This paper is devoted to the numerical symplectic approximation of the charged-particle dynamics (CPD) with a homogeneous magnetic field and its extension to a non-homogeneous magnetic field. By utilizing continuous-stage methods and exponential integrators, a general class of symplectic methods is formulated for CPD under a homogeneous magnetic field. Based on the derived symplectic conditions, two practical symplectic methods up to order four are constructed where the error estimates show that the proposed second order scheme has a uniform accuracy in the position w.r.t. the strength of the magnetic field. Moreover, the symplectic methods are extended to CPD under a non-homogeneous magnetic field and three algorithms are formulated. Rigorous error estimates are investigated for the proposed methods and one method is proved to have a uniform accuracy in the position w.r.t. the strength of the magnetic field. Numerical experiments are provided for CPD under homogeneous and non-homogeneous magnetic fields, and the numerical results support the theoretical analysis and demonstrate the remarkable numerical behavior of our methods.

本文致力于均匀磁场带电粒子动力学（CPD）的数值辛近似及其对非均匀磁场的推广。通过利用连续级方法和指数积分器，为均匀磁场下的 CPD 制定了一类通用辛方法。基于导出的辛条件，构建了两种高达四阶的实用辛方法，其中误差估计表明所提出的二阶方案在相对于磁场强度的位置方面具有统一的精度。此外，将辛方法扩展到非均匀磁场下的CPD，并制定了三种算法。对所提出的方法进行了严格的误差估计研究，并且证明一种方法在相对于磁场强度的位置方面具有一致的精度。提供了均匀和非均匀磁场下 CPD 的数值实验，数值结果支持了理论分析并证明了我们方法的显着数值行为。