2025/05/04 by Zenitani, Seiji, Kato, Tsunehiko N.
#Computational Physics (physics.comp-ph) #FOS: Physical sciences #Plasma Physics (physics.plasm-ph) #Space Physics (physics.space-ph)
paper · doi:10.48550/arxiv.2505.02270
We propose a family of numerical solvers for the nonrelativistic Newton--Lorentz equation in kinetic plasma simulations. The new solvers extend the standard 4-step Boris procedure, which has second-order accuracy in time, in three ways. First, we repeat the 4-step procedure multiple times, using an n-times smaller timestep (Δt/n). We derive a formula for the arbitrary subcycling number n, so that we obtain the result without repeating the same calculations. Second, prior to the 4-step procedure, we apply Boris-type gyrophase corrections to the electromagnetic field. In addition to a well-known correction to the magnetic field, we correct the electric field in an anisotropic manner to achieve higher-order (N=2,4,6 …th order) accuracy. Third, combining these two methods, we propose a family of high-accuracy particle solvers, the hyper Boris solvers, which have two hyperparameters of the subcycling number n and the order of accuracy, N. The n-cycle Nth-order solver gives a numerical error of ∼ (Δt/n)N at affordable computational cost.