2 Design of an efficient laser plasma electron accelerator

The laser plasma accelerator is based on a commercial hHz laser system, which has been equipped in many laboratories, for example, it can deliver laser pulses with energy of 50 mJ, pulse duration of 30 fs in FWHM and repetition rate of 100 Hz. The laser pulses can be focused into the gas jet with an f/3 off-axis paraboloid mirror to a spot size ${w}_0 = 2.5$ μm (1.2 times the diffraction limit) containing 80 $\%$ of the total energy, giving a confocal parameter of 2 ${z}_{\mathrm{R}}$   $\sim$ 50 μm ( ${z}_{\mathrm{R}}$ is Rayleigh length) and a peak intensity of ${8.5\times {10}^{18}}$  W/cm² (peak normalized vector potential ${a}_0$ = 2). The dense gas jet is generated by feeding high-pressure nitrogen gas through a solenoid valve to a Mach $\sim$ 3 supersonic ‘De Laval’ nozzle with a 100 μm diameter throat and a 300 μm exit diameter^[ Reference Gustas, Guénot, Vernier, Dutt, Böhle, Lopez-Martens, Lifschitz and Faure ^{32 ]}. The out-flow gas density profile is near-Gaussian distribution with approximately 120 μm in FWHM, according to the computational fluid dynamics simulation using ANSYS Fluent software. The peak nitrogen density can be adjusted in the range of ${n}_{\mathrm{N}} = 0.5 \times {10}^{19} - 5 \times {10}^{19}\ {\mathrm{cm}}^{-3}$ by controlling the gas backing pressure. After the LWFA process, the electron beam passes through the Kapton window, and then it is deflected by a magnet and bombards on the Lanex emitting fluorescence, which is collected by a charge-coupled device (CCD) for acquiring a beam energy spectrum^[ Reference Feng, Li, Wang, Li, Zhu, Tan, Geng, Liu and Chen ^{33 ]}, as shown in Figure 1. In experiments, some parameters, for example, the laser focal position, gas density, and laser pulse second order dispersion, can be adjusted to optimize the electron beam quality.

Figure 1 Design of the experimental setup for the generation of an ultra-short pulsed neutron source and the fast neutron absorption spectroscopy.

In order to exhibit the characteristics of the electron beam accelerated from the above system, we have carried out 3D particle-in-cell simulations using EPOCH code^[ Reference Arber, Bennett, Brady, Lawrence-Douglas, Ramsay, Sircombe, Gillies, Evans, Schmitz, Bell and Ridgers ^{34 ]}. The simulation window size is set to $40\ \unicode{x3bc} \mathrm{m} \times 40\ \unicode{x3bc} \mathrm{m}\times 40$ μm with $1200\times 300\times 300$ cells in the x-, y- and z-directions, respectively. The simulation window propagates along the x-direction at the speed of light. One macro-particle per cell is used as the nitrogen atoms. The ionization process is modeled with ADK rates^[ Reference Ammosov, Delone and Krainov ^{35 ]}. The longitudinal profile of nitrogen gas has a Gaussian distribution with 120 μm in FWHM. A laser pulse with p-polarization propagates along the x-axis, and it is focused at the center of the nitrogen gas profile. Both the focal spot and pulse envelope have Gaussian profiles, ${w}_0$ = 2.5 μm and the pulse duration is 30 fs. The laser intensity is set to $8.5\times {10}^{18}\;\mathrm{W}/{\mathrm{cm}}^2$ .

To acquire a large charge and high conversion-efficiency electron beam, we scanned the gas density. In order to meet the matching criteria for maintaining laser intensity and overcoming quick defocus^[ Reference Esarey, Schroeder and Leemans ^{36 ]}, that is, ${w}_0\approx R$ , where $R = 2c\sqrt{a_0}/\sqrt{4\pi {n}_\mathrm{e}{e}^2/{m}_\mathrm{e}}$ is the plasma bubble radius, usually requires a higher plasma density for matching the small focal spot. When considering a higher plasma density of $7\times {10}^{19}\;{\mathrm{cm}}^{-3}$ , the matched plasma bubble radius is approximately 2 μm, as a result of which the laser peak intensity can be further increased to ${a}_0\sim$ 2.5 due to self-focusing, as shown in Figure 2(b). The intense laser pulse will also induce the nonlinear evolution of plasma bubbles, which results in the combination of plasma bubbles and trapping a large number of electrons^[ Reference Li, Li, Huang, Tao, Li, Zhao, Ma, Guo, Wang, Chen, Hafz, Zhang and Chen ^{16 ]}, as shown in Figure 2(c). Then, when the laser pulse propagates at the density down-ramp of the nitrogen gas jet, the accelerated intense electron beam drives plasma wakefield acceleration due to the fact that the tightly focused laser pulse quickly defocuses in low-density plasma, as shown in Figure 2(d). The self-generated electro-magnetic fields in the plasma bubbles would also restrain the electron beam^[ Reference Corde, Phuoc, Lambert, Fitour, Malka, Rousse, Beck and Lefebvre ^{37 ]}, resulting in a micro-sized electron beam ( $\sim$ 4 μm in FWHM). Meanwhile, the electron beam has the advantages of ultra-short duration ( $\sim$ 30 fs in FWHM) and ultra-dense density ( ${\sim}1\times {10}^{20}\;{\mathrm{cm}}^{-3}$ ), which are unattainable for traditional radio-frequency accelerators.

Figure 2 Three-dimensional particle-in-cell simulations of laser plasma acceleration. (a)–(d) represent four different times at 0.25, 0.5, 0.75 and 1 ps, respectively. The nitrogen atom density is $1\times {10}^{19}\;{\mathrm{cm}}^{-3}$ and the laser ${a}_0$ = 2.

Here, we have scanned the nitrogen density, and the results are shown in Figure 3. On increasing the density, the accelerated electron beam charge is quickly increased to approximately 2.8 nC ( ${E}_{\mathrm{k}}$ > 1 MeV), as shown in Figure 3(a). Moreover, the maximum energy of the electron beam increases with the density, and can reach approximately 25 MeV, as shown in Figure 3(b). However, both the beam charge and the maximum energy decrease at densities above $1.5\times {10}^{19}\;{\mathrm{cm}}^{-3}$ due to the rapid dissipation of the driving laser in high-density plasma. Finally, we choose ${n}_{\mathrm{N}} = 1\times {10}^{19}\;{\mathrm{cm}}^{-3}$ , ${a}_0$ = 2 as the optimal conditions, and the electron parameters include charge 2.5 nC, source size 4 μm, maximum energy 25 MeV and divergence angle 5°. Significantly, most of the electrons have energy locating in the range of 7–20 MeV, which is beneficial for driving nuclear giant dipole resonance to produce fast neutrons via ( $\unicode{x3b3}$ , n) reactions.

Figure 3 Simulation results of the electron beam. (a) Variation of electron beam charge ( ${E}_{\mathrm{k}}$ > 1 MeV) with the nitrogen atom density. (b) Electron energy spectra for different nitrogen atom densities.

3 Generation of the ultra-short pulsed fast neutron source

To generate a fast neutron source, we have utilized the optimal electron beam to bombard a thin metal target for inducing photo-nuclear reactions^[ Reference Feng, Fu, Li, Zhang, Wang, Li, Zhu, Tan, Mirzaie, Zhang and Chen ^{38 ]}. Here, we carried out Monte Carlo simulation with Geant4 code. In the simulation setup, the metal target is a piece of tantalum (Ta) sheet with the thickness of 500 μm, which is set at 500 μm away from the electron beam source. The parameters of the electron beam, including the source size, distribution, energy spectrum and transversal momentum distribution, are imported into the input text of the Geant4 code, and $6.25\times {10}^8$ electrons are used in this Monte Carlo simulation.

The simulation results of the Bremsstrahlung source are shown in Figure 4. According to the $\unicode{x3b3}$ -ray spectrum, most photons have energy below 15 MeV, and thus the neutrons would be mainly contributed by the ${}^{181}\mathrm{Ta}{\left(\unicode{x3b3}, \mathrm{n}\right)}^{180}\mathrm{Ta}$ reaction, and a small number of neutrons are contributed by the ${}^{181}\mathrm{Ta}{\left(\unicode{x3b3}, 2\mathrm{n}\right)}^{179}\mathrm{Ta}$ reaction. In addition, the $\unicode{x3b3}$ -ray source size is large ( $\sim$ 50 μm in FWHM), due to the divergence of the electron beam in the Ta sheet.

Figure 4 Simulation results of the Bremsstrahlung source driven by the laser plasma electron accelerator. (a) $\unicode{x3b3}$ -ray spectrum (red line) photo-nuclear reactions of ${}^{181}\mathrm{Ta}\left(\unicode{x3b3}, \mathrm{n}\right)$ , ${}^{181}\mathrm{Ta}\left(\unicode{x3b3}, 2\mathrm{n}\right)$ and ${}^{181}$ Ta $\left(\unicode{x3b3}, 3\mathrm{n}\right)$ . (b) $\unicode{x3b3}$ -ray source transversal distribution, which is detected on the plane of the rear surface of the Ta converter.

The simulation results of the photo-nuclear neutron are shown in Figure 5. The fast neutron source has near-Gaussian transversal distribution and its source size is approximately 250 μm in FWHM, which is larger than that of the $\unicode{x3b3}$ -ray source due to the neutrons’ near-uniform emission distribution, as shown in Figures 5(a) and 5(b). The energy spectrum of the neutron source is shown in Figure 5(c). The neutron energy is mainly in the range from 40 keV to 4 MeV, and the peak energy is approximately 700 keV. The neutron yield considering the electron beam charge of 2.5 nC is shown in Figure 5(d). The yield increases rapidly with the target thickness, and the yield could be up to $7\times {10}^5$ for the 500 μm thickness. We estimated the neutron pulse duration according to the neutron energy spectra and target thickness, that is, $\Delta t = 73\cdot d\left[\mathrm{mm}\right]\cdot \Big(\frac{1}{\sqrt{E_{\mathrm{nl}}\left[\mathrm{MeV}\right]}}-\frac{1}{\sqrt{E_{_{\mathrm{nh}}}\left[\mathrm{MeV}\right]}}\Big)$ ^[ Reference Qi, Zhang, Zhang, He, Zhang, Cui, Yu, Dai, Peng and Gu ^{39 ]}, where $d$ is the propagation distance (or the converter thickness) and ${E}_{\mathrm{nl}}$ and ${E}_{_{\mathrm{nh}}}$ represent the low and high neutron kinetic energy in this pulse, respectively. The pulse duration is linearly proportional with the target thickness, and could be less than 50 ps for the 500 μm thickness, as shown in Figure 5(d).

Figure 5 Simulation results of the neutron source driven by the laser plasma electron accelerator. (a) Neutron spatial distribution. (b) Neutron angular distribution. (c) Neutron energy spectrum. (d) Neutron yield and pulse duration.

4 Design of ultrahigh energy-resolution neutron absorption spectroscopy

The FNAS energy resolution is limited by three factors, the neutron pulse duration, detection distance and detector temporal resolution. At present, the doped ${\mathrm{BaF}}_2$ crystal scintillator can realize an approximately 30 ps fluorescence process and an approximately hundreds of ps quenching process^[ Reference Chen, Zhang, Zhu, Du, Wang, Sun and Li ^{40 ]}. It has sufficiently high temporal resolution to be used to diagnose the arrival time of a neutron. For the effects of detection distance, the farther the distance, the higher the energy resolution^[ Reference Li, Feng, Wang, Tan, Ge, Liu, Yan, Zhang, Fu and Chen ^{12 ]}. Here, it is limited by the single-shot yield of the laser neutron source, and we set the detection distance to 5 m. For the case of 1.5 MeV neutron energy and 1 ns pulse duration, $\frac{\Delta E}{E}$ = 52.8 keV @ 5 m, 1 ns, and even if the detection distance of 20 m corresponds to an energy resolution of 13.2 keV @ 1.5 MeV, 1 ns^[ Reference Li, Feng, Wang, Tan, Ge, Liu, Yan, Zhang, Fu and Chen ^{12 ]}, it is still difficult for the state-of-the-art traditional fast neutron source to acquire the FNAS, which can exhibit the fine structure of some resonance absorption peaks^[ Reference Pomerantz, McCary, Meadows, Arefiev, Bernstein, Chester, Cortez, Donovan, Dyer, Gaul, Hamilton, Kuk, Lestrade, Wang, Ditmire and Hegelich ^{11 ,} Reference Li, Feng, Wang, Tan, Ge, Liu, Yan, Zhang, Fu and Chen ^{12 ]}.

In order to further decrease the influence of scintillator fluorescence tailing on the energy resolution of FNAS, we proposed a method named SNC absorption spectroscopy, for which the setup is shown in Figure 1. The generated photo-nuclear neutron source has near-uniform distribution in the entire $4\pi$ solid angle. Here, we choose the 45° direction and use a long vacuum tube composed of Teflon and lead collimators with a hole diameter 5 cm to transport the fast neutrons. The sample and the ${\mathrm{BaF}}_2$ detector are placed 0.6 and 5 m away from the neutron source point, respectively. By considering the neutron yield of $7\times {10}^5$ neutrons/shot and the response efficiency of the ${\mathrm{BaF}}_2$ detector of approximately 20% for fast neutrons, approximately four neutrons can be recorded on the oscilloscope for one laser shooting. The signal is several separated peaks or only one peak, and we can calculate their energy according to the time-of-flight signal on the oscilloscope. Finally, we accumulate enough shots to acquire the neutron energy spectrum or absorption spectrum.

As the results show in Figure 6, we present the potential of this kind of FNAS. The sample is composed of two materials, namely graphite and C7H5N3O6 (TNT), and the neutron transmittances of the two materials are shown in Figure 6(a). In the simulation, the neutron beam with the energy spectrum of Figure 5(c) passes through the sample; then one transmitted neutron is randomly selected via MATLAB code to be recorded and the recorded energy has corresponding uncertainty, which is shown in Ref. [Reference Li, Feng, Wang, Tan, Ge, Liu, Yan, Zhang, Fu and Chen12] (Figure 5(b)); finally, we repeat the selection process to accumulate enough transmitted neutrons to acquire a fine absorption spectrum, whose energy resolution is determined by the calculated result in Ref. [Reference Li, Feng, Wang, Tan, Ge, Liu, Yan, Zhang, Fu and Chen12]; the repetitive process is the same to accumulate laser shots. The absorption spectra are shown in Figures 6(b)–6(d). For the case of accumulating ${10}^4$ neutrons, the absorption peak at 433 keV can be distinguished clearly, but the absorption peak width of approximately 60 keV in FWHM is larger than that of 40 keV from the theoretical data^{[ 41 ]}, as shown in Figure 6(b). When the neutron number is increased to ${10}^5$ , the FWHM at 433 keV could be close to the theoretical value of approximately 40 keV. Moreover, we continue to accumulate the neutron number to ${10}^6$ (which means $2.5\times {10}^5$ shots or almost 4 h in our experimental case), the absorption peak at 2080 keV with FWHM of approximately 20 keV can be distinguished and its peak shape can also be found, as shown in Figure 6(d). However, it is impossible for the low-resolution FNAS to diagnose the accurate peak position, and the uncertainty could be up to 100 keV for the peak of 433 keV, as shown in Figure 6(e).

Figure 6 Single-neutron-count fast neutron absorption spectroscopy. (a) Transmissivities for two materials, that is, graphite and TNT. (b)–(d) Simulated neutron absorption spectrum for the pulse duration of 36 ps, where the total neutron counts are ${10}^4$ (b), ${10}^5$ (c) and ${10}^6$ (d), respectively. (e) Absorption spectrum for the pulse duration of 1 ns, where the total count is ${10}^6$ .