The Viscous MHD Spectra – Application to Coronal LoopHeating and Stability

Abstract

We have derived the viscous MHD equilibrium and perturbed equationsfor current carrying cylindrical plasmas. We have consideredcompressible plasmas and, when the viscosity is introduced in theequation of motion it leads to a linearized vector second orderperturbed equation for the fluid displacement, showing the appearanceof non Hermitian operators. The Lagrangian representation is used toinvestigate the stability and we used the normal mode analysis tostudy the linearized equation. We applied our model for the problem ofthe coronal loop heating and solved the eigenmode equation, which isnonlinear in the eigenvalue, using a numerical code based on thesoftware “Mathematica”, with appropriateboundary conditions. We have confirmed that viscosity is relevant asthe dominant mechanism for the coronal loop heating in ourself-consistent calculation as indicated by previous nonself-consistent work of De Azevedo et al (1991 Solar Phys.136 295). In the limit of zero viscosity, we obtain thediscrete and the continuous spectra and some unstablepoints.