Modeling kinetic plasma instabilities using a conservative continuum model

Summary form only given. Boltzmann kinetic plasma models encapsulate a complete physical description of a plasma through a statistical representation. Continuum Boltzmann kinetic models, in particular, present a viable alternative to particle-in-cell (PIC) models because they can be cast in conservation form and they are not susceptible to noise. By treating the associated phase space distribution function as a continuous incompressible fluid occupying a volume of position-velocity space, evolution of the distribution function is determined by solving a 6-D advection equation. In cases where collision terms are negligible, the Boltzmann model is reduced to a Vlasov model. A 4th-order accurate continuum kinetic Vlasov model has been developed to address the challenges associated with solving a 6-D hyperbolic governing equation. The governing equation is cast in conservation law form and solved with a finite volume representation. Adaptive mesh refinement (AMR) is used to allow for efficient use of computational resources while maintaining desired levels of resolution. Consequently, with AMR the model is able to capture filamentation, or the fine structures that develop in the distribution function as it evolves in time. The model is tested on several plasma instability problems including: the two-stream instability, the beam-plasma instability, and the Dory-Guest-Harris instability. The model results as well as run time performance are compared with particle-in-cell simulations.