Magnetohydrodynamic waves in braided magnetic fields

Abstract

Aims. We investigate the propagation of transverse magnetohydrodynamic (MHD) wave fronts through a coronal plasma containing a braided magnetic field. Methods. We performed a series of three dimensional 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 Alfvénic wave phase mixing in this regime. We considered the effects of viscous dissipation in a weakly non-ideal plasma and evaluate the effects of field complexity on wave energy dissipation. Results. Spatial gradients in the local Alfvén 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 Alfvén 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. Conclusions. The phase mixing of transverse 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 the 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.

Phase mixing and wave heating in a complex coronal plasma

“…Together, these processes generate small spatial scales in the velocity and perturbed magnetic fields which, in a non-ideal regime, enhance the rate of wave energy dissipation. These effects are discussed in detail in Howson et al (2019) in the context of a single wave pulse and in this case, they simply occur for each wave front.…”

“…As in Howson et al (2019), we utilise the volume integral of the magnitude of the vorticity, |ω| as a measure of the small scales present within the domain. An alternative metric may consider the volume integrated current density.…”

“…If this does represent the true nature of the solar magnetic field, then the observed wave modes are likely to exist as perturbations to a complex background state and, as such, it is important to understand the dynamics and energetics of waves in this context. In Howson et al (2019), we established key characteristics of the propagation of a single wave pulse through a variety of magnetic field geometries with a range of complexities. In particular, we established that phase mixing is able to generate small spatial scales throughout the cross-section of the wave packet.…”

Investigating the damping rate of phase-mixed Alfvén waves

“…For example, Browning & Priest (1984) expanded on the Kelvin-Helmholtz analysis and argue that the phase mixing of standing Alfvén waves can trigger turbulence, which can lead to a turbulent cascade and enhanced dissipation of wave energy. Similon & Sudan (1989) and Howson et al (2019) study phase mixing in a complex magnetic field. Parker (1991) investigated phase mixing in a coronal hole and argues that it is not valid to assume an ignorable coordinate, and therefore that Alfvén waves couple to other modes and are not subject to pure phase mixing.…”

Forward modelling of MHD waves in braided magnetic fields

“…Clearly, the velocity is no longer aligned with the boundary wave driver. This (partial) change to the polarisation of the wave, from v y to v x , is due to the interaction of the perturbations in B y with j z , which produces an x-component of the Lorentz force (see also Howson et al 2019b) and hence, generates velocity perturbations in the x-direction, as the waves travel along the twisted magnetic field lines.…”