Analytic solutions for resonant Alfv�n waves in 1D magnetic flux tubes in dissipative stationary MHD

Abstract

Resonantly driven Alfven waves are studied in non-uniform stationary magnetic flux tubes. 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. From these analytic solutions we obtain the fundamental conservation law and the jump conditions for resonantly driven Alfven waves in magnetic flux tubes with an equilibriun flow. The fundamental conservation law and the jump conditions depend on the equilibrium flow in a more complicated way than just a Doppler shift. The effects of an equlibrium flow are not to be predicted easily in general terms with the exception that the polarization of the driven Alfven waves is still in the magnetic surfaces and perpendicular to the magnetic field lines as it is in a static flux tube.