What metric to optimize for suppressing instability in a Vlasov-Poisson system?
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866910126589345792 |
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| author | Guerra, Martin Li, Qin Yue, Yukun Zepeda-Núñez, Leonardo |
| author_facet | Guerra, Martin Li, Qin Yue, Yukun Zepeda-Núñez, Leonardo |
| contents | Stabilizing plasma dynamics is a central challenge in magnetic confinement fusion. A common approach is to introduce external electric fields to suppress instabilities in the plasma distribution. However, efficiently identifying such stabilizing fields remains challenging, even for simplified kinetic models such as the Vlasov-Poisson (VP) system. In this work we study plasma stabilization from the perspective of PDE-constrained optimization. Our goal is to understand how the choice of objective function and the underlying kinetic dynamics influence the optimization landscape. First, we analyze the dispersion relation of the VP system and show that it reveals the spectral structure of the dynamics; eliminating unstable modes provides parameter configurations that lie close to the global optimum and serve as effective initial guesses for optimization. Second, we investigate several objective functions for stabilization and compare their optimization landscapes through numerical experiments. Our results show that while different objectives lead to similar stabilizing parameter configurations, objective functions incorporating time-integrated information exhibit more convex-like landscapes and are therefore more favorable for gradient-based optimization methods. These findings provide insight into the design of objective functions for optimization-based plasma control and suggest promising directions for future research on real-time stabilization of kinetic plasma models. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_10435 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | What metric to optimize for suppressing instability in a Vlasov-Poisson system? Guerra, Martin Li, Qin Yue, Yukun Zepeda-Núñez, Leonardo Numerical Analysis Computational Physics Stabilizing plasma dynamics is a central challenge in magnetic confinement fusion. A common approach is to introduce external electric fields to suppress instabilities in the plasma distribution. However, efficiently identifying such stabilizing fields remains challenging, even for simplified kinetic models such as the Vlasov-Poisson (VP) system. In this work we study plasma stabilization from the perspective of PDE-constrained optimization. Our goal is to understand how the choice of objective function and the underlying kinetic dynamics influence the optimization landscape. First, we analyze the dispersion relation of the VP system and show that it reveals the spectral structure of the dynamics; eliminating unstable modes provides parameter configurations that lie close to the global optimum and serve as effective initial guesses for optimization. Second, we investigate several objective functions for stabilization and compare their optimization landscapes through numerical experiments. Our results show that while different objectives lead to similar stabilizing parameter configurations, objective functions incorporating time-integrated information exhibit more convex-like landscapes and are therefore more favorable for gradient-based optimization methods. These findings provide insight into the design of objective functions for optimization-based plasma control and suggest promising directions for future research on real-time stabilization of kinetic plasma models. |
| title | What metric to optimize for suppressing instability in a Vlasov-Poisson system? |
| topic | Numerical Analysis Computational Physics |
| url | https://arxiv.org/abs/2504.10435 |