The gyro-kinetic model is an approximation of the Vlasov-Maxwell system in a strongly magnetized magnetic field. We propose a new algorithm for solving it combining the Semi-Lagrangian (SL) method and the Arakawa (AKW) scheme with a time-integrator. Both methods are successfully used in practice for different kinds of applications, in our case, we combine them by first decomposing the problem into a fast (parallel) and a slow (perpendicular) dynamical system. The SL approach and the AKW scheme will be used to solve respectively the fast and the slow subsystems. Compared to the scheme in [1], where the entire model is solved using only the SL method, our goal is to replace the method used in the slow subsystem by the AKW scheme, in order to improve the conservation of the physical constants.

翻译：回旋动理学模型是在强磁场环境下对弗拉索夫-麦克斯韦系统的一种近似。我们提出了一种结合半拉格朗日(SL)方法与阿拉卡瓦(AKW)格式及时间积分器的新型求解算法。这两种方法在不同应用场景中均已成功实践。在本研究中，我们通过将问题分解为快速（平行方向）和慢速（垂直方向）动力学系统来实现二者的结合。SL方法与AKW格式分别用于求解快速子系统与慢速子系统。相较于文献[1]中采用纯SL方法求解整个模型的方案，我们的目标是用AKW格式替代慢速子系统的求解方法，以提升物理常数的守恒性。