  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.
