arXiv subjects

Martin Guerra

Publications and source records attributed to Martin Guerra.

4 recordsLinked to original sources

arXiv2026

Kinetic Optimization of Magnetic Mirror Confinement: Beyond Classical Loss-Cone Theory

Magnetic mirrors are among the conceptually simplest plasma confinement configurations and remain promising candidates for thermonuclear fusion. Their design requires shaping an externally applied magnetic field to confine plasma within an open-ended cylindrical device. In contrast to toroidally closed devices such as tokamaks and stellarators, confinement in magnetic mirrors depends intrinsically on kinetic mechanisms, particularly velocity-space trapping and particle loss through the open ends. We formulate magnetic mirror design as a PDE-constrained optimization problem governed by a reduced multispecies drift-kinetic-Poisson model. The resulting optimization reveals two physical effects not captured by the classical loss-cone argument. First, the self-consistent electric field generated through Poisson coupling acts as a secondary confinement barrier and substantially alters particle retention in the nonlinear regime. Second, the optimized magnetic-field configuration depends qualitatively on the underlying kinetic model: an electron-only model favors an unconventional centrally peaked field, whereas the fully coupled electron-ion model recovers the classical boundary-peaked mirror configuration. These results demonstrate that optimal magnetic mirror design cannot be determined solely from loss-cone considerations, but must account for the self-consistent nonlinear kinetic dynamics of the plasma.

physics.plasm-ph↗

arXiv2025

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

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.

math.NA↗

arXiv2024

Swarm-based gradient descent meets simulated annealing

We introduce a novel method for non-convex optimization, called Swarm-based Simulated Annealing (SSA), which is at the interface between the swarm-based gradient-descent (SBGD) [J. Lu et. al., ArXiv:2211.17157; E.Tadmor and A. Zenginoglu, Acta Applicandae Math., 190, 2024] and Simulated Annealing (SA) [V. Cerny, J. optimization theory and appl., 45:41-51, 1985; S.Kirkpatrick et. al., Science, 220(4598):671-680, 1983; S. Geman and C.-R. Hwang, SIAM J. Control and Optimization, 24(5):1031-1043, 1986]. Similar to SBGD, we introduce a swarm of agents, each identified with a position, ${\mathbf x}$ and mass $m$, to explore the ambient space. Similar to SA, the agents proceed in the gradient descent direction, and are subject to Brownian motion. The annealing rate, however, is dictated by a decreasing function of their mass. As a consequence, instead of the SA protocol for time-decreasing temperature, we let the swarm decide how to `cool down' agents, depending on their accumulated mass over time. The dynamics of masses is coupled with the dynamics of positions: agents at higher ground transfer (part of) their mass to those at lower ground. Consequently, resulting SSA optimizer is dynamically divided between heavier, cooler agents viewed as `leaders' and lighter, warmer agents viewed as `explorers'. Mean-field convergence analysis and benchmark optimizations demonstrate the effectiveness of the swarm-based method as a multi-dimensional global optimizer.

math.OC↗

arXiv2024

Optimal design for linear models via gradient flow

Optimal experimental design (OED) aims to choose the observations in an experiment to be as informative as possible, according to certain statistical criteria. In the linear case (when the observations depend linearly on the unknown parameters), it seeks the optimal weights over rows of the design matrix $\mA$ under certain criteria. Classical OED assumes a discrete design space and thus a design matrix with finite dimensions. In many practical situations, however, the design space is continuous-valued, so that the OED problem is one of optimizing over a continuous-valued design space. The objective becomes a functional over the probability measure, instead of a function of a finite dimensional vector. This change of perspective requires a new set of techniques to optimize over probability measures, and Wasserstein gradient flow becomes a natural candidate. Both the first-order criticality and the convexity properties of the OED objective are presented. Computationally, the Monte Carlo particle method is used to translate the gradient flow equation formulation into a numerical algorithm. This algorithm is applied to two elliptic inverse problems.

math.NA↗