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

高温等离子体，如聚变装置中的等离子体和许多天体物理情况下的等离子体，其特征是极低的碰撞频率。经典的无碰撞理论处理已经产生了有趣的和根本重要的结果，例如线性状态下的朗道阻尼，以及非线性情况下一维（1D）的伯恩斯坦-格林-克鲁斯卡尔（BGK）模态。然而，一个真正的等离子体实际上有一定程度的碰撞，不管它有多弱。最近，有弱碰撞的朗道阻尼的物理图像已被证明与无碰撞的情况完全不同[Ng， Bhattacharjee和Skiff，Phys]。Rev. Lett. 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，并且当速度空间中出现急剧梯度时将变得重要。如此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。与此同时，对于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]。启。中文信息学报，95,245004 (2005)；Ng， Bhattacharjee和Skiff， Phys。等离子体学报，13(5):593 - 593（2006）。在本项目中，将通过分析以及具有Fokker-Planck型碰撞项的直接玻尔兹曼模拟，研究弱碰撞等离子体中朗道阻尼和2D/3D BGK模式的非线性动力学。这些研究将以越来越现实和复杂的水平进行：从朗道阻尼问题的一维玻尔兹曼模拟开始，然后是对称高维BGK模式的一维空间和二维速度空间模拟。研究结果将与实验室和空间观测结果进行比较。这是一个广泛关注的主题，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，如实验室实验和空间/天体物理环境，而且也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光束，星系动力学，海浪，玻色-爱因斯坦凝聚，捕获电子设备。在这个项目中开发的代码将可供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互动，例如爱荷华大学的F. Skiff教授所做的实验，以及对空间中孤立波型结构的大量观察。该项目将资助一名研究生，并部分资助一名博士后研究员，该博士后研究员还将接受指导活动。该项目的结果将发表在科学期刊上，并在网站上进行汇总。该项目还将允许支持的研究人员参与阿拉斯加费尔班克斯大学地区的教育和推广活动，例如通过地球物理研究所公共信息和教育推广办公室组织的活动，或由UAF科学教育推广网络协调的活动。

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.