Controlling instability in the Vlasov-Poisson system through moment-based optimization
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915462935216128 |
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| author | Lu, Jingcheng Wang, Li Calder, Jeff |
| author_facet | Lu, Jingcheng Wang, Li Calder, Jeff |
| contents | Controlling instability in plasma is one of the central challenges in fusion energy research. Among the various sources of instability, kinetic effects play a significant role. In this work, we aim to suppress the instability induced by kinetic effects by designing an external electric field. However, rather than directly solving the full kinetic Vlasov-Poisson system, we focus on a reduced-order model, specifically the moment-based system, to capture the underlying dynamics. This approach is motivated by the desire to reduce the computational cost associated with repeatedly solving the high-dimensional kinetic equations during the optimization of the electric field. Additionally, moment-based data is more readily accessible in practice, making a moment-based control framework more adaptable to data-driven scenarios. We investigate the effectiveness of moment-based control both analytically and numerically, by comparing it to control based on the full kinetic model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_18412 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Controlling instability in the Vlasov-Poisson system through moment-based optimization Lu, Jingcheng Wang, Li Calder, Jeff Numerical Analysis 49M41, 49J20, 35Q83, 65K10 Controlling instability in plasma is one of the central challenges in fusion energy research. Among the various sources of instability, kinetic effects play a significant role. In this work, we aim to suppress the instability induced by kinetic effects by designing an external electric field. However, rather than directly solving the full kinetic Vlasov-Poisson system, we focus on a reduced-order model, specifically the moment-based system, to capture the underlying dynamics. This approach is motivated by the desire to reduce the computational cost associated with repeatedly solving the high-dimensional kinetic equations during the optimization of the electric field. Additionally, moment-based data is more readily accessible in practice, making a moment-based control framework more adaptable to data-driven scenarios. We investigate the effectiveness of moment-based control both analytically and numerically, by comparing it to control based on the full kinetic model. |
| title | Controlling instability in the Vlasov-Poisson system through moment-based optimization |
| topic | Numerical Analysis 49M41, 49J20, 35Q83, 65K10 |
| url | https://arxiv.org/abs/2508.18412 |