On the construction of general large-amplitude spherically polarised Alfv\'en waves

TL;DR

This paper introduces a computational method to construct large-amplitude, multi-dimensional spherically polarised Alfvén waves in magnetized plasma, explaining sharp magnetic discontinuities observed in the solar wind.

Contribution

It presents a novel approach to generate arbitrary amplitude solutions of spherically polarised Alfvén waves, addressing the challenge of maintaining a constant-magnitude magnetic field in multiple dimensions.

Findings

Solutions tend to form sharp gradients or discontinuities in higher dimensions.

Method successfully models large-amplitude waves starting from low-amplitude fluctuations.

Results explain the sharp magnetic-field switchbacks observed in the solar wind.

Abstract

In a magnetised plasma on scales well above ion kinetic scales, any constant-magnitude magnetic field, accompanied by parallel Alfv\'enic flows, forms a nonlinear solution in an isobaric, constant-density background. These structures, which are also known as spherically polarised Alfv\'en waves, are observed ubiquitously in the solar wind, presumably created by the growth of small-amplitude fluctuations as they propagate outwards in the corona. Here, we present a computational method to construct such solutions of arbitrary amplitude with general multi-dimensional structure, and explore some of their properties. The difficulty lies in computing a zero-divergence, constant-magnitude magnetic field, which leaves a single, quasi-free function to define the solution, while requiring strong constraints on any individual component of the field. Motivated by the physical process of wave growth in the solar wind, our method circumvents this issue by starting from low-amplitude Alfv\'enic fluctuations dominated by a strong mean field, then "growing" magnetic perturbations into the large-amplitude regime. We present example solutions with nontrivial structure in one, two, and three dimensions, demonstrating a clear tendency to form very sharp gradients or discontinuities, unless the solution is one dimensional. As well as being useful as an input for other calculations, particularly the study of parametric decay, our results provide a natural explanation for the extremely sharp field discontinuities observed across magnetic-field switchbacks in the low solar wind.