A family of new explicit, revertible, volume-preserving numerical schemes for the system of Lorentz force

The Lorentz system underlies the fundamental rules for the motion of charged particle in electromagnetic field, which is proved volume-preserving. In this paper, we construct a family of new revertible numerical schemes for general autonomous systems, which in particular, are explicit and volume-preserving for Lorentz systems. These new schemes can prevent the extra numerical errors caused by mismatched initial half-step values in the Boris-like algorithm. Numerical experiments demonstrate the superiorities of our second-order methods in long-term simulations and energy preservation over the Boris algorithm and a higher order Runge-Kutta method (RK3). We also apply these new methods to the guiding center system and find that they behave much better than RK3.