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

该项目将发展理论并探索模拟等离子体的新算法的实际应用-等离子体是一种具有自由相互作用的电子和离子而不是在原子中结合在一起的物质状态。这种新算法有可能模拟更大、更复杂的等离子体系统，从而更好地理解等离子体物理的基本原理，提高对空间天气的预测能力，更好地建模聚变装置和基于等离子体的火箭推进器，以及更有效地操纵半导体制造和其他工业用途的等离子体。这种新的算法，即速度限制粒子胞内（SLPIC）方法，是非常有用的粒子胞内（PIC）技术的一个极端变体。SLPIC通过避免解决不重要的小尺度现象（即使物理上可以忽略不计，也必须经常解决的现象）来促进多尺度模拟，以避免数值不稳定。为了实现这一目标，SLPIC限制了快速粒子（例如电子）的速度，同时保持跟踪它们的实际速度。速度限制运动是一个近似的弗拉索夫方程的结果；它精确地模拟了粒子分布函数，只要它们变化得足够慢。该项目将发展SLPIC的理论和使用，研究其在标准PIC模拟方面的优点和缺点，并将其应用于测试问题，包括等离子体护套、太阳风和霍尔火箭推进器。此外，该项目将探索SLPIC技术可能有助于减轻标准PIC方法中众所周知的有限网格不稳定性的可能性。

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.