A Hankel Transform approach to Doppler broadening

IF 1.9 3区工程技术 Q1 NUCLEAR SCIENCE & TECHNOLOGY

Annals of Nuclear Energy Pub Date : 2024-07-30 DOI:10.1016/j.anucene.2024.110790

Godfree Gert, Caleb M. Mattoon, Bret R. Beck

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Abstract

The kernel broadening approach to Doppler broadening has been shown to be equivalent to the convolution of a function related to the unheated cross section and Gaussian distribution function. This convolution may be expressed as the inverse Fourier transform of the product of the Fourier transforms of the convolution arguments. By recognizing that the unheated cross section function is an odd function, the resulting equations are reduced to a Hankel Transform of order $α = \frac{1}{2}$ . A discretized version of the Hankel Transform is applied to produce a set of equations that are independent of the interpolation scheme used in the pointwise representation of the cross sections. The heated cross section at a given energy is consequently calculated as the sum of the contributions from each of these pointwise intervals and each contribution is represented as a separate Hankel Transform.

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多普勒增宽的汉克尔变换方法

多普勒增宽的核增宽方法已被证明等同于与未加热截面和高斯分布函数相关的函数的卷积。这种卷积可表示为卷积参数的傅里叶变换乘积的逆傅里叶变换。由于未加热横截面函数是奇函数，因此所得到的方程可以简化为阶次为 . 的汉克尔变换。应用汉克尔变换的离散化版本，可以得到一组与横截面点式表示中使用的插值方案无关的方程。因此，给定能量下的受热截面计算为来自这些点状区间的每个贡献的总和，而每个贡献都表示为一个单独的汉克尔变换。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Annals of Nuclear Energy 工程技术-核科学技术

CiteScore

4.30

自引率

21.10%

发文量

632

审稿时长

7.3 months

期刊介绍： Annals of Nuclear Energy provides an international medium for the communication of original research, ideas and developments in all areas of the field of nuclear energy science and technology. Its scope embraces nuclear fuel reserves, fuel cycles and cost, materials, processing, system and component technology (fission only), design and optimization, direct conversion of nuclear energy sources, environmental control, reactor physics, heat transfer and fluid dynamics, structural analysis, fuel management, future developments, nuclear fuel and safety, nuclear aerosol, neutron physics, computer technology (both software and hardware), risk assessment, radioactive waste disposal and reactor thermal hydraulics. Papers submitted to Annals need to demonstrate a clear link to nuclear power generation/nuclear engineering. Papers which deal with pure nuclear physics, pure health physics, imaging, or attenuation and shielding properties of concretes and various geological materials are not within the scope of the journal. Also, papers that deal with policy or economics are not within the scope of the journal.