Continuum kinetic model for simulating low-collisionality regimes in plasmas

Continuum kinetic models, such as Maxwell-Boltzmann, present a viable alternative to particle-in-cell (PIC) models because they can be cast in conservation form and 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 in one spatial and one velocity dimension to address the challenges associated with solving a hyperbolic governing equation in multidimensional phase space. 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 the fine structures that develop in the distribution function as it evolves in time, while using low resolution in the tail of the distribution function. The model is tested on several plasma instability problems including: the two-stream instability and the beam-plasma instability. The model demonstrates conservation of mass in that the total integral of the distribution function is preserved, as well as the conservation of energy. Model extension into two and three spatial dimensions is discussed.