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光子与相对论麦克斯韦分布电子散射截面的蒙特卡罗计算方法

李树

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光子与相对论麦克斯韦分布电子散射截面的蒙特卡罗计算方法

李树

Monte Carlo method for computing relativistic photon-Maxwellian electron scattering cross sections

Li Shu
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  • 高温全电离等离子体的辐射输运问题中,光子与电子的Compton散射与逆Compton散射是其中重要的特性,光子与相对论麦克斯韦电子散射的描述及截面的计算非常复杂且费时.本文提出了一种用于模拟计算光子与相对论麦克斯韦速度分布电子散射截面的蒙特卡罗计算方法.给出了各步骤的具体实现办法,推导了对应的计算公式,研究了相对论电子速率抽样方法,编写了光子与相对论电子散射的微观截面的蒙特卡罗计算程序.开展了高温全电离等离子体中,不同能量光子与不同温度电子散射的微观散射截面计算和分析.模拟计算结果显示,在电子温度低于25 keV情况下,本文方法与多重数值积分方法的计算结果非常接近;但随着电子温度继续升高,二者差异逐渐增大并较明显,经分析,可能是本文方法目前的电子速率抽样偏差所致,希望将来能够找到更好的相对论电子速率抽样方法以克服此缺陷.
    Compton and inverse Compton scattering from relativistic Maxwellian electrons both have an important feature, i.e. calculating the radiation transport in high-temperature and full-ionized plasma. Description and evaluation of relativistic photon-Maxwellian electron scattering are numerically complex and computationally time consuming. A Monte Carlo method is proposed to simulate photon scattering with relativistic Maxwellian electron and compute the scattering cross-sections. To compute the total cross-section of a photon of energy hν interacting with electrons at temperature Te in the laboratory coordinate, the calculation steps of Monte Carlo scheme are described as follows. The first step is to sample the velocity of an electron, the directions are isotropically sampled, and the speed is sampled from the relativistic Maxwellian distribution at temperature Te. The second step is to transform the photon energy hν into the photon energy in the coordinate in which the electron is at rest. The third step is to use the exact Klein-Nishina formula to compute the cross-sections. The fourth step is go back to the first step, and cycle this many times. The last step is to summarize all computed cross-sections and averaged them, and the average value is what we need. The operation and corresponding formula for each step are described in this paper. A better method of sampling the speed of a relativistic electron is expected to be found.A Monte Carlo processor is developed to compute the scattering cross-section of a photon of any energy, interacting with electrons at any temperature. To check this method, scatterings of the photons of various energies with electrons with various temperatures are simulated, and the results are compared with those from the numerical integration method. The comparison indicates that the simulated cross-sections are in pretty good agreement with those from the multiple integration method for the cases of electron temperature less than 25 keV. But unfortunately, the difference is obvious for the case of temperature more than 25 keV, and the error increases with temperature increasing. Why so? When the temperature is more than 25 keV, the sampling of electron speed is inaccurate when using the present method, which maybe results in this difference. So, we need to find a more accurate method of sampling relativistic electron speed to solve this problem in the future.
      通信作者: 李树, li_shu@iapcm.ac.cn
    • 基金项目: 国家自然科学基金(批准号:11775033,11775030)和中国工程物理研究院于敏基金(批准号:FZ025)资助的课题.
      Corresponding author: Li Shu, li_shu@iapcm.ac.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11775033, 11775030) and the Yumin Foundation of China Academy of Engineering Physics (Grant No. FZ025).
    [1]

    Yu M 1996 Selected Papers of Yu Min (Beijing: Institute of Applied Physics and Computational Mathematics) p102 (in Chinese)[于敏 1996 于敏论文集(北京: 北京应用物理与计算数学研究所) 第102页]

    [2]

    Pomraning G C 1973 The Equations of Radiation Hydrodynamics (Oxford: Pergamon Press) p183

    [3]

    Evans R D 1955 The Atomic Nucleus (New York: McGraw-Hill Press) p677

    [4]

    Lux I, Koblinger L 1991 Monte Carlo Particle Transport Methods: Neutron and Photon Calculations (Boston: CRC Press) p45

    [5]

    Hastings C J 1955 Approximations for Digital Computers (Princeton: Princeton University Press) p154

    [6]

    Wienke B R 1973 Nuclear Science and Engineering 52 247

    [7]

    Cooper G E 1974 J. Quant. Spectr. Rad. Transfer 14 887

    [8]

    Wienke B R 1975 J. Quant. Spectr. Rad. Transfer 15 151

    [9]

    Wienke B R, Lathrop B L 1984 J. Comp. Phys. 53 331

    [10]

    Brinkmann W 1984 J. Quant. Spectrosc. Radiat. Transfer 31 417

    [11]

    Wienke B R, Hendricks J S, Booth T E 1985 J. Quant. Spectr. Rad. Transfer 33 555

    [12]

    Wienke B R, Lathrop B L, Devaney J J 1986 Radiation Effects 94 303

    [13]

    Prasad M K, Kershaw D S, Beason J D 1986 Applied Physics Letters 48 1193

    [14]

    Kershaw D S 1987 J. Quant. Spectr. Rad. Transfer 38 347

    [15]

    Shestakov A I, Kershaw D S, Prasad M K 1988 J. Quant. Spectr. Rad. Transfer 40 577

    [16]

    Webster J B, Stephan B G, Bridgman C J 1973 Trans. Amer. Nucl. Soc. 17 574

    [17]

    Wienke B R, Lathrop B L, Devaney J J 1984 Nuclear Sci. Eng. 88 71

    [18]

    Booth T E, Hendricks J S 1985 Nuclear Sci. Eng. 90 248

    [19]

    Pomraning G C 1972 J. Quant. Spectr. Rad. Transfer 12 1047

    [20]

    Pomraning G C 1973 The Equations of Radiation Hydrodynamics (Oxford: Pergamon Press) p185

    [21]

    Mohamed N M A 2014 Theory Probab. Appl. 58 698

    [22]

    Wienke B R 1975 Am. J. Phys. 43 317

  • [1]

    Yu M 1996 Selected Papers of Yu Min (Beijing: Institute of Applied Physics and Computational Mathematics) p102 (in Chinese)[于敏 1996 于敏论文集(北京: 北京应用物理与计算数学研究所) 第102页]

    [2]

    Pomraning G C 1973 The Equations of Radiation Hydrodynamics (Oxford: Pergamon Press) p183

    [3]

    Evans R D 1955 The Atomic Nucleus (New York: McGraw-Hill Press) p677

    [4]

    Lux I, Koblinger L 1991 Monte Carlo Particle Transport Methods: Neutron and Photon Calculations (Boston: CRC Press) p45

    [5]

    Hastings C J 1955 Approximations for Digital Computers (Princeton: Princeton University Press) p154

    [6]

    Wienke B R 1973 Nuclear Science and Engineering 52 247

    [7]

    Cooper G E 1974 J. Quant. Spectr. Rad. Transfer 14 887

    [8]

    Wienke B R 1975 J. Quant. Spectr. Rad. Transfer 15 151

    [9]

    Wienke B R, Lathrop B L 1984 J. Comp. Phys. 53 331

    [10]

    Brinkmann W 1984 J. Quant. Spectrosc. Radiat. Transfer 31 417

    [11]

    Wienke B R, Hendricks J S, Booth T E 1985 J. Quant. Spectr. Rad. Transfer 33 555

    [12]

    Wienke B R, Lathrop B L, Devaney J J 1986 Radiation Effects 94 303

    [13]

    Prasad M K, Kershaw D S, Beason J D 1986 Applied Physics Letters 48 1193

    [14]

    Kershaw D S 1987 J. Quant. Spectr. Rad. Transfer 38 347

    [15]

    Shestakov A I, Kershaw D S, Prasad M K 1988 J. Quant. Spectr. Rad. Transfer 40 577

    [16]

    Webster J B, Stephan B G, Bridgman C J 1973 Trans. Amer. Nucl. Soc. 17 574

    [17]

    Wienke B R, Lathrop B L, Devaney J J 1984 Nuclear Sci. Eng. 88 71

    [18]

    Booth T E, Hendricks J S 1985 Nuclear Sci. Eng. 90 248

    [19]

    Pomraning G C 1972 J. Quant. Spectr. Rad. Transfer 12 1047

    [20]

    Pomraning G C 1973 The Equations of Radiation Hydrodynamics (Oxford: Pergamon Press) p185

    [21]

    Mohamed N M A 2014 Theory Probab. Appl. 58 698

    [22]

    Wienke B R 1975 Am. J. Phys. 43 317

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  • 收稿日期:  2018-05-10
  • 修回日期:  2018-08-16
  • 刊出日期:  2018-11-05

光子与相对论麦克斯韦分布电子散射截面的蒙特卡罗计算方法

  • 1. 北京应用物理与计算数学研究所, 北京 100094
  • 通信作者: 李树, li_shu@iapcm.ac.cn
    基金项目: 国家自然科学基金(批准号:11775033,11775030)和中国工程物理研究院于敏基金(批准号:FZ025)资助的课题.

摘要: 高温全电离等离子体的辐射输运问题中,光子与电子的Compton散射与逆Compton散射是其中重要的特性,光子与相对论麦克斯韦电子散射的描述及截面的计算非常复杂且费时.本文提出了一种用于模拟计算光子与相对论麦克斯韦速度分布电子散射截面的蒙特卡罗计算方法.给出了各步骤的具体实现办法,推导了对应的计算公式,研究了相对论电子速率抽样方法,编写了光子与相对论电子散射的微观截面的蒙特卡罗计算程序.开展了高温全电离等离子体中,不同能量光子与不同温度电子散射的微观散射截面计算和分析.模拟计算结果显示,在电子温度低于25 keV情况下,本文方法与多重数值积分方法的计算结果非常接近;但随着电子温度继续升高,二者差异逐渐增大并较明显,经分析,可能是本文方法目前的电子速率抽样偏差所致,希望将来能够找到更好的相对论电子速率抽样方法以克服此缺陷.

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