Theory of the Speed-Limited Particle-in-Cell Simulation Method

这个项目将发展一种模拟等离子体的新算法的理论和探索实际应用--等离子体是一种物质状态，其中电子和离子在原子中没有束缚在一起，自由相互作用。这种新算法有可能模拟更大和更复杂的等离子体系统，从而更好地了解等离子体物理，提高对空间天气的预测能力，更好地对聚变设备和基于等离子体的火箭推进器进行建模，并更有效地操纵用于半导体制造和其他工业目的的等离子体。新算法--限速粒子单元(SLPIC)方法--是非常有用的粒子单元(PIC)技术的极端变体。SLPIC通过避免解决不重要的小规模现象的需要来促进多尺度模拟--这些现象必须经常解决，即使在物理上可以忽略的情况下，以避免数值不稳定。为了做到这一点，SLPIC限制了快速粒子(例如电子)的速度，同时跟踪它们的实际速度。限速运动是近似的弗拉索夫方程的结果；它准确地模拟了粒子分布函数，只要它们变化得足够慢。本项目将发展SLPIC的理论和应用，检验其相对于标准PIC模拟的优缺点，并将其应用于测试问题，包括等离子体鞘、太阳风和霍尔火箭推进器。此外，该项目还将探索SLPIC技术可能有助于缓解标准PIC方法中众所周知的有限网格不稳定性。

This project will develop the theory and explore practical applications of a new algorithm for simulation of plasma -- a state of matter with freely interacting electrons and ions not bound together in atoms. This new algorithm has the potential to enable simulation of larger and more complicated plasma systems, leading to a better fundamental understanding of plasma physics, improved predictive capabilities for space weather, better modeling of fusion devices and plasma-based rocket thrusters, and more efficient manipulation of plasma for semiconductor fabrication and other industrial purposes.The new algorithm, the speed-limited particle-in-cell (SLPIC) method, is an extreme variant of the immensely useful particle-in-cell (PIC) technique. SLPIC facilitates multiscale simulation by avoiding the need to resolve unimportant small-scale phenomena -- phenomena that must otherwise often be resolved, even when physically negligible, to avoid numerical instabilities. To accomplish this, SLPIC limits the speed of fast particles (e.g., electrons), while keeping track of what their actual speed should be. The speed-limited motion is a consequence of an approximate Vlasov equation; it accurately simulates particle distribution functions as long as they change sufficiently slowly. This project will develop the theory and use of SLPIC, examining its advantages and disadvantages with respect to standard PIC simulation, and apply it to test problems, including plasma sheaths, the solar wind, and Hall rocket thrusters. In addition, this project will explore the possibility that SLPIC techniques might help mitigate the finite grid instability well-known in standard PIC methods.