Bartsch, Jan and Knopf, Patrik and Scheurer, Stefania and Weber, Joerg (2024) Controlling a Vlasov–Poisson Plasma by a Particle-in-Cell Method Based on a Monte Carlo Framework. SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 62 (4). pp. 1977-2011. ISSN 0363-0129, 1095-7138
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The Vlasov--Poisson system describes the time evolution of a plasma in the so-called collisionless regime. The investigation of a high-temperature plasma that is influenced by an exterior magnetic field is one of the most significant aspects of thermonuclear fusion research. In this paper, we formulate and analyze a kinetic optimal control problem for the Vlasov--Poisson system where the control is represented by an external magnetic field. The main goal of such optimal control problems is to confine the plasma to a certain region in phase space. We first investigate the optimal control problem in terms of mathematical analysis, i.e., we show the existence of at least one global minimizer and rigorously derive a first-order necessary optimality condition for local minimizers by the adjoint approach. Then we build a Monte Carlo framework to solve the state equations as well as the adjoint equations by means of a particle-in-cell method, and we apply a nonlinear conjugate gradient method to solve the optimization problem. Eventually, we present numerical experiments that successfully validate our optimization framework.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | SYSTEM; STATIONARY; CONTROLLABILITY; OSCILLATIONS; EXISTENCE; EQUATIONS; Vlasov--Poisson system; ensemble optimal control problems; multispecies plasma; Monte Carlo methods; particle-in-cell method; magnetic confinement |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 10 Dec 2025 07:24 |
| Last Modified: | 10 Dec 2025 07:24 |
| URI: | https://pred.uni-regensburg.de/id/eprint/64647 |
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