| 带电测试粒子在磁化史瓦西黑洞中的混沌运动 |
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| 引用本文： | 周娜英,张洪星,孙鑫,刘文芳,李丹.带电测试粒子在磁化史瓦西黑洞中的混沌运动[J].天文学报,2023,64(4):39. |
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| 作者姓名： | 周娜英 张洪星 孙鑫 刘文芳 李丹 |
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| 作者单位： | 上海工程技术大学数理与统计学院计算物理与应用研究中心 上海 201620;广西大学物理科学与工程技术学院 南宁 530004 |
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| 基金项目： | 国家自然科学基金项目(11973020)资助 |
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| 摘 要： | 当史瓦西黑洞周围存在渐近均匀的外部磁场时, 描述带电粒子在史瓦西黑洞附近运动的哈密顿系统会变为不可积系统. 类似于这样的相对论哈密顿系统不存在有显式分析解的2部分分离形式, 给显式辛算法的构建和应用带来困难. 近一年以来的系列工作提出将相对论哈密顿系统分解为具有显式分析解的2个以上分离部分形式, 成功解决了许多相对论时空构建显式辛算法的难题. 最近的工作回答了哈密顿系统显式可积分离数目对长期数值积分精度有何影响、哪种显式辛算法有最佳长期数值性能这两个问题, 指出哈密顿有最小可积分离数目即3部分分裂解形式并且应用于优化的4阶分段龙格库塔显式辛算法可取得最好精度. 由此选择上述数值积分方法并利用庞加莱截面、最大李雅普诺夫指数和快速李雅普诺夫指标研究在磁化史瓦西黑洞附近运动的带电粒子轨道动力学. 结果显示: 针对某特定的粒子能量和角动量, 较小的外部磁场很难形成混沌轨道; 较大的正磁场参数容易使轨道产生混沌, 并且随着磁场的增大, 轨道的混沌程度也随之加强; 粒子能量适当变大也可以加剧混沌程度, 但负磁场参数和粒子角动量变大都会减弱混沌.
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| 关 键 词： | 天体力学 黑洞 磁场 混沌 算法 |
| 收稿时间： | 2022/4/8 0:00:00 |
Chaotic Motion of Charged Test Particles in a Magnetized Schwarzschild Black Hole |
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| ZHOU Na-ying,ZHANG Hong-xing,SUN Xin,LIU Wen-fang,LI Dan.Chaotic Motion of Charged Test Particles in a Magnetized Schwarzschild Black Hole[J].Acta Astronomica Sinica,2023,64(4):39. |
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| Authors: | ZHOU Na-ying ZHANG Hong-xing SUN Xin LIU Wen-fang LI Dan |
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| Institution: | Center of Application and Research of Computational Physics, School of Mathematics, Physics and Statistics, Shanghai University of Engineering Science, Shanghai 201620;Guangxi Key Laboratory for Relativistic Astrophysics, Guangxi University, Nanning 530004 |
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| Abstract: | The Hamiltonian describing the motion of charged particles around the Schwarzschild black hole immersed in an external magnetic field is nonintegrable. Such relativistic Hamiltonian systems do not have two splitting parts with analytical solutions as explicit functions of time. This leads to the difficulty in the construction and application of explicit symplectic algorithms to the relativistic systems. Recently, Chinese scholars have published a series of works in the Astrophysical Journal, where explicit symplectic methods are successfully designed for these relativistic Hamiltonians split into three or more explicit integrable parts. There are two questions of whether the numbers of splitting these Hamiltonians affect the numerical accuracy and which of the explicit symplectic integrators shows the best performance. Our latest work in the Astrophysical Journal answered the two questions, and shows that the fourth-order optimal Partitioned-Runge-Kutta (PRK64) explicit symplectic algorithms with the three-part splitting method as
the least number of splitting these Hamiltonians performs the best accuracy. This paper applies such an
integrator to obtain Poincar e cross-section, maximum Lyapunov indicators and fast Lyapunov indicators
(FLIs), which distinguish between the regular and chaotic dynamical properties of charged particles moving
near the magnetized Schwarzschild black hole. For given speci c values of the particle energy and angular
momentum, a small magnetic eld does not induce chaos, whereas a large positive magnetic eld parameter
easily causes the occurrence of chaos. The strength of chaos increases with the magnetic eld increasing.
Chaos is also strengthened as the particle energy increases. However, it is weakened when a negative
magnetic eld parameter and the particle angular momentum increase. |
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| Keywords: | celestial mechanics black hole magnetic field chaotic integrators |
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