بسم الله الرحمن الرحيم

1. بسم الله الرحمن الرحيم {وَقُلْ رَبِّ زِدْنِي عِلْمًا}[طه : 114] صدق الله العظيم نتقدم بالشكر للسادة الحضور

2. Comparison of neutron yield and fusion power for D-D and D-T fusion reactions in broad range of high energy-density plasma By Moustafa Ismail

3. Outline 1- Objective 2- Laser fusion 3- Cross Section Calculations for D-D and D-T fusion reactions 4- Neutron yield ratio calculations for D-Dand D-T fusion reactions 5- Fusion power ratio calculations for D-D and D-T Fusion reactions 6- Conclusion

4. Objective • Calculating of neutron yield ratio and fusion power ratio for D-D and D-T fusion reactions in the energy range 0.01 MeV ≤ Ed ≤ 39 MeV • These calculations are very important for laser fusion reactors in the future D + T → 4He (3.5 MeV) + n (14.1 MeV) Q = 17.6 MeV D + D → 3He (0.82 MeV) + n (2.45 MeV) Q = 3.27 MeV The energy range is chosen to cover the energies of the laser accelerated deuterons up to the predicted maximum value in the near future, 39 MeV. • Why Neutron yield and fusion power? • Neutron yield is the crucial factor to judge the successful achieving of fusion . • Fusion power is the final output of fusion.

5. Laser Fusion How to achieve a successful fusion ? Fusion is joining together of a light nuclei to form a more massive nucleus. Because the masses of the products are less than that of the original nuclei. The loss of mass converts to energy.

6. But…What are conditions to achieve a successful fusion? In fact:

7. As the repulsive coulomb force prevents the fusion We need: 1) High temperature and 2) High density To overcome the repulsive coulomb force But The collection between high temperature and high density is extremely difficult Therefore we need 3) Confinement Now, conditions to achieve a successful fusion are high temperature, high density and confinement.

8. Confinement What are methods of confinement?

9. Here, we arrive to answer the question.How to achieve successful fusion ?

10. Laser Fusion

11. Implosion approach In implosion approach: Laser beams irradiate spherical target from all directions symmetrically in the same time . Where every beam faces another beam in opposite direction as if the extensions of beams are focused in the center. But the penetration of laser beam is around 1 µm (µm = 10-6 m) while the radius of the target is around 1mm (mm = 10-3 m). Here we have to ask the following question! How does laser fusion occur?

12. Fusion occurs as the following: When laser beams irradiate the target, deposition energy occurs in outer layer of the target we obtain • Thermal expansion in outer layer of the target.Then we have high density in the center. (2) Heating of outer layer of the target.Consequently we havehigh temperature in the center (3) Because of inertia of fuel, We obtain confinement . At this moment, ignition occurs in the center (Fusion proceeds). (4) Burnoccurs (fusion spreads rapidly in the whole target).

13. Fast Ignition (FI) approach The other approach of laser fusion. In implosion approach We make compressing and heating with the same laser beams لThe Comparison In fast ignition(FI) approach We separate between compressing and heating where, heating is made by PW laser beam.

14. Cross Section Calculations for D-D and D-T fusion reactions In laser fusion, the total cross section calculations have an important role in: 1- Calculating the neutron yield ratio Yn(DD/DT) of D-D and D-T fusion reactions and the vice versa. 2- Calculating the Fusion power ratio Pf(DD/DT)of D-D and D-T fusion reaction and the vice versa. Our calculations are made in broad range of high energy- density plasma; 0.01 MeV ≤ Ed ≤ 39 MeV. We used Drosg 2000 code program in the total cross section calculations

15. Verification of total cross section calculations Total cross section values of D-D reaction . The calculated values (gray line) by Drosg 2000 code (M. Drosg 2000) are compared with those published (black line) in nuclear data table (Liskien and Paulsen 1973) up to the maximum published value of the incident deuteron energy (10 MeV). Total cross section values of D-T reaction. The calculated values (gray line) by Drosg 2000 code (M. Drosg 2000) are compared with those published (black line) in nuclear data table (Liskien and Paulsen 1973) up to the maximum published value of the incident deuteron energy (10 MeV). We found a good agreement between the calculated values and the published ones. This agreement encouraged us to extend the calculated values up to 39 MeV (the predicted maximum value of laser accelerated deuterons in the near future).

16. Comparison of total cross section calculations for D-D and D-T in the energy range 0.01 MeV ≤ Ed ≤ 39 MeV comparison between calculated total cross section values of D-T fusion reaction (gray line) and D-D fusion reaction (black line) by Drosg 2000 code (M. Drosg 2000) within the energy range 0.4 ≤ Ed ≤ 2.2 MeV for the incident deuteron. Comparison between calculated total cross section values of D-T fusion reaction (gray line) and D-D fusion reaction (black line) by Drosg 2000 code (M. Drosg 2000) within the energy range 2.3 ≤ Ed ≤ 39 MeV for the incident deuteron. comparison between calculated total cross section values of D-T fusion reaction (gray line) and D-D fusion reaction (black line) by Drosg 2000 code (M. Drosg 2000) within the energy range 0.03 ≤ Ed ≤ 0.3 MeV for the incident deuteron.

17. Neutron yield ratio calculations for D-D and D-T reactions Comparisonof neutron yield for D-D and D-T fusion reaction in broad range of high energy – density plasma ; 0.01 MeV ≤ Ed ≤ 39, using a three dimensional (3-D) Monte Carlo code is introduced for the first time. Neutron yield is calculated as: Where : n1 : the number density of the accelerated ions per unit volume. n2 : the number of the target ions per unit volume. σE :the total cross section of the nuclear reaction for a given energy E. υ : the velocity of the accelerated ions. Yn = ∫ n1 n2σE υ dt dυ The neutron yield ratio Yn(DT/DD) is calculated as Yn(DT/DD) = Yn(DT) / Yn(DD)

18. Neutron yield ratio Of DD and DT fusion reactions in the energy range 0.01 MeV ≤ Ed ≤ 39 MeV DT/DD neutron yield ratio for incident deuteron energies from 0.01 MeV to 0.14 MeV. DT/DD neutron yield ratio for incident deuteron energies from 0.15 MeV to 0.40 MeV.

19. Neutron yield ratio Of DD and DT fusion reactions in the energy range 0.01 MeV ≤ Ed ≤ 39 MeV DT/DD neutron yield ratio for incident deuteron energies from 0.5 MeV to 2.2 MeV. DD/DT neutron yield ratio for incident deuteron energies from 2.2 MeV to 39 MeV.

20. Fusion power ratio calculations for D-D and D-T reactions in the energy range 0.01 MeV ≤ Ed ≤ 39 MeV We derived an equation to calculate the fusion power ratio. Pf(DT/DD) = Ef(DT) σDT / Ef(DD)σDD • Where • Ef(DT) is the fusion energy of DT • σDT is the total cross section of DT fusion reaction • Ef(DD) is the fusion energy of DD • σDD is total cross section of DD fusion reaction

21. Fusion power ratio calculations for D-D and D-T reactions in the energy range 0.01 MeV ≤ Ed ≤ 39 MeV Comparison between the fusion power of D-T and D-D fusion reactions in regime (0.14 – 0.3) MeV. Comparison between the fusion power of D-T and D-D fusion reactions in the regime (0.3 – 1) MeV. Comparison between the fusion power of D-T and D-D fusion reactions in the regime (0.01 – 0.13) MeV.

22. Fusion power ratio calculations for D-D and D-T reactions in the energy range 0.01 MeV ≤ Ed ≤ 39 MeV Comparison between the fusion power of D-T and D-D fusion reactions in the regime (1.1 – 14.4) MeV. Comparison between the fusion power of D-T and D-D fusion reactions in the regime (14.5 – 39) MeV.

23. Conclusion • In this work, an effective method for comparing the neutron yield and the fusion power of DT and DD fusion reactions is introduced. The study indicates that: • The neutron yield of the DT reaction is higher than that of the DD reaction in the energy range 0.01- 2.2 MeV and the DT/DD neutron yield ratio reaches its maximum value at 0.08 MeV. However, the neutron yield of DD reaction becomes higher at the energies higher than 2.2 MeV. Consequently, from the burning ratio point of view, DT reaction is the preferable fusion reaction at energies up to 2.2 MeV (especially at 0.08 MeV) but the DD reaction is the preferable one at the higher energies. • The fusion power of the DT reaction is higher than that of the DD reaction in the energy range 0.01- 14.3 MeV and the DT/DD fusion power ratio reaches its maximum value at 0.08 MeV. However, the fusion power of DD reaction becomes higher at the energies higher than 14.4 MeV. Consequently, from the fusion power point of view, DT reaction is preferable fusion reaction at energies up to 14.3 MeV but the DD reaction is the preferable one at the energies higher than 14.4 MeV. • the DT reaction is the proper reaction for the implosion approach of laser fusion especially at 0.08 MeV while the DD reaction is the proper reaction for the fast ignition approach. • At 0.08 MeV both the DT/DD neutron yield ratio and the DT/DD fusion power ratio are maxima.