Wave energy dissipation by phase mixing in magnetic coronal plasmas

Wave energy dissipation by viscous and resistive damping in magnetic coronal plasmas is examined. We begin by pointing out that since the dimensionless viscous damping coefficient. is generally much greater than the dimensionless resistivity eta, viscous dissipation can be expected to be the dominant mechanism in many coronal applications. A detailed analysis is presented for the case of perpendicular polarized shear wave disturbances which propagate in a horizontally stratified magnetic channel. We show that when the equilibrium field contains a neutral line (specifically, B = B(0)y (x) over cap) the development of small length scales by phase mixing l similar or equal to (eta + v)(1/3) leads to efficient wave energy losses: in particular, the bulk of the energy losses take place over the time interval (eta + v)(-1/3). However, the later stages of the decay depends critically on whether viscosity or resistivity provides the dominant damping mechanism. When resistivity is sufficiently small the decay rate weakens at later times due to the emergence of a self-similar mode which allows a separation of the global kinetic and magnetic energies (v >> eta). If the resistivity is large enough but still not dominant, self-similar behaviour can give way to monotonic exponential damping on the visco-resistive length scale l similar or equal to (eta v)(1/6). In either case, provided only that v > eta, energy equipartition eventually breaks down and the remnants of the initial wave energy wind up mainly in the magnetic field.