Elasticity of tangled magnetic fields

TL;DR

This paper investigates the elastic-like behavior of tangled magnetic fields, introducing a mean-field formalism to describe magnetoelastic waves and their damping, supported by numerical simulations of force-free magnetic equilibria.

Contribution

It develops a mean-field approach to magnetoelasticity, explicitly accounts for intermittency effects, and demonstrates anomalous viscous damping of large-scale waves in tangled magnetic fields.

Findings

Intermittency decreases magnetoelastic wave frequency.

Small-scale motions cause anomalous viscous damping.

Numerical simulations confirm analytic predictions.

Abstract

The fundamental difference between incompressible ideal magnetohydrodynamics and the dynamics of a non-conducting fluid is that magnetic fields exert a tension force that opposes their bending; magnetic fields behave like elastic strings threading the fluid. It is natural, therefore, to expect that a magnetic field tangled at small length scales should resist a large-scale shear in an elastic way, much as a ball of tangled elastic strings responds elastically to an impulse. Furthermore, a tangled field should support the propagation of `magnetoelastic waves', the isotropic analogue of Alfv\'en waves on a straight magnetic field. Here, we study magnetoelasticity in the idealised context of an equilibrium tangled field configuration. In contrast to previous treatments, we explicitly account for intermittency of the Maxwell stress, and show that this intermittency necessarily decreases the frequency of magnetoelastic waves in a stable field configuration. We develop a mean-field formalism to describe magnetoelastic behaviour, retaining leading-order corrections due to the coupling of large- and small-scale motions, and solve the initial-value problem for viscous fluids subjected to a large-scale shear, showing that the development of small-scale motions results in anomalous viscous damping of large-scale waves. Finally, we test these analytic predictions using numerical simulations of standing waves on tangled, linear force-free magnetic-field equilibria.