Speaker: Andrew Christlieb
Title: Fully Lagrangian Methods for Problems in Plasma Physics
Affiliation: Michigan State University
Date: Friday, November 16, 2007.
Place and Time: Room 101, Love Building, 3:35-4:30 pm.
Refreshments: Room 204, Love Building, 3:00 pm.

Abstract. Plasmas are ionized gases that appear in a wide range of applications including astrophysics and space physics, as well as in laboratory settings such as in magnetically confined fusion. Modeling and understanding the basic phenomenon in plasmas has long been a topic in scientific computing, yet many problems remain far too numerically intensive for modern parallel computers. The main difficulty is that plasmas span a wide range of spatial and temporal scales, requiring modeling tools from both fluid and kinetic theory.
In this work we focus on one class of fully kinetic plasma problems where the underlying system is collisionless and electrostaticly driven. This class of plasma problem is governed by the Vlasov- Poisson (VP) system. Many interesting instabilities arise in this system, such as the bump on tail instability, two stream instability, the dynamics of BGK modes (the only known class of fully non-linear solutions to the VP system), as well as the dynamics of magnetically confined charged particles. Understanding the long time dynamics of the VP system is essential for a range of applications, including the design of high power tubes for communications systems in satellites, and for increasing our understanding of basic physics, such as how BGK modes propagate in the ionosphere. The VP system is 6D plus time and as such is very computationally expensive to solve.
In this work we consider an efficient approach to the simulation of the VP system based on a Lagrangian particle models. The method draws on work in point vortex dynamics and differs from other Lagrangian plasma simulations in that it computes long range interactions via a combined fast summation boundary integral method. We will demonstrate the effectiveness of the approach by applying the method to several classic problems, including the two stream instability and the dynamics of a Penning trap. We will also discuss extension of the method to incorporate the spectral deffered correction as one approach for handling temporal multi scale problems.
This is joint work with R. Krasny, J. Qiu and B. Ong.