The Viscous MHD Spectra – Application to Coronal Loop Heating and Stability

Abstract

We have derived the viscous MHD equilibrium and perturbed equations for current carrying cylindrical plasmas. We have considered compressible plasmas and, when the viscosity is introduced in the equation of motion it leads to a linearized vector second order perturbed equation for the fluid displacement, showing the appearance of non Hermitian operators. The Lagrangian representation is used to investigate the stability and we used the normal mode analysis to study the linearized equation. We applied our model for the problem of the coronal loop heating and solved the eigenmode equation, which is nonlinear in the eigenvalue, using a numerical code based on the software “Mathematica”, with appropriate boundary conditions. We have confirmed that viscosity is relevant as the dominant mechanism for the coronal loop heating in our self-consistent calculation as indicated by previous non self-consistent work of De Azevedo et al (1991 Solar Phys. 136 295). In the limit of zero viscosity, we obtain the discrete and the continuous spectra and some unstable points.

Viscous damping of Alfvén surface waves at a magnetic interface

“…However, it is suggested that viscosity plays a crucial role in the damping of waves over the other existing mechanisms such as phase mixing, ohmic heating, resonance absorption…etc [13]. The viscous MHD spectra for cylindrical plasma has been analysed by Santiago et al [14] and confirmed the viscosity as the dominant mechanism for coronal loop heating. In this work, we study the viscous damping of ASW at a single magnetic interface separating two incompressible viscous plasma media and estimate the damping length in the solar atmosphere.…”