30 research outputs found
From Vlasov-Poisson and Vlasov-Poisson-Fokker-Planck Systems to Incompressible Euler Equations: the case with finite charge
We study the asymptotic regime of strong electric fields that leads from the
Vlasov-Poisson system to the Incompressible Euler equations. We also deal with
the Vlasov-Poisson-Fokker-Planck system which induces dissipative effects. The
originality consists in considering a situation with a finite total charge
confined by a strong external field. In turn, the limiting equation is set in a
bounded domain, the shape of which is determined by the external confining
potential. The analysis extends to the situation where the limiting density is
non-homogeneous and where the Euler equation is replaced by the Lake Equation,
also called Anelastic Equation.Comment: 39 pages, 3 figure
The Euler--Maxwell system for electrons: global solutions in
A basic model for describing plasma dynamics is given by the Euler-Maxwell
system, in which compressible ion and electron fluids interact with their own
self-consistent electromagnetic field. In this paper we consider the
"one-fluid" Euler--Maxwell model for electrons, in 2 spatial dimensions, and
prove global stability of a constant neutral background.Comment: Revised versio
Charged Particles and the Electro-Magnetic Field in Non-Inertial Frames of Minkowski Spacetime: I. Admissible 3+1 Splittings of Minkowski Spacetime and the Non-Inertial Rest Frames
By using the 3+1 point of view and parametrized Minkowski theories we develop
the theory of {\it non-inertial} frames in Minkowski space-time. The transition
from a non-inertial frame to another one is a gauge transformation connecting
the respective notions of instantaneous 3-space (clock synchronization
convention) and of the 3-coordinates inside them. As a particular case we get
the extension of the inertial rest-frame instant form of dynamics to the
non-inertial rest-frame one. We show that every isolated system can be
described as an external decoupled non-covariant canonical center of mass
(described by frozen Jacobi data) carrying a pole-dipole structure: the
invariant mass and an effective spin. Moreover we identify the constraints
eliminating the internal 3-center of mass inside the instantaneous 3-spaces. In
the case of the isolated system of positive-energy scalar particles with
Grassmann-valued electric charges plus the electro-magnetic field we obtain
both Maxwell equations and their Hamiltonian description in non-inertial
frames. Then by means of a non-covariant decomposition we define the
non-inertial radiation gauge and we find the form of the non-covariant Coulomb
potential. We identify the coordinate-dependent relativistic inertial
potentials and we show that they have the correct Newtonian limit. In the
second paper we will study properties of Maxwell equations in non-inertial
frames like the wrap-up effect and the Faraday rotation in astrophysics. Also
the 3+1 description without coordinate-singularities of the rotating disk and
the Sagnac effect will be given, with added comments on pulsar magnetosphere
and on a relativistic extension of the Earth-fixed coordinate system.Comment: This paper and the second one are an adaptation of arXiv 0812.3057
for publication on Int.J.Geom. Methods in Modern Phys. 77
Boundary integral equations in Kinetic Plasma Theory
In this thesis, we use boundary integral equations (BIE) as a powerful tool to gain new insights into the dynamics of plasmas. On the theoretical side, our work provides new results regarding the oscillation of bounded plasmas. With the analytical computation of the frequencies for a general ellipsoid we contribute a new benchmark for numerical methods. Our results are validated by an extensive numerical study of several three-dimensional problems, including a particle accelerator with complex geometry and mixed boundary conditions. The use of Boundary Element Methods (BEM) reduces the dimension of the problem from three to two, thus drastically reducing the number of unknowns. By employing hierarchical methods for the computation of the occurring nonlocal sums and integral operators, our method scales linearly with the number of particles and the number of surface triangles, where the error decays exponentially in the expansion parameter. Furthermore, our method allows the pointwise evaluation of the electric field without loss of convergence order. As we are able to compute the occurring boundary integrals analytically, we can precisely predict the electric field near the boundary. This property makes our method exceptionally well suited for the numerical simulation of plasma sheaths near irregular boundaries or of plasma-surface interaction such as etching of semiconductors.In der vorliegenden Arbeit nutzen wir Randintegralgleichungen als ein mächtiges Werkzeug, um neue Einsichten in die Dynamik von Plasmen zu gewinnen. Auf theoretischer Seite entwickelt diese Arbeit neue Resultate bezüglich der Oszillation beschränkter Plasmen. Durch die ana- lytische Berechnung der Frequenzen im Fall eines allgemeinen Ellipsoids stellen wir ein neues Testbeispiel für numerische Methoden bereit. Unsere Resultate werden durch umfangreiche numerische Untersuchen dreidimensionaler Beispiele validiert, etwa einen Partikelbeschleuniger mit komplexer Geometrie und gemischten Randwerten. Mithilfe der Randelementmethode reduziert sich die Dimension des Problems von drei auf zwei, womit sich die Anzahl der Un- bekannten drastisch reduziert. Dank der Nutzung hierarchischer Methoden zur Berechnung der auftauchenden nichtlokalen Summen und Integraloperatoren skaliert unsere Methode linear mit der Anzahl der Partikel und der Anzahl der Oberflächendreiecken, wobei der Fehler exponen- tiell im Entwicklungsparameter abfällt. Des Weiteren erlaubt unsere Methode die Berechnung des elektrischen Felds ohne Verringerung der Konvergenzordnung. Da wir die auftretenden Randintegrale analytisch berechnen können, können wir präzise Aussagen über das elektrische Feld nahe des Rands treffen. Dank dieser Eigenschaft ist unsere Methode außergewöhnlich gut geeignet, um Plasmaränder nahe irregulärer Ränder oder Plasma-Oberflächen-Interaktionen, etwa das Ätzen von Halbleitern, zu simulieren