Nonlinear Studies of a Weakly Collisional Plasma: Landau Damping and 3D BGK Modes

高温等离子体，如聚变装置和许多天体物理学情况下的高温等离子体，其特征是碰撞频率极低。经典的无碰撞理论处理产生了有趣的和根本上重要的结果，如朗道阻尼的线性制度，和Bernstein-Greene-Kruskal（BGK）模式在一维（1D）的非线性情况。然而，一个真实的等离子体实际上有一定程度的碰撞，无论它有多弱。最近的物理图片朗道阻尼弱碰撞已被证明是完全不同的碰撞情况下[Ng，Bhattacharjee和Skiff，物理。92，065002（2004）; 83，1974（1999）]。这是因为碰撞项实际上代表了无碰撞问题的奇异摄动，当速度空间中出现尖锐的梯度时，碰撞项将变得重要。这种急剧的梯度也使线性化的假设失效，因此必须包括非线性效应。同时，对解释观测结果很重要的高维效应也完全改变了BGK模式的性质[Ng和Bhattacharjee，Phys. Rev. Lett.，95，245004（2005）; Ng，Bhattacharjee和Skiff，Phys. Plasmas，13，055903（2006）]。本计画将利用解析法及直接Boltzmann模拟方法，研究弱碰撞等离子体中朗道阻尼模及二维/三维BGK模的非线性动力学。这些研究将进行越来越多的现实主义和复杂程度：从一维玻尔兹曼模拟的朗道阻尼问题，并跟进与一维空间和二维速度空间模拟的对称高维BGK模式。研究结果将与实验室和空间观测结果进行比较。这是一个广泛感兴趣的主题，因为众所周知，弗拉索夫方程/朗道阻尼/BGK模式的基础物理不仅适用于高温等离子体，如在实验室实验和空间/天体物理环境中，而且还以类似的形式存在于许多不同的物理系统中，例如，粒子加速器中的电子束、星系动力学、海浪、玻色-爱因斯坦凝聚体、被困电子设备。该项目中开发的代码将提供给科学界用于其他研究。该项目还涉及理论和实验之间的重要相互作用，如F。以及对空间中孤立波型结构的大量观测。该项目将资助一名研究生，部分资助一名博士后研究员，博士后研究员也将接受指导活动。该项目的结果将发表在科学期刊上，并在网站上进行总结。该项目还将允许支持的研究人员参加教育和宣传活动在阿拉斯加大学费尔班克斯地区，如通过地球物理研究所的公共信息和教育外展办公室组织，或那些由UAF科学教育外展网络协调。

High temperature plasmas, such as those in fusion devices and in many astrophysical cases, are characterized by extremely low collision frequencies. Classical collisionless theoretical treatments have produced interesting and fundamentally important results, such as Landau damping in the linear regime, and Bernstein-Greene-Kruskal (BGK) modes in one dimension (1D) for the nonlinear case. However, a real plasma actually has a certain level of collisions, no matter how weak it is. Recently the physical picture of Landau damping with weak collisions has been shown to be completely different from the collisionless case [Ng, Bhattacharjee and Skiff,Phys. Rev. Lett. 92, 065002 (2004); 83, 1974 (1999)]. This occurs because the collision termactually represents a singular perturbation of the collisionless problem, and will become important when sharp gradients develop in the velocity space. Such sharp gradients also invalidate assumptions of linearization so that nonlinear effects must be included. At the same time, higher dimensional effects, which are important to explain observations, also completely change the properties of BGK modes [Ng and Bhattacharjee, Phys. Rev. Lett., 95, 245004 (2005); Ng, Bhattacharjee and Skiff, Phys. Plasmas, 13, 055903 (2006)]. In this project, the nonlinear dynamics of Landau damping and 2D/3D BGK modes in a weakly collisional plasma will be studied, by means of analysis as well as direct Boltzmann simulations with a Fokker-Planck type collision term. These studies will be carried out with increasing levels of realism and sophistication: starting with 1D Boltzmann simulations for the Landau damping problem, and following up with 1D spatial and 2D velocity space simulations for the symmetric higher dimensional BGK modes. Results of the studies will be compared with laboratory and space observations. This is a subject of broad interest because, as is well known, the underlying physics of Vlasov equation/Landau damping/BGK modes not only applies in high temperature plasmas, as in laboratory experiments and space/astrophysical environments, but also exists in similar form in many different physical systems, e.g., beams in particle accelerators, galactic dynamics, ocean waves, Bose-Einstein condensates, trapped electron devices. The codes developed in this project will be available for the scientific community for other research. This project also involves significant interactions between theory and experiments, such as those performed by Prof. F. Skiff at the University of Iowa as well as numerous observations of solitary wave-type structures in space. This project will support a graduate student, and partially for a postdoctoral research fellow, who will also receive mentoring activities. Results from this project will be published in scientific journals, and summarized in a website. This project will also allow supported researchers to participate in education and outreach activities around the University of Alaska Fairbanks area, such as those organized through the Public Information and Education Outreach Office of the Geophysical Institute, or those coordinated by the UAF Science education Outreach Network.