Grid instability growth rates for explicit, electrostatic momentum- and energy-conserving particle-in-cell algorithms
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912589956513792 |
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| author | Adams, Luke C Werner, Gregory R Cary, John R |
| author_facet | Adams, Luke C Werner, Gregory R Cary, John R |
| contents | When the Debye length is not resolved in a simulation using the most common particle-in-cell (PIC) algorithm, the plasma will unphysically heat until the Debye length becomes resolved via a phenomenon known as grid heating. This article presents detailed numerical measurements of grid heating for several explicit PIC algorithms including the first systematic (covering the Debye length resolution and drift-velocity parameter space) study of grid-heating growth rates for the most-common electrostatic momentum-conserving PIC algorithm. Additionally, we derive and test a cubic-spline-based PIC algorithm that ensures that the interpolated electric field has a continuous first derivative, but find that a differentiable electric field has minimal impact on grid-heating stability. Also considered are energy-conserving PIC algorithms with linear and quadratic interpolation functions. In all cases, we find that unphysical heating can occur for some combinations of Debye under-resolution and plasma drift. We demonstrate analytically and numerically that grid heating cannot be eliminated by using a higher-order field solve, and give an analytical expression for the cold-beam stability limits of some energy-conserving algorithms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_13697 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Grid instability growth rates for explicit, electrostatic momentum- and energy-conserving particle-in-cell algorithms Adams, Luke C Werner, Gregory R Cary, John R Plasma Physics Computational Physics When the Debye length is not resolved in a simulation using the most common particle-in-cell (PIC) algorithm, the plasma will unphysically heat until the Debye length becomes resolved via a phenomenon known as grid heating. This article presents detailed numerical measurements of grid heating for several explicit PIC algorithms including the first systematic (covering the Debye length resolution and drift-velocity parameter space) study of grid-heating growth rates for the most-common electrostatic momentum-conserving PIC algorithm. Additionally, we derive and test a cubic-spline-based PIC algorithm that ensures that the interpolated electric field has a continuous first derivative, but find that a differentiable electric field has minimal impact on grid-heating stability. Also considered are energy-conserving PIC algorithms with linear and quadratic interpolation functions. In all cases, we find that unphysical heating can occur for some combinations of Debye under-resolution and plasma drift. We demonstrate analytically and numerically that grid heating cannot be eliminated by using a higher-order field solve, and give an analytical expression for the cold-beam stability limits of some energy-conserving algorithms. |
| title | Grid instability growth rates for explicit, electrostatic momentum- and energy-conserving particle-in-cell algorithms |
| topic | Plasma Physics Computational Physics |
| url | https://arxiv.org/abs/2503.13697 |