Charged-particle dynamics in a strong constant magnetic field can yield a fast gyromotion with high frequency around the center. Considering the superior of exponential integrators for highly oscillatory problems and the benefit of energy preservation of numerical integrators in solving the charged-particle dynamics, this paper is devoted to developing a fourth-order energy-preserving exponential integrator for the charged-particle dynamics in a strong constant magnetic field. To this end, we first rewrite the problem in the form of a semilinear Poisson system, to which the exponential average vector field (EAVF) method can be applied with energy preservation. Then, by deriving the truncated modified differential equation of the EAVF method, we propose a fourth-order energy-preserving exponential integrator according to the modifying integrator theory. Finally, numerical results soundly support the good energy preservation and high efficiency of the proposed fourth-order integrator in solving the problem considered in this paper.

中文翻译：

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强恒磁场中带电粒子动力学的四阶能量守恒指数积分器

在强恒磁场中的带电粒子动力学可以产生围绕中心的高频快速旋转。考虑到指数积分器在解决高振荡问题上的优越性以及数值积分器在解决带电粒子动力学方面的优势，本文致力于开发一种四阶能量守恒指数积分器，用于求解带电粒子动力学。强的恒定磁场。为此，我们首先以半线性Poisson系统的形式重写问题，可以将指数平均矢量场（EAVF）方法应用于能量保存。然后，通过推导EAVF方法的截断的修正微分方程，我们提出了一种基于能量的四阶能量守恒指数积分器。修改积分理论。最后，数值结果良好地证明了拟议的四阶积分器在解决本文所考虑的问题时具有良好的节能性和高效性。