Skip to main content
Log in

Reaction Rates Important for Fusion Targets

  • Published:
Mathematical Models and Computer Simulations Aims and scope

Abstract

To compute controlled fusion problems, four nuclear reactions are conventionally used. In the paper, cross sections of many thermonuclear reactions between the lightest elements are compared. We show that, along with the traditional four reactions, a tangible contribution can be made by the reaction \({\text{T}} + {\text{T}} \to 2n + \,{}^{{\text{4}}}{\text{He}}\). At low temperatures, the reactions \({\text{D}} + p \to \gamma + {}^{3}{\text{He}}\) and \({\text{T}} + p \to \gamma + {}^{4}{\text{He}}\) make a considerable contribution and it appears that the rest of the reactions can be neglected. For the outlined reactions, we perform a more thorough processing of the experimental data and construct high-order accurate approximations. The accuracy of finding the S-factor is 2–6% and that of the reaction rate is 3–4% for the new reactions.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.

Similar content being viewed by others

REFERENCES

  1. NEA Data Bank – Nuclear Data Services. http://www.oecd-nea.org/janisweb/search/exfor.

  2. NIST Standard Reference Data. https://www.nist.gov/srd.

  3. S. N. Abramovich, B. Ya. Guszhovskii, V. A. Zherebtsov, and A. G. Zvenigorodskii, Nuclear Physics Constants for Thermonuclear Fusion: A Reference Handbook, IAEA Rep. INDC(CCP)-326/L+F (IAEA, Vienna, 1991; TsNIIatominform, Moscow, 1989).

  4. B. N. Kozlov, “Thermonuclear reaction rates,” At. Energ. 12, 238–240 (1962).

    Google Scholar 

  5. A. A. Belov and N. N. Kalitkin, “Processing of experimental curves by applying a regularized double period method,” Dokl. Math. 94, 539–543 (2016).

    Article  MathSciNet  Google Scholar 

  6. A. A. Belov and N. N. Kalitkin, “Regularization of the double period method for experimental data processing,” Comput. Math. Math. Phys. 57, 1741–1750 (2017).

    Article  MathSciNet  Google Scholar 

  7. A. A. Belov, N. N. Kalitkin, and I. A. Kozlitin, “Refinement of thermonuclear reaction rates,” Fusion Eng. Des. 141, 51–58 (2019).

    Article  Google Scholar 

  8. N. N. Kalitkin, I. A. Kozlitin, and A. A. Belov, TEFIS Database. http://tefis.ru.

  9. G. A. Gamow, “Essay on the development of the doctrine of the structure of the atomic nucleus. Theory of radioactive decay,” Usp. Fiz. Nauk 10, 531–544 (1930).

    Article  Google Scholar 

  10. L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics, Vol. 3: Quantum Mechanics: Non-Relativistic Theory (Butterworth-Heinemann, Oxford, 1981; Fizmatlit, Moscow, 2004).

  11. E. Iu. Dnestrovskaia and N. N. Kalitkin, “Regression of experimental curves,” KIAM Preprint No. 181 (Keldysh Inst. Appl. Math., Moscow, 1987).

    Google Scholar 

  12. Los Alamos Scientific Lab. Reports No. 7722-PR (1978).

  13. H. S. Bosch and G. M. Hale, “Improved formulas for fusion cross-sections and thermal reactivities,” Nucl. Fus. 32, 611 (1992).

    Article  Google Scholar 

Download references

ACKNOWLEDGMENTS

The authors thank N.V. Zmitrenko for his valuable comments.

Funding

This work was supported by Russian Science Foundation, project no. 16-11-10 001.

Author information

Authors and Affiliations

Authors

Corresponding authors

Correspondence to A. A. Belov or N. N. Kalitkin.

Additional information

Translated by I. Tselishcheva

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Belov, A.A., Kalitkin, N.N., Topor, O.I. et al. Reaction Rates Important for Fusion Targets. Math Models Comput Simul 12, 293–301 (2020). https://doi.org/10.1134/S2070048220030084

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S2070048220030084

Keywords:

Navigation