A Numerical Method for Parallel Particle Motions in Gyrokinetic Vlasov Simulations

Abstract

A semi-Lagrangian scheme is applied for the first time to computations of charged particle motions along magnetic field lines, to numerically solve the δf gyrokinetic equations in a flux tube geometry. This new solver adopted in the gyrokinetic Vlasov simulations has an advantage over the conventional Eulerian codes in calculating the parallel dynamics, because semi-Lagrangian schemes are free of the Courant-Friedrichs-Lewy (CFL) condition that restricts the time step size. A study of the accuracy of the parallel motion simulations reveals that numerical errors mainly stem from spatial (not temporal) discretization for realistic values of the grid spacing and time step, and it demonstrates the advantage of the semi-Lagrangian scheme. This novel numerical method is successfully applied to linear gyrokinetic simulations of the ion temperature gradient instability, where time steps larger than those restricted by the CFL condition can be employed.