K. Tangtartharakul, G. Chen, and A. Arefiev, "Particle integrator for particle-in-cell simulations of ultra-high intensity laser-plasma interactions", Journal of Computational Physics 434, 110233 (2021).
Particle-in-cell codes are the most widely used simulation tools for kinetic studies of ultra-intense laser-plasma interactions. Using the motion of a single electron in a plane electromagnetic wave as a benchmark problem, we show surprising deterioration of the numerical accuracy of the PIC algorithm with increasing normalized wave amplitude for typical time-step and grid sizes. Two significant sources of errors are identified: strong acceleration near stopping points and the temporal field interpolation. We propose adaptive electron sub-cycling coupled with a third order temporal interpolation of the magnetic field and electric field as an efficient remedy that dramatically improves the accuracy of the particle integrator.