Approximately symplectic Runge-Kutta methods for the guiding center dynamics

讲座题目：Approximately symplectic Runge-Kutta methods for the guiding center dynamics

讲座时间 Datetime:2026年11月26日，周四，10：00 - 12：00

地点 Venue: 腾讯会议：387-664-881

主持人 Host：李露副教授

报告人 Speaker: 张瑞丽 副教授

单位 Affiliation:北京交通大学

报告摘要：

The canonical coordinates of guiding center dynamics and their associated symplectic numerical methods play fundamental and significant roles in the gyromotion scale physics of plasma. However, the canonicalization of guiding center dynamics in general magnetic fields and existing symplectic methods present substantial challenges in practical simulation implementations. This study reformulates the guiding center dynamics in a 6-dimensional phase space, deriving three equivalent guiding center formulations. The second formulations is referred to as the HamiltonDirac formulation, characterized by releasing global constraints and presenting a more concise right vector field expression. The solution flow of the Hamilton-Dirac formulation of the guiding center dynamics preserves symplectic structure and three invariants, that is, the Hamiltonian function and two constraints. Furthermore, when the conventional canonical Runge-Kutta method is applied to the compact Hamilton-Dirac formulation of the guiding center dynamics, it exhibits approximate symplecticity for the guiding center dynamics as the two constraints remain bounded. Comparative numerical experiments are conducted in various magnetic fields, employing both approximately symplectic and non-symplectic Runge-Kutta methods. The numerical results demonstrate that while both methods preserve the two constraints well, the approximately symplectic method shows its advantages in terms of accuracy of guiding center orbits and the conservation properties of energy over long term simulation compared to non-symplectic methods.

报告人简介：

张瑞丽，北京交通大学副教授，博士生导师。博士毕业于中国科学院数学与系统科学研究院，长期从事动力系统保结构算法和保结构神经网络的理论与应用研究。已在JCP、PRE、POP、JSC等期刊发表论文30余篇，先后主持中国博士后基金、国家自然科学基金青年和面上项目、主持和参与多个国家重点研发ITER专项。担任中国仿真学会仿真算法委员会委员、中国仿真学会青年工作委员会委员。