Volume-preserving particle integrator based on exact flow of velocity for nonrelativistic particle-in-cell simulations

We construct a particle integrator for nonrelativistic particles by means of the splitting method based on the exact flow of the equation of motion of particles in the presence of constant electric and magnetic field. This integrator is volume-preserving similar to the standard Boris integrator and is suitable for long-term integrations in particle-in-cell simulations. Numerical tests reveal that it is significantly more accurate than previous volume-preserving integrators with second-order accuracy. For example, in the $E \times B$ drift test, this integrator is more accurate than the Boris integrator and the integrator based on the exact solution of gyro motion by three and two orders of magnitude, respectively. In addition, we derive approximate integrators that incur low computational cost and high-precision integrators displaying fourth- to tenth-order accuracy with the aid of the composition method. These integrators are also volume-preserving. It is also demonstrated that the Boris integrator is equivalent to the simplest case of the approximate integrators derived in this study.