I. The effect of symmetric and spatially varying equilibria and flow on MHD wave modes: slab geometry

Abstract

Realistic theoretical models of magnetohydrodynamic wave propagation in the different solar magnetic configurations are required to explain observational results, allowing magnetoseismology to be conducted and provide more accurate information about local plasma properties. The numerical approach described in this paper allows a dispersion diagram to be obtained for any arbitrary symmetric magnetic slab model of solar atmospheric features. This proposed technique implements the shooting method to match necessary boundary conditions on continuity of displacement and total pressure of the waveguide. The algorithm also implements fundamental physical knowledge of the sausage and kink modes such that both can be investigated. The dispersion diagrams for a number of analytic cases that model magnetohydrodynamic waves in a magnetic slab were successfully reproduced. This work is then extended by considering density structuring modelled as a series of Gaussian profiles and a sinc(x) function. A further case study investigates properties of MHD wave modes in a coronal slab with a non-uniform background plasma flow, for which the governing equations are derived. It is found that the dispersive properties of slow body modes are more greatly altered than those of fast modes when any equilibrium inhomogeneity is increased, including background flow. The spatial structure of the eigenfunctions is also modified, introducing extra nodes and points of inflexion that may be of interest to observers.

II. The effect of axisymmetric and spatially varying equilibria and flow on MHD wave modes: cylindrical geometry

“…This study includes plasma (gas) pressure in the analysis; ho we ver, it a v oids resonantly damped modes by assuming that the wav e frequenc y is purely real. It should be noted that previous works have investigated the resonantly damped modes; ho we ver, in their analysis they assume that the plasmaβ is zero, which ultimately remo v es the slow magnetoacoustic modes from their analysis (Van Doorsselaere et al 2004 ;Soler et al 2013 ;Soler 2017Soler , 2019.…”

“…Since then, adaptations and specific case studies have been undertaken to explore the properties of MHD waves under more complicated yet realistic plasma configurations. A non-e xhaustiv e list includes inv estigating waves in non-uniform magnetic slabs (Arregui et al 2007 ;Lopin & Nagorny 2015a , b ;Li et al 2018 ;Skirvin, Fedun & Ve r t h 2021 ), curved magnetic slabs (Verwichte, Foullon & Nakariakov 2006 ), twisted magnetic cylinders (Erd élyi & Fedun 2007Terradas, Magyar & Va n Doorsselaere 2018 ), and magnetic cylinders with vortex flows (Cheremnykh et al 2017(Cheremnykh et al , 2018Tsap et al 2020 ). It is widely known that within a non-uniform plasma in ideal MHD, waves propagating at specific frequencies may resonate with the local plasma.…”

II. The effect of axisymmetric and spatially varying equilibria and flow on MHD wave modes: Cylindrical geometry

“…In this paper a previously developed numerical technique described in Skirvin et al (2021) has been employed to obtain the eigenvalues for trapped MHD waves in possible cylindrical environments representing some cases observed in the solar atmosphere. The algorithm has been tested against well known analytical results in a simple uniform cylindrical geometry and a more complex scenario that takes into account background twist of the equilibrium magnetic field.…”

“…Since then, adaptations and specific case studies have been undertaken to explore the properties of MHD waves under more complicated yet realistic plasma configurations. A non exhaustive list includes investigating waves in non-uniform magnetic slabs (Arregui et al 2007;Lopin & Nagorny 2015a,b;Li et al 2018;Skirvin et al 2021), curved magnetic slabs (Verwichte et al 2006), twisted magnetic cylinders (Erdélyi & Fedun 2007Terradas et al 2018) and magnetic cylinders with vortex flows (Cheremnykh et al 2017(Cheremnykh et al , 2018Tsap et al 2020). It is widely known that within a non-uniform plasma in ideal MHD, waves propagating at specific frequencies may resonate with the local plasma.…”

“…This nonuniformity has an important affect on the propagation and observation of MHD waves. It was shown in Skirvin et al (2021) (hereafter Paper 1) that an inhomogeneous plasma equilibrium changes the eigenvalues for trapped wave modes dependant upon the scale of the inhomogeneity. If the plasma is highly non-uniform then the permittable bands within which MHD waves can propagate become narrower, whereas the continuum regions, where physical damping processes can take place, spread a wider range of phase speeds.…”