On the properties of low-beta magnetohydrodynamic waves in curved coronal fields

The solar corona is a complex magnetic environment where several kinds of waves can propagate. In this work, the properties of fast, Alfven, and slow magnetohydrodynamic waves in a simple curved structure are investigated. We consider the linear regime, i.e., small-amplitude waves. We study the time evolution of impulsively generated waves in a coronal arcade by solving the ideal magnetohydrodynamic equations. We use a numerical code specially designed to solve these equations in the low-beta regime. The results of the simulations are compared with the eigenmodes of the arcade model. Fast modes propagate nearly isotropically through the whole arcade and are reflected at the photosphere, where line-tying conditions are imposed. On the other hand, Alfven and slow perturbations are very anisotropic and propagate along the magnetic field lines. Because of the different physical properties in different field lines, there is a continuous spectrum of Alfven and slow modes. Curvature can have a significant effect on the properties of the waves. Among other effects, it considerably changes the frequency of oscillation of the slow modes and enhances the possible dissipation of the Alfven modes due to phase mixing.