[P-EM17] Space Plasma Science

[PEM17-P06] A new fourth-order leap-frog integrator for relativistic equations of motion for charged particles

*Takayuki Umeda^1,2, Eiichiro Mizoguchi¹, Riku Ozaki¹ (1.Institute for Space-Earth Environmental Research, Nagoya University, 2.Information Initiative Center, Hokkaido University)

Keywords:equation of motion, high accuracy, numerical scheme

Numerical methods for solving the relativistic motion of charged particles with a higher accurately is an issue for computational physics in various fields. The classic fourth-order Runge-Kutta method (RK4) has been used over many years for tracking charged particle motions, although RK4 does not satisfy any conservation law. However, the Boris method (Boris 1970) has been used over a half century in particle-in-cell plasma simulations because of its property of the energy conservation during the gyro motion.
Recently, a new method for solving relativistic charged particle motions has been developed, which conserves both boosted Lorentz factor and kinetic energy during the gyro motion (Umeda 2023). The new integrator has the second-order accuracy in time and is less accurate than RK4. Then, new integrator is extended to the fourth-order accuracy in time by combining RK4 (Umeda & Ozaki 2023). However, it is not easy to implement the new fourth-order integrator into PIC codes, because the new method adopted co-located time stepping for position and velocity vectors.
In the present study, a fourth-order leap-frog integrator is developed, in which staggered time stepping is adopted for position and velocity vectors. It is shown by theoretical analysis and numerical experiment that position vectors have fourth-order accuracy in time by a three-stage integrator with Umeda (2023).