Volume-preserving algorithm for secular relativistic dynamics of charged particles

Secular dynamics of relativistic charged particles has theoretical significance and a wide range of applications. However, conventional algorithms are not applicable to this problem due to the coherent accumulation of numerical errors. To overcome this difficulty, we develop a volume-preserving algorithm (VPA) with long-term accuracy and conservativeness via a systematic splitting method. Applied to the simulation of runaway electrons with a time-span over 10 magnitudes, the VPA generates accurate results and enables the discovery of new physics for secular runaway dynamics.