Damping of Magnetoelastic Waves

A general method for constructing a model of the dissipative function describing the relaxation processes induced by the damping of coupled magnetoacoustic waves in magnetically ordered materials has been developed. The obtained model is based on the symmetry of the magnet and describes both exchange and relativistic interactions in the crystal. The model accounts for the contributions of both the magnetic and elastic subsystems to the dissipation, as well asthe relaxation associated with the magnetoelastic interaction. The dispersion law for coupled magnetoelastic waves is calculated in the case of a uniaxial ferromagnet of the “easy axis” type. It is shown that the contribution of the magnetoelastic interaction to dissipative processes can play a significant role in the case of magnetoacoustic resonance.

Elasticity of tangled magnetic fields

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 Alfvén 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.