Outflow Boundary Conditions for the Fourier Transformed Two-Dimensional Vlasov Equation

In order to facilitate numerical simulations of plasma phenomena where kinetic processes are important, we have studied the technique of Fourier transforming the Vlasov equation analytically in velocity space, and solving the resulting equation numerically. Particular attention has been paid to the boundary conditions of the Fourier transformed system. By using outgoing wave boundary conditions in the Fourier transformed space, small-scale information in velocity space is carried outside the computational domain and is removed, representing a dissipative loss mechanism. Thereby the so-called recurrence phenomenon is reduced. In the present article, a previously developed method in one spatial and one velocity dimension plus time is generalised to two spatial and two velocity dimensions plus time. Different high-order methods are used for computing derivatives as well as for the time stepping.