The viscous MHD spectra-application to coronal loop heating

We have derived the viscous MHD equilibrium and perturbed equations for a current carrying cylindrical plasma in a previous paper. We have considered compressible plasmas and, the viscosity is introduced in the equation of motion leading to a linearized third order perturbed equation for the fluid displacement. Including the flowing equilibrium and viscosity, we have shown the appearance of non Hermitian operators. The Lagrangian representation is used to investigate the stability. We solve the eigenmode equation, which is non linear in the eigenvalue, for the problem of coronal loop heating, using a numerical code based on the software 'Mathematica', with appropriate boundary conditions. We have shown 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. In the limit of zero viscosity, we obtain the discrete and continuous spectra ans some unstable points. (author)