Canonical Hamiltonian Guiding Center Dynamics and Its Intrinsic Magnetic Moment
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arXiv
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| Main Authors: | , , , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909128098578432 |
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| author | Zhang, Ruili Liu, Jian Liu, Tong Li, Wenxiang Wang, Xiaogang Tang, Yifa |
| author_facet | Zhang, Ruili Liu, Jian Liu, Tong Li, Wenxiang Wang, Xiaogang Tang, Yifa |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_02883 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Canonical Hamiltonian Guiding Center Dynamics and Its Intrinsic Magnetic Moment Zhang, Ruili Liu, Jian Liu, Tong Li, Wenxiang Wang, Xiaogang Tang, Yifa Plasma Physics 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. |
| title | Canonical Hamiltonian Guiding Center Dynamics and Its Intrinsic Magnetic Moment |
| topic | Plasma Physics |
| url | https://arxiv.org/abs/2403.02883 |