This work deals with the numerical approximation of plasmas which are confined by the effect of a fast oscillating magnetic field (see \cite{Bostan2012}) in the Vlasov model. The presence of this magnetic field induces oscillations (in time) to the solution of the characteristic equations. Due to its multiscale character, a standard time discretization would lead to an inefficient solver. In this work, time integrators are derived and analyzed for a class of highly oscillatory differential systems. We prove the uniform accuracy property of these time integrators, meaning that the accuracy does not depend on the small parameter $\varepsilon$. Moreover, we construct an extension of the scheme which degenerates towards an energy preserving numerical scheme for the averaged model, when $\varepsilon\to 0$. Several numerical results illustrate the capabilities of the method.

翻译：本研究针对Vlasov模型中受快速振荡磁场约束的等离子体（参见\cite{Bostan2012}）进行数值近似。该磁场的存在导致特征方程的解产生（时间上的）振荡。由于其多尺度特性，标准时间离散化将导致求解器效率低下。本文针对一类高频振荡微分系统推导并分析了时间积分器。我们证明了这些时间积分器具有一致精度特性，即其精度不依赖于小参数$\varepsilon$。此外，我们构建了该格式的扩展形式，当$\varepsilon\to 0$时，该扩展格式会退化为平均模型的能量守恒数值格式。若干数值算例验证了该方法的性能。