Alfvén wave phase-mixing and damping in the ion cyclotron range of frequencies

¹ School of Mathematics and Statistics, University of St. Andrews, St. Andrews, Fife KY16 9SS, UK
e-mail: jamest@mcs.st-and.ac.uk; ineke@mcs.st-and.ac.uk
² EURATOM/CCFE Fusion Association, Culham Science Centre, Abingdon, Oxfordshire, OX14 3DB, UK
e-mail: k.g.mcclements@ccfe.ac.uk

Received: 27 July 2010
Accepted: 18 October 2010

Abstract

Aims. We determine the effect of the Hall term in the generalised Ohm’s law on the damping and phase mixing of Alfvén waves in the ion cyclotron range of frequencies in uniform and non-uniform equilibrium plasmas.

Methods. Wave damping in a uniform plasma is treated analytically, whilst a Lagrangian remap code (Lare2d) is used to study Hall effects on damping and phase mixing in the presence of an equilibrium density gradient.

Results. The magnetic energy associated with an initially Gaussian field perturbation in a uniform resistive plasma is shown to decay algebraically at a rate that is unaffected by the Hall term to leading order in ${\mathit{k}}^{\mathrm{2}}{\mathit{\delta }}_{\mathrm{i}}^{\mathrm{2}}$ where k is wavenumber and δ_i is ion skin depth. A similar algebraic decay law applies to whistler perturbations in the limit ${\mathit{k}}^{\mathrm{2}}{\mathit{\delta }}_{\mathrm{i}}^{\mathrm{2}}\mathrm{\gg }\mathrm{1}$. In a non-uniform plasma it is found that the spatially-integrated damping rate due to phase mixing is lower in Hall MHD than it is in MHD, but the reduction in the damping rate, which can be attributed to the effects of wave dispersion, tends to zero in both the weak and strong phase mixing limits.