  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.
