Vlasov and Drift Kinetic Simulation Methods Based on the Symplectic Integrator

Abstract

Vlasov and drift kinetic simulation methods based on the symplectic integrators are benchmarked for test problems on the linear and nonlinear Landau dampings and the Kelvin‐Helmholtz (K‐H) instability. The explicit symplectic integrator for the separable Hamiltonian leads to straightforward generalization of the splitting scheme for the Vlasov‐Poisson system. The Nth‐order version improves the total energy conservation decreasing the error as ∝Δt ^N where Δt denotes the time step size. An Eulerian drift kinetic simulation scheme derived from the implicit symplectic integrator for the nonseparable Hamiltonian exactly satisfies the conservation of the energy and the enstrophy in the K‐H instability, and results in successful application to the plasma echo.

Keywords:

• Vlasov equation
• drift kinetic equation
• gyrokinetic equation
• simulation method
• symplectic integrator

Acknowledgment

This work is partially supported by grants‐in‐aid of Ministry of Education, Culture, Sports, Science and Technology (No. 12680497 and 14780387).