A hybrid method of semi-Lagrangian and additive semi-implicit Runge–Kutta schemes for gyrokinetic Vlasov simulations Original Research Article

A hybrid method of semi-Lagrangian and additive semi-implicit Runge–Kutta schemes is developed for gyrokinetic Vlasov simulations in a flux tube geometry. The time-integration scheme is free from the Courant–Friedrichs–Lewy condition for the linear advection terms in the gyrokinetic equation. The new method is applied to simulations of the ion-temperature-gradient instability in fusion plasmas confined by helical magnetic fields, where the parallel advection term severely restricts the time step size for explicit Eulerian schemes. Linear and nonlinear results show good agreements with those obtained by using the explicit Runge–Kutta–Gill scheme, while the new method substantially reduces the computational cost.