Volume-preserving algorithms for charged particle dynamics

The paper reports the development of volume-preserving algorithms using the splitting technique for charged particle motion under the Lorentz force. The source-free nature of the Lorentz vector field has been investigated. Based on the volume-preserving property of the dynamics, a class of numerical methods for advancing charged particles in a general electromagnetic field has been constructed by splitting the classical evolution operator. This new class of numerical methods, which includes the Boris algorithm as a special case, conserves phase space volume, and globally bounds the numerical errors of energy, momentum, and other adiabatic invariants up to the order of the method over a very long simulation time. These algorithms can be computed explicitly, and thus are effective for the long-term simulation of the multi-scale dynamics of plasmas.