Speaker
Description
Numerical methods for solving the relativistic motion of charged particles with a higher accuracy is an issue for scientific computing in various fields including plasma physics. 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 the boosted Lorentz factor during the E-cross-B 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 and Ozaki 2023]. However, it is not easy to implement the new fourth-order integrator into PIC codes, because the new method with RK4 adopted co-located time stepping for position and velocity vectors, which is not compatible with the charge conservation method.
In this paper, the two new relativistic integrators are reviewed. Then, a new leap-frog integrator with fourth-order accuracy in time is developed, which adopts staggered time stepping for position and velocity vectors.
