Calculating α Eigenvalues of One-Dimensional Media with Monte Carlo

B. R. Betzler; W. R. Martin; B. C. Kiedrowskl; F. B. Brown

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Calculating α Eigenvalues of One-Dimensional Media with Monte Carlo

机译：用蒙特卡罗计算一维介质的α本征值

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This paper presents results from the application of a Monte Carlo Markov Transition Rate Matrix Method to calculate forward and adjoint α eigenvalues and eigenfunctions of one-speed slabs, and perform eigenfunction expansion to approximate the time-dependent flux response to user-defined sources. The formulation of this method relies on the interpretation that the operator in the adjoint α-eigenvalue problem describes a continuous-time Markov process, i.e., elements of this operator are rates defining particles transitioning among the position-energy-direction phase space. A forward Monte Carlo simulation tallies these elements for a discretized phase space, using careful bookkeeping during the random walk. We compare calculated eigenvalues and eigenfunctions to those obtained by the Green's Function Method for multiplying and non-multiplying multi-region slabs.

机译：本文介绍了应用蒙特卡洛马尔科夫跃迁速率矩阵方法计算单速板的正向和伴随α本征值和本征函数，并进行本征函数扩展以近似随时间变化的对用户定义源的磁通响应的结果。该方法的表述基于以下解释：伴随α-特征值问题中的算子描述了连续时间的马尔可夫过程，即该算子的元素是确定粒子在位置-能量方向相空间之间转变的速率。向前的蒙特卡洛模拟通过在随机行走过程中进行仔细的簿记，将这些元素用于离散的相空间。我们将计算出的特征值和特征函数与格林函数方法获得的特征值和特征函数进行比较，以进行乘积和非乘积的多区域平板的计算。

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《Jorunal of computational and theoretical transport》 |2014年第7期|共12页
作者
B. R. Betzler; W. R. Martin; B. C. Kiedrowskl; F. B. Brown;
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正文语种 eng
中图分类理论物理学;
关键词
α eigenvalues; Monte Carlo methods; neutron transport;

机译：α特征值;蒙特卡罗方法;中子输运;

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1. Calculating α Eigenvalues of One-Dimensional Media with Monte Carlo [J] . B. R. Betzler, W. R. Martin, B. C. Kiedrowskl, Jorunal of computational and theoretical transport . 2014,第1a7Speca期

机译：用蒙特卡罗计算一维介质的α本征值
2. Calculating the k-Eigenvalue Sensitivity to Typical Geometric Perturbations with the Adjoint-Weighted Method in the Continuous-Energy Reactor Monte Carlo Code RMC [J] . Nuclear science and engineering . 2019,第11期

机译：在连续能量反应堆中使用伴随加权方法计算典型几何扰动的k特征值蒙特卡罗代码RMC
3. Calculating Alpha Eigenvalues and Eigenfunctions with a Markov Transition Rate Matrix Monte Carlo Method [J] . Benjamin R. Betzler, Brian C. Kiedrowski, William R. Martin, Nuclear science and engineering . 2018,第2期

机译：用马尔可夫跃迁速率矩阵蒙特卡罗方法计算Alpha特征值和特征函数
4. CALCULATING α-EIGENVALUE SPECTRA WITH MONTE CARLO [C] . Benjamin R. Betzler, Brian C. Kiedrowski, Forrest B. Brown, ANS Nuclear Criticality Safety Division topical meeting . 2013

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7. Calculating Alpha Eigenvalues and Eigenfunctions with a Markov Transition Rate Matrix Monte Carlo Method [O] . Benjamin R. Betzler, Brian C. Kiedrowski, William R. Martin, 2018

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8. Development of Continuous-Energy Eigenvalue Sensitivity Coefficient Calculation Methods in the Shift Monte Carlo Code. [R] . Perfetti, C., Martin, W., Reardon, B., 2012

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Calculating α Eigenvalues of One-Dimensional Media with Monte Carlo

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