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A mixture of deuterium (D) and tritium (T) is the most likely fuel for laser-driven inertial confinement fusion (ICF) reactors and hence DD and DT are the fusion reactions that will fire these
reactors in the future. Neutrons produced from the two reactions will escape from the burning
plasma, in the reactor core, and they are the only products possible to be measured directly. DT/DD neutron ratio is crucial for evaluation of T/D fuel ratio, burn control, tritium cycle and alpha particle self-heating power. To measure this ratio experimentally, the neutron spectra of DD and DT reactions have to be measured separately and simultaneously under high neutron counting with sufficient statistics (typically within 10% error) in a very short time and these issues are mutually contradicted. That is why it is not plausible to measure this high priority ratio for reactor performance accurately. Precise calculations of the DT/DD neutron ratio are needed. Here, we introduce such calculations using a three dimensional (3-D) Monte Carlo code at energies up to 40 MeV (the predicted maximum ion acceleration energy with the available laser systems). In addi
tion, the fusion power ratio of DD and DT reactions is calculated for the same energy range. The study indicates that for a mixture of 50% deuterium and 50% triton, with taking into account the reactions D(d,n)^{3}He and T(d,n)^{4}He, the optimum energy value for achieving the most efficient laser-driven ICF is 0.08 MeV.

Nuclear fusion is one of the few options that provide a sustainable and safe energy source for future. There are two approaches to achieve the nuclear fusion: Magnetic Confinement Fusion and laser fusion. Both of the approaches occur in burning plasma (high-energy-density plasma) to offer the very high temperature and density required to achieve the fusion. The burning plasma regime is a critically important regime of plasma physics. Investigating and understanding the physics of such plasmas are crucial in order to successfully achievement of nuclear fusion.

High power laser is a promising tool to achieving nuclear fusion as lasers can focus intense bursts of energy in a very short time onto small targets. Due to the recent progress of ultra-powerful lasers, the concept of fast ignition was introduced [

In principle, a mixture of hydrogen isotopes deuterium (D) and tritium (T) is the most promising fuel to fire the laser-driven ICF reactors in the future [^{3}He and T(d,n)^{4}He will occur in the burning DT plasma in the reactor core. Neutrons produced by the two reactions will be used to measure the fusion output and its time evolution. As it is impossible to probe the burning plasma directly, the produced neutron yield is practically the crucial factor to judge the achievement of nuclear fusion [

In previous works [^{3}He and T(d,n)^{4}He reactions are calculated up to 40 MeV which is the predicted maximum acceleration energy of D ions using the laser facility for fast ignition experiment (LFEX) at the Institute of Laser Engineering (ILE), Osaka University [^{21} W/cm^{2} and hence 40 MeV is the maximum energy of D ions as calculated according to the model introduced in Ref. [^{3}He, the DD reaction can occur through the other channel D(d,p)^{3}H with the same probability i.e., 50% for each channel. The channel D(d,p)^{3}H doesn’t give any neutrons so that it has nothing to do with the neutron ratio calculations.

Neutron spectra of DD and DT reactions have to be measured accurately to determine the DT/DD neutron yield ratio and the T/D fuel ratio. Experimentally, there many difficulties in measuring the DT/DD neutron yield ratio [_{d} ≤ 40 MeV is introduced for the first time. In Section 4, the fusion power ratio of the two reactions is computed for the same energy range. Finally, the conclusion is given in Section 5.

To calculate both the neutron yield ratio and the fusion power ratio, the total cross section values of DD and DT reactions have to be calculated precisely. Here, the total cross sections of DD and DT reactions are calculated over the energy range 0.01 ≤ Ed ≤ 40 MeV with steps 0.01 MeV using the Drosg 2000 code [

In order to get the clearest possible picture, the comparison has been divided into three regimes. The first regime is from 0.01 MeV to 0.3 MeV (

to ≈ 1350 mb at 0.3 MeV. The second regime is from 0.4 MeV to 2.2 MeV (

DT/DD neutron yield ratio is an effective way to know the DT/DD burning ratio. This ratio will play a crucial rule for any fusion reactor in the future. It is essential for the T/D fuel ratio, burn control, estimation of tritium fuel cycle and alpha particle self-heating power [

Experimentally, neutron detectors are positioned at certain angles and hence the measured neutrons are those emitted at these angles only. However, the total neutron yields of DD or DT reactions are required to determine the neutron yield ratio. In this section, the DT/DD neutron yield ratio over the energy range 0.01 ≤ E_{d} ≤ 40 MeV is calculated using a three dimensional (3-D) Monte Carlo code.

Monte Carlo Code

To calculate the neutron yield ratio of DD and DT reactions, numerical experiments have been performed by using 3-D Monte Carlo code [_{n} of DD or DT reaction is calculated through the formula:

where n_{1} is the number density of the accelerated ions, n_{2} is the number of the target ions per unit volume, σ_{E} is the total cross section of the nuclear reaction for a given energy E and υ is the velocity of the accelerated ions. The total cross section σ_{E} for a given energy E is calculated by using the Drosg 2000 code. The neutron yield ratio is calculated as Y_{n(}_{DT/DD) }= Y_{n(DT)}/Y_{n(DD)} and the vice versa i.e., Y_{n(DD/DT) }= Y_{n(DD)}/Y_{n(DT)}.The time step, in the calculations, is taken to be enough for large number of collisions. The Monte Carlo code has been run with a large enough sample size to reduce the fluctuations in the calculated spectra.

Figures 6-9 show the results of calculations of the neutron yield ratio of DD and DT reactions in the energy range 0.01 ≤ E_{d} ≤ 40 MeV To get the best possible analysis of the neutron yield ratio, the total energy range has been divided into four regimes. The first regime is from 0.01 MeV to 0.14 MeV (

ratio is less than 9.0 and it decreases to the value 1.0 at the end of the regime. The value 2.2 MeV is an inversion point as before it the DT/DD neutron ratio is more than 1.0 but after it we have the opposite situation i.e., the DD/DT neutron ratio becomes higher than 1.0. The fourth regime is from 2.2 MeV to 40 MeV (

In summary, the DT/DD neutron ratio increases gradually from 191 at 0.01 MeV to the maximum value 334 at 0.08 MeV and then it decreases to become 1.0 at 2.2 MeV (the value at which the neutron yields of DD and DT reactions are equal). At energies higher than 2.2 MeV, the neutron yield of DD reaction becomes higher than that of the DT reaction. The energy value 0.08 MeV is the optimum energy value at which the highest DT/DD neutron yield ratio can be obtained using a mixture of D and T ions. It is worth to mention that the fast tritons produced in the DD fusion reactions may cause secondary DT reactions in flight with the D fuel ions. Neutron yield of these secondary DT reactions, in a DT mixture, is at least three orders of magnitude less than the neutron yield of the original DT reactions [

The total fusion energy produced per unit volume per unit time in the burning fusion plasma is called the fusion power density of the fusion reaction. In this section, we perform a comparison between the fusion power of DD and DT reactions (achieved in high-energy density plasma relevant to laser-driven ICF) in the energy range 0.01 ≤ E_{d} ≤ 40 MeV. To achieve this comparison; we have derived a formula that is valid to calculate the DT/DD fusion power ratio and the DD/DT fusion power ratio using the calculated cross section values in section 2.

To calculate the fusion power density, the reaction rate (the number of fusion reactions per unit volume per unit time) has to be incorporated. The reaction rate

where σ is the reaction cross section, n_{1 }is the number density of the accelerated ions, n_{2}_{ }is the number of the target ions per unit volume, and is the velocity of the accelerated ions. If each fusion collision generates energy^{3} as:

In the case if DT fusion fuel mixture is composite of 50% D and 50% T, then

Consequently, the fusion power ratio

The above formula is introduced for the first time and it is used to compare the fusion power of DD and DT fusion reactions (

E_{d} ≤ 40 MeV). The formula can be generalized to compare the fusion power of other fusion reactions like D-^{3}He, D-^{12}C, D-^{9}Be, D-^{3}Li, P-T and P-^{7}Li.

For the sake of high degree of accuracy, the comparison of fusion power ratio is divided into five regimes (Figures 10-14). The first regime is from 0.01 MeV to 0.13 MeV (

In this work, an effective method for comparing the neutron yield and the fusion power of DT and DD fusion reactions is introduced. We found that the neutron yield of the DT reaction is much higher than that of the DD reaction in the energy range 0.01 - 2.2 MeV. The DT/DD neutron yield ratio reaches its maximum value at 0.08 MeV. At the energies higher than 2.2 MeV, the neutron yield of DD reaction becomes higher than that of the DT reaction but less than its double. Consequently, from the burning ratio point of view, DT reaction is the preferable fusion reaction at energies up to 2.2 MeV but the DD reaction is the preferable one at the higher energies. In addition, the fusion power of the DT reaction is higher than, but less than twice, that of the DD reaction in the energy range 0.01 - 14.3 MeV. The DT/DD fusion power ratio reaches its maximum value at 0.08 MeV. The fusion power of DD reaction becomes higher at the energies higher than 14.3 MeV. Thus, from the fusion power point of view, DT reaction is preferable fusion reaction at energies up to 14.4 MeV but the DD reaction is the preferable one at the energies higher than 14.4 MeV. From the picture presented, for a mixture of 50% deuterium and 50% triton, at 0.08 MeV both the DT/DD neutron yield ratio and the DT/DD fusion power ratio are maxima. Therefore, one can say that the energy value 0.08 MeV is the optimum value for achieving the laser-driven ICF. Now the question is whether or not the secondary fusions produced by the energetic ^{3}H and ^{3}He can affect this energy value. The very recent studies point out that the total probability of these secondary fusions is generally on the order of 10^{−2} or less [

The authors are very grateful to Ha’il University for funding this work.

A. Youssef,M. Haparir, (2016) Achievement of Laser Fusion with High Energy Efficiency Using a Mixture of D and T Ions. Open Journal of Energy Efficiency,05,48-58. doi: 10.4236/ojee.2016.52005