In this paper, we apply the coordinate increment discrete gradient (CIDG) method to solve the Lorentz force system which can be written as a non-canonical Hamiltonian system. Then we can obtain a new energy-preserving CIDG-I method for the system. The CIDG-I method can combine with its adjoint method CIDG-II which is also a energy-preserving method to form a new method, namely CIDG-C method. The CIDG-C method is symmetrical and can conserve the Hamiltonian energy directly and exactly. With comparison to the well-used Boris method, numerical experiments indicate that the CIDG-C method holds advantage over the Boris method in terms of energy-conserving.

中文翻译：

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一种新颖的带电粒子动力学直接守能方法

在本文中，我们应用坐标增量离散梯度（CIDG）方法来求解洛伦兹力系统，该系统可以写成非规范哈密顿系统。从而得到系统的一种新的节能CIDG-I方法。 CIDG-I方法可以与其伴随方法CIDG-II（也是一种能量守恒方法）结合形成一种新方法，即CIDG-C方法。 CIDG-C方法是对称的，可以直接、准确地守恒哈密顿能量。与常用的Boris方法相比，数值实验表明CIDG-C方法在节能方面优于Boris方法。