Hyper Boris integrators for kinetic plasma simulations and their connection to 3D rotation representations

Particle-in-cell (PIC) simulation is one of the most important research tools in theoretical plasma physics. To solve the motion of charged particles, the Boris method (a.k.a. the Boris integrator/pusher/solver) has been used for more than a half century. Although the Boris solver has good accuracy, the demand for high-accuracy numerical solvers has been increasing, and new integrators have been actively developed. In this contribution, we present novel high-accuracy particle integrators, the hyper Boris integrators, for nonrelativistic kinetic simulations. We further discuss their connection to 3D rotation representations.