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The reflected neutrons from the wall of the reactor have a significant effect on the waveform of the fast burst reactor. The leakage neutrons from the reactor core have a certain probability that they will come back. Their return time displays a continuous distribution because of the difference in energy among the reflected neutrons. In the stable state, the influence of the reflected neutrons is not obvious. However, in a prompt state, it is obvious because the reflected neutrons are not synchronized with the neutrons in the reactor core, which leads to some strange phenomena in experiment. For example, in the process of erupting a fission burst in a metal reactor, the number of neutrons in core increases very rapidly, while the return time of reflected neutrons lags behind, which causes the falling edge to slow down. The two-region kinetic model, which divides the reactor core into a fission region and a reflected region, is generally used to study the reflected reactor. The traditional two-region kinetic model only takes into account the interaction probability between the two regions but the time property of the interaction is not considered at all. Therefore, the traditional two-region model can well describe the stable state process rather than the prompt one. In the early stage, the delayed neutron approximation method was used to study the reflected neutron problem of metal burst reactors. Although some parameters were obtained to be in accordance with the experimental results, there existed a significant difference in behavior between delayed neutrons and reflected neutrons. In this paper, we present a time-dependent two-region model which can effectively describe the behavior of the reflected neutrons in both stable and prompt states. Firstly, we use the Monte-Carlo method to calculate the returning behavior of one leakage neutron from the reactor core. The equivalent eigen source is obtained by solving the kinetic equation with the Monte-Carlo calculating result. This source, including time information, causes the same effect as that of one leakage neutron in the reactor. Secondly, we establish the kinetic equation with reflection effect by introducing the eigen source. In short, the reflected neutrons are treated as an equivalent neutron source. The waveform acquired through solving the equation is consistent with the experiment data of CFBR-Ⅱ, which reasonably describes the experimental phenomenon of falling edge slow-down and plateau power increase.
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Keywords:
- reflected neutron /
- equivalent neutron /
- burst reactor /
- kinetic equations
[1] Zhong J, Chen W, Yang J, Wang D H, Chen D 2001 Physics 30 693 (in Chinese)[钟洁, 陈伟, 杨军, 王道华, 陈达 2001 物理 30 693]
[2] Yang C, Gong S 1995 Trends Nucl. Phys. 12 58 (in Chinese)[杨成德, 龚书良 1995 核物理动态 12 58]
[3] Ye T, Sun W, Deng L, She R, Xiao G 2014 Nucl. Data Sheets 118 582
[4] Price C C 1970 Ph. D. Dissertation (Albuquerque:University of New Mexico)
[5] Coats R L
[6] Avery R 1958 Nucl. Sci. Eng. 3 129
[7] Cohn C E
[8] Cohn C E 1962 Nucl. Sci. Eng. 13 12
[9] Spriggs G D, Busch R D 1994 The Shift of Prompt Critical in Reflected Reactors and the Limitations of the Mean Prompt-neutron Lifetime Model (Los Alamos National Laboratory) LA-UR-94-2250
[10] Busch R D, Spriggs G D 1995 Coupling Parameters for Partially Reflected Reactors (Los Alamos National Laboratory) LA-UR-95-2028
[11] Spriggs G D, Busch R D, Williams J G 1997 Ann. Nucl. Energ. 24 205
[12] Dam H V 1996 Ann. Nucl. Energ. 23 1127
[13] Tobias M, Haubenreich P N, Aven R E 1953 Conversion in a Two-Region Reactor (Oak Ridge National Laboratory) CF-53-2-134
[14] Aboanber A E 2010 Prog. Nucl. Energ. 52 197
[15] Kawai T 1965 J. Nucl. Sci. Technol. 2 245
[16] Kawai T 1965 J. Nucl. Sci. Technol. 2 285
[17] Wimett T F 1960 Nucl. Sci. Eng. 8 691
[18] Zhang X D 1995 J. Changzhou Norm. College of Technol. 1 1 (in Chinese)[张显达 1995 常州技术师范学院学报 1 1]
[19] Li B, Lu Y, Lu W, Li M, Liang W F, Xie Q L, Fan X Q 2014 At. Energ. Sci. Technol. 48(s1) 144 (in Chinese)[李兵, 鲁艺, 卢伟, 李勐, 梁文峰, 谢奇林, 范晓强 2014 原子能科学技术 48(增刊1) 144]
[20] Li B, Lu Y, Gao H 2016 High Power Laser and Particle Beams 28 056001 (in Chinese)[李兵, 鲁艺, 高辉 2016 强激光与粒子束 28 056001]
[21] Song L L, Gao H
[22] He R F, Deng M C 2012 Experiments and Physics on Fast-Neutron Critical Facilities and Pulsed Reactors (Bejing:National Defence Industry Press) p439 (in Chinese)[贺仁辅, 邓门才 2012 快中子临界装置和脉冲堆实验物理(北京:国防工业出版社) 第439页]
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[1] Zhong J, Chen W, Yang J, Wang D H, Chen D 2001 Physics 30 693 (in Chinese)[钟洁, 陈伟, 杨军, 王道华, 陈达 2001 物理 30 693]
[2] Yang C, Gong S 1995 Trends Nucl. Phys. 12 58 (in Chinese)[杨成德, 龚书良 1995 核物理动态 12 58]
[3] Ye T, Sun W, Deng L, She R, Xiao G 2014 Nucl. Data Sheets 118 582
[4] Price C C 1970 Ph. D. Dissertation (Albuquerque:University of New Mexico)
[5] Coats R L
[6] Avery R 1958 Nucl. Sci. Eng. 3 129
[7] Cohn C E
[8] Cohn C E 1962 Nucl. Sci. Eng. 13 12
[9] Spriggs G D, Busch R D 1994 The Shift of Prompt Critical in Reflected Reactors and the Limitations of the Mean Prompt-neutron Lifetime Model (Los Alamos National Laboratory) LA-UR-94-2250
[10] Busch R D, Spriggs G D 1995 Coupling Parameters for Partially Reflected Reactors (Los Alamos National Laboratory) LA-UR-95-2028
[11] Spriggs G D, Busch R D, Williams J G 1997 Ann. Nucl. Energ. 24 205
[12] Dam H V 1996 Ann. Nucl. Energ. 23 1127
[13] Tobias M, Haubenreich P N, Aven R E 1953 Conversion in a Two-Region Reactor (Oak Ridge National Laboratory) CF-53-2-134
[14] Aboanber A E 2010 Prog. Nucl. Energ. 52 197
[15] Kawai T 1965 J. Nucl. Sci. Technol. 2 245
[16] Kawai T 1965 J. Nucl. Sci. Technol. 2 285
[17] Wimett T F 1960 Nucl. Sci. Eng. 8 691
[18] Zhang X D 1995 J. Changzhou Norm. College of Technol. 1 1 (in Chinese)[张显达 1995 常州技术师范学院学报 1 1]
[19] Li B, Lu Y, Lu W, Li M, Liang W F, Xie Q L, Fan X Q 2014 At. Energ. Sci. Technol. 48(s1) 144 (in Chinese)[李兵, 鲁艺, 卢伟, 李勐, 梁文峰, 谢奇林, 范晓强 2014 原子能科学技术 48(增刊1) 144]
[20] Li B, Lu Y, Gao H 2016 High Power Laser and Particle Beams 28 056001 (in Chinese)[李兵, 鲁艺, 高辉 2016 强激光与粒子束 28 056001]
[21] Song L L, Gao H
[22] He R F, Deng M C 2012 Experiments and Physics on Fast-Neutron Critical Facilities and Pulsed Reactors (Bejing:National Defence Industry Press) p439 (in Chinese)[贺仁辅, 邓门才 2012 快中子临界装置和脉冲堆实验物理(北京:国防工业出版社) 第439页]
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