Propagation of Surface Magnetohydrodynamic Waves in Asymmetric Multilayered Plasma

Daria Shukhobodskaia,Róbert Erdélyi

doi:10.3847/1538-4357/aae83c

Daria Shukhobodskaia, Róbert Erdélyi

Open Access

https://doi.org/10.3847/1538-4357/aae83c

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Abstract

Abstract Investigation of magnetohydrodynamic wave propagation in different equilibrium configurations is important for the development of solar magnetoseismology. In the present work, a magnetized plasma slab sandwiched between an arbitrary number of nonmagnetic layers is considered and an analytical approach is used for the derivation of its dispersion relation. This work is a natural generalization of the symmetric slab model studied by Roberts and the asymmetric magnetic slab model, considered by Allcock & Erdélyi. Similar to the dispersion relation for an asymmetric slab, and unlike a symmetric slab, the dispersion relation for an asymmetric multilayered plasma cannot be decoupled into sausage and kink eigenmodes. The waves that permitted us to propagate in multilayered slabs have mixed characters; therefore, the notion of quasi-sausage and quasi-kink waves is more appropriate. Here, we focus on how a multilayered structuring affects the eigenmodes. The amplitudes of the eigenmodes depend on the equilibrium structuring and the model parameters; this motivates an application as a solar magnetoseismology tool. Finally, specific cases of two- and three-layered slabs are studied in detail and their potential applicability to magnetic bright points is discussed.

Highlights

The solar atmosphere, from the photosphere to the corona, is dominated by a complex and dynamic magnetic field that makes the plasma highly structured
It was shown by Roberts (1981b) that the dispersion relation governing wave propagation in the case of a single symmetric slab consists of two decoupled equations, describing sausage and kink MHD waves
A mathematical model of a magnetized plasma slab sandwiched between an arbitrary number of plasma interfaces is considered, generalizing MHD wave studies in a plasma slab embedded in an asymmetric environment studied by Allcock & Erdélyi (2017, 2018)

Summary

Introduction

The solar atmosphere, from the photosphere to the corona, is dominated by a complex and dynamic magnetic field that makes the plasma highly structured. Multiwavelength observations from high-resolution satellites and ground-based telescopes enable the detection of periodic motions in different magnetic structures in the solar atmosphere, such as in coronal loops (Thompson et al 1998; Wang 2004; Aschwanden 2005; Banerjee et al 2007; De Moortel 2009), plumes (Ofman et al 1997; DeForest & Gurman 1998; Nakariakov 2006), prominences (Arregui et al 2012), solar wind (Belcher 1971; Abbo et al 2016), and spicules (Zaqarashvili & Erdélyi 2009; Tsiropoula et al 2012) These observed periodic perturbations may be described in terms of magnetohydrodynamic (MHD) waves. The general dispersion relation is derived and is solved analytically for the cases of two (i.e. one magnetic and one nonmagnetic) or three (i.e., a magnetic slab sandwiched between two asymmetric) slabs in the cases of an incompressible fluid and under the thin-slab approximation

Derivation of General Dispersion Relation

Two-slab Case

Three-slab Case

Analytical Solutions

Incompressible Approximation

Conclusions