Search

We present results on the oscillatory properties (periods, damping rates, and spatial distribution of perturbations) for resonantly damped oscillations in a system of two inhomogeneous coronal slabs and compare them to the properties found in single slab loop models. A system of two identical coronal loops is modelled, in Cartesian geometry, as being composed by two density enhancements. The linear magnetohydrodynamic (MHD) wave equations for oblique propagation of waves are solved and the damping due to resonant absorption is computed. Due to the interaction between the loops, the normal modes of oscillation present in a single slab split into symmetric and antisymmetric oscillations when a system of two identical slabs is considered. The frequencies of these solutions may differ from the single slab results when the distance between the loops is of the order of a few slab widths. Oblique propagation of waves weakens this interaction, since solutions become more confined to the edges of the slabs. The damping is strong for surface-like oscillations, while sausage body-like solutions are unaffected.

We study the effects of magnetic field shear (B y ¬= 0) and longitudinal propagation of perturbations (k y ¬= 0) on the linear and adiabatic magnetohydrodynamic (MHD) normal modes of oscillation of a potential coronal arcade. In a cold plasma, the inclusion of these two effects produces the linear coupling of discrete fast modes, characterised by a discrete spectrum of frequencies and a global velocity structure, and Alfven continuum modes, characterised by a continuous spectrum of frequencies and with a velocity perturbation confined to given magnetic surfaces in such a way that modes with mixed properties arise (Arregui et al. 2004). The wave equations governing the velocity perturbations have been solved numerically and our results show that the couplings between fast and Alfven modes are governed by some parity rules for the symmetry of the eigenfunctions of fast and Alfven modes in the direction along the equilibrium magnetic field. The nature of the coupling between fast and Alfven modes can be resonant or non-resonant depending on the location of the fast mode frequency within the different Alfven continua. Also, an important result is that in this kind of configurations coupled modes could be difficult to observe since when both magnetic field shear and longitudinal propagation are present the spatial distribution of the velocity may not be confined to low heights in the solar corona.

The magnetohydrodynamic (MHD) normal modes of oscillation of sheared coronal arcades including longitudinal wave propagation are studied. Solutions have been computed to ascertain the effects of the longitudinal magnetic field component, By, and of the longitudinal wavenumber, ky, in these structures. Our results show that whenever By ≠ 0 and/or ky ≠ 0, fast modes, characterized by a global velocity structure and a discrete spectrum of frequencies, and Alfven continuum modes, characterized by a velocity perturbation confined to given magnetic surfaces, get coupled and no pure fast modes or pure Alfven modes exist, but modes with mixed properties arise. These oscillatory modes display a global spatial distribution, together with a nonsquare integrable singular behavior on certain magnetic surfaces. Moreover, this mode coupling is such that under some circumstances the Alfvenic contribution is also in the form of a smooth velocity profile covering a range of magnetic surfaces instead of a singularity on a fixed magnetic surface. The coupling between fast and Alfven modes is governed by the parity of their eigenfunctions in the direction along the equilibrium magnetic field. The parity rules determining the features of coupled modes in terms of their spatial structure, ky, and By are presented. We have found that the frequency of coupled modes is real when either By ≠ 0 or ky ≠ 0 but is complex when both By ≠ 0 and ky ≠ 0. Also, an important result is that coupled modes may not be observable since many of them leak energy away from the solar corona.

The theoretical understanding of the linear standing or propagating magnetohydrodynamic waves in a variety of solar coronal structures is far from complete since analytical solutions to the linearised MHD equations can only be found for very simple magnetic configurations. In this paper, we use a numerical code to solve the linear fast and Alfven wave equations in a very simple, bounded magnetic configuration that incorporates two features that are not usually considered in similar works, namely the longitudinal magnetic field component and wave propagation in the longitudinal direction ($k_y\neq 0$). We use a numerical code (Arregui et al. 2001) that has been modified by including a staggered mesh that allows us to properly capture the spatial behaviour of solutions to the wave equations. Coupling between fast and Alfven modes has been studied in detail and it has been found that it does not take place when the longitudinal field component is zero and the frequency of the fast mode is outside the Alfven continuum with the same spatial structure along field lines. Under these circumstances, fast modes retain their global spatial behaviour and are also characterised by $\omega^2$ varying linearly with $k_y^2$, such as in a uniform medium (although here the Alfven speed changes exponentially in the direction normal to field lines). Regarding mode coupling, its main feature is the blend of fast and Alfven solutions with close frequencies in some modes with a mixture of their properties, namely discontinuities or jumps around certain magnetic surfaces (such as in pure Alfven waves), global spatial distribution of the normal velocity component and non-zero density perturbations (such as in fast waves).

The excitation and temporal evolution of fast and Alfven magnetohydrodynamic oscillations in a two-dimensional coronal arcade are investigated. The approach is to consider an equilibrium magnetic and plasma structure and then to introduce a perturbation trying to mimic a nearby disturbance, such as a flare or filament eruption. By numerically solving the time-dependent linearized MHD wave equations, the properties of the solutions have been studied. First, the properties of uncoupled fast and Alfven waves are described. Then, longitudinal propagation of perturbations is included, and the properties of coupled waves are determined.

One of the proposed damping mechanisms of coronal transverse loop oscillations in the kink mode is resonant absorption as a result of the spatial variation of the Alfven velocity in the equilibrium configuration. Analytical expressions for the period and the damping time exist for 1‐D cylindrical equilibrium models with thin non‐uniform transitional layers. Comparison with observations indicates that the assumption of thin non‐uniform transitional layers is not a very accurate approximation of reality. This contributions starts with a short review of observations on transverse oscillations in solar coronal loops. Then it presents results on periods and damping times of resonantly damped kink mode oscillations for (i) fully non‐uniform 1‐D cylindrical equilibrium models in which the equilibrium quantities vary in the radial direction across the magnetic field from the centre of the loop up to its boundary and (ii) non‐uniform 2‐D cylindrical equilibrium models in which the equilibrium quantities vary both ...