基于蒙特卡罗-离散纵标方法的氘氚激光等离子体聚变反应率数值模拟

陈忠; 赵子甲; 吕中良; 李俊汉; 潘冬梅

doi:10.7498/aps.68.20190440

摘要

惯性约束聚变(ICF)是实现受控热核聚变可能途径之一. 聚变中子源项是氘氚激光等离子体物理设计与分析的重要参数之一, 其准确性直接影响分析结果的可靠性. 目前国内外对于ICF氘氚聚变反应产生的中子源项研究主要基于解析公式法, 在温度和反应类型等方面适用范围有限. 本文采用粒子云概念对氘、氚粒子云团开展了随机抽样与时空网格划分, 然后基于麦克斯韦速率分布律对氘氚聚变反应开展了多普勒能量展宽效应分析与微分截面温度修正工作, 耦合蒙特卡罗方法和离散纵标方法, 开展了激光等离子体中D-T粒子云团聚变反应率的数值模拟工作. 研究结果显示, 与原核数据库截面相比, D-T, D-D, T-D截面经修正后多普勒温度效应显著. 在20—100 keV的等离子体温度范围内, 相较传统的解析公式法, 本文模拟结果更符合最新的ENDF核数据库的氘氚反应截面数据, 且与解析公式法结果在低能区存在较大误差, 可能是计算方法不同与低温截面差异过大原因导致.

关键词:

Abstract

Inertial confinement fusion (ICF) is one of the possible ways to realize controlled thermonuclear fusion. The fusion neutron source term is one of the important parameters in the physical design and analysis of laser plasma. The accuracy of the fusion neutron source term directly affects the reliability of the analysis results. At present, the neutron source term of deuterium-tritium fusion reaction in ICF is mainly based on formula method. It has limited applications in temperature and reaction type. Because of a large quantity of data, it is impossible to simulate the fusion reaction of each particle. In this paper, the concept of particle cloud is introduced, that is, the collection of the like particles with the same position and speed, and it is considered that the action of particle cloud is the same reaction. Because the particles should satisfy the Maxwell velocity distribution at a certain temperature and the direction is all around the circumference angle, the collision cross sections between the incident particle and different target particles are different. Therefore, the design program takes all the possible velocities, polar angles and direction angles, reads the collision cross sections between deuterium and tritium and makes corrections, and obtains the multi-temperature differential correction cross sections of deuterium and tritium fusion with Doppler energy broadening. On these bases, Monte Carlo method and discrete ordinate method method are used. A numerical simulation program for the fusion rate of D-T particles in laser plasma is developed in this paper. It is found that there are significant differences between the DT, DD, TD cross sections and the original cross sections after Doppler broadening. In a range of plasma temperature between 20 keV and 100 keV, the simulation results are more consistent with the cross section data of ENDF/B-VI and ENDF/B-VII databases of deuterium-tritium fusion reaction than those from the analytical formula method. There is a large error between the numerical simulation results and the analytical formula method in the low energy region. It may be caused by the difference of calculation methods and too big difference among the used fusion cross sections at low temperature.

Keywords:

laser plasma /
deuterium-tritium fusion reaction /
differential cross-section temperature correction /
Monte Carlo method /
discrete ordinate method

作者及机构信息

1.
西南科技大学国防科技学院, 绵阳　621010

2.
国防科技大学文理学院, 长沙　410073

3.
中国科学技术大学, 合肥　230027

通信作者: 赵子甲, sszdzl1@mail.ustc.edu.cn

基金项目: 西南科技大学博士基金(批准号: 13zx7138)、湖南省科技创新计划(批准号: 2018JJ2473)、国家自然科学基金(批准号: 11475150, 11475260)、中国科学院中子输运理论与辐射安全重点实验室开放研究课题基金(批准号: NEUTRON201707)、哈尔滨工程大学核安全与仿真技术国防重点学科实验室基金(批准号: HEUNSS18SF04)和特殊环境机器人技术四川省重点实验室基金(批准号: 17kftk01)资助的课题

Authors and contacts

1.
School of National Defense Science and Technology, Southwest University of Science and Technology, Mianyang 621010, China

2.
College of Liberal Arts and Science, National University of Defense Technology, Changsha 410073, China

3.
University of Science and Technology of China, Hefei 230027, China

Corresponding author: Zhao Zi-Jia, sszdzl1@mail.ustc.edu.cn

Funds: Project supported by the Doctoral Fund of Southwest University of Science and Technology, China (Grant No. 13zx7138), the Natural Science Foundation of Hunan Province, China (Grant No. 2018JJ2473), the National Natural Science Foundation of China (Grant Nos. 11475260, 11475150), the Opening Foundation of Key Laboratory of Neutronics and Radiation Safety of CAS (Grant No. NEUTRON201707), the Fund of Fundamental Science on Nuclear Safety and Simulation Technology Laboratory, Harbin Engineering University, China (Grant No. HEUNSS18SF04), and the Fund of Robot Technology Used for Special Environment Key Laboratory of Sichuan Province, China (Grant No. 17kftk01)

文章全文

参考文献

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[20]	https://t2.lanl.gov/nis/data/endf/ [2019−3−28]

施引文献

图 1 动量矢量分解

Fig. 1. Momentum vector decomposition.

下载: 全尺寸图片幻灯片

图 2 二维网格误差分析

Fig. 2. Two-dimensional grid error analysis.

下载: 全尺寸图片幻灯片

图 3 二维网格大小造成的误差

Fig. 3. Error caused by two-dimensional mesh size.

下载: 全尺寸图片幻灯片

图 4 仰角对应球带(球坐标)

Fig. 4. Elevation corresponding to the ball belt (ball coordinate).

下载: 全尺寸图片幻灯片

图 5 氘氚等离子体聚变反应模拟流程图

Fig. 5. Simulation flow of deuterium-tritium plasma fusion reaction.

下载: 全尺寸图片幻灯片

图 6 氘氚等离子体聚变反应修正　(a) D-D反应截面修正; (b) D-T反应截面修正; (c) T-D反应截面修正

Fig. 6. Correction of fusion reaction of deuterium-tritium plasma: (a) D-D fusion cross section correction; (b) D-T fusion cross section correction; (c) T-D fusion cross section correction.

下载: 全尺寸图片幻灯片

图 7 氘氚等离子体聚变反应中子产生率

Fig. 7. Neutron production rate of deuterium-tritium plasma fusion reaction.

下载: 全尺寸图片幻灯片

图 8 两种方法聚变反应截面对比^[19,20]

Fig. 8. Comparison of fusion cross sections of the two methods^[19,20].

下载: 全尺寸图片幻灯片

map

[1]	Nuckolls J H 1982 Phys. Today 35 24 Google Scholar
[2]	Johnson T H 2005 Proc. IEEE 72 548 Google Scholar
[3]	Brysk H 1973 Plasma Phys. 15 611 Google Scholar
[4]	Davis J, Petrov G M, Petrova T, Willingale L, Maksimchuk A, Krushelnick K 2010 Plasma Phys. Controlled Fusion 52 045015 Google Scholar
[5]	Petrov G M, Higginson D P, Davis J, et al. 2013 Plasma Phys. Controlled Fusion 55 105009 Google Scholar
[6]	Ditmire T, Zweiback J, Yanovsky V P, et al. 1999 Nature 398 6727 Google Scholar
[7]	Bang W, Dyer G, Quevedo H J, Bernstein A C, Gaul E, Donovan M, Ditmire T 2013 Phys. Rev. E 87 023106 Google Scholar
[8]	Bang W, Barbui M, Bonasera A, et al. T 2013 Phys. Rev. E 88 033108 Google Scholar
[9]	Jung D, Falk K, Guler N, et al. 2013 Phys. Plasmas 20 056706 Google Scholar
[10]	Ni M, Wang Y, Yuan B, Jiang J, Wu Y 2013 Fusion Eng. Des. 88 2422 Google Scholar
[11]	Nie B, Ni M, Wei S 2017 J. Hazardous Mater. 327 135 Google Scholar
[12]	Nie B, Ran G, Zeng Q, Du H, Li Z, Chen Y, Zhu Z, Zhao X, Ni M, Li F 2019 Energ. Sci. Eng. 7 457 Google Scholar
[13]	He M Q, Cai H B, Zhang H, et al. 2015 Phys. Plasmas 22 44 Google Scholar
[14]	Pomerantz I, Mccary E, Meadows A R, et al. 2014 Phys. Rev. Lett. 113 184801 Google Scholar
[15]	Fausser C, Puma A L, Gabriel F, Villari R 2012 Fusion Eng. Des. 87 787 Google Scholar
[16]	林尊琪 2006 第五届全国光子学大会会议论文集黄山 2004年10月18日 p4 Lin Z Q 2006 The Proc. the Fifth National Conference on Photonics Huangshan, China, October 18, 2004 p4 (in Chinese)
[17]	樊铁栓, 黄钢, 冯玉清 2005 原子能科学技术 39 28 Google Scholar Fan T S, Huang G, Feng Y Q 2005 At. Energ. Sci. Technol. 39 28 Google Scholar
[18]	Xu B, Ma Y, Yang X, Tang W, Wang S, Ge Z, Zhao Y, Ke Y 2017 Laser and Particle Beams 35 366 Google Scholar
[19]	Bosch H S, Hale G M 1992 Nucl. Fusion 32 611 Google Scholar
[20]	https://t2.lanl.gov/nis/data/endf/ [2019−3−28]

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基于蒙特卡罗-离散纵标方法的氘氚激光等离子体聚变反应率数值模拟