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

Abstract

The standing quasi‐modes of the ideal magnetohydrodynamics (MHD) in a zero‐β cylindrical magnetic flux tube that undergoes a longitudinal density stratification and radial density structuring are 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.

THE EFFECT OF A TWISTED MAGNETIC FIELD ON THE PERIOD RATIOP1/P2OF NONAXISYMMETRIC MAGNETOHYDRODYNAMIC WAVES

“…Here we show that the dispersion relation (17) in the absence of internal twist, i.e. A i = 0, can be obtained from the dispersion relation, Eq.…”

“…In subsections 3.1 and 3.2, we show that the dispersion relation (17) for the cases A i = 0 and A 0 = 0, respectively, reduces to two known cases. Also in subsection 3.3, we give an analytical solution for the dispersion relation (17).…”

“…Note that Eq. (17) shows that even in the presence of annulus, the internal twist does not affect the kink (m = 1) modes. Because the internal twist, A i , only appears in Eq.…”

“…Here we try to solve the dispersion relation (17), analytically. To do this we apply the TT approximation, Eq.…”

“…( 20). This reduces the dispersion relation (17) to a second order equation in terms of ω 2 which can now be solved analytically. To write the solutions in a simple form, we define two expressions X j m and Z 0 m as follows…”