Neutron sources plays a vital role in multiple applications in biology,1 cancer therapy,2 materials science,3 and nuclear power4 owing to the neutron’s unique penetrating ability. High-flux neutron sources are often generated by the fission process in nuclear reactors5 and the spallation mechanism using high-energy proton accelerators,6,7 which are unavailable for widespread use owing to their large size and high costs. Recently, laser-driven neutron sources (LDNSs) have attracted great attention as a compact way to generate short-pulse neutron beams at low cost, and they have been the subject of numerous studies.8–14 Through (d, n) and (p, n) reactions, neutron yields of 10¹⁰n/sr have been achieved using the TRIDENT and PHELIX lasers,8,10,12 while (γ, n) reactions have reached neutron yields of 10⁹n/sr.9,12

Besides the fission process, the “pitcher–catcher” scheme15,16 is the most common neutron-production scheme, with two stages: ion acceleration and nuclear reaction. In this scheme, light ions (protons and deuterons) are the projectiles commonly used to bombard heavy targets (mainly lithium or beryllium), since they are easy to accelerate in what is known as normal kinematics. However, the neutron distributions produced by normal kinematics are typically isotropic in 4π space. Even with the use of deuteron-induced reactions in current experiments,8,10 the neutrons produced have a high beam intensity at the rear and side directions. This brings two problems. On the one hand, only a tiny part of the produced neutrons in the forward direction can be used for practical applications, resulting in rather low effective utilization rate. On the other hand, as the vast majority of neutrons in other directions contribute to the room neutron background, heavy shielding17 is essential to protect researchers and experimental devices, which requires the construction of complex shielding structures. In particular, for a LDNS, the damage caused to the laser system and other electronic equipment by backward neutrons actually makes it extremely hard to operate the source in a repetitive way.

In addition to the normal kinematics, inverse kinematic reactions18–22 are another method for neutron generation, using heavy ions to bombard light targets. Unlike the isotropic neutron distribution produced by normal kinematics, neutrons produced by inverse kinematics are focused in a narrow forward cone, owing to the negative reaction threshold energy and the considerable velocity of the center-of-mass system brought about by the heavy projectile. Thus, inverse kinematics can maximize the emitted neutrons’ utilization while significantly reducing the background neutrons, which circumvents the need for heavy shielding. Details of the principle of inverse kinematic reactions can be found in Sec. II. However, several challenges exist in achieving inverse kinematics for neutron production. First, providing an intense lithium-ion beam has been difficult with conventional accelerators;23,24 second, the large stopping power of heavy ions leads to a large reduction in the number of reaction events in a given converter. It has been thought that the practical application of such an inverse kinematic neutron generator would be very difficult. Although it has been shown that it should be possible to use a laser-accelerated lithium-ion beam to achieve inverse kinematics,25 the most critical issue, namely, how to access the efficient inverse kinematics scheme, which is difficult with conventional accelerators, has not been solved. In other words, the key laser and target conditions, a quantitative estimate of advantages, the absolute neutron yield, and the energy spectrum for inverse kinematics driven by lasers have not been established.

In this article, we propose laser-driven light-sail (LS) acceleration26–29 from ultrathin lithium foils as a promising candidate to achieve a forward-directed pulsed neutron source utilizing the inverse kinematic reaction. As shown schematically in Fig. 1, intense energetic lithium-ion beams are generated from laser-driven ultrathin foils and are then injected into a hydrocarbon converter target. Owing to its orders of magnitude higher accelerating fields than conventional accelerators and excellent acceleration efficiency for heavy ions, laser-driven LS acceleration can easily produce lithium-ion beams with sufficiently high forward energy and high flux that the inverse p(Li7,n) reaction can be efficiently induced for production of forward-directed kinematically focused neutron beams. The scheme is verified numerically by a self-consistent combination of three-dimensional (3D) particle-in-cell (PIC) simulations and Monte Carlo (MC) nuclear reaction simulations for laser-driven ion acceleration and neutron production processes, respectively. The simulation results show that a forward-directed pulsed neutron source with ultrashort duration 3 ns, small divergence angle 26°, and high peak flux 3 × 10¹⁴n/(cm²⋅s) can be produced by petawatt lasers at intensities of 10²¹ W/cm², which is greatly superior performance compared with a conventional accelerator. The simulations also show that the number of forward low-energy neutrons (<4 MeV) generated by inverse kinematics is roughly an order of magnitude larger than the number produced by normal kinematics, benefiting practical applications.30 Thus, a laser-driven neutron source operating on the basis of inverse kinematics shows promise as a novel compact pulsed neutron generator for practical applications, capable of safe and repetitive operation.

A neutron source produced by heavy ions incident on light nucleus targets is known as a heavy ion neutron source (HINS), and the corresponding reaction process is known as inverse kinematics. Here, we focus on the reaction p(Li7,n) as a demonstration of inverse kinematics. For the neutron generation reaction between proton and lithium, the normal kinematics ⁷Li(p, n) and inverse kinematics p(Li7,n) can be expressed asH+Li7→Be7+n,Ep,th=1.88MeV,(1)Li7+H→Be7+n,ELi,th=13.12MeV,(2)where E_p,th and E_Li,th are the respective reaction threshold energies of the incident ions. As shown in Fig. 2, in contrast to the isotropic distribution produced in normal kinematics, the neutron production in inverse kinematics is constrained in a forward neutron cone. This natural forward collimation of emitted neutrons is caused by the considerable velocity of the center-of-mass system brought by the heavy ion, called the kinematic focusing effect.

Figure 3 shows the properties of the p(Li7,n) neutron source discussed in this paper. The neutron cone angle and two neutron energy groups in the forward direction are plotted in Fig. 3(a). The neutron cone angle θ_L can be expressed as a function of the lithium incident energy E_Li, in the following nonrelativistic approximation that is appropriate for the ion energy range discussed in our scheme:θL=arcsinELi−ELi,thELi.(3)It can be seen that at any lithium ion energy, the neutron cone angle does not exceed 90°, ensuring that neutrons are not emitted backward. In addition, the p(Li7,n) neutron products have two energy groups in the forward direction, demonstrating that high-energy lithium ions also can produce low-energy neutrons, unlike the ⁷Li(p, n) reaction, which possesses only a high-energy neutron group. Figure 3(b) plots the total neutron production cross section and the double differential neutron cross section at θ = 0°. While the total cross section at a given ion energy per nucleon is the same for normal and inverse kinematics, the zero-angle double differential cross section for inverse kinematics is significantly larger than for normal kinematics owing to the kinematic focusing effect. However, as shown in Fig. 3(c), the stopping power of lithium in CH₂ is larger compared with that of a proton in LiF, resulting in a short projectile range for lithium and limiting the neutron yields of the p(Li7,n) reaction.

3D PIC simulations are carried out with the EPOCH code.31 A circularly polarized (CP) laser with wavelength λ = 800 nm and duration τ = 7T₀ (where T₀ = λ/c) propagates from the left boundary at x = 0 μm and irradiates the target at x = 2.4 μm. The laser pulse has a transversely fourth-order super-Gaussian profile with a spot radius r = 5 μm and a temporally flat-top envelope (1T₀ rise and fall times and 6T₀ plateau). Three laser intensities (I = 4.3 × 10²⁰, 1 × 10²¹, and 1.73 × 10²¹ W/cm², with normalized amplitudes a = 10, 15.3, and 20, respectively) are chosen for study. The lithium targets have a real density of 0.53 g/cm³, corresponding to an initial density n_e = 78n_c (where n_c is the critical density). The target thicknesses l corresponding to the above laser intensities are determined as 35, 55, and 74 nm, respectively, using the ideal LS condition27,32 (l_op = an_cλ/πn_e) to ensure the production of a high-quality lithium beam. The simulation box (x, y, z) is 15 × 10 × 10 μm³ and contains 1500 × 800 × 800 cells. Each cell has the same 20 macroparticles for electrons and ions. Three additional simulations are performed with the same laser and target settings as before, except that the ion species are substituted with carbon and proton (number density ratio nC6+:nH+=1:2), for comparing the results of inverse and normal kinematics. It should be noted that the purpose of using the super-Gaussian laser profile here is only to show the novel physics more clearly. Laser profile effects, including simulation results for more realistic Gaussian laser profiles, are discussed at the end of Sec. V. It should also be noted that for practical reasons, to prevent degradation of the ultrathin lithium targets due, for example, to oxidation, an inert gas (e.g., argon)33–35 can be utilized for protection. Another different approach is to use a lithium compound (e.g., lithium hydride) instead of elemental lithium as the target material. Moreover, nanometer-scale free-standing and mechanically robust lithium metal foils have been successfully prepared,36 and a considerable number of experiments have even employed high-repetition target techniques.37,38

Figure 4 shows the PIC simulation results. As can be seen from Fig. 4(a), the accelerating lithium foil remains opaque until the laser illumination is over, ensuring that the LS acceleration dominates when the pulse is on. The peak energy of the ions, for both the lithium and CH₂ cases, is consistent with the predictions of the LS model, as demonstrated in Figs. 4(b) and 4(c). Since the areal density σ = n_el of the CH₂ target is smaller than that of the lithium target, the energy per nucleon acquired by the proton is higher than that acquired by the lithium. Figures 4(d) and 4(e) plot the lithium and proton energy spectra, respectively, together with the corresponding cross sections of the p(Li7,n) and ⁷Li(p, n) reactions. Since the reaction threshold energy E_p,th = 1.88 MeV for ⁷Li(p, n) is much lower than E_Li,th = 13.12 MeV for p(Li7,n), a higher percentage of protons can participate in the nuclear reactions than is the case for lithium. In addition, as presented Fig. 4(d), the energy peaks of the three lithium energy spectra are located at different positions of the p(Li7,n) cross section, enabling us to study our scheme in different situations.

The data from the PIC simulations of accelerated lithium and protons (forward angle θ_ion < 45°) are used as input for MC simulations of nuclear reactions and neutron production. With that goal in mind, an MC code (named MCNRC) is developed, in which nuclear data are carefully selected and benchmarked with the experimental data. More details of MCNRC can be found in the Appendix. CH₂ and LiF are chosen as the converter targets for the inverse and normal kinematics. The target thicknesses are selected to ensure that all ions can fully react in the converter target, expecting maximum neutron yields.

The angular neutron spectra shown in Fig. 5(a) clearly show that the neutrons produced by inverse kinematics are confined within a forward cone angle, and the increase in the maximum energy of the incident lithium ions causes the cone angle to expand. By contrast, normal kinematics produces more total neutrons in the total 4π space, but owing to the isotropic neutron distribution, the forward neutron yield is lower than with inverse kinematics.

The relationship between the neutron cutoff energy in Fig. 5(b) and the maximum ion energy in Figs. 4(d) and 4(e) agrees well with nuclear reaction theory. In addition, the steep dips in the neutron spectra are primarily due to the shape of the reaction cross-section shown by green dashed curves in Figs. 4(d) and 4(e). As shown in Fig. 5(b), with rising laser intensity, in contrast to the rapid increase in high-energy neutrons in the case of normal kinematics, the neutrons produced by inverse kinematics are concentrated in the low-energy range. This is clearly shown in the inset in Fig. 5(b), where the number of neutrons produced by inverse kinematics is nearly an order of magnitude higher than the number of those produced by normal kinematics in the low-energy range (E_n < 4 MeV). The energy–angle distributions of neutrons for the case a = 15.3 are shown in Figs. 5(c) and 5(d) for inverse and normal kinematics, respectively. In contrast to the nearly isotropic structure for normal kinematics, the energy-angle distribution for inverse kinematics has a distinct spatial structure, with low-energy neutrons concentrated in smaller angles, where the FWHM divergence angle is about 26°. The properties of the finally obtained neutron source from the inverse kinematics in our scheme can be evaluated by placing a numerical detector at 5 cm away in our simulations, and the resulting temporal and the spatial distributions are plotted in Figs. 5(e) and 5(g), respectively. We see clearly that a forward-directed pulsed neutron source is obtained, with an ultrashort pulse duration ∼3 ns determined mainly by the neutron transport time to the detector, a small divergence angle 26°, and a high peak intensity of 1 × 10⁶n/cm² (with a focal radius of ∼2 cm). After calculation, we find that the neutron source has an extremely high peak flux of about 3 × 10¹⁴n/(cm² s).

Further PIC-MC simulations are performed for the proposed scheme under various conditions. The accelerated lithium target thicknesses are chosen at optimal LS conditions in simulations with varying laser intensities. It is found that higher laser intensities result in more reactive lithium ions and higher lithium peak energy, both of which increase the neutron yield. Figure 6(a) shows that the forward neutron production grows roughly linearly with increasing laser intensity, but the low-energy fraction rises more slowly. Figure 6(b) demonstrates this more clearly when the neutron yield per laser energy is taken as the unit.

The total neutron yield per joule remains 3 × 10⁶n/(sr⋅J) when the laser intensity further increases, while the low-energy (E_n < 4 MeV) neutron yield per joule decreases once the laser intensity becomes higher than 10²¹ W/cm². The reason for this behavior is that the neutron production cross section of p(Li7,n) is rather lower in the high-energy region, as shown by the dashed green curve in Fig. 4(d), and this cannot effectively increase the neutron yield. In addition, the maximum neutron angle and the beam spot angle increase gradually with increasing laser intensity, but the growth trend becomes gradually slower. From the above discussion, we know that focusing the lithium energy in the high-cross-section region between 20 and 60 MeV can lead to an optimized neutron source based on inverse kinematics. Meanwhile, this energy range corresponds to laser intensities of 10²¹ W/cm², which are currently achievable. From the perspective of maximizing the laser energy to neutron conversion efficiency, an intensity of I = 10²¹ W/cm² would be the most suitable laser intensity for our scheme.

The unique advantages of LS acceleration are revealed when compared with target normal sheath acceleration (TNSA).39,40 In 2D TNSA simulations, we switch the circularly polarized laser to a linearly polarized laser, while keeping other laser parameters the same. As can be seen from Fig. 6(c), the forward neutron yield produced by TNSA is an order of magnitude lower than that from LS acceleration. This is mostly due to the exponentially decaying energy spectrum and lower cutoff energy of the lithium ions created by TNSA, resulting in too few reactive lithium ions (E_Li > E_Li,th). By contrast, LS acceleration has the ability to generate more reactive lithium ions, resulting in a higher laser–neutron conversion rate. Although LS acceleration requires a high laser contrast achieved by the use of plasma mirrors, leading to slight decreases in laser energy and intensity,14,41,42 its superiority over TNSA remains.

We also compare inverse and normal kinematics for deu-teron–lithium reactions. LS acceleration is chosen for the acceleration of lithium and deuteron ions, and CD₂ and LiF are selected as the corresponding converter targets. As shown in Fig. 6(d), not only does the inverse kinematics d(Li7,n) give a poorer forward neutron yield than the normal kinematics ⁷Li(d, n), but it also exhibits an unusual boost in the backward direction. The poorer yield is due to the positive reaction energy of the deuteron–lithium reaction, resulting in the absence of any kinematic focusing effect for neutron production. Meanwhile, the stopping power of lithium ions in CD₂ is higher than that of deuterons in LiF, which leads to a lower total neutron production. The boost in the backward direction occurs because the normal kinematics has a large forward neutron production cross section, producing a more significant backward cross section in inverse kinematics after coordinate system transformation. Thus, inverse kinematics is not helpful in neutron sources based on the deuteron–lithium reaction.

Finally, we discuss the effects of the laser profile. The reason that we utilized an intense, circularly polarized laser beam with a fourth-order super-Gaussian profile and a steep time profile in our simulations was to reveal the physics of our inverse kinematics scheme more clearly. Actually, the laser profile has little effect on our scheme, provided that the corresponding laser fluences ∫I dt and intensities are kept the same near the laser axis. As an example, Fig. 7 shows large-scale 3D PIC simulation results with realistic Gaussian laser profiles in both space and time, where the focal radius of the Gaussian laser pulse is twice that of a fourth-order super-Gaussian laser, i.e., σ_Gaussian = 2σ_{super-Gaussian} = 10 μm. As shown in Fig. 7(a), the accelerated lithium target maintains opaque with high density until the laser illumination ends, implying that the LS acceleration is still valid for the case of a realistic Gaussian laser. Figure 7(b) plots the energy spectra of the lithium ions near the axis with |r| < 3 μm, which we believe can be transported and arrive at the hydrocarbon converter target, contributing to the subsequent inverse p(Li7,n) reaction for neutron production. We see clearly that the lithium ion energy spectra near the axis for the realistic Gaussian laser with intensities a = 10, 15.3, and 20 are all similar to those for the super-Gaussian laser (although obviously the conversion efficiency may drop fourfold). The obtained neutron angular spectra and forward energy spectra are shown in Figs. 7(c) and 7(d), from which we see clearly that the angular distribution remains predominantly in the forward direction, and the energy spectra are also similar to those for the super-Gaussian laser [Fig. 4(b)]. Therefore, our scheme is indeed feasible for a realistic Gaussian laser pulse, although we acknowledge that the total conversion efficiency from laser to neutrons may drop by about a factor of four. Furthermore, the advantages of our scheme do not depend greatly on the laser parameters, but rather, for example, the difference between inverse and normal kinematics arises mainly from the difference in the nuclear reaction process, while the difference between the LS and TNSA results comes from the difference in ion energy spectra due to the different acceleration mechanisms.

We have shown that the laser-driven inverse kinematic reaction p(Li7,n) is able to produce a forward-directed pulsed neutron source with extremely high peak flux, ultrashort pulse duration, and dominant energy range at the MeV level. All these unique properties are of great advantage for many important applications. For example, such an MeV neutron source, with its energy range matching well with that of the fast neutrons (typically from 0.5 to 4 MeV) produced by future Generation IV reactors,43,44 would be of great use for precisely measuring and providing previously lacking reaction cross-section data in this energy range through experiments, thereby supporting the design and operation of these reactors.45,46 For application to fast neutron resonance radiography (FNRR)47,48 and fast neutron activation analysis (FNAA),49 our neutron source, with its ultrashort nanosecond duration, is capable of providing exceptionally high temporal and spatial resolutions. Furthermore, the near absence of backward neutron production and the extremely low gamma background, which would otherwise cause damage to the laser system and other electronic equipment, mean that our compact pulsed neutron generator can operate in a safe and repetitive way with high-repetition petawatt femtosecond lasers50 to provide the neutron fluxes required for various applications.

Acknowledgment. This work is supported by the National Key R&D Program of China (Grant Nos. 2022YFA1603200 and 2022YFA1603201), the National Natural Science Foundation of China (Grant Nos. 12135001, 11825502, and 11921006), the Strategic Priority Research Program of CAS (Grant No. XDA25050900), and the National Natural Science Funds for Distinguished Young Scholars (Grant No. 11825502).