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

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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.