Speaker
Description
Particle-in-cell (PIC) simulations are important research tools in theoretical plasma physics. Inside the PIC code, the particle integrator is extensively used to solve the Newton-Lorentz equation to advance charged particles. The Boris method (Boris 1970; also known as the Buneman-Boris method) has been the de facto standard particle integrator for more than a half century. It has second-order accuracy in time --- the numerical error is proportional to the square of the timestep, ~ (dt)^2.
In this presentation, we propose three extensions to the nonrelativistic Boris solver. First, we introduce n-times subcycling: we repeat the numerical procedure n-times, with an n-times smaller timestep of dt/n. This allows us to solve the equation with better second-order accuracy, ~ (dt/n)^2. Second, we extend the second-order Boris method to higher order. In addition to the well-known "gyrophase correction" to the magnetic field, we use an anisotropic correction to the electric field, to achieve fully higher-order accuracy, ~ (dt)^N [N = 2, 4, 6...]. Third, we combine these two methods to amplify their benefits. We call the hybrid method the hyper Boris solvers, because it has two hyperparameters of the subcycling number n and the order of accuracy, N. The accuracy of the n-cycle Nth-order solver is remarkably high, ~ (dt/n)^N, even though its computational cost is affordable.
For further details, see S. Zenitani & T. N. Kato, Comput. Phys. Commun. 2025, doi:10.1016/j.cpc.2025.109695.