Mathematical Problems: Mathematical Modeling in Plasma Physics

9404433斯特恩伯格拟议的研究涉及对射频放电中发生的物理过程进行数学建模。本文的目的是研究静态约束等离子体问题中从等离子体中心的恒定离子迁移率区域到等离子体边界的空间电荷区域的转变。建立了用于确定护套中频小信号电容的数学模型。对等离子体和鞘层的更精确的分析和数值理解对于未来在等离子体化学、激光工程、微电子学和核物理中的成功应用至关重要。利用数学方法，提出的项目将改进物理实验的公式，并提供对物理问题的新见解。

9404433 Sternberg The proposed research is concerned with mathematical modeling of physical processes that occur in radio frequency discharges. The intent is to study the transition from the constant ion mobility regime at the center of the plasma to the space-charge regime at the plasma boundary in the static bounded plasma problem. It is also intended to construct a mathematical model for determining the small signal capacitance of the sheath at intermediate frequencies. A more precise analytical and numerical understanding of the the plasma and the sheath is vital for future successful applications in plasma chemistry, laser engineering, microelectronics, and nuclear physics. Using mathematical methods, the proposed project will improve the formulation of the physical experiments, and provide new insight into the physical problem.