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光子与相对论麦克斯韦分布电子散射的能谱角度谱研究

李树

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光子与相对论麦克斯韦分布电子散射的能谱角度谱研究

李树

Photon spectrum and angle distribution for photon scattering with relativistic Maxwellian electrons

Li Shu
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  • 光子与相对论麦克斯韦分布电子散射的描述及能谱角度谱计算非常复杂且费时.本文提出了一种光子与相对论麦克斯韦速度分布电子散射的蒙特卡罗(MC)模拟方法,该方法能够细致模拟高温等离子体中任意能量光子与任意温度电子的Compton和逆Compton散射问题.对于散射后光子的能谱和角度谱参数,可以根据电子温度抽样若干不同状态的电子,分别模拟其与光子发生散射,可以得到各次散射后的光子能量和偏转角度,取统计平均后的结果即可获得该光子与该温度电子散射的能谱和角度谱分布.根据该方法编写了光子与相对论电子散射MC模拟程序,开展了高温全电离等离子体中光子与相对论电子散射的能谱角度谱计算和分析,分析结果显示:热运动电子将展宽出射光子能谱,且低能光子与高温电子散射后的蓝移现象明显;出射光子的角度谱很复杂,其决定于入射光子能量、出射光子能量及电子温度.基于该方法计算并以数表形式给出的光子-相对论电子散射能谱角度谱数据,可以供辐射输运数值模拟程序使用.
    Description of photon scattering with relativistic Maxwellian electrons is numerically complex, and computationally time consuming for the final photon energy and angle distribution. A Monte Carlo method is used to simulate photon scattering with relativistic Maxwellian electrons. The main idea of this method is to transform the interaction of photonmoving electrons in the laboratory coordinate system into that in a new coordinate system in which the electrons are at rest, then to use the exact Klein-Nishina formula to describe this interaction and obtain the outgoing photon energy and angle, finally, to transform it into the primary laboratory coordinate system. In sum, there are eight steps, i.e.two two-dimensional (2D) transforms and two three-dimensional (3D) transforms and two Lorentz transforms, and two sampling. Repeating this process, summarizing and averaging all computed energy values and angles, the distribution of scattered energy and angle can be obtained.
    A Monte Carlo processor is developed to simulate a photon of any energy interacting with electrons at any temperature. Some typical cases are simulated. The computed results indicate that the photon spectrum is different from that of the photon scattering with rest electrons remarkably, especially for a low energy photon scattering with the high temperature electrons. The main phenomena are Doppler broading and blue shifting. The moving electron can extend the distribution of the outgoing photon energy, and for a low energy photon scattering with the high temperature electrons, the photon maybe obtains the energy from electrons with significant probability. The angle distribution is very complicated, and it is determined by the incident photon energy, the outgoing photon energy, and the electron temperature. This processor can calculate the energy scattering differential cross-sections or energy-angle scattering double differential cross-sections, and provide the data in a tabulated form for other transport methods.
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    Kershaw D S 1987 J. Quant. Spectr. Rad. Transfer 38 347

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    Wienke B R, Lathrop B L, Devaney J J 1984 Nucl. Sci. Engin. 88 71

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    Booth T E, Hendricks J S 1985 Nucl. Sci. Engin. 90 248

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    Fleck J A, Cummings J D 1971 J. Computat. Phys. 8 313

    [19]

    Lux I, Koblinger L 1991 Monte Carlo Particle Transport Methods: Neutron and Photon Calculations (Boston: CRC Press) p44

    [20]

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    数学手册编写组 1979 数学手册 (北京: 高等教育出版社) 第330页

    Editor Group 1979 Handbook of Mathematics (Beijing: Higher Education Press) p330

  • [1]

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

    [2]

    Salvat F, Fernandez-Varea J M, Sempau J 2006 PENELOPE-2006: A Code System for Monte Carlo Simulation of Electron and Photon Transport Workshop Proceedings Barcelona, Spain p60

    [3]

    Dirac P A M 1925 Monthly Notices R. Astron. Soc. 85 825

    [4]

    Edmonds F N 1953 Astrophys. J. 117 298

    [5]

    Wienke B R 1973 Nucl. Sci. Engin. 52 247

    [6]

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

    [7]

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

    [8]

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

    [9]

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

    [10]

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

    [11]

    Wienke B R, Lathrop B L, Devaney J J 1986 Radiation Effects 94 977

    [12]

    Prasad M K, Kershaw D S, Beason J D 1986 Appl. Phys. Lett. 48 1193

    [13]

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

    [14]

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

    [15]

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

    [16]

    Wienke B R, Lathrop B L, Devaney J J 1984 Nucl. Sci. Engin. 88 71

    [17]

    Booth T E, Hendricks J S 1985 Nucl. Sci. Engin. 90 248

    [18]

    Fleck J A, Cummings J D 1971 J. Computat. Phys. 8 313

    [19]

    Lux I, Koblinger L 1991 Monte Carlo Particle Transport Methods: Neutron and Photon Calculations (Boston: CRC Press) p44

    [20]

    Kahn H 1954 Applications of Monte Carlo (AECU-3259 Report, National Technical Information Service)

    [21]

    Koblinger L 1975 Nucl. Sci. Engin. 56 218

    [22]

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

    [23]

    数学手册编写组 1979 数学手册 (北京: 高等教育出版社) 第330页

    Editor Group 1979 Handbook of Mathematics (Beijing: Higher Education Press) p330

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出版历程
  • 收稿日期:  2018-09-30
  • 修回日期:  2018-11-05
  • 刊出日期:  2019-01-05

光子与相对论麦克斯韦分布电子散射的能谱角度谱研究

  • 北京应用物理与计算数学研究所, 北京 100094

摘要: 光子与相对论麦克斯韦分布电子散射的描述及能谱角度谱计算非常复杂且费时.本文提出了一种光子与相对论麦克斯韦速度分布电子散射的蒙特卡罗(MC)模拟方法,该方法能够细致模拟高温等离子体中任意能量光子与任意温度电子的Compton和逆Compton散射问题.对于散射后光子的能谱和角度谱参数,可以根据电子温度抽样若干不同状态的电子,分别模拟其与光子发生散射,可以得到各次散射后的光子能量和偏转角度,取统计平均后的结果即可获得该光子与该温度电子散射的能谱和角度谱分布.根据该方法编写了光子与相对论电子散射MC模拟程序,开展了高温全电离等离子体中光子与相对论电子散射的能谱角度谱计算和分析,分析结果显示:热运动电子将展宽出射光子能谱,且低能光子与高温电子散射后的蓝移现象明显;出射光子的角度谱很复杂,其决定于入射光子能量、出射光子能量及电子温度.基于该方法计算并以数表形式给出的光子-相对论电子散射能谱角度谱数据,可以供辐射输运数值模拟程序使用.

English Abstract

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