紧凑型反应堆中的单粒子动力学

doi:10.19596/j.cnki.1001-246x.8415

计算物理 ›› 2022, Vol. 39 ›› Issue (3): 253-260.DOI: 10.19596/j.cnki.1001-246x.8415

• 研究论文 • 下一篇

紧凑型反应堆中的单粒子动力学

于承新¹(), 舒小芳², 刘杰³

1. 北京应用物理与计算数学研究所, 北京 100088
2. 北京量子信息科学研究院, 北京 100193
3. 中国工程物理研究院研究生院, 北京 100096

收稿日期:2021-06-25 出版日期:2022-05-25 发布日期:2022-09-02
作者简介:
于承新(1980-), 男, 博士, 副研究员, 主要从事流体力学不稳定性研究, E-mail: cx_yu2013@163 com
基金资助:
国家自然科学基金(11775030); 国家自然科学基金(11875091); 国家自然科学基金青年项目(12004043)

Single Particle Dynamics in a Compact Fusion Reactor

Chengxin YU¹(), Xiaofang SHU², Jie LIU³

1. Beijing Institute of Applied Physics and Computational Mathematics, Beijing 100088, China
2. Beijing Academy of Quantum Information Sciences, Beijing 100193, China
3. Graduate School of China Academy of Engineering Physics, Beijing 100096, China

Received:2021-06-25 Online:2022-05-25 Published:2022-09-02

摘要/Abstract

摘要：

针对紧凑型聚变反应堆独特的磁势阱结构, 使用蒙特卡罗方法研究单个高能带电粒子的约束动力学行为。考虑到磁场位型的局域平坦性, 在足够小的计算区域或足够短的时间内, 带电粒子基本上在一个常数磁场中的运动。基于此, 给出精确保证能量守恒的粒子运动方程逐点解析解, 该计算方案具有长时间追踪的能力。模拟结果表明: 对于初始位置和速度方向随机分布的具有1千电子伏能量的高能氘粒子, 大约有7%的概率能够约束至10 ms量级。由于粒子运动方程的求解过程不依赖于具体的磁场位型, 所以它可以方便地应用到具有任意位型的磁约束装置中。

关键词: 紧凑型聚变反应装置, 单粒子运动, 磁势阱

Abstract:

For the unique magnetic structure of a compact fusion reactor, confinement dynamics of a single high-energy charged particle was studied with Monte Carlo method. Taking into account the local flatness characteristics of the magnetic field configuration, a charged particle moves basically in a constant magnetic field for a sufficiently small area or a short enough timestep. Therefore, a point-by-point analytical solution of particle motion equation that guarantees accurately conservation of energy is proposed, which has long-term tracking capabilities. Simulation results show that for high-energy deuterium particles with 1 keV energy distributed randomly in initial position and velocity direction, there is about a 7% probability that can be constrained to an order of 10 ms. Since the method for solving the motion equation is independent of magnetic configuration, it can be generalized naturally to arbitrary magnetic confinement setup.

Key words: compact fusion reactor, single charged particle motion, magnetic trap

于承新, 舒小芳, 刘杰. 紧凑型反应堆中的单粒子动力学[J]. 计算物理, 2022, 39(3): 253-260.

Chengxin YU, Xiaofang SHU, Jie LIU. Single Particle Dynamics in a Compact Fusion Reactor[J]. Chinese Journal of Computational Physics, 2022, 39(3): 253-260.

图/表 8

图1 紧凑型聚变反应堆(CFR)的概念设计图[14]

Fig.1 Conception design of a compact fusion reactor (CFR)

表1 采用的CFR参数

Table 1 The adopted parameters for CFR

C_ℓ	y_ℓ/m	r_ℓ/m	I_ℓ/MA
C₁	-1.25	0.3	-10
C₂	-1.0	0.5	-1
C₃	-0.7	0.7	-1
C₄	-0.4	0.25	7
C₅	0	0.702	-4.3
C₆	0.4	0.25	7
C₇	0.7	0.7	-1
C₈	1.0	0.5	-1
C₉	1.25	0.3	-10

图2 (a) CFR电流线圈产生的磁场位形(对数标度)；(b)为(a)中心的放大(蓝色流线表示磁场方向及强磁场强度。)

Fig.2 (a) Magnetic configuration (logarithmic scale); (b) Zoom-in version of the center of (a) (The blue stream lines show direction and strength of the magnetic field.)

图3 (a) 磁场分布的轴对称性质；(b)三维磁场的两维分解(B=B⊥ + B‖)；(c) 磁场横向分量的分解B⊥ = Bx + Bz

Fig.3 (a) Axial properties of the magnetic field; (b) Two-dimensional decomposition of three-dimensional magnetic field; (c) Decomposition of lateral magnetic component

图4 程序模拟过程中的三维网格系统

Fig.4 Three-dimensional grids used in simulation programs

图5 动能相对误差的含时演化

Fig.5 Evolution of relative error of kinetic energy

图6 CFR势阱中，初始105个氘离子在不同时刻的约束情况(a) 10-7 s；(b) 10-6 s；(c) 10-5 s；(d) 10-4 s；(e) 10-3 s；(f) 10-2 s

Fig.6 Distributions of 105 random deuterium samples at different moments in the magnetic trap of CFR (a) 10-7 s；(b) 10-6 s；(c) 10-5 s；(d) 10-4 s；(e) 10-3 s；(f) 10-2 s

图7 算法的收敛性分析，对应于三种时间步长的样本数分别为100000, 25000和5000

Fig.7 Convergence of algorithm at three different step lengths for 100000, 25000 and 5000 samples, respectively

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紧凑型反应堆中的单粒子动力学

Single Particle Dynamics in a Compact Fusion Reactor

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