What metric to optimize for suppressing instability in a Vlasov-Poisson system?

[2504.10435] What metric to optimize for suppressing instability in a Vlasov-Poisson system? Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Numerical Analysis arXiv:2504.10435 (math) [Submitted on 14 Apr 2025 ( v1 ), last revised 14 Apr 2026 (this version, v4)] Title: What metric to optimize for suppressing instability in a Vlasov-Poisson system? Authors: Martin Guerra , Qin Li , Yukun Yue , Leonardo Zepeda-Núñez View a PDF of the paper titled What metric to optimize for suppressing instability in a Vlasov-Poisson system?, by Martin Guerra and 3 other authors View PDF HTML (experimental) Abstract: 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. Comments: 60 pages, 83 figures Subjects: Numerical Analysis (math.NA) ; Computational Physics (physics.comp-ph) Cite as: arXiv:2504.10435 [math.NA] (or arXiv:2504.10435v4 [math.NA] for this version) https://doi.org/10.48550/arXiv.2504.10435 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Martin Guerra [ view email ] [v1] Mon, 14 Apr 2025 17:26:09 UTC (40,089 KB) [v2] Tue, 15 Apr 2025 05:07:18 UTC (40,086 KB) [v3] Thu, 14 Aug 2025 02:47:00 UTC (27,571 KB) [v4] Tue, 14 Apr 2026 05:18:34 UTC (30,248 KB) Full-text links: Access Paper: View a PDF of the paper titled What metric to optimize for suppressing instability in a Vlasov-Poisson system?, by Martin Guerra and 3 other authors View PDF HTML (experimental) TeX Source view license Current browse context: math.NA < prev | next > new | recent | 2025-04 Change to browse by: cs cs.NA math physics physics.comp-ph References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... 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