Standing kink oscillations of thin twisted magnetic tubes with continuous equilibrium magnetic field

Abstract

In this article we study standing kink waves in twisted magnetic tubes. We use the cold plasma and thin tube approximation. We assume that the plasma density is constant inside and outside the tube. We also assume that the magnetic twist is weak and take the ratio of the azimuthal and axial component of the magnetic field to be of the order of ratio of the tube radius and tube length. The azimuthal component of the magnetic field is proportional to the distance from the tube axis inside the tube, and inversely proportional to this distance outside the tube. Using the method of asymptotic expansions we derived the governing integral equation that determines the eigenfrequencies and eigenmodes of the tube kink oscillations. In the approximation of a very weak twist, we calculated analytically the corrections to the frequencies of the fundamental mode and first overtone of a straight magnetic tube related to the presence of twist. The analytical results are compared with the numerical results obtained using the full set of linear ideal magnetohydrodynamic equations. We also calculated the ratio of frequencies of the fist overtone and fundamental mode. We found that the magnetic twist enhances this ratio for moderate values of the density ratio, and reduces this ratio for large values of the density ratio. In general, the deviation of the frequency ratio from 2 caused by the magnetic twist is comparable to that found in simultaneous observations of the fundamental mode and first overtone of the coronal loop kink oscillations. Finally, we studied the eigenmode polarization. We found that, in a particular case of linear polarization, the polarization direction rotates along the tube.

Kink Oscillations of Coronal Loops

“…However, under the presence of twist the situation is more complicated since the modes with wave numbers k z and −k z have different frequencies. To solve properly this problem we have to combine more than one wave to satisfy the boundary conditions at footpoints, as it was shown in detail by Ruderman and Terradas (2015) (see also references therein) for a particular choice of the dependence of the azimuthal component of the field on the transverse coordinate (see also .…”

“…Therefore the cylinder oscillates transversally at the characteristic kink frequency, ω k . Second order modifications to this frequency have been calculated analytically in Ruderman and Terradas (2015). Nevertheless, the most important effect of magnetic twist on transverse oscillations is related to the polarisation of the movements.…”

Transverse waves in coronal flux tubes with thick boundaries: The effect of longitudinal flows

“…Besides the effect of flows, there are still various physical ingredients that could be incorporated to the semi-analytic Frobenius-based method. For instance, two additional improvements of the method would be to consider longitudinal stratification (e.g., Andries et al 2005;Arregui et al 2005) and magnetic twist (e.g., Terradas & Goossens 2012;Ruderman & Terradas 2015). These extensions could be tackled in forthcoming works.…”

The Effect of a Twisted Magnetic Field on the Phase Mixing of the Kink Magnetohydrodynamic Waves in Coronal Loops

“…Ruderman (2015) called the modes corresponding with m = +1, −1 in a twisted flux tube, accelerated and decelerated kink wave, respectively. Ruderman & Terradas (2015) investigated the standing MHD kink oscillations of thin twisted magnetic tubes. They found that depending on the value of the plasma density ratio of the interior and exterior of the loop, the period ratio of the first overtone to the fundamental kink mode can be increased or decreased by increasing the magnetic twist in the loop.…”