Rayleigh-Taylor instability of a magnetic tangential discontinuity in the presence of flow

¹ Solar Physics and Space Plasma Research Centre (SP 2RC), University of Sheffield, Hicks Building, Hounsfield Road, Sheffield S3 7RH, UK
e-mail: m.s.ruderman@sheffield.ac.uk
² Space Research Institute (IKI) Russian Academy of Sciences, 117342 Moscow, Russia

Received: 24 February 2015
Accepted: 23 May 2015

Abstract

We studied the magnetic Rayleigh-Taylor (MRT) instability of a magnetohydrodynamic tangential discontinuity in an infinitely conducting incompressible plasma in the presence of flow. We assumed that the flow magnitude is small enough to guarantee that there is no Kelvin-Helmholtz (KH) instability. In addition, we assumed that there is the magnetic shear, that is, the magnetic field has different directions at the two side of the discontinuity. In this case, only perturbations whose wavelength is greater than the critical one are unstable. As a consequence, the perturbation growth rate is bounded, and the initial-value problem describing their evolution is well posed. We also studied the absolute and convective nature of the MRT instability using the Briggs method. We obtained the necessary and sufficient condition for a perturbation propagating in a given direction to be only convectively unstable but absolutely stable. We also obtained the condition for perturbations propagating in any direction to be only convectively unstable, but absolutely stable. The results of the general analysis were applied to the MRT instability of prominence threads and the heliopause. Similar to previous research, we assumed that the thread disappearance is related to the MRT instability and the thread lifetime is equal to the inverse instability increment. Using this assumption we estimated the angle between the magnetic field inside the thread and in the surrounding plasma and studied how this estimate depends on the magnitude of the flow inside the thread. We found that this dependence is very weak. To apply this to the heliopause stability, we carried out the local analysis and restricted it to the near flanks of the heliopause only where the plasma flow can be considered incompressible. We showed that, for values of the magnetic field magnitude observed by Voyager 1, there is no KH instability. We then studied the MRT instability that can occur when the heliosheath is accelerated in the antisolar direction due to the increase in the solar wind dynamic pressure. We showed that, for typical values of the plasma flow and magnetic field parameters, there are directions such that perturbations propagating in this directions are absolutely unstable.