# Magnetohydrodynamic waves in braided magnetic fields

## TL;DR

This study uses MHD simulations to analyze how complex braided magnetic fields influence Alfvén wave phase mixing and energy dissipation, suggesting enhanced heating mechanisms in the solar corona due to magnetic complexity.

## Contribution

It demonstrates that magnetic field complexity significantly affects wave phase mixing, leading to increased energy dissipation over larger areas compared to classical models.

## Key findings

- Wave energy is deposited over larger cross-sections in complex fields.
- Small gradients in wave drivers can produce large gradients in plasma.
- Wave dissipation rate increases with magnetic field complexity.

## Abstract

We consider a series of MHD simulations in which a small amplitude, transverse velocity perturbation is introduced into a complex magnetic field. We analysed the deformation of the wave fronts as the perturbation propagates through the braided magnetic structures and explore the nature of Alfv\'enic wave phase mixing in this regime. Spatial gradients in the local Alfv\'en speed and variations in the length of magnetic field lines ensure that small scales form throughout the propagating wave front due to phase mixing. Additionally, the presence of complex, intricate current sheets associated with the background field locally modifies the polarisation of the wave front. The combination of these two effects enhances the rate of viscous dissipation, particularly in more complex field configurations. Unlike in classical phase mixing configurations, the greater spatial extent of Alfv\'en speed gradients ensures that wave energy is deposited over a larger cross-section of the magnetic structure. Further, the complexity of the background magnetic field ensures that small gradients in a wave driver can map to large gradients within the coronal plasma. The phase mixing of MHD waves in a complex magnetic field will progress throughout the braided volume. As a result, in a non-ideal regime wave energy will be dissipated over a greater cross-section than in classical phase mixing models. The formation rate of small spatial scales in a propagating wave front is a function of the complexity of the background magnetic field. As such, if the coronal field is sufficiently complex it remains plausible that phase mixing induced wave heating can contribute to maintaining observed temperatures. Furthermore, the weak compressibility of the transverse wave and the observed phase mixing pattern may provide seismological information about the nature of the background plasma.