We propose a dynamical low-rank algorithm for a gyrokinetic model that is used to describe strongly magnetized plasmas. The low-rank approximation is based on a decomposition into variables parallel and perpendicular to the magnetic field, as suggested by the physics of the underlying problem. We show that the resulting scheme exactly recovers the dispersion relation even with rank 1. We then perform a simulation of kinetic shear Alfv\'en waves and show that using the proposed dynamical low-rank algorithm a drastic reduction (multiple orders of magnitude) in both computational time and memory consumption can be achieved. We also compare the performance of robust first and second-order projector splitting, BUG (also called unconventional), and augmented BUG integrators as well as a FFT-based spectral and Lax--Wendroff discretization.

翻译：本文提出一种适用于强磁化等离子体回旋动理学模型的动态低秩算法。该低秩近似基于问题物理特性所建议的平行与垂直磁场的变量分解。我们证明即使秩为1，该方案也能精确恢复色散关系。随后对动力学剪切阿尔芬波进行模拟，结果表明采用所提出的动态低秩算法可在计算时间和内存消耗上实现数量级（多个量级）的显著降低。我们还比较了稳健的一阶与二阶投影分裂法、BUG（亦称非常规）积分器、增强型BUG积分器以及基于FFT的谱方法与Lax-Wendroff离散格式的性能。