV ion dose with increasing plasma density in a simplified computer model, with the goal not to reproduce experimental spectra but to understand the observed trends. To that effect, we have performed a series of quasi-one dimensional kinetic Particle-in-Cell simulations with the code WarpX [23], using a 2D grid of 10 × 1500 microns with a resolution of 50 cells per micron and 100 particles per cell. The laser pulse has a peak intensity of 1.4 × 1 0 18 W/ c m 2 with a 1 micron wavelength and is polarized in the simulation plane, with a 2ps temporal full-width-half-maximum and a planar phase front injected at z0 = −750 μ m and the peak laser power arrives at the target at about 3ps. In the simulation, the plasma is made of deuterium ions and electrons, which is a simplification to represent any fully ionized species (other than protons) where an ion charge-to-mass ratio of 1 2 yields identical kinetic behavior as deuterium. The plasma has reached a 20 μ m long plateau density between 1 n crit and 60 n crit at z = −320 μ m, preceded by an exponential ramp with a scale length of about 0.5 μ m. Figure 7a shows the ion density at the end of the laser pulse in two example cases with 15 n crit (blue) and 60 n crit (red). The initial profile of the ion density as a dashed gray line. For the purposes of these simulations, we work under the assumption that, for multi-ps laser pulses, the morphology of the target does not play a role and the target is assumed to have uniform density, apart from a small gradient detailed in [12]. Prior work with laser-driven structured targets by Kemp et al. shows that, even when the pre-pulse is ignored, the intense short pulse dissolves the initial structure of the target in its rising half [24]. At peak laser power, the target simply consists of a fully ionized plasma at a density equal to the average density of the structured target. Thus, we assume that the original target morphology gets destroyed in the early parts of the main laser pulse. Figure 7b shows the time history of electron energy > 0.5 MeV for the “blue” case (top curve) and the “red” case; total fraction of laser energy absorbed is about 30%, a little more for the “blue” case than for the “red”. While the laser total absorption is similar, the main difference between the 15 n crit and the 60 n crit cases lies in the total energy of “hot electrons”, that is, those with kinetic energy > 0.5 MeV. Similarly, experimentally the electron temperature is also higher for lower density shots suggesting that this class of targets enable a hotter population of escaping electrons. Figure 7c shows the simulated number of ions above 0.5 MeV (left axis, triangles) and above 10 MeV (right axis, circles). Figure 7d shows ion energy spectra at 9ps, the last time step where the fastest ions have not yet reached the end of the simulation box. Note that the energy cutoff is almost independent of plasma density. Our simulations show a notable drop in MeV ion dose with increasing plasma density, a proxy for the initial wire diameter. This is related to the fact that a higher target density leads to a higher heat capacity and hence less thermal expansion early in the laser interaction. As a consequence, the remainder of the laser pulse interacts with a steeper plasma gradient and fewer MeV electrons are generated. Our simulations additionally show a sudden drop in dose where the plasma density is close to critical density for our laser pulse. In that case, the laser is able to penetrate the plasma and continues to transfer energy to electrons and ions behind the target. Based on the initial condition of our targets, we do not think that our experiments, within the a 0 ∼ 1 scan, enter this transparent regime [25]. Despite this, even within this quasi-relativistic regime both in simulation and data we see that lowering the target density is a key optimization parameter for increasing ion dose and conversion efficiency.

A detailed study of 3D-printed microstructured targets was performed at the OMEGA-EP laser facility in the quasi-relativistic regime. We have shown that both target ρ L and a 0 are key parameters for optimization of the proton maximum energy, slope temperature and conversion efficiency. In particular, for a fixed target length of 20 μ m, decreasing the wire diameter of the LPA targets by half leads to an increase in the conversion efficiency of roughly 9 × and the maximum proton energy by approximately 1.8 ×. These results are supported by simulations which performed a scan in target density in the a 0 ∼ 1 regime and found that a higher target density leads to fewer hot electrons to establish a strong sheath field thus diminishing the proton acceleration. These results demonstrate that LPA targets that are optimized in ρ L may provide access to high-flux target designs on other multi-ps, multi-kJ quasi-relativistic laser facilities. In addition, we find that the proton beam divergence for these targets increases with pulse duration as shown in previous work with solid density targets [22], which is attributed to pre-expansion of the rear-side surface, which is perhaps exacerbated with LPA targets by penetration of the laser through the target depending on the ρ L.

Future work will focus on several mechanisms to potentially improve the conversion efficiency and beam quality of these targets. More specifically, previous work in this unique laser parameter regime with solid density targets has studied the role of focal spot size [26] as well as laser contrast [27] on fast electron generation. In addition, Iwata et al. has demonstrated in prior work that large laser spots (∼ 10s of microns) can allow enhanced electron confinement by the laser field and thus a larger population of fast electrons to support a more sustained sheath field and thus enhanced proton characteristics like conversion efficiency [26] and Peebles et al. has shown that controlled pre-pulses can establish a long-scale length plasma enabling a larger population of super-ponderomotive electrons which in turn can similarly support a strong sheath field for enhanced ion performance [15, 27]. Expanding these experimental scaling studies to examine whether focal spot size and laser pre-pulse are also key parameters for improving the flux and maximum energy of these sources using 3D printed LPA targets is a natural extension of this work. To improve proton beam quality, the addition of a solid density foil at the end of the LPA target could increase ρ L to the point where the laser cannot penetrate the target anymore, while maintaining the enhanced density gradient and higher absorption on the front, offering a route to simultaneously improve divergence and ion conversion efficiency for applications to fast ignition and proton radiography.