A novel discretization method of a hybrid parallel-kinetic-perpendicular-moment model

A recent innovation in modeling collisionless, magnetized plasmas, dubbed the parallel-kinetic-perpendicular-moment, or PKPM, model employs a hybrid discretization of the Vlasov-Maxwell system of equations via a spectral expansion in only the perpendicular degrees of freedom, with perpendicular defined with respect to the local magnetic field. This approach reduces the six-dimensional Vlasov equation to a set of four-dimensional equations, with the exact number of four-dimensional equations encoding the amount of perpendicular resolution of the simulated plasma. The specific spectral expansion: Laguerre polynomials in the perpendicular velocity and Fourier harmonics in the gyrophase, is highly efficient. A number of kinetic plasma problems utilizing only a few spectral coefficients while still obtaining good agreement with fully kinetic simulations have been performed. 

In this presentation, we give an overview of how the remaining four-dimensional equations are discretized for maximum efficiency and robustness with a discontinuous Galerkin finite element method. We showcase a number of magnetized plasma problems where retaining the full local parallel velocity kinetics has manifest benefit, as fine features in phase space form in the parallel degree of freedom even as the plasma remains mostly gyrotropic.