Mechanisms of D-D fusion and associated neutron-producing reactions in PW laser interactions with carbon-deuterated targets

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Kodama This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8108674/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract The mechanisms of the D(d,n) 3 He fusion reaction and its associated neutron-producing reactions in petawatt laser interactions with CD and CD 2 targets have recently attracted attention. The mechanisms by which ions are accelerated, causing fusion and other nuclear reactions are also a subject of debate. It was assumed that the D(d,n) 3 He fusion reaction is the only source of neutrons through thermonuclear and/or beam fusion mechanisms with a background of photoneutrons. In addition, ions acceleration occurs at the target front surface and within the electrostatic sheath on the rear surface. Here, through in-depth analysis of experimental measurements and simulations using 3-D Monte Carlo code, it was shown that nuclear reactions occur between accelerated ions and target background ions. The ions are accelerated at the target surface, causing nuclear reactions as they pass through the target, thus eliminating the effect of the electrostatic sheath on the rear side. The relative contribution of each reaction was assessed in comparison with the fusion reaction. Deuteron-Carbon stripping reactions contribute to overall neutron production, with a much higher neutron yield than that of the fusion reaction. Other reactions such as photonuclear reactions, deuteron breakup, and deuteron electro-disintegration must be considered. Physical sciences/Chemistry Physical sciences/Physics (1) D-D fusion reaction (2) neutron producing reactions Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Introduction Neutrons have the unique ability to play a vital role in science, technology, and medicine as they are unique tools for investigating or modifying the structure and properties of materials. Their distinctive properties such as deep penetration, non-destructive interaction with matter, and sensitivity to light elements make them ideal for a wide range of applications extend to many fields including medical sciences 1 , material science 2 – 4 , biology 5 , laboratory astrophysics 6 , transmutation of nuclear waste 7 , archaeology 8 , 9 , security 10 , 11 , neutron imaging 12 , nuclear transmutation 13 , and boron neutron capture therapy for the treatment of tumors 14 . Laser-generated neutrons have attracted the attention of many recent studies 15 – 19 . These studies focused on the theoretical investigation of neutron production via the thermonuclear mechanism and the nuclear reactions caused by accelerated ions when petawatt (PW) class lasers irradiate carbon-deuterated targets. P. Martin et al. 15 suggested that, through 2-D particle-in-cell simulations, neutrons are seen to be produced by hole-boring (HB) mechanism inside the target bulk and target normal sheath acceleration (TNSA) mechanism on the rear surface of the target. Furthermore, neutrons produced due to the shock-like features within the bulk target plasma by the rapid expansion of contaminant species from the front and back surfaces of the target. When using carbon-deuterated targets like CD 2 and CD, the previous studies have considered the neutron source to be only the D-D fusion reaction. In this work, using in-depth analysis of experimental data for the interaction of PW lasers with CD and CD 2 targets and simulations using MCUNED 3D Monte Carlo code, it was demonstrated that the produced neutrons are due to the acceleration of ions at the target surface only. The accelerated ions then produce nuclear reactions as they pass through the target. The D(d,n) 3 He fusion reaction and other associated neutron-producing reactions contribute to the overall process of neutron production. Therefore, identifying the reactions and their mechanisms is crucial in determining the relative contribution of each reaction to the total neutron yield. The following sections of this paper were arranged as follows: The experimental work was explained in Section 2. The experimental results were presented in Section 3. Details of the Monte Carlo simulation were given in section 4. Analysis and discussion were provided in Section 5. Finally, the conclusion was given in Section 6. Experimental work The experiments were carried out at the Laser Engineering Institute (ILE), Osaka University, using 100-micrometer-thick CD and CD 2 targets. The targets were irradiated with a PW laser to study the D(d,n) 3 He fusion reaction, its associated neutron-producing reactions, and neutron production mechanisms. The PW laser produces a linearly polarized laser pulse with energies up to 500 J and a duration of 0.5–1 picosecond at a wavelength of 1.053 µm. In the experiment, peak intensity at the target is ≈ 1x10 19 W/cm 2 . Ultra-intense laser interactions with CD and CD 2 targets can produce significantly higher neutrons compared to other targets such as metallic (Al and Au) and inorganic targets (LiF) because the accelerated ions originate from the target's structure itself. Therefore, intensities and current densities of the driven neutron beams can be much higher than other targets under the same radiation conditions 20 , 21 . To detect the produced neutron spectra, neutron diagnostics consisted of current mode time-of-flight (TOF) neutron detectors were used. The detectors comprise a combination of the quenched version of the Bicron BC-422 ultra-fast timing plastic scintillator/Hamamatsu R2083 photomultiplier tube (PMT) placed at varying distances from the target. Three neutron detectors were placed at an angle of 40° to the direction of the PW laser beam. To prevent background gamma rays and photoneutrons (resulting from interactions with the target's surroundings) from affecting the measured neutron spectra, cone-shaped collimators made of lead and plastics were installed in the laser chamber. The detectors were shielded by 10 cm thick lead block at the front and another 5 cm thick lead block on all sides. Neutron spectra modification due to shielding has been considered 22 , and the TOF values were corrected by accounting for neutron delays within lead blocks. The measured neutron signals were normalized to be the number of neutrons/MeV Sr (solid angle), taking into account the detector position and sensitivity 23 . The accuracy of each energy value was calculated using the differentiation method 24 . The error in neutron energy ΔE is calculated using partial differentiation based on experimental errors in both TOF (ΔT) and the detector distance from the target (ΔX) as follows: (ΔE) 2 = (∂E/∂T) 2 (ΔT) 2 + (∂E/∂X) 2 (ΔX) 2 (1) Experimental Results Figures 1 , 2 show neutron spectra measured when 100-micro-thick CD and CD 2 targets were irradiated by the PW laser respectively. The area under the curve in both figures shows that the neutron production from CD 2 target is twice that of CD target under the same radiation conditions. This is because the deuterium concentration in CD 2 target is twice that of CD target (detailed explanation was given in the discussion). In both cases, the peak of 2.45 MeV neutrons was measured within the experimental error at 2.44 ± 0.17 MeV. The error in the measured value is due to the detector resolution and the error in TOF measurement (Eq. 1). The emission of 2.45 MeV neutrons means that thermonuclear fusion occurs in the high-energy density plasma produced by PW laser interactions with the deuterated targets. Thermonuclear fusion of the reaction D(d,n)He The D(d,n) 3 He fusion reaction between two deuterons (naked deuterium nuclei) is written as follows 25 : D + D → 3 He + n + 3.27 MeV The D-D reaction, which has a positive Q value (3.27 MeV), occurs even if the total kinetic energy, and therefore the total momentum, of the interacting deuterons is zero at the time of the reaction (thermonuclear fusion). In this case, only 2.45 MeV neutrons are emitted because the Q-value of the reaction is distributed between the two products ( 3 He and n) inversely with their masses. Therefore, the thermonuclear fusion reaction D(d,n) 3 He can be written as follows: D + D → 3 He (0.82 MeV) + n (2.45 MeV) According to the law of momentum conservation, since the total momentum of the two interacting deuterons at the time of the reaction is zero, the 2.45 MeV neutrons are emitted in all directions. The produced nucleus 3 He recoils in the opposite direction to keep the final momentum at zero. Therefore, thermonuclear fusion mechanism of the D(d,n) 3 He fusion reaction produce only 2.45 MeV neutrons which are isotropic and can be detected at all observation angles. Thermonuclear fusion occurs when bare nuclei possess sufficient energy to overcome the Coulomb barrier (the potential energy barrier created by electrostatic repulsion). Nuclei that do not overcome the Coulomb barrier can still undergo thermonuclear fusion via tunneling through the barrier. The measured neutron spectra showed that the emitted neutron energies ranged from 20 ± 1.4 kV to 5.4 ± 0.38 MeV for both CD and CD 2 targets. This demonstrates that the 2.45 MeV neutron signal is not the total neutron yield and the thermonuclear fusion is not the only mechanism of the D(d,n) 3 He fusion reaction. Another mechanism of the D(d,n) 3 He reaction is called beam fusion mechanism must be considered. Beam fusion mechanism of the reaction D(d,n)He In a beam fusion reaction, the total kinetic energy and momentum of the interacting nuclei are not zero but have specific values. Neutrons produced by the beam fusion of the D(d,n) 3 He reaction have energies that depend on the kinetic energy of the interacting nuclei and the angle of emission, which in turn depends on the momentum. Therefore, beam fusion is completely different from thermonuclear fusion. The beam fusion of the D(d,n) 3 He reaction produces neutrons with energies higher than 2.45 MeV in the forward directions, as well as other neutrons with energies lower than 2.45 MeV in the reverse directions. The neutron energy E b emitted in the laboratory system as a function of the projectile energy E a and the emission angle θ between projectile and emitted neutron is given as follows 26 : E b ½ = ((m a m b E a ) ½ cosθ ±{m a m b E a cos 2 θ + (m Y + m b )[m Y Q + (m Y – m a )E a ]} ½ )/(m Y + m b ) (2) where m a , m b , and m Y are the masses of projectile, emitted neutron, and residual nucleus respectively. From the above equation, the maximum measured energy of the emitted neutrons is ≈ 5.4 ± 0.38 MeV at an angle of 40 0 relative to laser direction (the same direction of ion acceleration). Then the maximum acceleration energy of D ions is ≈ 3.0 ± 0.21 MeV. In this case, the minimum energy of the produced neutrons by the D(d,n) 3 He reaction is ≈ 1.63 ± 0.11 MeV (Eq. 2). Thus, the neutron spectrum produced by the beam fusion mechanism of the D(d,n) 3 He reaction was in the energy range ≈ 1.63 ± 0.11–5.4 ± 0.38 MeV. It is known that the minimum energy of the D(d,n) 3 He neutrons is 1.63 MeV 27 . Based on the above, the beam fusion mechanism of the D(d,n) 3 He reaction produces neutrons with energies higher than 2.45 MeV up to ≈ 5.4 MeV, and neutrons with energies lower than 2.45 MeV down to ≈ 1.63 MeV. However, the measured neutron spectrum contains neutrons with energies as low as 20 ± 1.4 keV, which is much lower than the minimum energy limit of the D(d,n) 3 He reaction neutrons (1.63 MeV). This emphasizes that other neutron-producing reactions produces lower energy neutrons when PW lasers interact with organic CD or CD 2 targets. Theoretical calculations using Monte Carlo method To elucidate the measured neutron spectra and identify the neutron producing reactions in PW laser interactions with CD and CD 2 targets, numerical experiments were performed using the 3D MCUNED Monte Carlo code. In previous study 28 , we demonstrated that the MCUNED code is the best among the available Monte Carlo codes 29 – 36 that can successfully simulate fusion neutron spectra and is consistent with experimental data. It allows for precise calculations of deceleration, scattering, and interactions of deuterons and light ions inside the high-energy density plasma. Currently, simulating neutron production using Monte Carlo techniques is considered the most efficient method, as errors in Monte Carlo calculations are reduced to almost zero by running a large number of histories (more than 10 9 ) 37 . Monte Carlo computational tools are best suited for simulating neutron spectra resulting from the interactions of a huge number accelerated light ions inside high-energy density plasma. The MCUNED code uses extended modeling by MCNPX 38 , 39 , a software package used to simulate particle interactions involving neutrons, photons, and electrons across a wide range of energy levels. The MCUNED patch for MCNPX 2.7.0 can efficiently calculate deuteron scattering, deceleration, and interactions in ultra-intense laser-plasma interactions. The MCUNED patch for MCNPX 2.7.0 can generally perform these calculations successfully for light nuclei in the energy range from 2 MeV to a few keV 40 . Besides, the best-fit values ​​for the experimental data of the nuclear reaction cross-section are given by the MCUNED code 41 – 44 . In the numerical experiment, a 50:50 fuel mixture of D and C was placed inside a spherical cell with a mass density of ≈ 1.05 g/cm³, which is the average density of polystyrene (CD) targets. For polyethylene (CD2) targets, a 1:2 mixture of C and D, respectively, was used, with a density of ≈ 1.0 g/cm³. The molar mass of polystyrene (CD) target is ≈ 112 g/mol and that of polyethylene (CD 2 ) target is ≈ 32 g/mol. To initiate the D-D reaction, the fuel density ρ and the fuel radius r must follow the relation ρr (areal density) ≥ 0.3 g/cm 2 . This is the minimum value that allows self-heating by alpha particles produced to heat nuclear fuel. In the calculations, the fuel radius is 0.3 cm for both targets. The volume of the source cell, in each case, is determined in cubic centimeters by dividing the mass by the density. The MCUNED code was used to calculate the neutron spectra resulting from the D(d,n) 3 He reaction inside CD or CD 2 targets of limited thickness and emitted at specific angles relative to the laser direction (the same direction as ion acceleration). The best agreement with the experimental results was obtained by assuming that the accelerated ions have an anisotropic Maxwellian energy distribution i.e., ions are accelerated in the direction of the incident laser with a Maxwellian energy distribution. Nuclear reactions occur due to the interaction of accelerated ions at the target surface with background ions within the target. At a given angle θ, the neutron yield Y(θ) is calculated by the formula: Y(θ)= ∫ n 1 n 2 σ(E, θ) υ dt dυ (3) where n 1 and n 2 are the number density of the accelerated and target background ions per unit volume respectively, σ(E, θ) is the reaction differential cross section for an emission angle θ and a given energy E , υ is the velocity of the accelerated ions corresponding to their energy and t is the time step. The 3D Monte Carlo code was run with a sufficiently large sample size to minimize fluctuations in the calculated spectra. Analysis and Discussion To explain why the measured neutron spectrum is so broad, extending from 20 ± 1.4 keV to 5.4 ± 0.38 MeV, an in-depth analysis and comprehensive discussion of the experimental results is presented here. In addition, the measured data were compared with Monte Carlo calculations for the D(d,n) 3 He reaction to determine the range of its neutron spectrum. Figures 3 , 4 show Monte Carlo simulation of the D(d,n) 3 He reaction compared to the experimental results when PW laser irradiated CD and CD 2 targets respectively. The area under the Monte Carlo calculation curve shows that the neutron production by the CD 2 target is twice that of the CD target. The Monte Carlo calculations indicated that the neutron spectrum produced by the D(d,n) 3 He reaction in both cases lies in the same energy range 1.63–5.4 MeV. To elucidate the lower part of the measured neutron spectra, from 20 ± 1.4 keV to 1.63 ± 0.11 MeV, additional neutron-producing interactions must be considered. Deuteron break-up (dissociation) reaction: Deuteron decay is a two-step reaction involving the excitation of the incident deuteron followed by dissociation into a proton and a neutron. This reaction occurs on the Coulomb and/or the nuclear field of target (deuteron or carbon) if the energy of the incident deuteron is equal to or greater than the threshold energy (E th ) 45 . D + D → D + P + n − 2.224 MeV E th = 4.45 MeV D + 12 C → 12 C + P + n − 2.224 MeV E th = 2.60 MeV, The threshold energy of the reaction D(d,np)D is higher than 3.0 MeV (the maximum energy of the accelerated deuterons) and therefore cannot occur. Although the 12 C(d,np) 12 C reaction has a threshold energy (2.60 MeV) slightly below 3.0 MeV, its cross-section and hence its neutron yield are negligible up 3.0 MeV 46 , 47 . However, at higher radiation levels, these interactions must be considered. Deuteron electro-disintegration: Deuteron disintegration can also occur due to interaction with fast electrons that have an energy of 2.224 MeV (deuteron binding energy) or more. e + D → e + p + n – 2.224 MeV E th = 2.224 MeV The cross-section of this reaction is extremely small ~ 10 µb 48 and has negligible effects in neutron production because electrons propagate at large angles outside the target area Photonuclear reactions: The interactions produced by hard bremsstrahlung X-rays and/or gamma rays, resulting from the relativistic stopping force of electrons inside the target, are called photonuclear interactions. The neutrons produced by photonuclear reactions are called photoneutrons, which can be used in diagnostics. Photonuclear reactions can occur inside the target irradiated by ultra-intense laser and with its surroundings. In the experiments, we installed cone-shaped collimators made of lead and plastics inside the laser chamber. Therefore, gamma rays and photoneutrons produced by interactions with the target environment did not contaminate the measured neutron spectra. Thus, in this work, the photonuclear reactions involved in the neutron production process are the reactions that occur inside the target only. For CD or CD 2 targets, the deuteron and carbon photo-dissociation reactions can occur inside the target as: γ + D → P + n – 2.224 MeV E th = 2.224 MeV, γ + 12 C → 11 B + n − 18.7 MeV E th = 18.7 MeV, The threshold energy (E th ) of deuteron photo-dissociation reaction equals the deuteron binding energy, 2.224 MeV 49 . The maximum cross-section value of the reaction is very small ≈ 2.5 mb 49,50 . For the incident photon energy up to 20 MeV, within which nuclei exhibit a giant resonance of photo-neutrons emission, the average cross section of the carbon photo-dissociation reaction is ≈ 5 mb 51 . The importance of photonuclear reactions depends on the stopping power of the accelerated electrons within the target. The bremsstrahlung flux results from the stopping power of the relativistic electrons inside deuterated targets (CD or CD 2 ) is like that produced within a pure carbon target of the same density. In pure carbon target, the bremsstrahlung radiation length is ≈ 43 g/cm 2 , and the relativistic electron stopping power is approximately 2 MeV cm 2 /g 52 . A target with a thickness of 300 micrometers is required to efficiently stop relativistic electrons 53 . Our 100-micrometer-thick target is so thin that it cannot stop relativistic electrons, and therefore the probability of producing bremsstrahlung inside the target is negligible. For such a thin target, deuteron and carbon photodissociation does not contribute to the overall neutron production. Neutron-producing reactions by accelerating ions In addition to the thermonuclear fusion and beam fusion of the D(d,n) 3 He reaction, the accelerated D and C ions have enough energy to produce neutrons due to the stripping reactions 12 C(d,n) 13 N and D( 12 c,n) 13 N . There is also a possibility that the accelerated deuterons will break up (dissociate) on the field of carbon nucleus or another deuteron producing neutrons. Moreover, other neutron producing reactions like photonuclear reactions and deuteron electro-disintegration must be investigated. Accordingly, the neutron-producing reactions involved in the total neutron yield must be identified. Deuteron-Carbon stripping reactions In previous studies 54 – 57 , we have experimentally and theoretically investigated the neutron production process in ultra-intensity laser interactions with planar CD and CD 2 targets. Detailed study of the neutron spectra proved that the reactions 12 C(d,n) 13 N and D( 12 c,n) 13 N between the deuterium and carbon ions participate effectively in the overall neutron production. However, the neutron yield of each reaction was not calculated compared to the D(d,n) 3 He reaction. These reactions are endoergic reactions with threshold energies of 0.33 MeV and 1.96 MeV, respectively. D + 12 C → 13 N + n – 0.28 MeV; E th = 0.33 MeV 12 C + D → 13 N + n – 0.28 MeV; E th = 1.96 MeV The two endoergic reactions D– 12 C and 12 C–D produce neutrons with lower energies than those produced by D–D reactions for the same acceleration energy. As the maximum acceleration energy of D ions is ≈ 3.0 MeV, interactions between D and C ions can produce neutrons with energies up to ≈ 2.6 MeV (Eq. 2). This explains the lower energy part of the measured spectrum. Neutron yield comparison One of the most important factors that the total neutron yield of any reaction depends on is the total reaction cross-section. The total cross section of the D– 12 C reaction is much larger than the cross-section of the D-D reaction. Up to 3.0 MeV (maximum deuteron acceleration energy), the maximum value of the D-D reaction cross-section is ≈ 100.0 mb 58,59 , and that of the D– 12 C reaction is ≈ 225.0 mb 60,61 . The differential cross-sectional data for the D- 12 C reaction are unavailable. Therefore, its neutron spectrum cannot be calculated at the same angle of observation as the measured spectrum. However, we can calculate the total neutron yield of the D– 12 C reaction using its total cross section. Comparing the total neutron yield of the D-D reaction with that of the D- 12 C and 12 C-D reactions can better illustrate the true situation than a partial yield measured at a certain angle. This is because the measured neutron yield at specific observation angles depends on the differential cross-sections, which vary from angle to angle. This does not reflect the true values ​​of the total neutron yields of the different reactions. Now, the question is what about the neutron yield of the 12 C–D reaction? Experimental cross-sectional data of the 12 C–D reaction are not available and hence its total neutron yield cannot be calculated. It is theoretically known that the cross-sections of the D– 12 C and 12 C–D reactions are identical in a center-of-mass system. In the laboratory system, when the ion acceleration is efficient, the cross section of the 12 C–D reaction can be twice that of the D– 12 C reaction 53 . Then, the neutron yield of the 12 C–D reaction can be twice that of the D– 12 C reaction for the same velocity and number density of the D and C ions (Eq. 3). However, in laser interactions with CD or CD 2 targets, the velocity of the accelerated D and C ions is not the same. The ions are accelerated due to front surface acceleration, causing nuclear reactions with the background ions within the target, while canceling out the effect of the target normal sheath acceleration (TNSA) 54 , 55 , 62 . When CD targets irradiated by lasers with intensities ranging from 3.0x10 18 to 1.0x10 19 W/cm 2 (the max. intensity in the experiments), the carbon ions are accelerated to about 60% of the velocity of the D ions due to the front side acceleration 57 . The neutron yield of any reaction depends on the collision frequency or reactivity \(\:⟨\sigma\:v⟩\) . Therefore, the neutron yields of the D– 12 C and 12 C–D reactions are almost the same because the collision frequency is approximately the same for the two reactions. The deuterated polystyrene (CD) target has the same number density of deuterium and carbon atoms per cubic centimeter (i.e., a 50%-50% mixture of deuterium and carbon atoms). In Eq. (3), replacing the differential cross-section with the total cross-section, and using n 1 = n 2 = ½ n , where n is the number density of the target, the total neutron yield of the D-D reaction can be calculated. For the D– 12 C reaction, the total neutron yield is given by applying the original equation (Eq. 3) because the number density of deuterium equals the number density of carbon in the CD target. The polyethylene target (CD 2 ) contains twice the concentration of D atoms as C atoms and hence n 1 is twice n 2 . Figures 5 , 6 illustrate the Monte Carlo calculations for neutron yield of the D-D reaction compared to the calculated total neutron yield of both D– 12 C and 12 C–D reactions (have equal neutron yield) up to an energy of 3.0 MeV for irradiated CD and CD 2 targets by PW laser respectively. The D– 12 C and 12 C–D reactions are involved in the neutron production process when the deuteron acceleration energy reaches its threshold energies, 0.33 MeV and 1.96 MeV respectively. By calculating the area under the curve for each reaction in figures (5,6), the neutron yield of the different reactions can be calculated. The calculations show that the total neutron yield of the D- 12 C and 12 C-D reactions is approximately twice the neutron yield of the D-D reaction in the case of the CD 2 target and four times the neutron yield of the D-D reaction in the case of the CD target. There are some reasons to explain these results. 1- For both targets, the cross sections of ​​the D– 12 C and 12 C–D reactions are much larger than that of the D–D reaction, and this is of great importance in determining the contribution of each reaction to the total neutron production. 2- The D-D fusion reaction has two paths with equal probability: D(d,n) 3 He and D(d,p)T . The second path produces protons and does not take part in neutron production. Therefore, the number of neutrons is only 50% of the D-D reaction rate. On the other hand, the neutron yields produced by the D– 12 C and 12 C–D reactions are the same as the reaction rates. 3- For the CD target, the D-D reaction occurs due to D-ion interactions only (50% of the total number of ions), but the D- 12 C and 12 C-D reactions occur due to interactions of all D and C ions (a 50%-50% mixture for the CD target). Therefore, the probability of the D- 12 C and 12 C-D reactions (due to the interactions between D and C ions) is twice the probability of the D-D reaction (due to the interactions of D ions only). Toupin et. a l., predicted, using kinetic numerical simulations, that at high irradiances of CD 2 targets by ultra-intense lasers, the total neutron yield of the D- 12 C and 12 C-D reactions can almost double the neutron yield of the D-D reaction 53 . This is even though the number density of C atoms is only 50% of the number density of D atoms in the CD 2 target. In the case of CD target, the number density of C and D ions is the same, and compared to the CD 2 target, this will double the ratio of the total neutron yield of D– 12 C and 12 C–D reactions to that of D-D reaction to be four times. This confirms the strong contribution of the two reactions D– 12 C and 12 C–D to the total neutron yield considering that they are endoergic reactions, and contribute to neutron production after the accelerated ions reach their threshold energies. Conclusion In this work the reaction mechanisms and neutron yields of D-D fusion reaction and its associated neutron-producing reactions when PW laser irradiated CD and CD 2 targets were studied in detail. Experimental data were compared to Monte Carlo simulation. The measured and calculated neutron spectra demonstrated that the D-D reaction produces neutrons via both thermonuclear fusion and beam fusion, but it is not the only neutron source. The D- 12 C and 12 C-D stripping reactions, between accelerated ions on the target surface and target background ions, have a much higher neutron production compared to the D-D reaction. Besides, neutron production due to photonuclear reactions, deuteron break up, and deuteron electro-dissociation must be considered. Although their neutron production is negligible under our irradiation conditions, it should be considered under higher irradiation conditions. Not as previously considered, all these reactions can contribute to the neutron production process not only thermonuclear and beam fusion of the D-D reaction with background of photoneutrons. Declarations Acknowledgments The authors are very grateful to the members of the Laser, Target, and measurement Tech. in ILE, Osaka, Japan. Authors Contribution declaration The authors hereby declare that this work has been carried out only by them. A. Youssef prepared all sections of the manuscript. R. Kodama revised the manuscript. Competing interests The author(s) declare no competing interests. Funding declaration The Authors didn’t receive any funds for this work. Data availability statement All data generated or analysed during this study are included in this published article. References Gray, L. & Read, J. Treatment of cancer by fast neutrons. Nature 152 (3a0), 53–54. https://doi.org/10.1038/15205 (1943). Takenaka, N., Asano, H., Fujii, T., Mizubata, M. & Yoshii, K. Application of fast neutron radiography to three-dimensional visualization of steady two-phase flow in a rod bundle. Nucl Instrum. Methods Phys. Res. A . 424 (98), 73–76. https://doi.org/10.1016/S0168- (1999). Mor, I. et al. Reconstruction of material elemental composition using fast neutron resonance radiography. Phys. Proc. 69, 304–313. 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1","display":"","copyAsset":false,"role":"figure","size":13781,"visible":true,"origin":"","legend":"\u003cp\u003eNeutron spectrum measured when a 100-micro-thick CD target was irradiated by the PW laser.\u003c/p\u003e","description":"","filename":"image1.png","url":"https://assets-eu.researchsquare.com/files/rs-8108674/v1/7150085c9d631dbfe46f72e5.png"},{"id":96336561,"identity":"e37cfb1f-4f55-45ac-bcdf-5df42a36f9de","added_by":"auto","created_at":"2025-11-20 03:11:41","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":15121,"visible":true,"origin":"","legend":"\u003cp\u003eNeutron spectrum measured when a 100-micro-thick CD\u003csub\u003e2\u003c/sub\u003e target was irradiated by the PW laser. Neutron yield is twice that of the CD target.\u003c/p\u003e","description":"","filename":"image2.png","url":"https://assets-eu.researchsquare.com/files/rs-8108674/v1/8e3104a2829c01d05d849982.png"},{"id":96366370,"identity":"3102fe4e-7bef-434c-9514-a1341051076f","added_by":"auto","created_at":"2025-11-20 10:11:24","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":16905,"visible":true,"origin":"","legend":"\u003cp\u003eNeutron spectrum of the \u003cem\u003eD(d,n)\u003c/em\u003e\u003csup\u003e\u003cem\u003e3\u003c/em\u003e\u003c/sup\u003e\u003cem\u003eHe\u003c/em\u003e reaction calculated by 3D Monte Carlo code (dashed line) compared to that measured one when CD targets were irradiated by PW laser (solid line).\u003c/p\u003e","description":"","filename":"image3.png","url":"https://assets-eu.researchsquare.com/files/rs-8108674/v1/7a0c521d794d377ed5a0c490.png"},{"id":96336564,"identity":"e8f16684-1d9e-4b4d-a71a-02508eef2604","added_by":"auto","created_at":"2025-11-20 03:11:41","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":16848,"visible":true,"origin":"","legend":"\u003cp\u003eMeasured neutron spectrum when CD\u003csub\u003e2\u003c/sub\u003e targets were irradiated by PW laser (solid line) compared to that calculated by 3D Monte Carlo code (dashed line).\u003c/p\u003e","description":"","filename":"image4.png","url":"https://assets-eu.researchsquare.com/files/rs-8108674/v1/25dc365a3bc1b08d8b006771.png"},{"id":96336563,"identity":"bddbfd44-3aab-47dc-b9f1-7c17c722cce9","added_by":"auto","created_at":"2025-11-20 03:11:41","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":11541,"visible":true,"origin":"","legend":"\u003cp\u003eTotal neutron yield of the D–\u003csup\u003e12\u003c/sup\u003eC\u003cem\u003e \u003c/em\u003eand \u003csup\u003e12\u003c/sup\u003eC–D reactions (dashed line) compared to that of the D–D reaction (solid line) for deuteron energy up to 3.0 MeV when CD target was irradiated by PW laser.\u003c/p\u003e","description":"","filename":"image5.png","url":"https://assets-eu.researchsquare.com/files/rs-8108674/v1/6752cce78f5a5f57e5f1e3e2.png"},{"id":96365405,"identity":"3e18dc02-a025-4777-97fe-cffa0363dba1","added_by":"auto","created_at":"2025-11-20 10:10:20","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":12045,"visible":true,"origin":"","legend":"\u003cp\u003eTotal neutron yield of the D–12C and 12C–D reactions (dashed line) compared to that of the D–D reaction (solid line) for deuteron energy up to 3.0 MeV when CD target was irradiated by PW laser.\u003c/p\u003e","description":"","filename":"image6.png","url":"https://assets-eu.researchsquare.com/files/rs-8108674/v1/eea8586f00071e64b489f1c0.png"},{"id":109760973,"identity":"eae858a7-515b-4eea-9475-99b6e4a68d95","added_by":"auto","created_at":"2026-05-22 07:29:21","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":477996,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8108674/v1/03666dcb-02c5-49b5-8f10-7b6bc31540a2.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Mechanisms of D-D fusion and associated neutron-producing reactions in PW laser interactions with carbon-deuterated targets","fulltext":[{"header":"Introduction","content":"\u003cp\u003eNeutrons have the unique ability to play a vital role in science, technology, and medicine as they are unique tools for investigating or modifying the structure and properties of materials. Their distinctive properties such as deep penetration, non-destructive interaction with matter, and sensitivity to light elements make them ideal for a wide range of applications extend to many fields including medical sciences\u003csup\u003e\u003cb\u003e\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u003c/b\u003e\u003c/sup\u003e, material science\u003csup\u003e\u003cb\u003e\u003cspan additionalcitationids=\"CR3\" citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e\u003c/b\u003e\u003c/sup\u003e, biology\u003csup\u003e\u003cb\u003e\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e\u003c/b\u003e\u003c/sup\u003e, laboratory astrophysics\u003csup\u003e\u003cb\u003e\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e\u003c/b\u003e\u003c/sup\u003e, transmutation of nuclear waste \u003csup\u003e\u003cb\u003e\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e\u003c/b\u003e\u003c/sup\u003e, archaeology\u003csup\u003e\u003cb\u003e\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e,\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e\u003c/b\u003e\u003c/sup\u003e, security\u003csup\u003e\u003cb\u003e\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e,\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e\u003c/b\u003e\u003c/sup\u003e, neutron imaging\u003csup\u003e\u003cb\u003e\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e\u003c/b\u003e\u003c/sup\u003e, nuclear transmutation\u003csup\u003e\u003cb\u003e\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e\u003c/b\u003e\u003c/sup\u003e, and boron neutron capture therapy for the treatment of tumors\u003csup\u003e\u003cb\u003e\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e\u003c/b\u003e\u003c/sup\u003e.\u003c/p\u003e\u003cp\u003eLaser-generated neutrons have attracted the attention of many recent studies\u003csup\u003e\u003cb\u003e\u003cspan additionalcitationids=\"CR16 CR17 CR18\" citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e\u003c/b\u003e\u003c/sup\u003e. These studies focused on the theoretical investigation of neutron production via the thermonuclear mechanism and the nuclear reactions caused by accelerated ions when petawatt (PW) class lasers irradiate carbon-deuterated targets. P. Martin \u003cem\u003eet al.\u003c/em\u003e\u003csup\u003e\u003cb\u003e15\u003c/b\u003e\u003c/sup\u003e suggested that, through 2-D particle-in-cell simulations, neutrons are seen to be produced by hole-boring (HB) mechanism inside the target bulk and target normal sheath acceleration (TNSA) mechanism on the rear surface of the target. Furthermore, neutrons produced due to the shock-like features within the bulk target plasma by the rapid expansion of contaminant species from the front and back surfaces of the target. When using carbon-deuterated targets like CD\u003csub\u003e2\u003c/sub\u003e and CD, the previous studies have considered the neutron source to be only the D-D fusion reaction.\u003c/p\u003e\u003cp\u003eIn this work, using in-depth analysis of experimental data for the interaction of PW lasers with CD and CD\u003csub\u003e2\u003c/sub\u003e targets and simulations using MCUNED 3D Monte Carlo code, it was demonstrated that the produced neutrons are due to the acceleration of ions at the target surface only. The accelerated ions then produce nuclear reactions as they pass through the target. The \u003cem\u003eD(d,n)\u003c/em\u003e\u003csup\u003e\u003cem\u003e3\u003c/em\u003e\u003c/sup\u003e\u003cem\u003eHe\u003c/em\u003e fusion reaction and other associated neutron-producing reactions contribute to the overall process of neutron production. Therefore, identifying the reactions and their mechanisms is crucial in determining the relative contribution of each reaction to the total neutron yield.\u003c/p\u003e\u003cp\u003eThe following sections of this paper were arranged as follows: The experimental work was explained in Section 2. The experimental results were presented in Section 3. Details of the Monte Carlo simulation were given in section 4. Analysis and discussion were provided in Section 5. Finally, the conclusion was given in Section 6.\u003c/p\u003e"},{"header":"Experimental work","content":"\u003cp\u003eThe experiments were carried out at the Laser Engineering Institute (ILE), Osaka University, using 100-micrometer-thick CD and CD\u003csub\u003e2\u003c/sub\u003e targets. The targets were irradiated with a PW laser to study the \u003cem\u003eD(d,n)\u003c/em\u003e\u003csup\u003e\u003cem\u003e3\u003c/em\u003e\u003c/sup\u003e\u003cem\u003eHe\u003c/em\u003e fusion reaction, its associated neutron-producing reactions, and neutron production mechanisms. The PW laser produces a linearly polarized laser pulse with energies up to 500 J and a duration of 0.5–1 picosecond at a wavelength of 1.053 µm. In the experiment, peak intensity at the target is ≈ 1x10\u003csup\u003e19\u003c/sup\u003e W/cm\u003csup\u003e2\u003c/sup\u003e.\u003c/p\u003e\u003cp\u003eUltra-intense laser interactions with CD and CD\u003csub\u003e2\u003c/sub\u003e targets can produce significantly higher neutrons compared to other targets such as metallic (Al and Au) and inorganic targets (LiF) because the accelerated ions originate from the target's structure itself. Therefore, intensities and current densities of the driven neutron beams can be much higher than other targets under the same radiation conditions \u003csup\u003e\u003cb\u003e\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e,\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e\u003c/b\u003e\u003c/sup\u003e.\u003c/p\u003e\u003cp\u003eTo detect the produced neutron spectra, neutron diagnostics consisted of current mode time-of-flight (TOF) neutron detectors were used. The detectors comprise a combination of the quenched version of the Bicron BC-422 ultra-fast timing plastic scintillator/Hamamatsu R2083 photomultiplier tube (PMT) placed at varying distances from the target. Three neutron detectors were placed at an angle of 40° to the direction of the PW laser beam. To prevent background gamma rays and photoneutrons (resulting from interactions with the target's surroundings) from affecting the measured neutron spectra, cone-shaped collimators made of lead and plastics were installed in the laser chamber.\u003c/p\u003e\u003cp\u003eThe detectors were shielded by 10 cm thick lead block at the front and another 5 cm thick lead block on all sides. Neutron spectra modification due to shielding has been considered\u003csup\u003e\u003cb\u003e\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e\u003c/b\u003e\u003c/sup\u003e, and the TOF values were corrected by accounting for neutron delays within lead blocks. The measured neutron signals were normalized to be the number of neutrons/MeV Sr (solid angle), taking into account the detector position and sensitivity\u003csup\u003e\u003cb\u003e\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e\u003c/b\u003e\u003c/sup\u003e. The accuracy of each energy value was calculated using the differentiation method\u003csup\u003e\u003cb\u003e\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e\u003c/b\u003e\u003c/sup\u003e. The error in neutron energy ΔE is calculated using partial differentiation based on experimental errors in both TOF (ΔT) and the detector distance from the target (ΔX) as follows:\u003c/p\u003e\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e\u003cp\u003e(ΔE)\u003csup\u003e2\u003c/sup\u003e = (∂E/∂T)\u003csup\u003e2\u003c/sup\u003e (ΔT)\u003csup\u003e2\u003c/sup\u003e + (∂E/∂X)\u003csup\u003e2\u003c/sup\u003e (ΔX)\u003csup\u003e2\u003c/sup\u003e (1)\u003c/p\u003e\u003cdiv id=\"Sec4\" class=\"Section3\"\u003e\u003cp\u003e\u003c/p\u003e\u003c/div\u003e\u003c/div\u003e"},{"header":"Experimental Results","content":"\u003cp\u003eFigures \u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e,\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e show neutron spectra measured when 100-micro-thick CD and CD\u003csub\u003e2\u003c/sub\u003e targets were irradiated by the PW laser respectively. The area under the curve in both figures shows that the neutron production from CD\u003csub\u003e2\u003c/sub\u003e target is twice that of CD target under the same radiation conditions. This is because the deuterium concentration in CD\u003csub\u003e2\u003c/sub\u003e target is twice that of CD target (detailed explanation was given in the discussion). In both cases, the peak of 2.45 MeV neutrons was measured within the experimental error at 2.44 ± 0.17 MeV. The error in the measured value is due to the detector resolution and the error in TOF measurement (Eq.\u0026nbsp;1). The emission of 2.45 MeV neutrons means that thermonuclear fusion occurs in the high-energy density plasma produced by PW laser interactions with the deuterated targets.\u003c/p\u003e\n\u003ch3\u003eThermonuclear fusion of the reaction D(d,n)He\u003c/h3\u003e\n\u003cp\u003eThe \u003cem\u003eD(d,n)\u003c/em\u003e\u003csup\u003e\u003cem\u003e3\u003c/em\u003e\u003c/sup\u003e\u003cem\u003eHe\u003c/em\u003e fusion reaction between two deuterons (naked deuterium nuclei) is written as follows\u003csup\u003e\u003cb\u003e\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e\u003c/b\u003e\u003c/sup\u003e:\u003c/p\u003e\u003cp\u003eD\u0026thinsp;+\u0026thinsp;D \u0026rarr; \u003csup\u003e3\u003c/sup\u003eHe + n + 3.27 MeV\u003c/p\u003e\u003cp\u003eThe D-D reaction, which has a positive Q value (3.27 MeV), occurs even if the total kinetic energy, and therefore the total momentum, of the interacting deuterons is zero at the time of the reaction (thermonuclear fusion). In this case, only 2.45 MeV neutrons are emitted because the Q-value of the reaction is distributed between the two products (\u003csup\u003e3\u003c/sup\u003eHe and n) inversely with their masses. Therefore, the thermonuclear fusion reaction \u003cem\u003eD(d,n)\u003c/em\u003e\u003csup\u003e\u003cem\u003e3\u003c/em\u003e\u003c/sup\u003e\u003cem\u003eHe\u003c/em\u003e can be written as follows:\u003c/p\u003e\u003cp\u003eD\u0026thinsp;+\u0026thinsp;D \u0026rarr; \u003csup\u003e3\u003c/sup\u003eHe (0.82 MeV)\u0026thinsp;+\u0026thinsp;n (2.45 MeV)\u003c/p\u003e\u003cp\u003eAccording to the law of momentum conservation, since the total momentum of the two interacting deuterons at the time of the reaction is zero, the 2.45 MeV neutrons are emitted in all directions. The produced nucleus \u003csup\u003e\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e\u003c/sup\u003eHe recoils in the opposite direction to keep the final momentum at zero. Therefore, thermonuclear fusion mechanism of the \u003cem\u003eD(d,n)\u003c/em\u003e\u003csup\u003e\u003cem\u003e3\u003c/em\u003e\u003c/sup\u003e\u003cem\u003eHe\u003c/em\u003e fusion reaction produce only 2.45 MeV neutrons which are isotropic and can be detected at all observation angles. Thermonuclear fusion occurs when bare nuclei possess sufficient energy to overcome the Coulomb barrier (the potential energy barrier created by electrostatic repulsion). Nuclei that do not overcome the Coulomb barrier can still undergo thermonuclear fusion via tunneling through the barrier.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eThe measured neutron spectra showed that the emitted neutron energies ranged from 20\u0026thinsp;\u0026plusmn;\u0026thinsp;1.4 kV to 5.4\u0026thinsp;\u0026plusmn;\u0026thinsp;0.38 MeV for both CD and CD\u003csub\u003e2\u003c/sub\u003e targets. This demonstrates that the 2.45 MeV neutron signal is not the total neutron yield and the thermonuclear fusion is not the only mechanism of the \u003cem\u003eD(d,n)\u003c/em\u003e\u003csup\u003e\u003cem\u003e3\u003c/em\u003e\u003c/sup\u003e\u003cem\u003eHe\u003c/em\u003e fusion reaction. Another mechanism of the \u003cem\u003eD(d,n)\u003c/em\u003e\u003csup\u003e\u003cem\u003e3\u003c/em\u003e\u003c/sup\u003e\u003cem\u003eHe\u003c/em\u003e reaction is called beam fusion mechanism must be considered.\u003c/p\u003e\n\u003ch3\u003eBeam fusion mechanism of the reaction D(d,n)He\u003c/h3\u003e\n\u003cp\u003eIn a beam fusion reaction, the total kinetic energy and momentum of the interacting nuclei are not zero but have specific values. Neutrons produced by the beam fusion of the \u003cem\u003eD(d,n)\u003c/em\u003e\u003csup\u003e\u003cem\u003e3\u003c/em\u003e\u003c/sup\u003e\u003cem\u003eHe\u003c/em\u003e reaction have energies that depend on the kinetic energy of the interacting nuclei and the angle of emission, which in turn depends on the momentum. Therefore, beam fusion is completely different from thermonuclear fusion. The beam fusion of the \u003cem\u003eD(d,n)\u003c/em\u003e\u003csup\u003e\u003cem\u003e3\u003c/em\u003e\u003c/sup\u003e\u003cem\u003eHe\u003c/em\u003e reaction produces neutrons with energies higher than 2.45 MeV in the forward directions, as well as other neutrons with energies lower than 2.45 MeV in the reverse directions.\u003c/p\u003e\u003cp\u003eThe neutron energy \u003cem\u003eE\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u003c/sub\u003e emitted in the laboratory system as a function of the projectile energy \u003cem\u003eE\u003c/em\u003e\u003csub\u003e\u003cem\u003ea\u003c/em\u003e\u003c/sub\u003e and the emission angle \u003cem\u003eθ\u003c/em\u003e between projectile and emitted neutron is given as follows\u003csup\u003e\u003cb\u003e\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e\u003c/b\u003e\u003c/sup\u003e:\u003c/p\u003e\u003cp\u003e\u003cem\u003eE\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u003c/sub\u003e\u003csup\u003e\u003cem\u003e\u0026frac12;\u003c/em\u003e\u003c/sup\u003e \u003cem\u003e= ((m\u003c/em\u003e\u003csub\u003e\u003cem\u003ea\u003c/em\u003e\u003c/sub\u003e \u003cem\u003em\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u003c/sub\u003e \u003cem\u003eE\u003c/em\u003e\u003csub\u003e\u003cem\u003ea\u003c/em\u003e\u003c/sub\u003e \u003cem\u003e)\u003c/em\u003e\u003csup\u003e\u003cem\u003e\u0026frac12;\u003c/em\u003e\u003c/sup\u003e \u003cem\u003ecosθ \u0026plusmn;{m\u003c/em\u003e\u003csub\u003e\u003cem\u003ea\u003c/em\u003e\u003c/sub\u003e \u003cem\u003em\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u003c/sub\u003e \u003cem\u003eE\u003c/em\u003e\u003csub\u003e\u003cem\u003ea\u003c/em\u003e\u003c/sub\u003e \u003cem\u003ecos\u003c/em\u003e\u003csup\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sup\u003e\u003cem\u003eθ + (m\u003c/em\u003e\u003csub\u003e\u003cem\u003eY\u003c/em\u003e\u003c/sub\u003e \u003cem\u003e+ m\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e)[m\u003c/em\u003e\u003csub\u003e\u003cem\u003eY\u003c/em\u003e\u003c/sub\u003e \u003cem\u003eQ + (m\u003c/em\u003e\u003csub\u003e\u003cem\u003eY\u003c/em\u003e\u003c/sub\u003e \u003cem\u003e\u0026ndash; m\u003c/em\u003e\u003csub\u003e\u003cem\u003ea\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e)E\u003c/em\u003e\u003csub\u003e\u003cem\u003ea\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e]}\u003c/em\u003e\u003csup\u003e\u003cem\u003e\u0026frac12;\u003c/em\u003e\u003c/sup\u003e \u003cem\u003e)/(m\u003c/em\u003e\u003csub\u003e\u003cem\u003eY\u003c/em\u003e\u003c/sub\u003e \u003cem\u003e+ m\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e)\u003c/em\u003e (2)\u003c/p\u003e\u003cp\u003ewhere \u003cem\u003em\u003c/em\u003e\u003csub\u003e\u003cem\u003ea\u003c/em\u003e,\u003c/sub\u003e \u003cem\u003em\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e,\u003c/sub\u003e and \u003cem\u003em\u003c/em\u003e\u003csub\u003e\u003cem\u003eY\u003c/em\u003e\u003c/sub\u003e are the masses of projectile, emitted neutron, and residual nucleus respectively. From the above equation, the maximum measured energy of the emitted neutrons is \u0026asymp;\u0026thinsp;5.4\u0026thinsp;\u0026plusmn;\u0026thinsp;0.38 MeV at an angle of 40\u003csup\u003e0\u003c/sup\u003e relative to laser direction (the same direction of ion acceleration). Then the maximum acceleration energy of D ions is \u0026asymp;\u0026thinsp;3.0\u0026thinsp;\u0026plusmn;\u0026thinsp;0.21 MeV. In this case, the minimum energy of the produced neutrons by the \u003cem\u003eD(d,n)\u003c/em\u003e\u003csup\u003e\u003cem\u003e3\u003c/em\u003e\u003c/sup\u003e\u003cem\u003eHe\u003c/em\u003e reaction is \u0026asymp;\u0026thinsp;1.63\u0026thinsp;\u0026plusmn;\u0026thinsp;0.11 MeV (Eq.\u0026nbsp;2). Thus, the neutron spectrum produced by the beam fusion mechanism of the \u003cem\u003eD(d,n)\u003c/em\u003e\u003csup\u003e\u003cem\u003e3\u003c/em\u003e\u003c/sup\u003e\u003cem\u003eHe\u003c/em\u003e reaction was in the energy range\u0026thinsp;\u0026asymp;\u0026thinsp;1.63\u0026thinsp;\u0026plusmn;\u0026thinsp;0.11\u0026ndash;5.4\u0026thinsp;\u0026plusmn;\u0026thinsp;0.38 MeV. It is known that the minimum energy of the \u003cem\u003eD(d,n)\u003c/em\u003e\u003csup\u003e\u003cem\u003e3\u003c/em\u003e\u003c/sup\u003e\u003cem\u003eHe\u003c/em\u003e neutrons is 1.63 MeV\u003csup\u003e\u003cb\u003e\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e\u003c/b\u003e\u003c/sup\u003e.\u003c/p\u003e\u003cp\u003eBased on the above, the beam fusion mechanism of the \u003cem\u003eD(d,n)\u003c/em\u003e\u003csup\u003e\u003cem\u003e3\u003c/em\u003e\u003c/sup\u003e\u003cem\u003eHe\u003c/em\u003e reaction produces neutrons with energies higher than 2.45 MeV up to \u0026asymp;\u0026thinsp;5.4 MeV, and neutrons with energies lower than 2.45 MeV down to \u0026asymp;\u0026thinsp;1.63 MeV. However, the measured neutron spectrum contains neutrons with energies as low as 20\u0026thinsp;\u0026plusmn;\u0026thinsp;1.4 keV, which is much lower than the minimum energy limit of the \u003cem\u003eD(d,n)\u003c/em\u003e\u003csup\u003e\u003cem\u003e3\u003c/em\u003e\u003c/sup\u003e\u003cem\u003eHe\u003c/em\u003e reaction neutrons (1.63 MeV). This emphasizes that other neutron-producing reactions produces lower energy neutrons when PW lasers interact with organic CD or CD\u003csub\u003e2\u003c/sub\u003e targets.\u003c/p\u003e\n\u003ch3\u003eTheoretical calculations using Monte Carlo method\u003c/h3\u003e\n\u003cp\u003eTo elucidate the measured neutron spectra and identify the neutron producing reactions in PW laser interactions with CD and CD\u003csub\u003e2\u003c/sub\u003e targets, numerical experiments were performed using the 3D MCUNED Monte Carlo code. In previous study\u003csup\u003e\u003cb\u003e\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e\u003c/b\u003e\u003c/sup\u003e, we demonstrated that the MCUNED code is the best among the available Monte Carlo codes\u003csup\u003e\u003cb\u003e\u003cspan additionalcitationids=\"CR30 CR31 CR32 CR33 CR34 CR35\" citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e\u003c/b\u003e\u003c/sup\u003e that can successfully simulate fusion neutron spectra and is consistent with experimental data. It allows for precise calculations of deceleration, scattering, and interactions of deuterons and light ions inside the high-energy density plasma. Currently, simulating neutron production using Monte Carlo techniques is considered the most efficient method, as errors in Monte Carlo calculations are reduced to almost zero by running a large number of histories (more than 10\u003csup\u003e9\u003c/sup\u003e)\u003csup\u003e\u003cb\u003e\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e\u003c/b\u003e\u003c/sup\u003e.\u003c/p\u003e\u003cp\u003eMonte Carlo computational tools are best suited for simulating neutron spectra resulting from the interactions of a huge number accelerated light ions inside high-energy density plasma. The MCUNED code uses extended modeling by MCNPX\u003csup\u003e\u003cb\u003e\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e,\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e\u003c/b\u003e\u003c/sup\u003e, a software package used to simulate particle interactions involving neutrons, photons, and electrons across a wide range of energy levels. The MCUNED patch for MCNPX 2.7.0 can efficiently calculate deuteron scattering, deceleration, and interactions in ultra-intense laser-plasma interactions. The MCUNED patch for MCNPX 2.7.0 can generally perform these calculations successfully for light nuclei in the energy range from 2 MeV to a few keV\u003csup\u003e\u003cb\u003e\u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e40\u003c/span\u003e\u003c/b\u003e\u003c/sup\u003e. Besides, the best-fit values ​​for the experimental data of the nuclear reaction cross-section are given by the MCUNED code\u003csup\u003e\u003cb\u003e\u003cspan additionalcitationids=\"CR42 CR43\" citationid=\"CR41\" class=\"CitationRef\"\u003e41\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e44\u003c/span\u003e\u003c/b\u003e\u003c/sup\u003e.\u003c/p\u003e\u003cp\u003eIn the numerical experiment, a 50:50 fuel mixture of D and C was placed inside a spherical cell with a mass density of \u0026asymp;\u0026thinsp;1.05 g/cm\u0026sup3;, which is the average density of polystyrene (CD) targets. For polyethylene (CD2) targets, a 1:2 mixture of C and D, respectively, was used, with a density of \u0026asymp;\u0026thinsp;1.0 g/cm\u0026sup3;. The molar mass of polystyrene (CD) target is \u0026asymp;\u0026thinsp;112 g/mol and that of polyethylene (CD\u003csub\u003e2\u003c/sub\u003e) target is \u0026asymp;\u0026thinsp;32 g/mol. To initiate the D-D reaction, the fuel density ρ and the fuel radius \u003cem\u003er\u003c/em\u003e must follow the relation \u003cem\u003eρr\u003c/em\u003e (areal density)\u0026thinsp;\u0026ge;\u0026thinsp;0.3 g/cm\u003csup\u003e2\u003c/sup\u003e. This is the minimum value that allows self-heating by alpha particles produced to heat nuclear fuel. In the calculations, the fuel radius is 0.3 cm for both targets. The volume of the source cell, in each case, is determined in cubic centimeters by dividing the mass by the density.\u003c/p\u003e\u003cp\u003eThe MCUNED code was used to calculate the neutron spectra resulting from the \u003cem\u003eD(d,n)\u003c/em\u003e\u003csup\u003e\u003cem\u003e3\u003c/em\u003e\u003c/sup\u003e\u003cem\u003eHe\u003c/em\u003e reaction inside CD or CD\u003csub\u003e2\u003c/sub\u003e targets of limited thickness and emitted at specific angles relative to the laser direction (the same direction as ion acceleration). The best agreement with the experimental results was obtained by assuming that the accelerated ions have an anisotropic Maxwellian energy distribution i.e., ions are accelerated in the direction of the incident laser with a Maxwellian energy distribution. Nuclear reactions occur due to the interaction of accelerated ions at the target surface with background ions within the target.\u003c/p\u003e\u003cp\u003eAt a given angle θ, the neutron yield Y(θ) is calculated by the formula:\u003c/p\u003e\u003cdiv id=\"Sec8\" class=\"Section2\"\u003e\u003cp\u003eY(θ)= \u0026int; n\u003csub\u003e1\u003c/sub\u003e n\u003csub\u003e2\u003c/sub\u003e σ(E, θ) υ dt dυ (3)\u003c/p\u003e\u003cp\u003ewhere \u003cem\u003en\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e and \u003cem\u003en\u003c/em\u003e\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003e are the number density of the accelerated and target background ions per unit volume respectively, \u003cem\u003eσ(E, θ)\u003c/em\u003e is the reaction differential cross section for an emission angle \u003cem\u003eθ\u003c/em\u003e and a given energy \u003cem\u003eE\u003c/em\u003e, \u003cem\u003eυ\u003c/em\u003e is the velocity of the accelerated ions corresponding to their energy and \u003cem\u003et\u003c/em\u003e is the time step. The 3D Monte Carlo code was run with a sufficiently large sample size to minimize fluctuations in the calculated spectra.\u003c/p\u003e\u003c/div\u003e"},{"header":"Analysis and Discussion","content":"\u003cp\u003eTo explain why the measured neutron spectrum is so broad, extending from 20\u0026thinsp;\u0026plusmn;\u0026thinsp;1.4 keV to 5.4\u0026thinsp;\u0026plusmn;\u0026thinsp;0.38 MeV, an in-depth analysis and comprehensive discussion of the experimental results is presented here. In addition, the measured data were compared with Monte Carlo calculations for the \u003cem\u003eD(d,n)\u003c/em\u003e\u003csup\u003e\u003cem\u003e3\u003c/em\u003e\u003c/sup\u003e\u003cem\u003eHe\u003c/em\u003e reaction to determine the range of its neutron spectrum.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eFigures \u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e,\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e show Monte Carlo simulation of the \u003cem\u003eD(d,n)\u003c/em\u003e\u003csup\u003e\u003cem\u003e3\u003c/em\u003e\u003c/sup\u003e\u003cem\u003eHe\u003c/em\u003e reaction compared to the experimental results when PW laser irradiated CD and CD\u003csub\u003e2\u003c/sub\u003e targets respectively. The area under the Monte Carlo calculation curve shows that the neutron production by the CD\u003csub\u003e2\u003c/sub\u003e target is twice that of the CD target. The Monte Carlo calculations indicated that the neutron spectrum produced by the \u003cem\u003eD(d,n)\u003c/em\u003e\u003csup\u003e\u003cem\u003e3\u003c/em\u003e\u003c/sup\u003e\u003cem\u003eHe\u003c/em\u003e reaction in both cases lies in the same energy range 1.63\u0026ndash;5.4 MeV. To elucidate the lower part of the measured neutron spectra, from 20\u0026thinsp;\u0026plusmn;\u0026thinsp;1.4 keV to 1.63\u0026thinsp;\u0026plusmn;\u0026thinsp;0.11 MeV, additional neutron-producing interactions must be considered.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\n\u003ch3\u003eDeuteron break-up (dissociation) reaction:\u003c/h3\u003e\n\u003cp\u003eDeuteron decay is a two-step reaction involving the excitation of the incident deuteron followed by dissociation into a proton and a neutron. This reaction occurs on the Coulomb and/or the nuclear field of target (deuteron or carbon) if the energy of the incident deuteron is equal to or greater than the threshold energy (E\u003csub\u003eth\u003c/sub\u003e)\u003csup\u003e\u003cb\u003e\u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e45\u003c/span\u003e\u003c/b\u003e\u003c/sup\u003e.\u003c/p\u003e\u003cp\u003eD\u0026thinsp;+\u0026thinsp;D \u0026rarr; D\u0026thinsp;+\u0026thinsp;P\u0026thinsp;+\u0026thinsp;n \u0026minus;\u0026thinsp;2.224 MeV E\u003csub\u003eth\u003c/sub\u003e = 4.45 MeV\u003c/p\u003e\u003cp\u003eD\u0026thinsp;+\u0026thinsp;\u003csup\u003e12\u003c/sup\u003eC \u0026rarr; \u003csup\u003e12\u003c/sup\u003eC + P + n \u0026minus;\u0026thinsp;2.224 MeV E\u003csub\u003eth\u003c/sub\u003e = 2.60 MeV,\u003c/p\u003e\u003cp\u003eThe threshold energy of the reaction \u003cem\u003eD(d,np)D\u003c/em\u003e is higher than 3.0 MeV (the maximum energy of the accelerated deuterons) and therefore cannot occur. Although the \u003csup\u003e\u003cem\u003e\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e\u003c/em\u003e\u003c/sup\u003e\u003cem\u003eC(d,np)\u003c/em\u003e\u003csup\u003e\u003cem\u003e\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e\u003c/em\u003e\u003c/sup\u003e\u003cem\u003eC\u003c/em\u003e reaction has a threshold energy (2.60 MeV) slightly below 3.0 MeV, its cross-section and hence its neutron yield are negligible up 3.0 MeV\u003csup\u003e\u003cb\u003e\u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e46\u003c/span\u003e,\u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e47\u003c/span\u003e\u003c/b\u003e\u003c/sup\u003e. However, at higher radiation levels, these interactions must be considered.\u003c/p\u003e\u003cdiv id=\"Sec11\" class=\"Section2\"\u003e\u003ch2\u003eDeuteron electro-disintegration:\u003c/h2\u003e\u003cp\u003eDeuteron disintegration can also occur due to interaction with fast electrons that have an energy of 2.224 MeV (deuteron binding energy) or more.\u003c/p\u003e\u003cp\u003ee\u0026thinsp;+\u0026thinsp;D \u0026rarr; e\u0026thinsp;+\u0026thinsp;p\u0026thinsp;+\u0026thinsp;n \u0026ndash; 2.224 MeV E\u003csub\u003eth\u003c/sub\u003e = 2.224 MeV\u003c/p\u003e\u003cp\u003eThe cross-section of this reaction is extremely small\u0026thinsp;~\u0026thinsp;10 \u0026micro;b\u003csup\u003e\u003cb\u003e48\u003c/b\u003e\u003c/sup\u003e and has negligible effects in neutron production because electrons propagate at large angles outside the target area\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec12\" class=\"Section2\"\u003e\u003ch2\u003ePhotonuclear reactions:\u003c/h2\u003e\u003cp\u003eThe interactions produced by hard bremsstrahlung X-rays and/or gamma rays, resulting from the relativistic stopping force of electrons inside the target, are called photonuclear interactions. The neutrons produced by photonuclear reactions are called photoneutrons, which can be used in diagnostics. Photonuclear reactions can occur inside the target irradiated by ultra-intense laser and with its surroundings. In the experiments, we installed cone-shaped collimators made of lead and plastics inside the laser chamber. Therefore, gamma rays and photoneutrons produced by interactions with the target environment did not contaminate the measured neutron spectra. Thus, in this work, the photonuclear reactions involved in the neutron production process are the reactions that occur inside the target only. For CD or CD\u003csub\u003e2\u003c/sub\u003e targets, the deuteron and carbon photo-dissociation reactions can occur inside the target as:\u003c/p\u003e\u003cp\u003eγ\u0026thinsp;+\u0026thinsp;D \u0026rarr; P\u0026thinsp;+\u0026thinsp;n \u0026ndash; 2.224 MeV E\u003csub\u003eth\u003c/sub\u003e = 2.224 MeV,\u003c/p\u003e\u003cp\u003eγ + \u003csup\u003e12\u003c/sup\u003eC \u0026rarr; \u003csup\u003e11\u003c/sup\u003eB + n \u0026minus;\u0026thinsp;18.7 MeV E\u003csub\u003eth\u003c/sub\u003e = 18.7 MeV,\u003c/p\u003e\u003cp\u003eThe threshold energy (E\u003csub\u003eth\u003c/sub\u003e) of deuteron photo-dissociation reaction equals the deuteron binding energy, 2.224 MeV\u003csup\u003e\u003cb\u003e\u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e49\u003c/span\u003e\u003c/b\u003e\u003c/sup\u003e. The maximum cross-section value of the reaction is very small\u0026thinsp;\u0026asymp;\u0026thinsp;2.5 mb \u003csup\u003e\u003cb\u003e49,50\u003c/b\u003e\u003c/sup\u003e. For the incident photon energy up to 20 MeV, within which nuclei exhibit a giant resonance of photo-neutrons emission, the average cross section of the carbon photo-dissociation reaction is \u0026asymp;\u0026thinsp;5 mb\u003csup\u003e\u003cb\u003e51\u003c/b\u003e\u003c/sup\u003e.\u003c/p\u003e\u003cp\u003eThe importance of photonuclear reactions depends on the stopping power of the accelerated electrons within the target. The bremsstrahlung flux results from the stopping power of the relativistic electrons inside deuterated targets (CD or CD\u003csub\u003e2\u003c/sub\u003e) is like that produced within a pure carbon target of the same density. In pure carbon target, the bremsstrahlung radiation length is \u0026asymp;\u0026thinsp;43 g/cm\u003csup\u003e2\u003c/sup\u003e, and the relativistic electron stopping power is approximately 2 MeV cm\u003csup\u003e2\u003c/sup\u003e/g\u003csup\u003e\u003cb\u003e52\u003c/b\u003e\u003c/sup\u003e. A target with a thickness of 300 micrometers is required to efficiently stop relativistic electrons\u003csup\u003e\u003cb\u003e\u003cspan citationid=\"CR53\" class=\"CitationRef\"\u003e53\u003c/span\u003e\u003c/b\u003e\u003c/sup\u003e. Our 100-micrometer-thick target is so thin that it cannot stop relativistic electrons, and therefore the probability of producing bremsstrahlung inside the target is negligible. For such a thin target, deuteron and carbon photodissociation does not contribute to the overall neutron production.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec13\" class=\"Section2\"\u003e\u003ch2\u003eNeutron-producing reactions by accelerating ions\u003c/h2\u003e\u003cp\u003eIn addition to the thermonuclear fusion and beam fusion of the \u003cem\u003eD(d,n)\u003c/em\u003e\u003csup\u003e\u003cem\u003e3\u003c/em\u003e\u003c/sup\u003e\u003cem\u003eHe\u003c/em\u003e reaction, the accelerated D and C ions have enough energy to produce neutrons due to the stripping reactions \u003csup\u003e\u003cem\u003e\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e\u003c/em\u003e\u003c/sup\u003e\u003cem\u003eC(d,n)\u003c/em\u003e\u003csup\u003e\u003cem\u003e13\u003c/em\u003e\u003c/sup\u003e\u003cem\u003eN\u003c/em\u003e and \u003cem\u003eD(\u003c/em\u003e\u003csup\u003e\u003cem\u003e12\u003c/em\u003e\u003c/sup\u003e\u003cem\u003ec,n)\u003c/em\u003e\u003csup\u003e\u003cem\u003e13\u003c/em\u003e\u003c/sup\u003e\u003cem\u003eN\u003c/em\u003e. There is also a possibility that the accelerated deuterons will break up (dissociate) on the field of carbon nucleus or another deuteron producing neutrons. Moreover, other neutron producing reactions like photonuclear reactions and deuteron electro-disintegration must be investigated. Accordingly, the neutron-producing reactions involved in the total neutron yield must be identified.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec14\" class=\"Section2\"\u003e\u003ch2\u003eDeuteron-Carbon stripping reactions\u003c/h2\u003e\u003cp\u003eIn previous studies\u003csup\u003e\u003cb\u003e\u003cspan additionalcitationids=\"CR55 CR56\" citationid=\"CR54\" class=\"CitationRef\"\u003e54\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR57\" class=\"CitationRef\"\u003e57\u003c/span\u003e\u003c/b\u003e\u003c/sup\u003e, we have experimentally and theoretically investigated the neutron production process in ultra-intensity laser interactions with planar CD and CD\u003csub\u003e2\u003c/sub\u003e targets. Detailed study of the neutron spectra proved that the reactions \u003csup\u003e\u003cem\u003e\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e\u003c/em\u003e\u003c/sup\u003e\u003cem\u003eC(d,n)\u003c/em\u003e\u003csup\u003e\u003cem\u003e13\u003c/em\u003e\u003c/sup\u003e\u003cem\u003eN\u003c/em\u003e and \u003cem\u003eD(\u003c/em\u003e\u003csup\u003e\u003cem\u003e12\u003c/em\u003e\u003c/sup\u003e\u003cem\u003ec,n)\u003c/em\u003e\u003csup\u003e\u003cem\u003e13\u003c/em\u003e\u003c/sup\u003e\u003cem\u003eN\u003c/em\u003e between the deuterium and carbon ions participate effectively in the overall neutron production. However, the neutron yield of each reaction was not calculated compared to the \u003cem\u003eD(d,n)\u003c/em\u003e\u003csup\u003e\u003cem\u003e3\u003c/em\u003e\u003c/sup\u003e\u003cem\u003eHe\u003c/em\u003e reaction. These reactions are endoergic reactions with threshold energies of 0.33 MeV and 1.96 MeV, respectively.\u003c/p\u003e\u003cp\u003eD\u0026thinsp;+\u0026thinsp;\u003csup\u003e12\u003c/sup\u003eC \u0026rarr; \u003csup\u003e13\u003c/sup\u003eN + n \u0026ndash; 0.28 MeV; E\u003csub\u003eth\u003c/sub\u003e = 0.33 MeV\u003c/p\u003e\u003cp\u003e\u003csup\u003e12\u003c/sup\u003eC + D \u0026rarr; \u003csup\u003e13\u003c/sup\u003eN + n \u0026ndash; 0.28 MeV; E\u003csub\u003eth\u003c/sub\u003e = 1.96 MeV\u003c/p\u003e\u003cp\u003eThe two endoergic reactions D\u0026ndash;\u003csup\u003e12\u003c/sup\u003eC and \u003csup\u003e\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e\u003c/sup\u003eC\u0026ndash;D produce neutrons with lower energies than those produced by D\u0026ndash;D reactions for the same acceleration energy. As the maximum acceleration energy of D ions is \u0026asymp;\u0026thinsp;3.0 MeV, interactions between D and C ions can produce neutrons with energies up to \u0026asymp;\u0026thinsp;2.6 MeV (Eq.\u0026nbsp;2). This explains the lower energy part of the measured spectrum.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec15\" class=\"Section2\"\u003e\u003ch2\u003eNeutron yield comparison\u003c/h2\u003e\u003cp\u003eOne of the most important factors that the total neutron yield of any reaction depends on is the total reaction cross-section. The total cross section of the D\u0026ndash;\u003csup\u003e12\u003c/sup\u003eC reaction is much larger than the cross-section of the D-D reaction. Up to 3.0 MeV (maximum deuteron acceleration energy), the maximum value of the D-D reaction cross-section is \u0026asymp;\u0026thinsp;100.0 mb\u003csup\u003e\u003cb\u003e58,59\u003c/b\u003e\u003c/sup\u003e, and that of the D\u0026ndash;\u003csup\u003e12\u003c/sup\u003eC reaction is \u0026asymp;\u0026thinsp;225.0 mb\u003csup\u003e\u003cb\u003e60,61\u003c/b\u003e\u003c/sup\u003e. The differential cross-sectional data for the D-\u003csup\u003e12\u003c/sup\u003eC reaction are unavailable. Therefore, its neutron spectrum cannot be calculated at the same angle of observation as the measured spectrum. However, we can calculate the total neutron yield of the D\u0026ndash;\u003csup\u003e12\u003c/sup\u003eC reaction using its total cross section. Comparing the total neutron yield of the D-D reaction with that of the D-\u003csup\u003e12\u003c/sup\u003eC and \u003csup\u003e\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e\u003c/sup\u003eC-D reactions can better illustrate the true situation than a partial yield measured at a certain angle. This is because the measured neutron yield at specific observation angles depends on the differential cross-sections, which vary from angle to angle. This does not reflect the true values ​​of the total neutron yields of the different reactions.\u003c/p\u003e\u003cp\u003eNow, the question is what about the neutron yield of the \u003csup\u003e\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e\u003c/sup\u003eC\u0026ndash;D reaction? Experimental cross-sectional data of the \u003csup\u003e\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e\u003c/sup\u003eC\u0026ndash;D reaction are not available and hence its total neutron yield cannot be calculated. It is theoretically known that the cross-sections of the D\u0026ndash;\u003csup\u003e12\u003c/sup\u003eC and \u003csup\u003e\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e\u003c/sup\u003eC\u0026ndash;D reactions are identical in a center-of-mass system. In the laboratory system, when the ion acceleration is efficient, the cross section of the \u003csup\u003e\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e\u003c/sup\u003eC\u0026ndash;D reaction can be twice that of the D\u0026ndash;\u003csup\u003e12\u003c/sup\u003eC reaction \u003csup\u003e\u003cb\u003e\u003cspan citationid=\"CR53\" class=\"CitationRef\"\u003e53\u003c/span\u003e\u003c/b\u003e\u003c/sup\u003e. Then, the neutron yield of the \u003csup\u003e\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e\u003c/sup\u003eC\u0026ndash;D reaction can be twice that of the D\u0026ndash;\u003csup\u003e12\u003c/sup\u003eC reaction for the same velocity and number density of the D and C ions (Eq.\u0026nbsp;3). However, in laser interactions with CD or CD\u003csub\u003e2\u003c/sub\u003e targets, the velocity of the accelerated D and C ions is not the same.\u003c/p\u003e\u003cp\u003eThe ions are accelerated due to front surface acceleration, causing nuclear reactions with the background ions within the target, while canceling out the effect of the target normal sheath acceleration (TNSA) \u003csup\u003e\u003cb\u003e\u003cspan citationid=\"CR54\" class=\"CitationRef\"\u003e54\u003c/span\u003e,\u003cspan citationid=\"CR55\" class=\"CitationRef\"\u003e55\u003c/span\u003e,\u003cspan citationid=\"CR62\" class=\"CitationRef\"\u003e62\u003c/span\u003e\u003c/b\u003e\u003c/sup\u003e. When CD targets irradiated by lasers with intensities ranging from 3.0x10\u003csup\u003e18\u003c/sup\u003e to 1.0x10\u003csup\u003e19\u003c/sup\u003e W/cm\u003csup\u003e2\u003c/sup\u003e (the max. intensity in the experiments), the carbon ions are accelerated to about 60% of the velocity of the D ions due to the front side acceleration\u003csup\u003e\u003cb\u003e\u003cspan citationid=\"CR57\" class=\"CitationRef\"\u003e57\u003c/span\u003e\u003c/b\u003e\u003c/sup\u003e. The neutron yield of any reaction depends on the collision frequency or reactivity \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\u0026lang;\\sigma\\:v\u0026rang;\\)\u003c/span\u003e\u003c/span\u003e. Therefore, the neutron yields of the D\u0026ndash;\u003csup\u003e12\u003c/sup\u003eC and \u003csup\u003e\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e\u003c/sup\u003eC\u0026ndash;D reactions are almost the same because the collision frequency is approximately the same for the two reactions.\u003c/p\u003e\u003cp\u003eThe deuterated polystyrene (CD) target has the same number density of deuterium and carbon atoms per cubic centimeter (i.e., a 50%-50% mixture of deuterium and carbon atoms). In Eq.\u0026nbsp;(3), replacing the differential cross-section with the total cross-section, and using \u003cem\u003en\u003c/em\u003e\u003csub\u003e\u003cem\u003e1 =\u003c/em\u003e\u003c/sub\u003e \u003cem\u003en\u003c/em\u003e\u003csub\u003e\u003cem\u003e2 =\u003c/em\u003e\u003c/sub\u003e \u003cem\u003e\u0026frac12; n\u003c/em\u003e, where \u003cem\u003en\u003c/em\u003e is the number density of the target, the total neutron yield of the D-D reaction can be calculated. For the D\u0026ndash;\u003csup\u003e12\u003c/sup\u003eC reaction, the total neutron yield is given by applying the original equation (Eq.\u0026nbsp;3) because the number density of deuterium equals the number density of carbon in the CD target. The polyethylene target (CD\u003csub\u003e2\u003c/sub\u003e) contains twice the concentration of D atoms as C atoms and hence \u003cem\u003en\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e is twice \u003cem\u003en\u003c/em\u003e\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003e.\u003c/p\u003e\u003cp\u003eFigures \u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e,\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e illustrate the Monte Carlo calculations for neutron yield of the D-D reaction compared to the calculated total neutron yield of both D\u0026ndash;\u003csup\u003e12\u003c/sup\u003eC and \u003csup\u003e\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e\u003c/sup\u003eC\u0026ndash;D reactions (have equal neutron yield) up to an energy of 3.0 MeV for irradiated CD and CD\u003csub\u003e2\u003c/sub\u003e targets by PW laser respectively. The D\u0026ndash;\u003csup\u003e12\u003c/sup\u003eC and \u003csup\u003e\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e\u003c/sup\u003eC\u0026ndash;D reactions are involved in the neutron production process when the deuteron acceleration energy reaches its threshold energies, 0.33 MeV and 1.96 MeV respectively.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eBy calculating the area under the curve for each reaction in figures (5,6), the neutron yield of the different reactions can be calculated. The calculations show that the total neutron yield of the D-\u003csup\u003e12\u003c/sup\u003eC and \u003csup\u003e\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e\u003c/sup\u003eC-D reactions is approximately twice the neutron yield of the D-D reaction in the case of the CD\u003csub\u003e2\u003c/sub\u003e target and four times the neutron yield of the D-D reaction in the case of the CD target. There are some reasons to explain these results.\u003c/p\u003e\u003cp\u003e1- For both targets, the cross sections of ​​the D\u0026ndash;\u003csup\u003e12\u003c/sup\u003eC and \u003csup\u003e\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e\u003c/sup\u003eC\u0026ndash;D reactions are much larger than that of the D\u0026ndash;D reaction, and this is of great importance in determining the contribution of each reaction to the total neutron production.\u003c/p\u003e\u003cp\u003e2- The D-D fusion reaction has two paths with equal probability: \u003cem\u003eD(d,n)\u003c/em\u003e\u003csup\u003e\u003cem\u003e3\u003c/em\u003e\u003c/sup\u003e\u003cem\u003eHe\u003c/em\u003e and \u003cem\u003eD(d,p)T\u003c/em\u003e. The second path produces protons and does not take part in neutron production. Therefore, the number of neutrons is only 50% of the D-D reaction rate. On the other hand, the neutron yields produced by the D\u0026ndash;\u003csup\u003e12\u003c/sup\u003eC and \u003csup\u003e\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e\u003c/sup\u003eC\u0026ndash;D reactions are the same as the reaction rates.\u003c/p\u003e\u003cp\u003e3- For the CD target, the D-D reaction occurs due to D-ion interactions only (50% of the total number of ions), but the D-\u003csup\u003e12\u003c/sup\u003eC and \u003csup\u003e\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e\u003c/sup\u003eC-D reactions occur due to interactions of all D and C ions (a 50%-50% mixture for the CD target). Therefore, the probability of the D-\u003csup\u003e12\u003c/sup\u003eC and \u003csup\u003e\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e\u003c/sup\u003eC-D reactions (due to the interactions between D and C ions) is twice the probability of the D-D reaction (due to the interactions of D ions only).\u003c/p\u003e\u003cp\u003eToupin \u003cem\u003eet. a\u003c/em\u003el., predicted, using kinetic numerical simulations, that at high irradiances of CD\u003csub\u003e2\u003c/sub\u003e targets by ultra-intense lasers, the total neutron yield of the D-\u003csup\u003e12\u003c/sup\u003eC and \u003csup\u003e\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e\u003c/sup\u003eC-D reactions can almost double the neutron yield of the D-D reaction\u003csup\u003e\u003cb\u003e\u003cspan citationid=\"CR53\" class=\"CitationRef\"\u003e53\u003c/span\u003e\u003c/b\u003e\u003c/sup\u003e. This is even though the number density of C atoms is only 50% of the number density of D atoms in the CD\u003csub\u003e2\u003c/sub\u003e target. In the case of CD target, the number density of C and D ions is the same, and compared to the CD\u003csub\u003e2\u003c/sub\u003e target, this will double the ratio of the total neutron yield of D\u0026ndash;\u003csup\u003e12\u003c/sup\u003eC and \u003csup\u003e\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e\u003c/sup\u003eC\u0026ndash;D reactions to that of D-D reaction to be four times. This confirms the strong contribution of the two reactions D\u0026ndash;\u003csup\u003e12\u003c/sup\u003eC and \u003csup\u003e\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e\u003c/sup\u003eC\u0026ndash;D to the total neutron yield considering that they are endoergic reactions, and contribute to neutron production after the accelerated ions reach their threshold energies.\u003c/p\u003e\u003c/div\u003e"},{"header":"Conclusion","content":"\u003cp\u003eIn this work the reaction mechanisms and neutron yields of D-D fusion reaction and its associated neutron-producing reactions when PW laser irradiated CD and CD\u003csub\u003e2\u003c/sub\u003e targets were studied in detail. Experimental data were compared to Monte Carlo simulation. The measured and calculated neutron spectra demonstrated that the D-D reaction produces neutrons via both thermonuclear fusion and beam fusion, but it is not the only neutron source. The D-\u003csup\u003e12\u003c/sup\u003eC and \u003csup\u003e\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e\u003c/sup\u003eC-D stripping reactions, between accelerated ions on the target surface and target background ions, have a much higher neutron production compared to the D-D reaction. Besides, neutron production due to photonuclear reactions, deuteron break up, and deuteron electro-dissociation must be considered. Although their neutron production is negligible under our irradiation conditions, it should be considered under higher irradiation conditions. Not as previously considered, all these reactions can contribute to the neutron production process not only thermonuclear and beam fusion of the D-D reaction with background of photoneutrons.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eAcknowledgments\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors are very grateful to the members of the Laser, Target, and measurement Tech. in ILE, Osaka, Japan.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e\u003cem\u003eAuthors Contribution declaration\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors hereby declare that this work has been carried out only by them.\u003c/p\u003e\n\u003cp\u003e\u0026nbsp;A. Youssef prepared all sections of the manuscript.\u003c/p\u003e\n\u003cp\u003eR. Kodama revised the manuscript.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e\u003cem\u003eCompeting interests\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe author(s) declare no competing interests.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e\u003cem\u003eFunding declaration\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe Authors didn\u0026rsquo;t receive any funds for this work.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e\u003cem\u003eData availability statement\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eAll data generated or analysed during this study are included in this published article.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eGray, L. \u0026amp; Read, J. 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Plasmas\u003c/em\u003e. \u003cb\u003e13\u003c/b\u003e, 030702 (2006).\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"(1) D-D fusion reaction (2) neutron producing reactions","lastPublishedDoi":"10.21203/rs.3.rs-8108674/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8108674/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe mechanisms of the \u003cem\u003eD(d,n)\u003c/em\u003e\u003csup\u003e\u003cem\u003e3\u003c/em\u003e\u003c/sup\u003e\u003cem\u003eHe\u003c/em\u003e fusion reaction and its associated neutron-producing reactions in petawatt laser interactions with CD and CD\u003csub\u003e2\u003c/sub\u003e targets have recently attracted attention. The mechanisms by which ions are accelerated, causing fusion and other nuclear reactions are also a subject of debate. It was assumed that the \u003cem\u003eD(d,n)\u003c/em\u003e\u003csup\u003e\u003cem\u003e3\u003c/em\u003e\u003c/sup\u003e\u003cem\u003eHe\u003c/em\u003e fusion reaction is the only source of neutrons through thermonuclear and/or beam fusion mechanisms with a background of photoneutrons. In addition, ions acceleration occurs at the target front surface and within the electrostatic sheath on the rear surface. Here, through in-depth analysis of experimental measurements and simulations using 3-D Monte Carlo code, it was shown that nuclear reactions occur between accelerated ions and target background ions. The ions are accelerated at the target surface, causing nuclear reactions as they pass through the target, thus eliminating the effect of the electrostatic sheath on the rear side. The relative contribution of each reaction was assessed in comparison with the fusion reaction. Deuteron-Carbon stripping reactions contribute to overall neutron production, with a much higher neutron yield than that of the fusion reaction. Other reactions such as photonuclear reactions, deuteron breakup, and deuteron electro-disintegration must be considered.\u003c/p\u003e","manuscriptTitle":"Mechanisms of D-D fusion and associated neutron-producing reactions in PW laser interactions with carbon-deuterated targets","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-11-20 03:11:36","doi":"10.21203/rs.3.rs-8108674/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"87144f8a-a3d5-42b6-9664-a62c8cb58f3d","owner":[],"postedDate":"November 20th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":58276688,"name":"Physical sciences/Chemistry"},{"id":58276689,"name":"Physical sciences/Physics"}],"tags":[],"updatedAt":"2026-05-20T08:56:04+00:00","versionOfRecord":[],"versionCreatedAt":"2025-11-20 03:11:36","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8108674","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8108674","identity":"rs-8108674","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}