2025/04/14 by Guerra, Martin, Li, Qin, Yue, Yukun +1 · 2 citations
#Computational Physics (physics.comp-ph) #FOS: Mathematics #FOS: Physical sciences #Numerical Analysis (math.NA)
paper · doi:10.48550/arxiv.2504.10435
Stabilizing plasma dynamics is an important task in green energy generation via fusion. A common strategy is to introduce an external field to prevent the plasma distribution from becoming turbulent. However, finding such external fields efficiently remains an open question, even for simplified models such as the Vlasov-Poisson (VP) system. In this work, we present an integrated method where we first perform an analytical derivation of the VP system's dispersion relation to construct a high-quality initial guess for the stabilizing field. This analytically-derived field is then used to initialize a PDE-constrained optimization loop that refines the control to a local optimum. Through extensive numerical experiments, we demonstrate that objective functions evaluated only at the target time-when stable plasma is desired-lead to highly non-convex optimization landscapes, making the global minimum difficult to locate. This behavior arises regardless of the choice of loss function (e.g., KL divergence or electric energy). In contrast, integrating the loss function over time yields a landscape with a convex basin near the global minimum, facilitating convergence. Furthermore, when using electric energy as the objective, the landscape outside this basin is dominated by flat, unphysical local minima, highlighting the critical importance of our analytical approach for generating an initial guess that lies within the global minimum's basin of attraction.