Explicit symplectic methods for solving charged particle trajectories

In this paper, we consider the Lorentz force system based on its Hamiltonian formulation. We decompose the Lorentz force system into four subsystems which can be solved with the help of coordinate transformations. Via the coordinate transformations, three kinds of explicit symplectic numerical methods have been established for simulating the motion of charged particles under the time-independent electromagnetic field. We generalize our methods to solve the system with time-dependent external electromagnetic fields, and also the system with a relativistic effect. In numerical experiments, the computing efficiency and accuracy over a long time for the newly derived methods are demonstrated. Also, the long-term simulation for the dynamics of runaway electrons is performed.