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In this paper, we introduce the on-the-fly (OTF) Doppler method which is used to calculate the temperature-dependent cross section. After substituting Adler-Adler multilevel representation into Doppler formulation, the theoretical formulation of temperature dependent cross section is obtained. This theoretical formulation can be approximated by a Taylor series expansion and asymptotic series expansion, which is the base of OTF method. The OTF method can be used to calculate the cross section of any nuclide at any temperature in a range of 300-3000 K based on cross section library of 300 K. For the OTF method, firstly, a series of temperature dependent cross section libraries is produced by NJOY. Secondly, a uniform energy grid is evaluated by the temperature dependent cross section libraries. Thirdly, a polynomial is used to fit the temperature dependent cross section on each energy grid. The coefficient of the polynomial is obtained by single value decomposition algorithm. Finally, the coefficients of the polynomial in all energy grids and the energy grids themselves are written in a text file. To test the cross section polynomial produced by OTF method, we compare the total and absorption cross sections of 238U and 235U calculated by the polynomial with those produced by NJOY. The errors of these cross sections obtained by these two programs are presented in the paper. The text file produced by OTF method can be read by the Monte Carlo code JMCT, which is a coupled neutron/photon transport code developed by IAPCM. After providing the temperature and energy of the particle, the temperature dependent cross sections in two adjacent energy grids are calculated by the polynomial respectively. The cross section of target energy is obtained by linear interpolation. Two benchmarks including a pin-cell model and an assembly model are used to verify the applications of OTF method in JMCT. The results are presented in the paper.
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Keywords:
- Monte Carlo /
- JMCT /
- on-the-fly doppler broadening
[1] Li G, Deng L, Li S, Mo Z Y 2011 Acta Phys. Sin. 60 022401 (in Chinese) [李刚, 邓力, 李树, 莫则尧 2011 60 022401]
[2] Macfarlane R E, Muir D W, George D C 2000 NJOY99.0 code system for producing pointwise and multigroup neutron and photon cross sections from ENDF/B data p77
[3] Trumbull T H 2006 Nucl. Technol. 156 75
[4] Conlin J L, Ji W, Lee J C, Martin W R 2005 Trans. Am. Nucl. Soc. 92 225
[5] Zangian M, Minuchehr A, Zolfaghari A 2013 Annals of Nuclear Energy 62 170
[6] Li S Y 2012 Ph. D. Dissertation (Beijing: Tsinghua University) (in Chinese) [李松阳 2012 博士学位论文 (北京: 清华大学)]
[7] Yesilyurt G, Martin W R, Brown F B 2012 Nucl. Sci. Engineer. 171 239
[8] Cullen D E, Weisbin C R 1976 Nucl. Sci. Engineer. 60 199
[9] Mosteller R D, Eisenhart L D, Little R C, Eich W J, Chao J 1991 Nucl. Sci. Engineer. 107 265
[10] Yamamoto A, Ikehara T, Ito T, Saji E 2002 J. Nucl. Sci. Technol. 39 900
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[1] Li G, Deng L, Li S, Mo Z Y 2011 Acta Phys. Sin. 60 022401 (in Chinese) [李刚, 邓力, 李树, 莫则尧 2011 60 022401]
[2] Macfarlane R E, Muir D W, George D C 2000 NJOY99.0 code system for producing pointwise and multigroup neutron and photon cross sections from ENDF/B data p77
[3] Trumbull T H 2006 Nucl. Technol. 156 75
[4] Conlin J L, Ji W, Lee J C, Martin W R 2005 Trans. Am. Nucl. Soc. 92 225
[5] Zangian M, Minuchehr A, Zolfaghari A 2013 Annals of Nuclear Energy 62 170
[6] Li S Y 2012 Ph. D. Dissertation (Beijing: Tsinghua University) (in Chinese) [李松阳 2012 博士学位论文 (北京: 清华大学)]
[7] Yesilyurt G, Martin W R, Brown F B 2012 Nucl. Sci. Engineer. 171 239
[8] Cullen D E, Weisbin C R 1976 Nucl. Sci. Engineer. 60 199
[9] Mosteller R D, Eisenhart L D, Little R C, Eich W J, Chao J 1991 Nucl. Sci. Engineer. 107 265
[10] Yamamoto A, Ikehara T, Ito T, Saji E 2002 J. Nucl. Sci. Technol. 39 900
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