Analytical and Numerical Methods in Collisionless Kinetic Theory

无碰撞运动理论中的分析和数值方法

• 批准号: 2107938
• 负责人: Stephen Pankavich
• 金额: $ 20万
• 依托单位: Colorado School of Mines
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2021
• 资助国家: 美国
• 起止时间: 2021-09-01 至 2025-08-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2107938&HistoricalAwards=false
• 关键词: Analytical; Numerical; Methods; Collisionless; Kinetic

This project develops analytic and computational methods to answer mathematical questions in the kinetic theory of plasma dynamics. Plasmas are charged gases, often referred to as the fourth state of matter, that account for more than 99% of all material in the universe and are of significant practical interest since they serve as excellent conductors of electricity. Plasma engines have been developed by space agencies around the world and were recently employed to power selected spacecraft. The use of plasmas within nuclear fusion reactors is also being explored as a source of clean energy. Other notable examples of plasmas occurring in natural phenomena are the solar wind, the Earth's ionosphere, galactic nebulae, and the tails of comets. A full understanding of the dynamics of the solar wind is of practical importance, as it dictates the intensity of space weather, which is often responsible for expensive damage to satellites orbiting the Earth. The motion of a plasma can be modeled by a system of partial differential equations, and among the goals of this project are to demonstrate that these equations possess realistic solutions, to determine their qualitative behavior, to compute their sensitivity with respect to model parameters, such as masses, charges, and temperature, and to approximate them computationally to predict future behavior with precision. The project provides graduate research training opportunities. A plasma is a fully ionized gas in which electromagnetic forces are often strong enough to dominate collisional effects. The motion of a high temperature, low density collisionless plasma is described by the Vlasov-Maxwell equations, a nonlinear system of hyperbolic partial differential equations. In this setting, collisions are neglected while the charge and current densities, which drive the Maxwell system, are determined in a self-consistent manner from velocity averages of the distribution of ions in the system, which satisfies the Vlasov equation. A major question this project addresses is if there are shocks in a collisionless plasma, that is, if a singularity can develop from smooth initial data as time progresses. In some cases, such as in lower dimensional relativistic formulations, smooth global solutions are known to exist. Additional questions concern the large time limiting behavior of the particle positions and momenta, charge and current densities, electromagnetic fields, and particle distribution functions within the system. More specifically, the project determines whether dispersive effects in the equations cause these quantities to decay over time, or if there is sufficient interaction to sustain their strength even in the time asymptotic limit. Finally, the sensitivity of the fields and densities with respect to model input parameters are computed using global sensitivity metrics, corresponding dispersion relations, and particle-in-cell simulations.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

这个项目开发了解析和计算方法来回答等离子体动力学动力学中的数学问题。等离子体是一种带电气体，通常被称为物质的第四状态，占宇宙中所有物质的99%以上，具有重要的实用价值，因为它们是优秀的电导体。等离子体发动机已经被世界各地的航天机构开发出来，最近被用来为选定的航天器提供动力。在核聚变反应堆中使用等离子体作为一种清洁能源也在探索之中。太阳风、地球电离层、银河系星云和彗星尾巴等自然现象中产生的等离子体也是值得注意的例子。充分了解太阳风的动力学具有实际意义，因为它决定了空间天气的强度，而空间天气往往是造成地球轨道卫星代价高昂的损害的原因。等离子体的运动可以用一个偏微分方程组来模拟，这个项目的目标之一是证明这些方程具有实际的解，确定它们的定性行为，计算它们对模型参数(如质量、电荷和温度)的敏感性，并通过计算对它们进行近似，以精确地预测未来的行为。该项目提供了研究生研究培训机会。等离子体是一种完全电离的气体，其中的电磁力往往强大到足以支配碰撞效应。用Vlasov-Maxwell方程描述高温、低密度无碰撞等离子体的运动，这是一个非线性的双曲型偏微分方程组。在这种情况下，忽略碰撞，而驱动麦克斯韦系统的电荷和电流密度以自洽的方式从系统中离子分布的速度平均值确定，这满足Vlasov方程。这个项目解决的一个主要问题是，在无碰撞的等离子体中是否存在冲击，也就是说，随着时间的推移，是否可以从平滑的初始数据发展出奇点。在某些情况下，例如在低维相对论公式中，已知存在光滑的整体解。其他问题涉及粒子位置和动量、电荷密度和电流密度、电磁场和系统内粒子分布函数的大时间限制行为。更具体地说，该项目确定方程中的色散效应是否导致这些量随着时间的推移而衰减，或者是否存在足够的相互作用来维持它们的强度，即使在时间渐近的限制下。最后，使用全局灵敏度度量、相应的色散关系和细胞内粒子模拟计算了场和密度相对于模型输入参数的灵敏度。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

项目成果

Asymptotic growth and decay of two-dimensional symmetric plasmas

二维对称等离子体的渐近生长和衰变

• DOI: 10.3934/krm.2023015
• 发表时间: 2023
• 期刊: Kinetic and Related Models
• 影响因子: 1
• 作者: Ben-Artzi, Jonathan;Morisse, Baptiste;Pankavich, Stephen
• 通讯作者: Pankavich, Stephen

A toy model for the relativistic Vlasov-Maxwell system

相对论性 Vlasov-Maxwell 系统的玩具模型

• DOI: 10.3934/krm.2021053
• 发表时间: 2022
• 期刊: Kinetic and Related Models
• 影响因子: 1
• 作者: Ben-Artzi, Jonathan;Pankavich, Stephen;Zhang, Junyong
• 通讯作者: Zhang, Junyong

Asymptotic Dynamics of Dispersive, Collisionless Plasmas

• DOI: 10.1007/s00220-022-04317-w
• 发表时间: 2021-06
• 期刊: Communications in Mathematical Physics
• 影响因子: 2.4
• 作者: S. Pankavich

Parallelized domain decomposition for multi-dimensional Lagrangian random walk mass-transfer particle tracking schemes

多维拉格朗日随机游走传质粒子跟踪方案的并行域分解

• DOI: 10.5194/gmd-16-833-2023
• 发表时间: 2023
• 期刊: Geoscientific Model Development
• 影响因子: 5.1
• 作者: Schauer, Lucas;Schmidt, Michael J.;Engdahl, Nicholas B.;Pankavich, Stephen D.;Benson, David A.;Bolster, Diogo
• 通讯作者: Bolster, Diogo

Exact Large Time Behavior of Spherically Symmetric Plasmas

• DOI: 10.1137/20m1352508
• 发表时间: 2020-06
• 期刊: SIAM J. Math. Anal.
• 作者: S. Pankavich