1 Introduction

Nuclear fusion, which is responsible for synthesizing chemical elements and for ensuring stellar equilibrium, is the most crucial reaction in nuclear astrophysics, which is a field that strives for a comprehensive understanding of nuclear reactions in the universe [1-7]. The deuteron-deuteron (DD) fusion reaction, a crucial type of nuclear fusion, plays a key role in aiding the understanding of primordial abundances in Big Bang nucleosynthesis (BBN) models [8] and designing clean nuclear fusion power plants. Therefore, over the past several decades, this reaction has been measured via traditional accelerators in various beam-target experiments[9, 10]. In recent years, with the advent of high-power laser technology, scientists have become particularly interested in investigating these fusion reactions in the plasma environments generated by this new technology, mimicking astrophysical conditions [11-14]. There are two main methods to study fusion reactions: laser direct-driven inertial confinement fusion (ICF) experiments [15-22] and magnetic-confinement fusion experiments [23-25].

In laser-induced nuclear fusion experiments, multiple laser beams release energy onto a small capsule (or a slice containing appropriate fuels) within a short time interval. Subsequently, the target is compressed and heated to reach a high temperature and density, replicating the conditions necessary for a fusion reaction. In addition to neutrons, these reactions produce charged particles such as protons (p), deuterons (D), tritons (T), ³He and alpha particles (α), whose spectral characteristics can reveal specific information concerning the compressed plasma’s temperature and density.

For laser-induced DD fusion experiments, the primary fusion reaction equations (1) and (2) are the main fusion channels that occur at the same probability. Considering the high probability of a fusion reaction between T and ³He with D, the energetic primary products may continue to undergo fusion reactions with thermal D in the fuel. These secondary reactions are displayed in Eqs. (3) and (4). Considering only the Q-value of the reaction energy, the 3.5 and 3.6 MeV alpha particles and 14.7 MeV protons are the primary charged products. However, the ³He and T particles produced in the primary reactions have a kinetic energy slightly below 1 MeV, and they may lose further kinetic energy before participating in the secondary reactions through ion collisions in the plasma. As shown in Eqs. (5) and (6), considering both the kinetic energy of the initial particle and the Q-value of the reaction energy, the alpha particle may have an energy of approximately 1.4-6.7 MeV while the proton energy may range from 12.6 to 17.5 MeV. These equations are referred to as the secondary fusion reactions.

Primary reactions:

Secondary reactions:

• Considering only the Q-value of the reaction energy,

• Considering the kinetic energy of the initial particle and the Q-value of the reaction energy,

For such measurements, CR-39 detectors are widely employed to measure protons or other charged particles because they are most sensitive to ions, but insensitive to electrons, X-rays, gamma rays, and electromagnetic noise. Normally, combining CR-39 with a fixed-thickness filter to form a range-filter (RF) assembly, or with a magnet to form a magnet-based charged-particle spectrometer, is used to measure the charged-particle spectra in the laser-plasma experiments [26]. However, when the yields of charged particles are too high, the particle tracks on a magnet-based charged-particle spectrometer will be more likely to overlap. This is a result of the magnets separating different particles, causing the same particles to concentrate in one area. To avoid overlapping tracks, the RF spectrometer assembled from an aluminum film and two CR-39 detectors (see Sect. 3 for details) is employed in this experiment. They measure the fusion products produced by eight laser beams focusing on a flat deuterated polyethylene (CD₂) target, as well as diagnosing the particle types according to the calibrated track diameter results.

In this work, the RF spectrometers were employed to measure primary DD-protons and secondary D³He-protons in laser-induced DD fusion experiments at the ShenGuang-II Upgrade (SG-II-Up) laser facility. Section 2 describes the experimental setup and layout. Section 3 describes the RF spectrometers used in this experiment and how they were employed to detect protons. Section 4 describes and analyses the results. Finally, concluding remarks and perspectives are written in Sect. 4.

2 Experimental Setup and Layout

The laser-induced DD fusion reaction was experimentally investigated at the SG-II-Up laser facility at the Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences. Figure 1(a) displays the schematic layout of the target chamber, with four laser beams focused on a thin CD₂ target from above and four beams from below. The laser parameters (total energy and pulse duration) ranged from approximately 2 kJ in 250 ps to 19 kJ in 2 ns. The thickness of the CD₂ target varied from 3.6 to 1000 μm, as the laser beam focus varied from 150 to 400 μm. When the eight laser beams focused on the target simultaneously, the impacted area of the target was rapidly compressed and heated to form a surrounding plasma. Subsequently, two ion beams were produced by the lasers interacting with the target, one moving from top to bottom and the other from bottom to top in the plasma. The two beams could collide and create a fusion reaction at the center of the plasma if the kinetic energy of the colliding deuterium ions was sufficient. Here, Faraday cups and Thomson parabolas with image plates were applied to measure the produced ions. Bubble detectors, liquid and plastic scintillators were used to measure the neutrons. A review of the performance of the detectors can be found in Ref. [27].

Fig. 1.Full-screen View

Experimental setup. (a) Schematic view of the target chamber, with eight laser beams focused on a flat deuterated polyethylene target. (b) Schematic view of the X-Y plane of the target chamber, with the location of the target, and five RF spectrometers (A-E) highlighted.

This work focused on the application and analysis of the RF spectrometers and their results. Figure 1(b) illustrates a schematic view of the target chamber and locations of the RF spectrometers (A-E), which were used to measure the yields of primary DD-protons and secondary D³He-protons. The radius of the target chamber was 1.1 m, and the spectrometers were placed between 28-85 cm from the target.

3 Proton Detection with range-filter spectrometer

CR-39, a clear and rigid plastic polymer with the chemical formula C₁₂H₁₈O₇, is an ideal material to measure ions in plasma experiments because it is most sensitive to ions but insensitive to electrons, X-rays, gamma rays, and electromagnetic radiation. When ions are incident on a CR-39 sample, they cause damage called a latent track. A latent track can become a micron-scale track, which may be observed by a microscope, after CR-39 is etched in a NaOH solution (see Ref. [28] for more CR-39 track information and growth process). A track’s position shows where the ions were incident, and its diameter can often be used to identify the particle type. Track diameters primarily depend on the etch time (t), bulk etch rate (V_B), and track etch rate (V_T), of which the latter two are both sensitive to the normality and temperature of the NaOH solution. Thus, to obtain repeatable results, these factors must be controlled. In this study, the CR-39 samples of size 25 mm (L) × 25 mm (W) × 1.5 mm (H) were manufactured by Track Analysis Systems Ltd. (TASL) in Bristol, UK. Following the manufacturer’s recommendations, an NaOH solution with a molarity of 6.25 mol/L was used because V_T/V_B peaks at concentrations of about 6.25 mol/L for temperatures above 60 [29]. Furthermore, a high etch temperature of 98 was maintained to reduce the etch time to one hour, unless otherwise noted. Following the etching process, the track parameters on the CR-39 sample, including the track position, track diameter, and gray level, were recorded by the TASLIMAGE radon dosimetry system, which consists of a computer-based scan system and a charge-coupled device (CCD) camera.

In laser-induced DD fusion experiments, while aiming to detect the number of DD-protons and D³He-protons with CR-39 detectors, other charged particles such as 0.82 MeV ³He, 1.4-6.7 MeV alpha particles, and 1.01 MeV T, D, and neutrons, should also be considered. For neutrons to leave tracks in a CR-39 detector, they need to generate a moving charged particle via n-p scattering or a nuclear reaction with ¹²C, resulting in a low neutron detection efficiency. Regarding 2.45 MeV and 14.1 MeV neutrons, CR-39’s neutron detection efficiency is approximately 10^-4 counts/neutron [30, 31]. Hence, the tracks left by neutrons can be ignored in comparison with those caused by charged particles.

To prevent proton tracks from mixing with other heavy charged particle tracks, it is necessary to place an appropriately thick aluminum filter in front of the CR-39 to stop the heavy charged particles from reaching the CR-39. In addition, the aluminum filter is used to reduce the proton energy down to around 1 MeV in order to create more visible tracks, as the maximum proton track diameter appears at this energy (see Ref. [26, 32, 33]). According to the charged particle range in aluminum materials shown in Table 1, calculated by the LISE++ program [34, 35], the range of 6.7 MeV alpha particles is 33.1 μm, and the range of 3.02 MeV protons is 81.8 μm. According to the remaining energy listed in Table 1, a 3.02 MeV proton retained 0.86 MeV of energy after passing through 70 μm thick aluminum, which is near the energy of the maximum proton track diameter. However, a 14.7 MeV proton retained 14.12 MeV of energy after passing through the same aluminum filter, which is not in the sensitive energy range of CR-39 for protons (CR-39 is insensitive to the high energy protons above 8 MeV) [26, 36, 37]. Thus, in order to detect these high energy protons, two CR-39 samples are needed. The first serves as an energy degrader, while the later as a track detector.

Based on the above idea, the RF spectrometer assembled from a 70 μm thick aluminum film and two 1.5 mm CR-39 samples (CR-39^1# and CR-39^2#) was employed in this study, to measure the DD-protons and D³He-protons. In the schematic diagram shown in Fig. 2, 1.01 MeV T, 6.7 MeV or lower energy alpha particle, and 0.82 MeV ³He can be stopped by the 70 μm thick aluminum filter. Meanwhile, the DD-protons reduce their energy passing through the filter, allowing for more efficient proton detection by the CR-39^1# sample. Furthermore, the response of the CR-39 sample covered with a 70 μm thick aluminum filter for 3 MeV protons was studied with the 2×6 MV tandem accelerator at Peking University’s Institute of Heavy Ion Physics. The detailed experimental information can be found in Ref. [36]. After CR-39 tracks were etched for one hour, the track diameter statistical histogram shown in Figure 3 was developed. The histogram illustrates that the proton track diameters were distributed between 3 and 8 μm, and the mean proton track diameter was 4.59 μm. These results could be used in the future laser-induced DD fusion experiments to diagnose proton tracks.

Fig. 2.Full-screen View

Schematic diagram of the RF spectrometer assembled from an aluminum film and two CR-39 detectors.

Fig. 3.Full-screen View

The histogram of the proton track diameter on a 70 μm aluminum-covered CR-39 sample irradiated by 3 MeV protons. The mean track diameter was 4.587 μm.

4 Experimental Results

Figure 4(a) shows the track image detected by the RF spectrometer on the CR-39^1# sample at position E. The tracks were small, consistent with the calibration results (figure 4(b)). Statistical histograms of the five RF spectrometers are shown in Fig. 5 and Fig. 6. Figure 5 illustrates the track diameter distribution on the CR-39^1# sample measured by the RF spectrometers, while Fig. 6 displays the results for the CR-39^2# sample. On the CR-39^1# sample, the RF spectrometer closest to the target at position E measured the largest number of tracks; the more distant detectors measured fewer tracks.

Fig. 4.Full-screen View

A digitized microscopic track image (20× magnification). The physical area of the image is 0.62 mm × 0.46 mm (776 × 582 pixels, where 1 pixel = 0.8 microns). The laser energy in this shot was 13.8 kJ in 2 ns impacting on a 210 μm CD₂ film target. (a)Track image on the CR-39^1# sample from a RF spectrometer.(b)Track image on the CR-39 sample covered with 70 μm aluminum irradiated by 3 MeV protons.

Fig. 5.Full-screen View

(Color online) The proton spectra of five RF spectrometers on CR-39^1#

Fig. 6.Full-screen View

(Color online) The five proton spectra of five RF spectrometers on CR-39^2#

Based on the calibration results in Fig. 3, we counted the number of tracks with diameters ranging from 3 to 8 μm in an area of 1 cm × 1 cm (Table 2). Overall, 972 tracks were discovered on the CR-39^1# sample at position E, while the other four detectors counted fewer tracks. The number of tracks measured by the five detectors at different positions (third column in Table 2) was multiplied by the area of a sphere, with the radius of the detector, to obtain the total yields. As shown in Fig. 7, we concluded that the number of tracks on the CR-39^1# sample at the five positions was approximately consistent with the 4π distribution. A primary DD-proton yield of (8.5±1.7)× 10⁶ was detected via this method for a 210 μm CD₂ target. The results of the other shots at different conditions are shown in Table 3. The primary DD-proton yields were approximately 10⁶-10⁷, which are consistent with the previous results by similar laser facilities, e.g. Gekko XIII [22] and SG-II [20, 21], but lower than those from OMEGA [26] and the National Ignition Facility [15] which have higher-intensity laser beams. As equations 1 and 2 have the same reaction probability, the DD-neutron yield should have the same order of magnitude as the DD-proton yield. The presented proton yield is consistent with the DD-neutron yield (10⁵ to 10⁸) previously measured by liquid and plastic neutron detectors [27].

Fig. 7.Full-screen View

The primary DD-proton yields detected by five RF spectrometers, with eight lasers impacting on a 210 μm CD₂ target at the SG-II-Up laser facility. The total laser energy is 13.8 kJ in 2 ns.

Furthermore, there were some tracks recorded at a diameter range of 10-20 μm, whose statistics were similar to those on the CR-39^1# sample at different positions. As heavy ions (such as alpha and T particles and other heavy primary products of DD fusion) are stopped by the 70 μm thick aluminum filter, these tracks might be the primary products at other energy ranges that have not been determined, or the products of primary particles scattered by the aluminum filter. This single type of CR-39 detector had difficulty diagnosing their properties; however, a combination of other devices might be able to measure them.

As described in Sect. 3, a 14.7 MeV proton retains 4.90 MeV of energy after passing through a 70 μm thick aluminum filter and a CR-39 sample. According to the proton calibration results in Ref. [36], a 5.0 MeV proton track etched in 98 NaOH solution for one hour does not appear on the CR-39 sample, but has a diameter of around 4 μm after two hours of etching. However, as shown in Figure 6, the track diameters on the CR-39^2# sample had a distribution of 3-10 μm, with a few track diameters ranging from 10 to 20 μm. Based on the 5.0 MeV proton calibration results, we conclude that these tracks were not 4.9 MeV proton tracks; they may be proton tracks below 3 MeV, tracks induced by neutrons, or background spots. As CR-39 is insufficient for detecting neutrons, these tracks are more likely to be proton tracks below 3 MeV or background spots. If they were all proton tracks below 3 MeV, the energy of D³He-protons emitted from the plasma environment should be below 14.7 MeV, and the number of D³He-proton tracks on the five CR-39^2# samples should meet the 4π distribution requirements. However, the statistical track counts on the CR-39^2# samples are not related to the detector positions shown in the fourth column in Table 2. According to the previous Ref. [26], the D³He-proton yields are typically three orders of magnitude lower than primary DD-proton yields. Therefore, only three D³He-protons were expected to be detected in this experiment, easily submerged in the background spots. Thus, these tracks were most likely a mixture of proton tracks below 3 MeV and background spots.

Generally, a proton track is darker than a background spot, but different microscopes (CCD cameras) have different gray level reading capabilities. Thus, determining the most effective gray value to diagnose a track is very subjective. High gray values may filter the background spots as well as the real signals, so they cannot be effectively used to distinguish the D³He-proton tracks.

Based on the above analyses, it was difficult to distinguish the secondary D³He-proton tracks from the background spots based solely on track diameter. Therefore, diagnosing the number of rare D³He-protons requires more accurate detectors. Silicon carbide (SiC) is one of the most promising wide bandgap materials. Considering previous laser plasma experiments [38, 39], a SiC detector combined with a magnet that separates low energy charged particles, might be able to measure the number of rare D³He-protons successfully.

5 Conclusion and Perspectives

In the laser-induced primary DD fusion reactions, and secondary D³He and DT fusion reactions, the yields of charged particles are the basic indicators of an implosion performance. The ratio of the secondary to primary yield is related to the target’s areal density. Moreover, when measuring the yields of the charged particle and neutron separately, it is possible to use the values to estimate the target’s temperature at burning time.

In this study, according to the calibration results of the 3 MeV proton track diameter on CR-39 covered with 70 μm thick aluminum, an approximate (8.5±1.7)10⁶ primary DD-proton yield was obtained, by employing five RF spectrometers with eight laser beams to induce DD fusion reactions. This shows that the RF spectrometer assembled from fixed-thickness aluminum film and two CR-39 detectors is an effective probe for detecting DD-protons. Furthermore, as the yields of the secondary D³He-protons were typically lower by three orders of magnitude than those of the primary DD-protons, only three events of D³He-protons were expected to be detected in this experiment. Hence, it was difficult to separate D³He-proton tracks from the background spots in the RF spectrometer.

In general, CR-39 detectors are widely employed to measure charged fusion products when they are energetic enough to escape the plasma. According to the primary DD-proton tracks on the CR-39^1# sample of the RF spectrometers (associated with the track diameter calibration of CR-39 covered with thick aluminum irradiated by 3 MeV protons), the method described in this research can be used effectively to detect primary DD-protons. In future, to detect D³He-protons, due to their high energy and low yields it is necessary to use a suitable filter in front of the CR-39 to reduce the proton energy. Detection could also be achieved by combining magnetic devices to identify the residual energy, which could help separate signals and backgrounds when there are a small number of fusion events.

The authors would like to thank the engineering staff at the SG-II-Up laser facility for their support, alongside the Engineering Technology Department at the Shanghai Institute of Applied Physics for providing the etching laboratory and CR-39 readout equipment.