Research on Plasma Sheaths: An Interdisciplinary Mathematical-Experimental Program

NSF奖摘要-DMS-0071463数学科学：等离子体鞘的研究：一个跨学科的数学-实验计划摘要Euler-Poisson方程描述了由离子和电子组成的等离子体。这些方程在有界域中的一个普遍性质是在边界附近存在一个整体准中性等离子体区域和一个薄的空间电荷鞘。这个项目研究了鞘形成的各个方面：两种和多种物种等离子体准中性极限的严格证明，极限方程的严格推导，定义鞘边界的规则的严格推导，与动力学理论的联系，以及在鞘形成问题中发现的在不同尺度上求解欧拉-泊松方程的松弛方案的发展。受限等离子体形成空间电荷鞘，离子密度大于电子密度的相对薄的区域。这一现象在各种技术应用(等离子体刻蚀、微电子学、气体激光)中都很重要。这个项目是一个研究空间电荷鞘的跨学科数学实验计划。这项研究的目标是：(1)开发新的工具，包括数学模型、数值方法和分析技术，用于预测等离子体鞘的形成和动力学；(2)进行新的实验室实验，以检查等离子体鞘的形成、行为和各种性质；(3)整合(1)和(2)的结果，为研究的数学和实验方面提供输入。该研究将引起美国数学界对围绕等离子体鞘分析的无数悬而未决的问题的关注。

NSF Award Abstract - DMS-0071463Mathematical Sciences: Research on Plasma Sheaths: An Interdisciplinary Mathematical-Experimental ProgramAbstract0071463 SlemrodThe 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, andvarious 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.