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Zhang, Ruili; Liu, Tong; Wang, Bin; Liu, Jian; Tang, Yifa

Structure-preserving algorithm and its error estimate for the relativistic charged-particle dynamics under the strong magnetic field. (English) Zbl 07909818

J. Sci. Comput. 100, No. 3, Paper No. 70, 29 p. (2024).
Summary: 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.

MSC:

65L05 Numerical methods for initial value problems involving ordinary differential equations
78A35 Motion of charged particles

Keywords:

structure-preserving algorithm; strong magnetic field; relativistic charged-particle dynamics; splitting scheme; error estimate

Software:

GEMPIC
Cite Review PDF
Full Text: DOI

References:

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