Continuous magnetohydrodynamic spectra of two-dimensional coronal magnetostatic flux tubes

In this paper we derive the equations for the continuous ideal magnetohydrodynamic (MHD) spectrum of two-dimensional coronal loops, including gravity and expansion, in general curvilinear coordinates. The equations clearly show the coupling between Alfven and slow magnetosonic continuum waves when both pressure and geodesic curvature of the magnetic field lines are present. Gravity always gives rise to Alfven-slow mode coupling when the magnetic field is twisted. Numerical calculations show that the coupling of Alfven and slow magnetosonic continuum waves can be strong. especially for Alfven-like continuum waves, when the magnetic flux concentration near the bases of flux tubes is taken into account. Amplitude ratios of the parallel and perpendicular displacement components of 0.4 were obtained for concentration of the flux with a factor of 4. Gravity has less effect on the coupling of Alfven and slow magnetosonic continuum waves than the concentration of flux but it has a large influence on the low frequency slow magnetosonic-like continuum branches.