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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 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 eigen-mode 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. Solar Phys 136, 295 (1991). In the limit of zero viscosity, we obtain the discrete and the continuous spectra and some unstable points.
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