Skip to main content

Advertisement

SpringerLink
Log in

On-the-fly Doppler broadening method based on optimal double-exponential formula

  • Published:
Nuclear Science and Techniques Aims and scope Submit manuscript

Abstract

As temperature changes constantly in nuclear reactor operation, on-the-fly Doppler broadening methods are commonly adopted for generating nuclear cross sections at various temperatures in neutron transport simulation. Among the existing methods, the widely used SIGMA1 approach is inefficient because it involves error function and Taylor series expansion. In this paper, we present a new on-the-fly Doppler broadening with optimal double-exponential formula based on SuperMC to improve efficiency with given accuracy. In this method, double-exponential formula in 1/16 steps is used for broadening cross section at low energy, with both accuracy and efficiency. Meanwhile, the Gauss–Hermite quadrature of different orders is used for broadening cross section at resonance energy. The method can generate neutron cross section rapidly and precisely at the desired temperature. Typical nuclide cross sections and benchmarking tests are presented in detail.

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

Access this article

Log in via an institution

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
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

  1. R. Macfarlane, D. Muir, R. Boicourt et al., The NJOY nuclear data processing system, version 2012, LA-UR-12-27079, Los Alamos National Laboratory (2012).

  2. D. Cullen, PREPRO 2015: 2015 ENDF/B Pre-Processing Codes, IAEA-NDS-39, Rev. 14 International Atomic Energy Agency (2015).

  3. D. Cullen, Program SIGMA1 (version 79-1): Doppler broaden evaluated cross sections in the evaluated nuclear data file/version B (ENDF/B) format, UCRL-50400, Lawrence Livermore National Laboratory (1979).

  4. G. Yesilyurt, W. Martin, F. Brown, On-the-fly Doppler broadening for Monte Carlo codes. Nucl. Sci. Eng. 171, 239–257 (2012). doi:10.13182/NSE11-67

    Article  Google Scholar 

  5. T. Viitanen, J. Leppanen, Explicit treatment of thermal motion in continuous-energy Monte Carlo tracking routines. Nucl. Sci. Eng. 171, 165–173 (2012). doi:10.13182/NSE11-36

    Article  Google Scholar 

  6. B. Forget, S. Xu, K. Smith, Direct Doppler broadening in Monte Carlo simulations using the multipole representation. Ann. Nucl. Energy 64, 78–85 (2014). doi:10.1016/j.anucene.2013.09.043

    Article  Google Scholar 

  7. A. Villanueva, J. Granada, Experimental evidence sustaining a compact-extended model for Doppler broadening of neutron absorption resonances. Ann. Nucl. Energy 38, 1389–1398 (2011). doi:10.1016/j.anucene.2011.01.034

    Article  Google Scholar 

  8. P. Romano, T. Trumbull, Comparison of algorithms for Doppler broadening pointwise tabulated cross section. Ann. Nucl. Energy 75, 358–364 (2015). doi:10.1016/j.anucene.2014.08.046

    Article  Google Scholar 

  9. C. Dean, R. Perry, R. Neal et al., Validation of run-time Doppler broadening in MONK with JEFF3.1. J. Korean Phys. Soc. 59, 1162–1165 (2011). doi:10.3938/jkps.59.1162

    Article  Google Scholar 

  10. G. Ferran, W. Haeck, A new method for the Doppler broadening of the Solbrig’s kernel using a Fourier transforms. Nucl. Sci. Eng. 179, 1–17 (2015). doi:10.13182/NSE14-64

    Article  Google Scholar 

  11. Y. Wu, J. Song, H. Zheng et al., CAD-based Monte Carlo program for integrated simulation of nuclear system SuperMC. Ann. Nucl. Energy 82, 161–168 (2015). doi:10.1016/j.anucene.2014.08.058

    Article  Google Scholar 

  12. Y. Wu, F.D.S. Team, CAD-based interface programs for fusion neutron transport simulation. Fusion Eng. Des. 84, 1987–1992 (2009). doi:10.1016/j.fusengdes.2008.12.041

    Article  Google Scholar 

  13. Y. Wu, Z. Chen, L. Hu et al., Identification of safety gaps for fusion demonstration reactors. Nat. Energy 1, 16154 (2016). doi:10.1038/nenergy.2016.154

    Article  Google Scholar 

  14. Y. Wu, J. Jiang, M. Wang et al., A fusion-driven subcritical system concept based on viable technologies. Nucl. Fusion 51, 103036 (2011). doi:10.1088/0029-5515/51/10/103036

    Article  Google Scholar 

  15. Y. Wu, F.D.S. Team, Design analysis of the China dual-functional lithium lead (DFLL) test blanket module in ITER. Fusion Eng. Des. 82, 1893–1903 (2007). doi:10.1016/j.fusengdes.2007.08.012

    Article  Google Scholar 

  16. D. Cullen, C. Weisbin, Exact Doppler broadening of tabulated cross section. Nucl. Sci. Eng. 60, 199–229 (1976). doi:10.13182/NSE76-1

    Article  Google Scholar 

  17. H. Takahasi, M. Mori, Double-exponential formulas for numerical integration. Publ. Res. I. Math. Sci. 9, 721–741 (1974)

    Article  MathSciNet  MATH  Google Scholar 

  18. M. Mori, M. Sugihara, The double-exponential transformation in numerical analysis. J. Comput. Appl. Math. 127, 287–296 (2001). doi:10.1016/S0377-0427(00)00501-X

    Article  MathSciNet  MATH  Google Scholar 

  19. J. Briggs, L. Scott, A. Nouri, The international criticality safety benchmark evaluation project. Nucl. Sci. Eng. 145, 1–10 (2003). doi:10.13182/NSE03-14

    Article  Google Scholar 

  20. R. Mosteller, ENDF/B-V, ENDF/B-VI, ENDF/B-VII.0 Results for the Doppler-Defect Benchmark, LA-UR-07-0922, Los Alamos National Laboratory (2007).

Download references

Acknowledgements

The authors would like to show their great appreciation to other members of the FDS Team for supports to this research.

Author information

Authors and Affiliations

  1. Key Laboratory of Neutronics and Radiation Safety, Institute of Nuclear Energy Safety Technology, Chinese Academy of Sciences, Hefei, 230031, China

    Rui Chen, Li-Juan Hao, Bin Wu, Jing Song & Li-Qin Hu

  2. University of Science and Technology of China, Hefei, 230027, China

    Rui Chen & Li-Qin Hu

Authors
  1. Rui Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Li-Juan Hao
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Bin Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Jing Song
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Li-Qin Hu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Li-Qin Hu.

Additional information

This work was supported by the Strategic Priority Science and Technology Program of the Chinese Academy of Sciences (No. XDA03040000), the Innovation Foundation of the Chinese Academy of Sciences (No. CXJJ-16Q231), the National Natural Science Foundation of China (NSFC) (Nos. 11305205, 11305203, 11405204 and 11605233), the National Magnetic Confinement Fusion Science Program of China (No. 2014GB112001), the Special Program for Informatization of the Chinese Academy of Sciences (No. XXH12504-1-09), the Anhui Provincial Special project for High Technology Industry, the Special Project of Youth Innovation Promotion Association of Chinese Academy of Sciences, the Industrialization Fund, the Open Funds of Engineering Research Center of Nuclear Technology Application of Ministry of Education (No. HJSJYB2011-11) and Jiang Xi young science foundation project (No.GJJ150558).

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Chen, R., Hao, LJ., Wu, B. et al. On-the-fly Doppler broadening method based on optimal double-exponential formula. NUCL SCI TECH 28, 166 (2017). https://doi.org/10.1007/s41365-017-0318-4

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s41365-017-0318-4

Keywords

Search

Navigation