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Experimental study on fission reaction rate induced by D-T neutron in depleted uranium shell

Han Zi-Jie Zhu Tong-Hua Lu Xin-Xin Qin Jian-Guo Wang Mei Jiang Li Yang Bo

Experimental study on fission reaction rate induced by D-T neutron in depleted uranium shell

Han Zi-Jie, Zhu Tong-Hua, Lu Xin-Xin, Qin Jian-Guo, Wang Mei, Jiang Li, Yang Bo
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  • Fission reaction rate is an important index for validating and checking the neutron transportation and fission power in nuclear engineering. The experimental data can be used in benchmark validation of cross sections, and in studying the correlation of fission power with the thickness of uranium sphere shell. There are five assemblies of depleted uranium shells used in this work, the inner radii of which are all fixed at 13.1 cm, while their outer radii are 18.1, 19.4, 23.35, 25.4 and 28.5 cm, respectively. The D-T neutron source is generated in the center of the assemblies, the yield of which is about 3 × 1010−4 × 1010 s–1. In horizontal plane across the center of the assemblies, the fission rates at positions along the radial direction are measured in the direction with 45° inclining with respect to the incident D+ beam. Due to the disturbance to assemblies and neutron field, the activation foil of uranium is a suitable choice rather than fission chamber or capture detector. The material of activation foil is the same as that in the experimental assemblies. Considering the accurate fission yield of 143Ce, the objective nuclides are selected. The total fission yield of 143Ce is contributed by 238U and a little 235U. For calculating the total fission yiled of 143Ce, the neutron energy range of 0−15 MeV is divided into eight subranges. By measuring the 293 keV gamma rays from the fission product 143Ce in activation foils with a TRANS-SPEC-DX100 HPGe detector, with a relative efficiency 40%, the fission rates and the trends at positions along the radial direction in the five assemblies are obtained based on the 143Ce fission product yield. The fission rate ranges from 5.28 × 10–29 to 7.58 × 10–28 sn-1·nuclide–1, with the relative uncertainty in a range from 6% to 11%. The Monte Carlo transport code MCNP5 and continuous energy cross section library ENDF/BV.8 are used for analyzing the fission rate distribution in the assemblies, and the experiemtal configuration, including the wall of the experimental hall is described in detail in the model. The calculated results are compared with the experimental ones and their agreement is found to be in an uncertainty range.
      Corresponding author: Qin Jian-Guo, stingg@126.com
    [1]

    Yu J N, Yu G 2009 J. Nucl. Mater 386−388 949

    [2]

    Robert G Mills 1981 IEEE Trans. Power Apparatus Systems PAS-100 1173

    [3]

    张俊, 张大林, 王成龙, 田文喜, 秋穗正, 苏光辉 2017 原子能科学技术 51 2230

    Zhang J, Zhang D L, Wang C L, Tian W X, Qiu S Z, Su G H 2017 At. Energ. Sci. Technol. 51 2230

    [4]

    刘国明, 程和平, 邵增 2012 原子能科学技术 46 272

    Liu G M, Cheng H P, Shao Z 2012 At. Energ. Sci. Technol. 46 272

    [5]

    马纪敏, 刘永康 2012 原子能科学技术 46 437

    Ma J M, Liu Y K 2012 At. Energ. Sci. Technol. 46 437

    [6]

    徐红, 杨永伟, 周志伟 2009 原子能科学技术 43 97

    Xu H, Yang Y W, Zhou Z W 2009 At. Energ. Sci. Technol. 43 97

    [7]

    Li M S, Liu R, Shi X M, Yi W W, Peng X J 2012 Fusion Eng. Des. 87 1420

    [8]

    马纪敏, 刘永康, 李茂生 2012 核动力工程 33 16

    Ma J M, Liu Y K, Li M S 2012 Nucl. Power Eng. 33 16

    [9]

    伊炜伟, 胡泽华, 李茂生 2010 核动力工程 31 125

    Yi W W, Hu Z H, Li M S 2010 Nucl. Power Eng. 31 125

    [10]

    Weale J W, Goodfellow H, Mctaggart M H, Mullender M L 1961 J. Nucl. Energ. 14 91

    [11]

    Akiyama M, Oka Y, Kanasugi K, Hashikura H, Kondo S 1987 Ann. Nucl. Energy 14 543

    [12]

    Afanas’ev V V, Belevitin A G, Verzilov Y M, Romodanov V L, Khro-mov V V, Markovskii D V, Shatalov G E 1991 At. Energ. 71 901

    [13]

    Zhu T H, Yang C W, Lu X X, Liu R, Han Z J, Jiang L, Wang M 2014 Ann. Nucl. Energy 63 486

    [14]

    Kimio Y, Shigeru I, Hisao O, Tetsuo M 1983 Jpn. J. Appl. Phys. 22 324

    [15]

    Li Y G, Shi Y Q, Zhang Y B, Xia P 2001 Radiat. Meas. 34 589

    [16]

    Szabó J, Pálfalvi J K, Strádi A, Bilski P, Swakoń J, Stolarczyk L 2018 Nucl. Instrum. Meth. Phys. Res. A 888 196

    [17]

    Wojciechowski A, Lim Y C, Stepanenko V, Tiutiunnikov S, Khilmanovich A, Martsynkevich B 2016 Measurement 90 118

    [18]

    Lin H X, Chen W L, Liu Y H, Sheu R J 2016 Nucl. Instrum. Meth. Phys. Res. A 811 94

    [19]

    Yang Y W, Yan X S, Liu R, Lu X X, Jiang L, Lin J F 2012 Fusion Eng. Des. 87 1679

    [20]

    冯松, 刘荣, 鹿心鑫, 羊奕伟, 王玫, 蒋励, 秦建国 2014 物理学报 63 162501

    Feng S, Liu R, Lu X X, Yang Y W, Wang M, Jiang L, Qin J G 2014 Acta Phys.Sin. 63 162501

    [21]

    鹿心鑫, 朱通华, 刘荣, 蒋励, 王玫, 林菊芳, 温中伟 2011 原子能科学技术 45 645

    Lu X X, Zhu T H, Liu R, Jiang L, Wang M, Lin J F, Wen Z W 2011 At. Energ. Sci. Technol. 45 645

    [22]

    Zhu T H, Han Z J, Jiang L, Wang M, Lu X X, Yang C W, Liu R 2015 J. Nucl. Sci. Technol. 52 1383

    [23]

    Gooden M E, Arnold C W, Becker J A, Bhatia C, Bhike M, Bond E M, Bredeweg T A, Fallin B, Fowler M M, Howell C R, Kelley J H, Krishichayan, Macri R, Rusev G, Ryan C, Sheets S A, Stoyer M A, Tonchev A P, Tornow W, Vieira D J, Wilhelmy J B 2016 Nuclear Data Sheets 131 319

    [24]

    刘荣, 林理彬, 王大伦, 励义俊, 蒋励, 陈素和, 王玫, 杨可 1999 核电子学与探测技术 19 428

    Liu R, Lin L B, Wang D L, Li Y J, Jiang L, Chen S H, Wang M, Yang K 1999 Nuclear Electron. Detect. Technol. 19 428

    [25]

    Lu X D, Tian D F, Xie D 2004 Nucl. Instrum. Meth. Phys. Res. A 519 647

    [26]

    Zhu C X, Chen Y, Mou Y F, Zheng P, He T, Wang X H, An L, Guo H P 2011 Nucl. Sci. Eng. 169 188

  • 图 1  (a)贫化铀装置实物图; (b)蒙特卡罗模型5片活化探测器分布情况(45°方向中的1, 2, 3, 4, 5)

    Figure 1.  (a) Physical map of depleted uranium device; (b) distribution of five activation detectors in Monte Carlo Model 5 (1, 2, 3, 4, 5 in the direction of 45°).

    图 2  HPGe探测器测量的贫化铀活化探测器发射的γ

    Figure 2.  γ spectrum of depleted uranium activation detector, detected by using HPGe detector.

    图 3  五种模型中的裂变反应率分布情况

    Figure 3.  Fission reaction rate distribution for five models.

    图 4  五种模型不同测量点处的中子通量密度(蒙特卡罗模拟计算)

    Figure 4.  Neutron flux density at various measuring positions of five models (Monte Carlo simulation).

    图 5  贫化铀装置中不同位置裂变率C/E

    Figure 5.  C/E ratio of fission reaction rate for various measuring position in depleted uranium assembly.

    表 1  五种贫化铀球壳的外径及厚度

    Table 1.  Radius and thickness of depleted uranium shells.

    模型编号外半径Rout/cm厚度L/cm
    118.105.00
    219.406.30
    323.3510.25
    425.4012.30
    528.4515.35
    DownLoad: CSV

    表 2  五种模型中活化探测器的布放位置

    Table 2.  Position of activation detector in various models

    模型编号L/cm
    p1p2p3p4p5
    113.6014.6215.6416.1617.18
    214.6015.6216.6417.6618.68
    314.6016.6218.6420.6621.68
    415.6018.6220.6422.6624.68
    515.6018.6220.6424.1627.18
    DownLoad: CSV

    表 3  YCe-143

    Table 3.  Values of YCe-143.

    Model No.p1/%p2/%p3/%p4/%p5/%
    14.294.324.334.344.34
    24.334.354.374.384.37
    34.364.414.454.454.46
    44.404.474.494.504.49
    54.414.484.514.554.55
    DownLoad: CSV

    表 4  裂变反应率总不确定度

    Table 4.  Synthesize uncertainty of fission reaction rate.

    PositionModel 1Model 2Model 3Model 4Model 5
    p1/%6.56.56.57.46.1
    p2/%6.26.35.77.27.0
    p3/%6.55.86.78.610.0
    p4/%6.56.36.59.59.5
    p5/%6.56.17.010.910.9
    DownLoad: CSV
  • [1]

    Yu J N, Yu G 2009 J. Nucl. Mater 386−388 949

    [2]

    Robert G Mills 1981 IEEE Trans. Power Apparatus Systems PAS-100 1173

    [3]

    张俊, 张大林, 王成龙, 田文喜, 秋穗正, 苏光辉 2017 原子能科学技术 51 2230

    Zhang J, Zhang D L, Wang C L, Tian W X, Qiu S Z, Su G H 2017 At. Energ. Sci. Technol. 51 2230

    [4]

    刘国明, 程和平, 邵增 2012 原子能科学技术 46 272

    Liu G M, Cheng H P, Shao Z 2012 At. Energ. Sci. Technol. 46 272

    [5]

    马纪敏, 刘永康 2012 原子能科学技术 46 437

    Ma J M, Liu Y K 2012 At. Energ. Sci. Technol. 46 437

    [6]

    徐红, 杨永伟, 周志伟 2009 原子能科学技术 43 97

    Xu H, Yang Y W, Zhou Z W 2009 At. Energ. Sci. Technol. 43 97

    [7]

    Li M S, Liu R, Shi X M, Yi W W, Peng X J 2012 Fusion Eng. Des. 87 1420

    [8]

    马纪敏, 刘永康, 李茂生 2012 核动力工程 33 16

    Ma J M, Liu Y K, Li M S 2012 Nucl. Power Eng. 33 16

    [9]

    伊炜伟, 胡泽华, 李茂生 2010 核动力工程 31 125

    Yi W W, Hu Z H, Li M S 2010 Nucl. Power Eng. 31 125

    [10]

    Weale J W, Goodfellow H, Mctaggart M H, Mullender M L 1961 J. Nucl. Energ. 14 91

    [11]

    Akiyama M, Oka Y, Kanasugi K, Hashikura H, Kondo S 1987 Ann. Nucl. Energy 14 543

    [12]

    Afanas’ev V V, Belevitin A G, Verzilov Y M, Romodanov V L, Khro-mov V V, Markovskii D V, Shatalov G E 1991 At. Energ. 71 901

    [13]

    Zhu T H, Yang C W, Lu X X, Liu R, Han Z J, Jiang L, Wang M 2014 Ann. Nucl. Energy 63 486

    [14]

    Kimio Y, Shigeru I, Hisao O, Tetsuo M 1983 Jpn. J. Appl. Phys. 22 324

    [15]

    Li Y G, Shi Y Q, Zhang Y B, Xia P 2001 Radiat. Meas. 34 589

    [16]

    Szabó J, Pálfalvi J K, Strádi A, Bilski P, Swakoń J, Stolarczyk L 2018 Nucl. Instrum. Meth. Phys. Res. A 888 196

    [17]

    Wojciechowski A, Lim Y C, Stepanenko V, Tiutiunnikov S, Khilmanovich A, Martsynkevich B 2016 Measurement 90 118

    [18]

    Lin H X, Chen W L, Liu Y H, Sheu R J 2016 Nucl. Instrum. Meth. Phys. Res. A 811 94

    [19]

    Yang Y W, Yan X S, Liu R, Lu X X, Jiang L, Lin J F 2012 Fusion Eng. Des. 87 1679

    [20]

    冯松, 刘荣, 鹿心鑫, 羊奕伟, 王玫, 蒋励, 秦建国 2014 物理学报 63 162501

    Feng S, Liu R, Lu X X, Yang Y W, Wang M, Jiang L, Qin J G 2014 Acta Phys.Sin. 63 162501

    [21]

    鹿心鑫, 朱通华, 刘荣, 蒋励, 王玫, 林菊芳, 温中伟 2011 原子能科学技术 45 645

    Lu X X, Zhu T H, Liu R, Jiang L, Wang M, Lin J F, Wen Z W 2011 At. Energ. Sci. Technol. 45 645

    [22]

    Zhu T H, Han Z J, Jiang L, Wang M, Lu X X, Yang C W, Liu R 2015 J. Nucl. Sci. Technol. 52 1383

    [23]

    Gooden M E, Arnold C W, Becker J A, Bhatia C, Bhike M, Bond E M, Bredeweg T A, Fallin B, Fowler M M, Howell C R, Kelley J H, Krishichayan, Macri R, Rusev G, Ryan C, Sheets S A, Stoyer M A, Tonchev A P, Tornow W, Vieira D J, Wilhelmy J B 2016 Nuclear Data Sheets 131 319

    [24]

    刘荣, 林理彬, 王大伦, 励义俊, 蒋励, 陈素和, 王玫, 杨可 1999 核电子学与探测技术 19 428

    Liu R, Lin L B, Wang D L, Li Y J, Jiang L, Chen S H, Wang M, Yang K 1999 Nuclear Electron. Detect. Technol. 19 428

    [25]

    Lu X D, Tian D F, Xie D 2004 Nucl. Instrum. Meth. Phys. Res. A 519 647

    [26]

    Zhu C X, Chen Y, Mou Y F, Zheng P, He T, Wang X H, An L, Guo H P 2011 Nucl. Sci. Eng. 169 188

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  • Received Date:  16 September 2018
  • Accepted Date:  07 May 2019
  • Available Online:  10 August 2019
  • Published Online:  01 August 2019

Experimental study on fission reaction rate induced by D-T neutron in depleted uranium shell

    Corresponding author: Qin Jian-Guo, stingg@126.com
  • 1. Institute of Nuclear Physics and Chemistry, China Academy of Engineering Physics, Mianyang 621900, China
  • 2. Institute of Applied Physics and Computational Mathematics, China Academy of Engineering Physics, Beijing 100094, China

Abstract: Fission reaction rate is an important index for validating and checking the neutron transportation and fission power in nuclear engineering. The experimental data can be used in benchmark validation of cross sections, and in studying the correlation of fission power with the thickness of uranium sphere shell. There are five assemblies of depleted uranium shells used in this work, the inner radii of which are all fixed at 13.1 cm, while their outer radii are 18.1, 19.4, 23.35, 25.4 and 28.5 cm, respectively. The D-T neutron source is generated in the center of the assemblies, the yield of which is about 3 × 1010−4 × 1010 s–1. In horizontal plane across the center of the assemblies, the fission rates at positions along the radial direction are measured in the direction with 45° inclining with respect to the incident D+ beam. Due to the disturbance to assemblies and neutron field, the activation foil of uranium is a suitable choice rather than fission chamber or capture detector. The material of activation foil is the same as that in the experimental assemblies. Considering the accurate fission yield of 143Ce, the objective nuclides are selected. The total fission yield of 143Ce is contributed by 238U and a little 235U. For calculating the total fission yiled of 143Ce, the neutron energy range of 0−15 MeV is divided into eight subranges. By measuring the 293 keV gamma rays from the fission product 143Ce in activation foils with a TRANS-SPEC-DX100 HPGe detector, with a relative efficiency 40%, the fission rates and the trends at positions along the radial direction in the five assemblies are obtained based on the 143Ce fission product yield. The fission rate ranges from 5.28 × 10–29 to 7.58 × 10–28 sn-1·nuclide–1, with the relative uncertainty in a range from 6% to 11%. The Monte Carlo transport code MCNP5 and continuous energy cross section library ENDF/BV.8 are used for analyzing the fission rate distribution in the assemblies, and the experiemtal configuration, including the wall of the experimental hall is described in detail in the model. The calculated results are compared with the experimental ones and their agreement is found to be in an uncertainty range.

    • 大量基础研究认为, 基于聚变中子源[1]和次临界堆包层的聚变-裂变混合型次临界能源堆[2]是解决能源问题比较值得研究的途径. 在这些概念研究中, 我国的研究团队开发了基于MCNP[3]程序的耦合程序, 如MCORGS, MCBURN, MOCOUPLES等[4-7], 并配套开发了多群截面库[8,9], 为校验程序和截面库的可靠性, 有必要在一系列模拟装置上开展基准实验.

      次临界能源堆能源供应主要依靠裂变包层中贫化铀裂变释放裂变能来实现, 裂变反应率的准确性在设计能量放大指标中异常重要. 英国的Weale等[10]用直径29.2 mm的天然铀棒搭建了一个高1066 mm, 直径990 mm的准圆柱装置, 用圆柱形裂变电离室测量了238U(n, f)及235U(n, f)裂变反应率分布. 日本东京大学的Akiyama等[11]用铀块堆砌了等效半径为457.2 mm的准球形装置, 利用柱形裂变室测量了14 MeV中子源条件下装置内侧238U(n, f)及235U(n, f)反应率, 不确定度为5.5%—6.0%. Afanas’ev等[12]在聚变堆包层模拟装置上开展14 MeV中子学积分实验, 用固体径迹探测器测量238U(n, f)及235U(n, f)反应率, 相对不确定度在8%. 国内朱通华等[13]在贫化铀聚乙烯交替球壳上用长杆平板型贫化铀裂变室测量了裂变反应率径向分布, 不确定度为3.4%.

      Weale实验与Akiyama实验所用的装置均采用现有材料堆砌而成, 基准性不足. 另外, 上述实验测量无论采用裂变室[14]还是固体径迹探测器[15,16], 均在被测位置引入了其他材料, 破坏了测量对象的原始状态, 使得测量点的物理参数发生改变, 要对测量值进行修正才能得到所需的物理量. 为了解决以上探测手段对测量的影响, 本文采用与宏观贫化铀球壳丰度完全相同的贫化铀片状样品作为活化探测器[17,18], 活化探测器可以看作被测模型的一部分, 最大限度降低了对被测对象的影响. 利用中国工程物理研究院现有系列贫化铀球壳, 构建五种不同厚度的实验模型, 选择与D+粒子(D+粒子指氘气电离后形成的带正电的原子核, 经引出、加速、然后轰击氚靶产生中子)水平呈45°角的测量孔道, 采用活化法基于14 MeV D-T中子开展实验研究. 选择裂变碎片中的143Ce[19]作为测量对象, 通过测量其发射的γ射线, 实现143Ce核子数的测量, 再根据裂变产额数据和中子产额监测数据, 获得裂变反应率沿45°方向分布规律, 为裂变放能与球壳厚度关系研究提供数据支持.

    2.   方法与实验
    • 绝对裂变反应率是指一个源中子诱发一个核材料原子核产生裂变的概率[20]. 通过测量装置内被测位置的核裂变计数, 可得到该处的裂变反应率. 裂变率计算公式为

      式中, ${N_{\rm{f}}}$为裂变数, $\phi $为中子产额, ${t_1}$为辐照时间, m为活化探测器核子数.

      本实验选取裂变产额比较准确的裂变碎片143Ce作为测量对象, 核裂变数${N_{\rm{f}}}$143Ce核子数${N_{{\rm{Ce}} \text{-} 143}}$有如下关系:

      式中${Y_{{\rm{Ce}} \text{-} 143}}$143Ce总裂变产额.

      贫化铀主要成分为238U和235U, 将中子能量从0 keV到15 MeV分成8个能段(238U只计算后7个能段), 143Ce总裂变产额${Y_{{\rm{Ce}} \text{-} 143}}$可用(3)式表示:

      式中, ${R_5}$235U裂变占总裂变的百分比; ${Y_{5i}}$为第i个能量段235U裂变143Ce的产额; ${R_{5i}}$为第i个能量段裂变占总235U裂变的百分比; ${R_8}$238U裂变占总裂变的百分比; ${Y_{8i}}$为第i个能量段238U裂变143Ce的产额; ${R_{8i}}$为第i个能量段裂变占总238U裂变的百分比.

      143Ce的半衰期为33 h, 能量为293 keV的γ射线的分支比是42%. 通过测量这条γ射线可以得到143Ce核子数. 143Ce核子数${N_{{\rm{Ce}} \text{-} 143}}$与293 keV γ射线计数有如下关系:

      式中, ${C_{293.3}}$为293.3 keV γ射线计数, $A{(d)_{293.3}}$为293.3 keV γ射线自吸收修正因子, ${b_{293.3}}$为293.3 keV γ射线分支比, ${\eta _{293.3}}$为293.3 keV γ射线探测效率, k为辐照过程修正因子, $\lambda {}_{{\rm{Ce}} \text{-} 143}$${C_{{\rm{Ce}} \text{-} 143}}$衰变常数, $\tau $为冷却时间, ${t_2}$为测量时间.

      由(1), (2)和(4)式可得裂变反应率f, 如(5)式所示:

      (5)式中各参数的意义同上.

    • 贫化铀装置[21]共分五种模型, 内半径Rin均为13.1 cm, 外径及组合厚度见表1. 贫化铀的密度为(18.8 ± 0.1) g/cm3, 其中238U和235U同位素丰度分别为99.58%和0.416%[22]. 在装置的水平径向留有放置D+离子束流漂移管的靶室孔道, 水平方向与D+粒子漂移方向呈45°和90°方向留有两条测量孔道, 竖直方向有一条测量(吊装)孔道, 靶室孔道及测量孔道直径均为44 mm. 本次实验在45°孔道开展实验.

      模型编号外半径Rout/cm厚度L/cm
      118.105.00
      219.406.30
      323.3510.25
      425.4012.30
      528.4515.35

      Table 1.  Radius and thickness of depleted uranium shells.

      实验测量时需在测量孔道内放置一个贫化铀套筒, 与套筒匹配有不同厚度(5, 10, 20和30 mm)的圆柱形贫化铀塞块, 用于填充活化探测器之外的空间, 以尽可能保证贫化铀球壳的完整性, 最大限度避免空腔效应及其他材料对贫化铀球壳中子场的扰动. 贫化铀装置及其蒙特卡罗模型分别见图1(a)图1(b), 贫化铀装置置于一铁支架上, 其中心与中子源中心重合(偏差 < 3 mm). 活化探测器与塞块交替放置在套筒内, 它们的材料成分均与贫化铀装置一样的, 5片活化探测器在装置中的分布情况见图1(b)中“1, 2, 3, 4, 5”. 为降低实验大厅散射中子本底影响, 实验装置距离实验大厅周围墙壁、地面及屋顶的距离均在3.5 m以上.

      Figure 1.  (a) Physical map of depleted uranium device; (b) distribution of five activation detectors in Monte Carlo Model 5 (1, 2, 3, 4, 5 in the direction of 45°).

    • 实验时, 每种模型均布放5片活化探测器, 活化探测器位置pi见(距中子源距离)表2. 测量孔道与D+粒子入射方向呈45°, 测量孔道内放置贫化铀套筒, 活化探测器置于贫化铀套筒内, 活化探测器之间用贫化铀塞块填充. 套筒内径Φ3.2 cm, 外径Φ4.2 cm, 活化探测器直径Φ2.4 cm, 标称厚度0.2 mm, 塞块直径Φ3.15 cm.

      模型编号L/cm
      p1p2p3p4p5
      113.6014.6215.6416.1617.18
      214.6015.6216.6417.6618.68
      314.6016.6218.6420.6621.68
      415.6018.6220.6422.6624.68
      515.6018.6220.6424.1627.18

      Table 2.  Position of activation detector in various models

    • 中子源由中国工程物理研究院核物理与化学研究所的中子发生器提供, 中子源靶室置于装置中心. 直管式铝制靶室外径26 mm, 靶管外为铝制水套, 内外直径分别为37 mm和39 mm, 靶管与水套之间为循环冷却水. TiT靶活性区直径为12 mm, TiT靶为厚靶(D+粒子全部阻止在T-Ti层内), 平均入射D+粒子能量为135 keV, 对应最大中子能量为14.9 MeV.

      绝对中子产额通过伴随α粒子法监测, 探测器置于漂移管中与D+束流方向夹角178.2°, 束流强度为300 μA时, 中子产额约为3 × 1010—4 × 1010 s–1. 中子产额监测采用分时记录系统, 该记录系统时间步长为10 s, 能够精确反映实验期间中子产额波动, 实验期间中子产额波动修正由(4)式中的“辐照过程修正因子”k完成.

    • 测量γ射线的探测系统为ORTEC公司的TRANS-SPEC-DX100电制冷HPGe探测器和GammaVision谱分析软件. Ge晶体直径67.0 mm, 长度51.7 mm, 死层厚度0.7 mm. HPGe探测器置于屏蔽体内, 工作高压为–4500 V, 对60Co的1.33 MeV γ射线能量分辨率为1.87 keV, 相对探测效率40%.

      利用到60Co, 133Ba, 152Eu等γ点源对HPGe探测器效率刻度, 得到探测器表面中心位置点源的探测效率曲线. 面源的探测效率采用积分的方法获得. 在探测器表面径向每隔3 mm测量一个点源探测效率, 拟合出径向的探测效率变化曲线, 在半径为12 mm的圆面内积分得到面源探测效率. 经标定, 位于探测器端面直径为24 mm的面源发射的293 keV γ射线的探测效率为7.44%. 293 keV的γ射线在贫化铀片中的自吸收因子由理论模拟得到(已由实验验证), 每片贫化铀片的自吸收因子根据实际厚度进行计算, 实验所用25片贫化铀片自吸收因子介于85%—92%之间.

    3.   结果与分析
    • 辐照实验完成后, 为降低短半衰期的γ本底, 将活化探测器冷却2 h, 然后在HPGe探测器表面对活化探测器进行了实验测量, 得到裂变碎片143Ce发射的293.3 keV γ射线能谱, 如图2所示. 与γ射线测量相关的自吸收修正因子、探测效率、辐照过程修正因子等实验前都进行了测量及标定.

      Figure 2.  γ spectrum of depleted uranium activation detector, detected by using HPGe detector.

      为了获得143Ce的总裂变产额, 分能区理论模拟了不同位置238U和235U的裂变反应率, 得到了${R_5}$, ${R_{5i}}$, ${R_8}$${R_{8i}}$, ${Y_{5i}}$${Y_{8i}}$取文献值[23]. 根据(3)式得到了五种模型不同测量位置的143Ce总裂变产额YCe-143, 结果见表3.

      将293.3 keV γ射线总计数、自吸收修正因子、射线分支比、探测效率、辐照过程修正因子、${C_{{\rm{Ce}} \text{-} 143}}$衰变常数、冷却时间、测量时间、裂变产额、活化探测器核子数及源中子数代入(5)式, 可得到各模型相应位置处的裂变反应率, 归一到一个源中子一个铀原子核, 结果见图3.

      Model No.p1/%p2/%p3/%p4/%p5/%
      14.294.324.334.344.34
      24.334.354.374.384.37
      34.364.414.454.454.46
      44.404.474.494.504.49
      54.414.484.514.554.55

      Table 3.  Values of YCe-143.

      Figure 3.  Fission reaction rate distribution for five models.

      图3可以看出: 1)每种模型, 随着距中子源距离L的增加裂变反应率逐渐变小, 厚模型变化幅度比薄模型变化幅度更大, 主要原因是距中子源越远中子通量密度越小, 裂变反应率自然降低; 2)相同测量位置, 模型越厚, 裂变反应率越大, 原因是外层贫化铀球壳的屏蔽与反射作用使得测点处中子通量密度增大, 为此用蒙特卡罗模拟计算了各模型测量位置处的中子通量密度, 结果见图4.

      实验结果的不确定度主要来自中子产额、裂变产额和γ射线测量三个方面. 实验前对α探测器和靶片在靶管中的几何位置进行了准确测量, 对准直光栏孔径采用显微镜进行了测量, 各向异性修正因子通过查表得到, 保证了中子产额的不确定度小于2.5%[24]. 裂变产额不确定度小于5%. γ射线测量的不确定度主要来自HPGE探测器探测效率、γ射线自吸收因子[25]γ谱解谱. 探测效率用系列标准源进行了标定, 不确定度小于2%[26], 自吸收因子进行了理论模拟及实验验证, 不确定度小于0.5%, 解谱不确定度为2%—10% (不同位置处活化探测器不确定度不同). 五种模型各位置裂变反应率的总不确定度见表4.

      Figure 4.  Neutron flux density at various measuring positions of five models (Monte Carlo simulation).

      PositionModel 1Model 2Model 3Model 4Model 5
      p1/%6.56.56.57.46.1
      p2/%6.26.35.77.27.0
      p3/%6.55.86.78.610.0
      p4/%6.56.36.59.59.5
      p5/%6.56.17.010.910.9

      Table 4.  Synthesize uncertainty of fission reaction rate.

    • 利用MCNP5程序和ENDF/VI.8数据库对五种模型进行理论模拟, 用F4栅元卡配合计数乘子卡F4得到了不同测量位置的裂变反应率, 不确定度小于3.4%. 为更清晰地分析计算值与实验值的差异, 用计算值与实验值的比值(C/E)来进行表征, 结果见图5. 可以看到, 五种实验模型C/E值介于0.9至1.1之间, 表明计算与实验在10%以内符合, 且对于大部分测量位置其比值都落在测量标准不确定度范围之内.

      Figure 5.  C/E ratio of fission reaction rate for various measuring position in depleted uranium assembly.

    4.   结 论
    • 采用与宏观贫化铀球壳丰度完全相同的贫化铀活化片作为探测器, 采用活化法测量方法得到了不同模型裂变反应率随径向距离的变化. 同种模型随径向距离增大裂变率逐渐降低, 主要是通量密度逐渐变小及能谱逐渐变软造成. 不同模型相同测量位置裂变反应率随模型厚度的增大逐渐变大, 主要原因是外层贫化铀球壳的屏蔽与反射作用使得测点处中子通量密度增大. 利用MCNP5程序和ENDF/VI.8数据库对上述实验模型进行了模拟, 理论与实验结果在不确定度范围内一致, 验证了蒙特卡罗输运程序及ENDF/VI.8数据库的可靠性.

      本方法克服了裂变室及固体径迹探测器的不足, 最大限度降低了探测器对测量对象的影响, 使得测量结果更加真实反映宏观模型内部裂变放能特性; 细分了测量位置的中子能谱, 采用最新的143Ce裂变产额数据, 提高了总裂变产额${Y_{{\rm{Ce}} \text{-} 143}}$的精度. 该研究成果对校验贫化铀材料核参数及中子输运特性具有重要意义, 为贫化铀裂变放能包层设计提供实验支撑.

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