# Contribution of mode coupling and phase-mixing of Alfv\'en waves to coronal heating

## TL;DR

This study uses 3D MHD simulations to evaluate the role of Alfvén wave phase-mixing in coronal heating, finding limited contribution to the overall temperature increase in the solar corona.

## Contribution

It provides a detailed simulation-based assessment of how phase-mixing of Alfvén waves affects coronal heating, highlighting its limited global impact.

## Key findings

- Phase-mixing causes temperature increases up to 10^5 K.
- Energy from phase-mixing balances radiative losses locally.
- Boundary layer structure and driver persistence influence heating efficiency.

## Abstract

Phase-mixing of Alfv\'en waves in the solar corona has been identified as one possible candidate to explain coronal heating. While this scenario is supported by observations of ubiquitous oscillations in the corona carrying sufficient wave energy and by theoretical models that have described the concentration of energy in small scale structures, it is still unclear whether this wave energy can maintain the million degree solar corona. The aim of this work is to assess how much energy can be converted by a phase-mixing process triggered by the propagation of Alfv\'enic waves in a cylindric coronal structure, such as a coronal loop, and to estimate the impact on the coronal heating. To this end, we run 3D MHD simulations of a magnetised cylinder where the Alfv\'en speed varies through a boundary shell and a footpoint driver is set to trigger kink modes which mode couple to torsional Alfv\'en modes in the boundary shell. These Alfv\'en waves are expected to phase-mix and the system allows us to study the subsequent thermal energy deposition. We run a reference simulation to explain the main process and then we vary simulation parameters. When we take into consideration high values of magnetic resistivity and strong footpoint drivers, we find i) that phase-mixing leads to a temperature increase of the order of $10^5$ K or less, depending on the structure of the boundary shell, ii) that this energy is able to balance the radiative losses only in the localised region involved in the heating, iii) and how the boundary layer and the persistence of the driver influence the thermal structure of the system. Our conclusion is that due to the extreme physical parameters we adopted and the moderate impact on the heating of the system, it is unlikely that phase-mixing can contribute on a global scale to the heating of the solar corona.