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Optimal control of a Vlasov-Poisson plasma by an external magnetic field

URN to cite this document: urn:nbn:de:bvb:703-epub-3387-5

Title data

Knopf, Patrik:
Optimal control of a Vlasov-Poisson plasma by an external magnetic field.
Bayreuth , 2017 . - 115 P.
( Doctoral thesis, 2017 , University of Bayreuth, Faculty of Mathematics, Physics and Computer Sciences)

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Abstract

We consider the three dimensional Vlasov-Poisson system in the plasma physical case. It describes the time evolution of the distribution function of a very large number of electrically charged particles. These particles move under the influence of a self-consistent electric field that is given by Poisson's equation. Our intention is to control the distribution function of the plasma by an external magnetic field. At first we will introduce the basics for variational calculus. Then we discuss two model problems where the distribution function is to be controlled in such a way that it matches a desired distribution function at some certain point of time as closely as possible. Those model problems will be analyzed with respect to the following topics: - existence of a globally optimal solution, - necessary conditions of first order for locally optimal solutions, - derivation of an optimality system, - sufficient conditions of second order for locally optimal solutions, - uniqueness of the optimal control under certain conditions.

Abstract in another language

Wir betrachten das dreidimensionale Vlasov-Poisson-System im elektrostatischen Fall. Es beschreibt die zeitliche Entwicklung der Verteilungsdichtefunktion eines sehr großen Ensembles elektrisch geladener Teilchen. Diese bewegen sich unter dem Einfluss eines selbst erzeugten elektrischen Felds. Das Ziel ist es nun, diese Verteilungsdichte über ein externes Magnetfeld zu steuern. Dazu führen wir zunächst die dafür notwendigen Grundlagen zur Variationsrechnung ein. Anschließend werden zwei Modelprobleme diskutiert bei denen die Stuerung so angepasst werden soll, dass die Verteilungsdichte zu einem festen Zeitpunkt mit einer gewünschten Verteilungsdichte möglichst genau übereinstimmt. Folgende Aspekte werden dabei analysiert: - die Existenz einer globalen optimalen Lösung, - notwendige Bedingungen erster Ordnung für lokale optimale Lösungen, - die Herleitung eines Optimalitätssystems, - hinreichende Bedingungen zweiter Ordnung für lokale optimale Lösungen, - Eindeutigkeit der optimalen Steuerung unter gewissen Bedingungen.

Further data

Item Type: Doctoral thesis (No information)
Keywords: Vlasov-Poisson equation; optimal control with PDE constraints; nonlinear partial differential equations; plasma physics
Subject classification: Mathematics Subject Classification: 49J20, 35Q83
DDC Subjects: 500 Science > 510 Mathematics
500 Science > 530 Physics
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics VI (Nonlinear Analysis and Mathematical Physics) > Chair Mathematics VI (Nonlinear Analysis and Mathematical Physics) - Univ.-Prof. Dr. Thomas Kriecherbauer
Profile Fields > Advanced Fields > Nonlinear Dynamics
Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics VI (Nonlinear Analysis and Mathematical Physics)
Profile Fields
Profile Fields > Advanced Fields
Language: English
Originates at UBT: Yes
URN: urn:nbn:de:bvb:703-epub-3387-5
Date Deposited: 25 Sep 2017 08:35
Last Modified: 25 Sep 2017 08:35
URI: https://epub.uni-bayreuth.de/id/eprint/3387

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