Dispersion and spatial structure of the coupled Alfvén and slow magnetosonic oscillations in the Solar corona

Abstract

ABSTRACT Numerical and analytical analysis of the magnetohydrodynamic (MHD) waves in Solar coronal arcades is performed. A semicylinder slab model of arcade is used where the field lines are represented by half-circles intersecting the photosphere, the magnetic shells are represented by nested coaxial semicylinders. The finite plasma pressure is taken into account. The ‘corrugational’ perturbations are considered, that is, the perturbations with short wavelength in the direction along the arcade. In this limit, there are two oscillation modes, the Alfvén and slow magnetosonic modes, coupled due to the field line curvature. The transverse dispersion of the modes, that is, the dependence of the radial wave vector’s component kr on the wave frequency ω, is considered. It was found that the wave is concentrated in two regions of mode’s existence, where $k_r^2\gt 0$: the Alfvén and magnetosonic transparent regions. On one side, each of them is bounded by the resonance surface, where $k_r^2 \rightarrow \infty$. On the resonance surface, the wave’s frequency is determined by the Alfvén and slow magnetosonic modes dispersion relations, respectively. On the other side, the transparent regions are bounded by cut-off frequencies where $k_{r}^2 =0$. In both transparent regions, the perturbations have both transverse electric field (characteristic for the Alfvén mode) and field aligned velocity (characteristic for the slow mode). The wave structure along the field line for several models of plasma parameters is calculated.