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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2503.18659 |
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| _version_ | 1866910040629182464 |
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| author | Li, Ting Wang, Bin |
| author_facet | Li, Ting Wang, Bin |
| contents | This article is concerned with a new filtered two-step variational integrator for solving the charged-particle dynamics in a mildly non-uniform moderate or strong magnetic field with a dimensionless parameter $\varepsilon$ inversely proportional to the strength of the magnetic field. In the case of a moderate magnetic field ($\varepsilon=1$), second-order error bounds and long-time near-conservation of energy and momentum are obtained. Moreover, the proof of the long-term analysis is accomplished by the backward error analysis. For $0<\varepsilon \ll 1$, the proposed integrator achieves uniform second-order accuracy in the position and the parallel velocity for large step sizes, while attaining first-order accuracy with respect to the small parameter $\varepsilon$ for smaller step sizes. The error bounds are derived from a comparison of the modulated Fourier expansions of the exact and numerical solutions. Moreover, long-time near-conservation of the energy and the magnetic moment is established using modulated Fourier expansion and backward error analysis. All the theoretical results of the error behavior and long-time near-conservation are numerically demonstrated by four numerical experiments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_18659 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A filtered two-step variational integrator for charged-particle dynamics in a moderate or strong magnetic field Li, Ting Wang, Bin Numerical Analysis This article is concerned with a new filtered two-step variational integrator for solving the charged-particle dynamics in a mildly non-uniform moderate or strong magnetic field with a dimensionless parameter $\varepsilon$ inversely proportional to the strength of the magnetic field. In the case of a moderate magnetic field ($\varepsilon=1$), second-order error bounds and long-time near-conservation of energy and momentum are obtained. Moreover, the proof of the long-term analysis is accomplished by the backward error analysis. For $0<\varepsilon \ll 1$, the proposed integrator achieves uniform second-order accuracy in the position and the parallel velocity for large step sizes, while attaining first-order accuracy with respect to the small parameter $\varepsilon$ for smaller step sizes. The error bounds are derived from a comparison of the modulated Fourier expansions of the exact and numerical solutions. Moreover, long-time near-conservation of the energy and the magnetic moment is established using modulated Fourier expansion and backward error analysis. All the theoretical results of the error behavior and long-time near-conservation are numerically demonstrated by four numerical experiments. |
| title | A filtered two-step variational integrator for charged-particle dynamics in a moderate or strong magnetic field |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2503.18659 |