ANALYTICAL SOLUTIONS FOR CUSP RESONANCE IN DISSIPATIVE MHD

The present paper considers resonant slow waves in 1D non-uniform magnetic flux tubes in dissipative MHD. Analytical solutions are obtained for the Lagrangian displacement and the Eulerian perturbation of the total pressure for both static and stationary equilibrium states. From these analytical solutions we obtain the fundamental conservation law and the jump conditions for resonant slow waves in dissipative MHD. The validity of the ideal conservation law and jump conditions obtained by Sakurai, Goossens, and Hollweg (1991) for static equilibria and Goossens, Hollweg, and Sakurai (1992) for stationary equilibria is justified in dissipative MHD.