Research on Plasma Sheaths: An Interdisciplinary Mathematical-Experimental Program

University Of Wisconsin-Madison, Madison WI

Investigators

Abstract

NSF Award Abstract - DMS-0071463 Mathematical Sciences: Research on Plasma Sheaths: An Interdisciplinary Mathematical-Experimental Program Abstract 0071463 Slemrod The Euler-Poisson equations describe a plasma consisting of ions and electrons. A universal property of these equations in a bounded domain is the existence of a bulk quasi-neutral plasma domain and a thin space charge sheath near the boundary. This project studies various aspects of sheath formation: rigorous justification of the quasi-neutral limit for two- and also multi-species plasmas, rigorous derivation of limit equations, rigorous derivation of rules for defining the sheath boundary, connections with kinetic theory, and development of relaxation schemes for solving the Euler-Poisson equations on the various scales to be found in sheath formation problems. Confined plasmas form space charge sheaths, relatively thin zones where the ion density is greater than the electron density. The phenomenon is important in various technological applications (plasma etching, microelectronics, gaseous lasers). This project is an interdisciplinary mathematical-experimental program for studying space charge sheaths. The objectives of the research are to: (1) develop new tools, including mathematical models, numerical methods, and analytical techniques, for prediction of plasma sheath formation and dynamics; (2) perform new laboratory experiments to examine the formation, behavior, and various properties of plasma sheaths; (3) integrate the results of (1) and (2) to provide input for both the mathematical and experimental aspects of the research. The research will bring to the attention of the U.S. mathematical community the myriad of open problems surrounding the analysis of plasma sheaths.