正则哈密顿引导中心动力学及其内禀磁矩
Canonical Hamiltonian Guiding Center Dynamics and Its Intrinsic Magnetic Moment
AI总结：
该研究证明引导中心动力学可表述为带约束的正则哈密顿系统，将其建模为具内禀磁矩的赝粒子，为相关理论发展和内禀磁矩起源研究提供了基础。
摘要：
引导中心概念在天体物理学、空间等离子体、聚变研究以及电弧等离子体中，是解决磁化等离子体多尺度动力学问题的有力工具。在这篇快报中，我们严格证明了引导中心动力学通常可被描述为六维相空间中带有两个约束的约束正则哈密顿系统，且引导中心的解流位于一个正则辛子流形上。因此，引导中心可被建模为一个具有内禀磁矩的赝粒子，该模型能在大于回旋周期的时间尺度上恰当替代带电粒子动力学。引导中心赝粒子的完整动力学行为，如速度和受力，均可从该模型清晰推导得出。此外，基于正则引导中心系统，可系统发展一系列相关理论，如辛数值方法、正则回旋动理学理论以及正则粒子网格（PIC）算法。正则引导中心理论也为内禀磁矩的起源提供了启示。
英文摘要：
The concept of guiding center is potent in astrophysics, space plasmas, fusion researches, and arc plasmas to solve the multi-scale dynamics of magnetized plasmas. In this letter, we rigorously prove that the guiding center dynamics can generally be described as a constrained canonical Hamiltonian system with two constraints in six dimensional phase space, and that the solution flow of the guiding center lies on a canonical symplectic sub-manifold. The guiding center can thus be modeled as a pseudo-particle with an intrinsic magnetic moment, which properly replaces the charged particle dynamics on time scales larger than the gyro-period. The complete dynamical behaviors, such as the velocity and force, of the guiding center pseudo-particle can be clearly deduced from the model. Furthermore, a series of related theories, such as symplectic numerical methods, the canonical gyro-kinetic theory, and canonical particle-in-cell algorithms can be systematically developed based on the canonical guiding center system. The canonical guiding center theory also provides an enlightenment for the origin of the intrinsic magnetic moment.
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