Viscous-Resistive MHD Waves in I-Dimensional Magnetic Flux Tubes

This paper generalizes the analysis of Goossens. Ruderman and Hollweg [I] on resonant Alfven waves in non-uniform I-dimensional magnetic flux tubes. The resonances that appear in the linear compressible MHD formulation of waves are studied for equilibrium states with dissipative terms viscosity and resistivity. The authors have considered a thin non-uniform layer to obtain the analytic results. Analytic dissipative MHD solutions are obtained for the Lagrangian displacement and the Eulerian perturbation of the total pressure. These analytic solutions are valid in the dissipative layer and in the two overlap regions to the left and the right of the dissipative layer. The conservation laws and the jump conditions across the resonance point are determined in the non-uniform cylindrical magnetic flux tubes. The jump conditions and the conservation law make it possible to determine the absorption of Alfven waves without having to solve the full set of dissipative MHD waves.