Energy dynamics in linear MHD with ion parallel viscosity

Abstract

Analytic results for the time dependences of the kinetic and magnetic energies of an incompressible magneto fluid threaded by a strong uniform magnetic field B₀ are obtained. The governing equations are the linearised magnetohydrodynamic (MHD) ones, but with the conventional Laplacian dissipation replaced by ion parallel viscous effects. The behaviour is shown to depend on the relative sizes of the Alfvén frequency and the viscous and resistive dissipation rates. For many cases equipartition of the kinetic and magnetic energy holds at the (Fourier) modal level. An important exception to this behaviour occurs for two-dimensional fluctuations, that is when the wavevectors are perpendicular to B₀.