The effect of density stratification on the resonant absorption of MHD waves in coronal loops

TL;DR

This paper investigates how density stratification affects the resonant absorption and damping of MHD waves in coronal loops, providing numerical solutions for wave frequencies and damping rates in structured magnetic flux tubes.

Contribution

It derives and solves the dispersion relation for MHD waves in density-stratified coronal loops, incorporating radial density structuring and longitudinal stratification, which was not comprehensively addressed before.

Findings

Density stratification influences wave frequencies and damping rates.

Numerical solutions for fundamental and overtone modes are provided.

Resonant absorption characteristics depend on density structuring.

Abstract

The standing quasi-modes of the ideal MHD in a zero-$\beta$ cylindrical magnetic flux tube that undergoes a longitudinal density stratification and radial density structuring is considered. The radial structuring is assumed to be a linearly varying density profile. Using the relevant connection formulae of the resonant absorption, the dispersion relation for the fast MHD body waves is derived and solved numerically to obtain both the frequencies and damping rates of the fundamental and first-overtone, $k=1,2$ modes of both the kink ($m=1$), and fluting ($m=2$) waves. Where $k$ and $m$ are the longitudinal and azimuthal mode numbers, respectively.