Particle Stimulation of Bounded Plasmas with a Wide Range of Space and Time Scales.

We are studying the effect of the boundary layer (or sheath) on bulk plasma behavior. Our approach is to use particle-in-cell plasma simulation to model the interplay between the bulk and the boundary. The sheath is an inherently small space and time scale structure. Previous particle simulation methods required global resolution of these small scales when studying bounded problems. With the computing resources currently available, this restricting has limited such simulations to studying microscopic phenomena. The objective of this research is to develop new techniques that allow simulation of macroscopic bounded plasma systems with accurate boundary layer physics. The first chapter introduces the types of physical problems we will study, reviews fundamental sheath physics, and reviews the relevant topics in particle-in-cell plasma simulation. In the following chapters we present new techniques that allow large gains in computing time over conventional particle methods but still resolve the sheath physics. Chapter 2 introduces the multi-scale method which allows local resolution of physical phenomena by allowing particles to have independent timestep size depending on their location in phase space. Chapter 3 further develops the multi-scale method and applies it to two plasma-sheath problems: an equilibrium sheath, and an ion acoustic shock front propagating toward a conducting wall. Chapter 4 presents an alternative approach of using the equilibrium physics of the sheath to specify the appropriate particle and field boundary conditions. Finally, Chapter 5 discusses the error associated with simulating magnetized systems when omega_{ce} Delta t is large and presents simulations of a one dimensional cross-field sheath.