Structure-Preserving Algorithm and Its Error Estimate for the Relativistic Charged-Particle Dynamics Under the Strong Magnetic Field

Abstract

This paper investigates the numerical algorithm and its error estimates for the dynamics of relativistic charged particles under a strong maximal ordering scaling magnetic field. To maintain the fundamental principles of relativistic dynamics, including energy conservation, volume preservation, and the Lorentz invariant property, we construct a structure-preserving algorithm using the splitting scheme. This algorithm ensures the preservation of volume, energy, and the Lorentz invariant property (VELPA) exactly. Specifically, we establish an uniform and optimal error bound in both 4-position and 4-velocity for VELPA. Numerical experiments are also presented to demonstrate the advantages of VELPA in both uniform error estimate and conservation of energy, compared to the implicit Euler method and traditional energy-preserving AVF method.