Verification of a hybrid kinetic-gyrokinetic model using the advanced semi-Lagrange code ssV

The super simple Vlasov (ssV) code was developed to study instabilities, turbulence, and reconnection in weakly magnetized plasmas, such as the solar wind in the dissipation range and the edge of fusion plasmas. The ssV code overcomes the limitations of standard gyrokinetic theory by using a hybrid kinetic-gyrokinetic model that incorporates fully kinetic ions and gyrokinetic electrons. This hybrid kinetic-gyrokinetic model enables accurate modeling in regimes characterized by steep gradients and high-frequency dynamics. To achieve this, ssV implements a set of semi-Lagrangian numerical schemes, including Positive Flux Conservative (PFC), Flux Conservative fifth-order (FCV), FCV with Umeda limiters, and a Semi-Lagrangian Monotonicity-Preserving fifth-order scheme (SLMP5). Benchmark problems such as Landau damping, ion-acoustic waves, ion Bernstein waves, and kinetic Alfvén waves were employed to evaluate the schemes. The SLMP5 scheme consistently delivered the best overall accuracy and numerical stability performance. The code also addresses well-known electromagnetic gyrokinetic simulation issues, such as the Ampère cancellation problem, using carefully chosen velocity-space resolutions and accurate integral evaluation.