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Applied Mathematics Seminar
Date/Time/Room:
Friday (2/3/2006) at 1:00pm in 304 Pickard Hall "Simulations of Plasma Dynamics using a Grid Free Technique"Abstract: When a sufficient amount of energy has been put into a gas, the gas breaks down into its constituent electrons and ions, commonly known as the plasma state. 99% of all matter is in the plasma state, e.g., stars, interstellar material, etc. Therefore understanding fundamental behavior of plasmas can tell us a great deal about the Universe.The fundamental set of equations describing a plasma is the BoltzmannMaxwell system. This system is a kinetic model and it can be reduced to the more familiar fluid description through the ChapmanEnskog procedure. However, a wide range of observable phenomena can only be described by a kinetic model. Limiting our attention to the simpler kinetic model of the VlasovPoisson (VP) system, two examples of purely kinetic phenomena are Landau damping and the bumpontail instability. The VP system is a nonlinear PDEintegral model for a collisionless electrostatic plasma. Due to the nonlinearity of the VP system, a natural approach to investigating the detailed dynamics of the system is through numerical simulations. In this talk I will highlight aspects of the derivation of the kinetic description, discuss what is known about this system, and give an overview of Landau damping and the bumpontail instability. In addition, I will discuss existing approaches to simulating this system and the shortcomings of these methods. Finally, I will discuss a gridfree alternative currently being developed and consider its application to the the bumpontail instability and the problem of crystal formation in plasmas. Novel aspects of the gridfree approach include the combination of fast summation algorithms with numerical Green's function methods and systematic refinement techniques in a fully Lagrangian framework.

