NSF Young Investigator:Spectral Methods in Plasma Kinetics

9358344霍洛威在此NYI研究奖下进行的工作是针对提高我们的建模能力，无论是碰撞或带电粒子中性粒子碰撞为主的等离子体，如非中性等离子体在高功率系统和静电陷阱，或处理等离子体。 正在探索的算法是基于使用pseudospectral配置的动力学方程和麦克斯韦方程的空间和速度离散化，进行离散化，使大部分的精确系统的哈密顿结构被保存在无碰撞的限制。 由此产生的半离散系统可以精确地保留原始系统的汉密尔顿函数，以及它的一些卡西米尔函数，例如粒子数和带电粒子分布函数的平方积分;在有限的网格尺寸下精确保持动量的方法也正在寻找。 时间离散方法，精确地保留这些重要的物理量在有限的数值网格大小使用，这些方法包括显式和非线性隐式方法。 在非常不同的时间尺度上（例如在处理等离子体中）发生现象的系统的建模正在通过以下组合进行研究： 渐近方法（多时间尺度分析）和谱方法。 ***

9358344 Holloway The work carried out under this NYI research award is directed to improving our capabilities in modeling plasmas that are either collisionless or dominated by charged particle-neutral particle collisions, such as non-neutral plasmas in high power systems and in electrostatic traps, or processing plasmas. The algorithms being explored are based on the use of pseudospectral collocation for the spatial and velocity discretization of the kinetic equations and Maxwell's equations, with the discretization carried out so that much of the Hamiltonian structure of the exact system is preserved in the collisionless limit. The resulting semi-discrete systems can be made to exactly preserve the Hamiltonian of the original system, as well as some of its Casimirs, such as number of particles and square integral of the charged particle distribution function; methods tat exactly conserve momentum at finite grid size are also being sought. Time discretization methods that exactly preserve these important physical quantities at finite numerical grid size are used; these methods include explicit and nonlinearly implicit methods. The modeling of systems with phenomena occurring over very disparate time scales (such as in processing plasmas) is being studied by a combination of asymptotic methods (multiple time scale analysis) and spectral methods. ***