We present a highly accurate tool for the simulation of shear Alfvén waves (SAWs) in collisionless plasma. SAW are important in space plasma environments because for small perpendicular scale lengths they can support an electric field parallel to the ambient magnetic field. Electrons can be accelerated by the parallel electric field and these waves have been implicated as the source of vibrant auroral displays. However, the parallel electric field carried by SAW is small in comparison with the perpendicular electric field of the wave, making it difficult to measure directly in the laboratory, or by satellites in the near-Earth plasma environment. In this paper, we present a simulation code that provides a means to study in detail the SAW–particle interaction in both space and laboratory plasma. Using idealized, small-amplitude propagating waves with a single perpendicular wavenumber, the simulation code accurately reproduces the damping rates and parallel electric field amplitudes predicted by linear theory for varying temperatures and perpendicular scale lengths. We present a rigorous kinetic derivation of the parallel electric field strength for small-amplitude SAW and show that commonly used inertial and kinetic approximations are valid except for where the ratio of thermal to Alfvén speed is between 0.7 and 1.0. We also present nonlinear simulations of large-amplitude waves and show that in the cases of strong damping, the damping rates and parallel electric field strength deviate from linear predictions when wave energies are greater than only a few per cent of the plasma kinetic energy, a situation which is often observed in the magnetosphere. The drift-kinetic code provides reliable, testable predictions of the parallel electric field strength which can be investigated directly in the laboratory, and will help to bridge the gap between studies of SAW in man-made and naturally occurring plasma.
Spectral characteristics of the collisional stationary Alfvén wave in the laboratory and space regimes