Far away from the Earth, high-energy-density plasma (HEDP) exists in many areas of the universe, for example, in the cores of planets and stars.1 Understanding and controlling this form of matter would help us to unveil the origins of heavy elements2 and harness future nuclear-energy technologies.3 Thanks to the development of high-power lasers, we can now create HEDP in the lab by compressing and heating a spherical capsule using multiple-megajoule nanosecond lasers. This state of matter has been the subject of worldwide research focus, and it is expected to help achieve self-sustainable reactions in inertial confinement fusion (ICF).4–7 In addition, research around HEDP has also promoted the development of laser nuclear physics,8–15 laboratory astrophysics,16,17 and high-energy-density physics.18–20

Apart from the well-known ICF scheme, HEDP can be created using ultra-intense and ultrashort laser pulses by virtue of relativistic laser–plasma interactions. An ultra-intense laser field can deeply ionize a target and accelerate its electrons to MeV levels on femtosecond timescales,21 forming a strong micron-scale space-charge field that can drive its ions. The most common experimental scheme for this involves irradiating a solid foil target at ultra-high intensity. The laser pulse interacts with the front surface of the foil, generating supra-thermal electrons in an expanded dilute plasma. Heated by these supra-thermal electrons and the return current, the solid target becomes an HEDP. The drawback of this scheme is that if we are interested in nuclear reactions in the HEDP, the entirety of the solid foil will not be hot enough for these to occur. The indirect heating involved results in a considerable temperature gradient in the foil,22 and only a small number of ions close to the surface will reach a temperature sufficient for nuclear reactions. To overcome this problem, cluster targets produced from cryogenic high-density gas12–14 or low-density foam23–26 have been used. The laser pulse can propagate through these materials and volumetrically heat the nanometer-sized clusters or the foam’s building blocks, resulting in the production of an HEDP. However, the densities of these plasmas typically do not exceed 1% of the solid density, which is unfavorable for nuclear reactions.

Recently, an increasing amount of attention has been paid to the use of novel microstructured targets to acquire near-solid-density HEDPs.27–33 In this area of research, nanowire-array (NWA)targets have shown superior performance. Numerical and experimental studies have indicated that NWA targets can absorb the majority of the laser energy and significantly enhance the energy-conversion efficiency to plasma when compared to solid targets,34–36 producing homogeneous HEDP with near-solid density. Figure 1(a) shows a schematic diagram of an NWA target. The typical diameter (D), length (L), and spacing (S) of the nanowires (NWs) are tens to hundreds of nanometers, 1–10, and 0.1–1.0 μm, respectively. The heating process of an NWA target under ultra-intense laser irradiation is illustrated in Fig. 1(b).

An NWA’s structure allows a laser pulse to propagate inside the target and interact with the sidewalls of the NWs. Electrons in the skin depth of NWs are pulled out into gaps and can be accelerated to tens of MeV in the laser field. On top of their quiver motions, these electrons collectively move along the laser propagation direction due to the v × B force. The resulting return current (typically of the order of 10¹–10² kA)37,38 inside the NWs and the reciprocal bombardment of the supra-thermal electrons accelerated by J × B heating39 efficiently heat the NWs to a high temperature. It has been found that the electron temperatures can reach values of 0.138 and 0.9 MeV39 under the effects of the return current and J × B heating with laser amplitudes of a = 2 and 5, respectively. Furthermore, the escaped electrons also give rise to a space-charge field (sheath field) normal to the surfaces of the NWs. Ions can subsequently be accelerated to MeV-level energies in this sheath field,40,41 which also contributes to plasma heating, with temperatures reaching the MeV level when they are stopped by nearby NWs. More details of these interactions, such as the plasma compression due to Z-pinch formation under higher-intensity petawatt (PW) lasers,38 are still under exploration. The electron temperatures can reach 4 MeV at a laser amplitude of a = 17.

The emissions of energetic electrons,37,42 ions,43,44 x-/γ-rays,45–48 and neutrons49,50 from NWA plasmas have been extensively observed. Purvis et al. measured the x-rays from Ni and Au NWA targets irradiated with 0.5 J femtosecond laser pulses.45 They observed the production of 100-fold-enhanced line emission over planar solid targets. Using numerical simulations, they concluded that the electron energy density (EED) after the expansion of the NWs is 0.3 GJ/cm³, which is comparable to that of spherical compression at the National Ignition Facility with megajoule laserpulses.51 Later, they increased the laser energy to 10 J52 and observed intense line emission from Au⁷²⁺ ions due to the >100 GJ/cm³ EED. Naturally, such a high energy density attracts interest regarding thermonuclear reactions. Deuterium–deuterium fusion in an NWA was first reported in 2018 by using deuterated polyethylene NWA targets.47 This produced a neutron yield of 10⁶/J/shot, a record for a joule-scale laser. Recently, 10⁷/shot neutrons were measured at a higher intensity with a PW laser.50

The electron-heating dynamics and EED in NWA targets have been widely studied by measuring the core–shell x-ray emissions from high-Z NWAs. Regrettably, this method is not applicable to low-Z NWA targets, which are particularly important for fusion-energy-oriented reactions such as ²H(d,n)³He and ¹¹B(p,2α)α. Furthermore, the energy density of ions in NWA targets, which is of foremost importance for nuclear reactions, has rarely been discussed. Finding the optimal target parameters for fusion nuclear reactions and additional methods for characterizing the high-energy-state in addition to x-ray spectroscopy will require further study.

In this work, first, we examined the interactions between NWA targets and femtosecond laser pulses by employing collisional 2D particle-in-cell (PIC) simulations. The electron and ion (proton) energy densities of the NWA targets across a broad target parameter range were obtained and compared to those of planar targets. The confined and emitted protons were defined, and their interrelationship and contributions to the energy densities of the HEDP were thoroughly examined. Thereafter, we experimentally measured the emitted protons, deuterium ions, and neutrons from ²H(d,n)³He fusion using ordinary and deuterated polyethylene NWA targets. The results were found to confirm those of our simulations.

To illustrate the interaction of NWA targets with relativistic femtosecond pulses, 2D PIC simulations were performed using the current EPOCH53 code. In the model for these simulations, the simulation box had a size of 40λ_L × 50λ_L with 4000 × 5000 cells in the x × y dimensions (laser wavelength λ_L = 0.8 μm). The box boundary in the y direction was periodic. A laser pulse polarized linearly in the y direction with a Gaussian profile of $a_y=a_0{e}^{-{(r/{\sigma }_0)}^2}{e}^{-{(t-t_0)}^2/{\tau }^2}$ traveled along the x axis from the left side and was normally incident on the NWA target, where a₀ = eE₀/m_ecω_L = 5, σ₀ = 4.3 μm, and τ = 10λ_L/c = 26.7 fs. The NWA’s L, D, and S values were set according to the achievable target parameters in the experiments. The NWs were located in the region 0 < x < L. The atomic ratio of C and H was 1:2, as in polyethylene. A 10 μm-thick polyethylene substrate was placed in the region L < x < L + 10 μm. The initial densities of electrons, protons, and C²⁺ ions were 80n_c, 40n_c, and 20n_c, respectively. Here, $n_{\text{c}}=m_e{\omega }_{\text{L}}^2/4\pi e^2=$ 1.7 × 10²¹ cm⁻³ is the critical electron density, in which ω_L, e, and m_e are the laser frequency, electron charge, and electron mass, respectively. The entire target was cold (10 eV) and not fully ionized, and the optical field ionization was included in the setup. The numbers of macroparticles per cell of each ion species and electrons were 12 and 48, respectively.

The x–p_x phase diagram of protons at t = 460 fs is shown in Fig. 3(a). This clearly describes the characteristics of the confined and emitted protons. The emitted protons distributed at x < 0 have high p_x up to −100m_ec (2.7 MeV), while the confined protons in the range 0 < x < 5 μm have much higher values. The x–p_y phase diagram (inset) indicates that the confined protons have $\left|p_x\right|<40m_{e}c$. The two groups of protons can also be distinguished from the angular distribution in Fig. 3(b). The emitted protons peak at 0°, while the confined protons are near to −90° and 90°. The dashed line in Fig. 3(b) shows the integrated energy of protons as a function of distribution angle. This indicates that the confined protons contain far more energy than the emitted protons, providing most of the plasma’s proton energy density (PED). According to the above classification, the energy spectra of the two groups of protons are given in Fig. 3(c). The fitting lines show that the temperatures of the confined and emitted protons are 50 and 300 keV, respectively.

The EED and PED of a typical NWA target (with the same parameters as in Fig. 2) and a planar target at t = 460 fs are depicted in Fig. 4. One can see that the NWA’s EED peaks at 0.3 GJ/cm³, about three times that of the planar target. This enhancement is mainly due to the higher absorption of the laser energy. Since the energetic electrons can penetrate deeply into the bulk of the target, the volume of the high-energy-density region in the case of a planar target is not significantly smaller than in the case of an NWA target. Compared to the EED, the enhancement of the PED in the NWA target is much more prominent; the maximum PED is 0.2 GJ/cm³, more than an order of magnitude greater than that of the planar target. Moreover, it can be seen from Fig. 4(b) that the high-PED volume in the NWA is much larger than that of the planar target. In the planar target, the depth of the high-PED region is limited to 1 μm below the surface; in the NWA target, the high-PED region covers the whole target. This is because laterally accelerated protons are abundant in the NWA, and they carry a significant amount of energy.

To reveal the dependence of the PED on the target parameters of an NWA, we performed a series of simulations. Figures 5(a)–5(d) show the spatial distributions of the PED of NWA targets with L = 5, 2, and 1 μm (D = 200 nm, S = 450 nm), and L = 5 μm (D = 300 nm, S = 450 nm), respectively. Figures 5(e) and 5(f) depict plots of the PED along the x and the y directions, respectively, and the data from an NWA of L = 10 μm, D = 200 nm, and S = 450 nm are also included. It can be seen that NWA targets with different lengths have almost the same maximum PED. Increasing the length of the NWs does not enhance the PED, but it does increase the volume of the high-PED region. In a given NWA, the PED decreases with x. For the L = 10 μm NWA, the PED drops to 0.05 GJ/cm³ at x = 10 μm, which is about a quarter of the peak value at the surface. The decreasing gradient depends strongly on the value of D. The D = 300 nm NWA has a gradient that is double that of the D = 200 nm NWA. The total proton energy contained in the plasma is significantly lower as a result.

Figure 6 shows the laser absorption ratio, temperature of confined electrons, temperature and number of confined protons, and total energy of emitted and confined protons as functions of the NW’s diameters and lengths. It should be noted that confined protons with energies lower than 1 keV are not counted in these data. As shown in Fig. 6(a), the laser absorption ratio is closely related to the NW diameter: smaller diameters correspond to higher absorption. This is because a larger diameter results in narrower gaps. The time before the complete filling of the gaps by overdense plasma is therefore, shorter, resulting in lower laser absorption and incomplete heating of the NWs. The temperatures of the confined electrons and protons and the numbers of >1 keV confined protons decrease with increasing diameter. It should be noted that the sheath field established by the electrons directly affects the acceleration and heating of protons. Therefore, the electron temperature results in consistent changes in proton temperature with the NW parameters. However, a decreased diameter will reduce the average density of the target for a given value of S, which is unfavorable to higher proton numbers. Figure 6(b) shows that a moderate diameter of D = 200 nm is the best trade-off, for which the average density is 16% of the solid density, and energetic confined protons contain 63 mJ energy for 1 J of input laser energy.

With a fixed diameter of 200 nm, we varied the length of the NWs to study its influence on the NWA’s PED. Figures 6(d) and 6(e) indicate that increasing the length of the NWs will not affect the laser absorption or the temperatures of the confined electrons and protons. This is understandable, as these parameters are determined by the laser–plasma interaction at the sidewalls of the NWs. In contrast, the number of confined protons is proportional to the length of the NWs. Moreover, as shown in Fig. 6(d), with increasing NW length, the energy converted to confined protons rises, while that converted to emitted protons drops. This is consistent with the observation in Fig. 5 that NWA targets with longer NWs have larger high-PED volumes. It can be seen that 9% of the laser energy is converted to protons in the best case (L = 10 μm), and the vast majority (>90%) of this is converted to confined protons.

In summary, our simulations explored the parameter space of NWAs for the purpose of establishing the values required for a high PED. It was established that the optimal NW diameter is 200 nm. With increasing NW length, the energy imparted to confined protons rises, whereas that imparted to emitted protons declines. NWA targets with an NW length of 10 μm and an NW diameter of 200 nm were found to perform the best, in which 8% of the laser energy can be converted to confined protons.

Guided by the simulation results, we performed an experimental campaign to study the high-energy-density states in NWA targets. Confined ions are challenging to detect in experiments; instead, we measured the emitted ions to verify our conclusions.

The experiments were conducted on the Compact Laser Plasma Accelerator (CLAPA) laser facility at Peking University, which has a central wavelength of 800 nm and a pulse duration of 30 fs (full width at half maximum, FWHM). Figure 7(a) depicts a schematic of the experimental setup. A linearly polarized laser pulse was normally incident on the NWA target. To prevent the pre-expansion of NWs, a plasma mirror system was employed to improve the laser contrast ratio, ensuring that the intensity of the pre-pulse was below 10¹¹ W/cm² at 5 ps.55 We checked whether the NWs could maintain their structure under the irradiation of the ps pedestal before the main pulse by employing the hydrodynamic simulation code MULTI2D.56 The results indicated the scale length of the pre-plasma L_pre = n_e/(dn_e/dx) ∼ 22 nm, which is insignificant compared to the gaps between NWs. The laser energy was measured to be 3.5 ± 0.5 J before the compressor using a laser-energy meter. Considering that the energy transmission efficiencies of the beamlines and plasma mirror system are 40% and 75%, respectively, the on-target laser energy was about 1 J. Ultimately, the laser beam was focused into a spot size of 4.0–4.4 μm (FWHM) to reach an on-target peak intensity of 4.8 × 10¹⁹ W/cm² (a₀ ∼ 5) by using an f/3, 90°, gold-coated off-axis-parabolic mirror (OAP). This OAP had a 3 mm-diameter hole that enabled ions from the front side of the target to pass to the ion spectrometer.

The ion spectra were measured using a Thomson parabola spectrometer (TPS) in the direction normal to the front side of the target. The TPS was composed of a collimating aperture, magnets, electrodes, a microchannel plate, a phosphor screen, and an electron-multiplying CCD (EMCCD). In this device, after the 1 mm-wide collimating aperture (1.3 × 10⁻⁶ Sr), collimated ions with different energies and charge-to-mass ratios (CMRs) are deflected by the electromagnetic fields and hit different positions on the microchannel plate. The ion signal multiplied by the microchannel plate is then converted to an optical signal at the phosphor screen and captured by the EMCCD. Ions with different CMRs have different parabolic traces imaged in TPS raw data. The set electric and measured magnetic fields of the TPS employed in the experiments were 0.83 kV/cm and 0.255 T, respectively. The detection area was limited by the microchannel plate, which had a diameter of 77 mm. Considering the electric field, magnetic field, and detection area, the energy range of protons was about 1–20 MeV. Furthermore, the angular distribution of emitted protons was recorded by CR39 ion-track detectors placed at angles of 20°, 40°, 55°, and 80° to the target normal.

Polyethylene NWA targets with a variety of parameters were examined in the experimental campaign. These were prepared by the following procedure. First, a thick polyethylene sheet was attached to an anodized aluminum oxide (AAO) template57 with hexagonally packed nanochannels. Heating and mechanically compressing this sheet then caused the polyethylene molecules to move into the template. After this, an NWA target was obtained by dissolving the AAO membrane in a 2M NaOH solution for 30 min. The diameters, spacings, and lengths of the NWs were determined by the AAO templates. The morphologies of the NWAs were characterized by scanning electron microscopy (SEM), and typical top and side views are shown in Figs. 7(b) and 7(c), respectively. The thickness of the polyethylene substrate supporting the NWs was about 450 μm. The average density of the NWAs lay in the range of 16%–45% of the intrinsic solid density. Planar polyethylene targets with a thickness of 450 μm were used for comparison. Table I summarizes the parameters of all of the targets.

The experimental results of emitted protons for NWA targets with different lengths and diameters are summarized in Figs. 8(a) and 8(b), in which the error bars reflect the shot-to-shot fluctuations and the data points are the arithmetic means. The maximum proton energies of the planar targets are depicted by zero-diameter and zero-length points in Figs. 8(a) and 8(b). The solid lines represent the 2D PIC simulation results, which fit the experimental results. The corresponding best experimental proton spectra are displayed in Figs. 8(c) and 8(d), respectively. Compared to the planar targets, a remarkable enhancement of maximum energy for NWA targets can be observed.

The dependence of the maximum proton energy on the NW diameter can be obtained from Figs. 8(a) and 8(c). For both S = 450 nm and S = 800 nm, the maximum proton energies decline with increasing NW diameter, which fits the simulation results well. For NWAs with fixed D = 200 nm and S = 450 nm, the maximum proton energies rise with increasing length until L = 2 μm, and they then decline. This trend reflects that the strongest E_sx is produced in the laser–plasma interactions for the 2 μm-length NWAs. When the NWs’ length exceeds the optimal value, the laser pulse propagates more deeply into the NWA and transfers more of its energy to confined protons. It should be noted that our experimental results in relation to the emitted protons are consistent with those of another recent study.58

The angular distribution of emitted protons was measured by the CR39 detectors after 16 consecutive shots. 30 μm-thick aluminum foils were placed on the CR39 detectors, which can block most carbon ions below 32 MeV and protons below 1.6 MeV. Images of the etched CR39 detectors placed at 20°, 55°, and 80° to the target normal are displayed in Figs. 9(b)–9(d), respectively. They were etched for 12 h in 6M NaOH solution at 70 °C after shooting. The sizes of the three CR39 plates were identical, corresponding to a solid angle of 2 × 10⁻⁶ Sr. As one can see in Fig. 9(d), only a few protons were emitted at 80° with respect to the target normal. More proton tracks were observed with decreasing angle. The proton tracks (the small dots in the image) at 20° are very dense, even close to saturation. At 55°, a number of energetic proton tracks were observed, which implies that the divergence of the protons from the NWA was larger than for typical planar targets. In general, the CR39 results are inconsistent with our simulation results in Fig. 3(b). The most energetic confined ions in lateral directions in Fig. 3(b) could not be detected as they had been stopped in the targets.

An NWA absorbs a majority of the laser energy and forms a near-solid-density HEDP, which creates excellent conditions for charged-particle nuclear reactions. In the experimental campaign, we also employed deuterated polyethylene NWA targets to demonstrate the neutron generation from the ²H(d,n)³He fusion. They were prepared following the same procedure as the polyethylene NWAs.

We first tried to measure the deuterium ions (D⁺) emitted from NWA targets using the TPS. The raw data, including all ions with different CMRs, are presented in Fig. 10(a). The traces with CMRs of 1, 1/2, ... can be identified. However, the traces of D⁺ and C⁶⁺ are indistinguishable because they have the same CMR of 1/2. Therefore, we positioned a 20 μm-thick Al foil in front of the MCP to distinguish them. Due to different stopping powers, C⁶⁺ with energies <1.83 MeV/u will be blocked by the foil, while D⁺ with energies >0.78 MeV/u can get through [see Fig. 10(c)]. This allows us to identify D⁺ in the range 0.78–1.83 MeV/u on the MCP. Figure 10(b) displays the raw TPS data. The broadening of traces is due to the straggling of ions when they pass through the Al foil. The cut-off of the trace at the low-energy end corresponds to 0.8 MeV/u, which is very close to the theoretical value of 0.78 MeV/u. It is thus unambiguous that the remaining parabolic trace of CMR = 1/2 only results from the D⁺.

The energy spectra of ions were obtained by analyzing the TPS traces, and these are shown in Figs. 10(d) and 10(e). The maximum proton energy of 3.5 MeV is similar to that without the Al foil, which indicates the good repeatability of the results. The maximum energy of the deuterium ions is 1.5 MeV/u, significantly lower than that of the protons. No deuterium-ion signal was detected for the planar deuterated polyethylene targets.

The observed emission of MeV-level deuterium is a signature of the strong laser–plasma coupling in the NWAs. Similar to the case of a polyethylene NWA, we performed 2D simulations to study HEDP in a deuterated polyethylene NWA by employing the Smilei code.59 The Smilei code includes a nuclear-reaction module, which can seamlessly simulate the ²H(d,n)³He fusion reaction using a Monte Carlo method. The nuclear-reaction module uses the relativistic kinematics calculations of the binary collision scheme in the COM frame.60 New macroparticles (the reaction products) are created using a certain probability of a reaction occurring. The collision of deuterium with deuterium to create a neutron and helium was enabled in the simulation. Other simulation settings of Smilei, such as the box, laser, and target parameters, were the same as those in the EPOCH simulations.

Figure 11(a) shows the simulated energy density of deuterium ions in a deuterated NWA target with D = 200 nm, S = 450 nm, and L = 5 μm at t = 460 fs. The distribution of the energy density is very uniform, with a peak value of 0.22 GJ/cm³. The peak temperature of the confined deuterium ions is 80 keV. The distribution of helium ions, which are the product of the fusion reactions, is depicted in Fig. 11(b). This indicates that nuclear reactions mainly occur in the focal-spot area where the temperature of the deuterium ions is highest. Figures 11(c) and 11(d) show the total helium yield (dashed lines) from NWAs with different lengths and diameters at t = 3 ps. Compared to a planar target, yields that are more than 20 times higher can be obtained from an optimal target. Increasing the NW length leads to increased yield; this, however, becomes less prominent when L exceeds 5 μm. The optimal diameter is D = 200 nm. The corresponding density is about 16% of the solid density.

The D–D nuclear reactions produce the same numbers of helium ions and neutrons. In a recent work, we reported the measurement of the neutrons from NWA targets with D = 200–500 nm, S = 450–800 nm, and L = 1–10 μm;61 the average neutron yield per shot was (24 ± 18) × 10⁶/J. One can see that the simulation results of the present work agree well with our previous observations.

We can also theoretically estimate the neutron yield. The volumetric reaction rate is given by $R=n_{\text{D}}^2\sigma {\vartheta }_{\text{r}}/\left(1+\delta \right)$, where: n_D is the average deuterium ion density of 16% × 8 × 10²² cm⁻³ for an NWA target with D = 200 nm, S = 450 nm, and L = 5 μm; ϑ_r is the deuterium–deuterium relative velocity, which we take as 2ϑ_D ∼c/54 based on the deuterium ion temperature of 80 keV; σ is the corresponding fusion cross section of 0.085 b62 for a deuterium ion energy of 160 keV in the center-of-mass frame; and δ is the Kronecker symbol of 1. Therefore, the reaction numbers can be roughly estimated as $N=V{n}_{\text{D}}^2\sigma {\vartheta }_{\text{r}}\tau /$2, multiplied by the reaction volume V and the reaction time τ. The value of V is about 6 × 10⁻¹⁰ cm⁻³ considering a cylindrical reaction area of 6 μm radius and 5 μm length. The value of τ can be roughly estimated as V^1/3/ϑ_D ∼ 2.8 ps. According to the above analysis, the number of neutrons N ∼ 7 × 10⁶ in 4π, which is in agreement with the experimental and simulation results.

In conclusion, we numerically and experimentally studied the HEDP formed in femtosecond-laser-irradiated NWA targets. It was found that the unique structure of the NWs leads to the generation of rich, energetic ions, which are eventually confined in the plasma and contribute most to the high-energy-density state. The emitted ions can be used as valuable diagnostics of the interaction. Our systematic study on the dependence of the ion energy density on the parameters of the NWA targets illustrates the optimal parameters for the generation of HEDP in NWAs and gives a valuable guide for future works employing NWA targets. The achieved large-volume homogeneous GJ/cm³-level energy density of ions driven by merely J-level lasers can provide a valuable testbed for high-energy-density and nuclear physics.

Acknowledgment. This work was supported by the NSFC innovation group project (Grant No. 11921006), the National Grand Instrument Project (Grant No. 2019YFF01014402), the United States Department of Energy (Grant No. DE-FG03-93ER40773), and the NNSA (Grant No. DENA0003841) (CENTAUR). The PIC simulations were carried out using the High-Performance Computing Platform of Peking University.