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| Main Authors: | , |
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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2505.02270 |
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| _version_ | 1866912414014898176 |
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| author | Zenitani, Seiji Kato, Tsunehiko N. |
| author_facet | Zenitani, Seiji Kato, Tsunehiko N. |
| contents | We propose a family of numerical solvers for the nonrelativistic Newton--Lorentz equation in kinetic plasma simulations. The new solvers extend the standard 4-step Boris procedure, which has second-order accuracy in time, in three ways. First, we repeat the 4-step procedure multiple times, using an $n$-times smaller timestep ($Δt/n$). We derive a formula for the arbitrary subcycling number $n$, so that we obtain the result without repeating the same calculations. Second, prior to the 4-step procedure, we apply Boris-type gyrophase corrections to the electromagnetic field. In addition to a well-known correction to the magnetic field, we correct the electric field in an anisotropic manner to achieve higher-order ($N=2,4,6 \dots$th order) accuracy. Third, combining these two methods, we propose a family of high-accuracy particle solvers, the hyper Boris solvers, which have two hyperparameters of the subcycling number $n$ and the order of accuracy, $N$. The $n$-cycle $N$th-order solver gives a numerical error of $\sim (Δt/n)^{N}$ at affordable computational cost. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_02270 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hyper Boris integrators for kinetic plasma simulations Zenitani, Seiji Kato, Tsunehiko N. Computational Physics Plasma Physics Space Physics We propose a family of numerical solvers for the nonrelativistic Newton--Lorentz equation in kinetic plasma simulations. The new solvers extend the standard 4-step Boris procedure, which has second-order accuracy in time, in three ways. First, we repeat the 4-step procedure multiple times, using an $n$-times smaller timestep ($Δt/n$). We derive a formula for the arbitrary subcycling number $n$, so that we obtain the result without repeating the same calculations. Second, prior to the 4-step procedure, we apply Boris-type gyrophase corrections to the electromagnetic field. In addition to a well-known correction to the magnetic field, we correct the electric field in an anisotropic manner to achieve higher-order ($N=2,4,6 \dots$th order) accuracy. Third, combining these two methods, we propose a family of high-accuracy particle solvers, the hyper Boris solvers, which have two hyperparameters of the subcycling number $n$ and the order of accuracy, $N$. The $n$-cycle $N$th-order solver gives a numerical error of $\sim (Δt/n)^{N}$ at affordable computational cost. |
| title | Hyper Boris integrators for kinetic plasma simulations |
| topic | Computational Physics Plasma Physics Space Physics |
| url | https://arxiv.org/abs/2505.02270 |