The paper investigates two new use cases for the Boris Spectral Deferred Corrections (Boris-SDC) time integrator for plasma simulations. First, we show that using Boris-SDC as a particle pusher in an electrostatic particle-in-cell (PIC) code can, at least in the linear regime, improve simulation accuracy compared with the standard second order Boris method. In some instances, the higher order of Boris-SDC even allows a much larger time step, leading to modest computational gains. Second, we propose a modification of Boris-SDC for the relativistic regime. Based on an implementation of Boris-SDC in the runko PIC code, we demonstrate for a relativistic Penning trap that Boris-SDC retains its high order of convergence for velocities ranging from 0.5c to >0.99c. We also show that for the force-free case where acceleration from electric and magnetic field cancel, Boris-SDC produces less numerical drift than Boris.
