Propagating kink waves in thin twisted magnetic tubes with continuous equilibrium magnetic field

Ruderman, M. S.

doi:10.1051/0004-6361/201424611

Cited by 37 publications

(19 citation statements)

References 41 publications

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“…Many theoretical works have also been done on the effect of twisted magnetic fields on the MHD waves in coronal loops (see e.g. Bennett et al 1999;Erdélyi & Carter 2006;Erdélyi & Fedun 2006, 2007Carter & Erdélyi 2007Ruderman 2007Ruderman , 2015; Karami & Barin 2009;Karami & Bahari 2010Terradas & Goossens 2012). Ruderman (2007) considered a straight flux tube in the zero-beta approximation with a magnetic twist inside the loop proportional to the distance from the tube axis.…”

Section: Introductionmentioning

confidence: 99%

Resonant absorption of kink magnetohydrodynamic waves by a magnetic twist in coronal loops

Ebrahimi

Karami

2016

Mon. Not. R. Astron. Soc.

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There is ample evidence of twisted magnetic structures in the solar corona. This motivates us to consider the magnetic twist as the cause of Alfvén frequency continuum in the coronal loops, which can support the resonant absorption as a rapid damping mechanism for the observed coronal kink magnetohydrodynamic (MHD) oscillations. We model a coronal loop with a straight cylindrical magnetic flux tube which has constant but different densities in the interior and exterior regions. The magnetic field is assumed to be constant and aligned with the cylinder axis everywhere except a thin layer near the boundary of the flux tube which has an additional small magnetic field twist. Then, we investigate a number of possible instabilities that may arise in our model. In the thin tube thin boundary approximation, we derive the dispersion relation and solve it analytically to obtain the frequencies and damping rates of the fundamental (l = 1) and first/second overtone (l = 2, 3) kink (m = 1) MHD modes. We conclude that the resonant absorption by the magnetic twist can justify the rapid damping of kink MHD waves observed in coronal loops. Furthermore, the magnetic twist in the inhomogeneous layer can cause deviations from P 1 /P 2 = 2 and P 1 /P 3 = 3 which are comparable with the observations.

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Section: Introductionmentioning

confidence: 99%

Resonant absorption of kink magnetohydrodynamic waves by a magnetic twist in coronal loops

Ebrahimi

Karami

2016

Mon. Not. R. Astron. Soc.

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“…In the case of propagating waves the Alfvén frequency for a given axial wave number is constant inside the tube, but it depends on the radial variable outside the tube. As a result, there is an Alfvén continuum and some of propagating wave modes are subject to resonant damping (Ruderman 2015). However, in the case of standing waves the situation is completely different.…”

Section: It Follows From Eqs (54) and (56) That Both H(s) + H(−s) Anmentioning

confidence: 99%

“…We only consider standing waves. Propagating kink waves in the same magnetic plasma configuration have been studied by Ruderman (2015).…”

Section: Introductionmentioning

confidence: 99%

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

Terradas

2015

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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.

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“…As a result, in the presence of magnetic twist, the standing MHD kink oscillation with line-tying boundary conditions at the footpoints of the loop cannot be Fourier-analyzed in azimuthal and longitudinal directions. 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.…”

Section: Introductionmentioning

confidence: 99%

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

Ebrahimi

Karami

Soler

2017

ApJ

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There are observational evidences for the existence of twisted magnetic field in the solar corona. This inspires us to investigate the effect of a twisted magnetic field on the evolution of magnetohydrodynamic (MHD) kink waves in coronal loops. To this aim, we solve the incompressible linearized MHD equations in a magnetically twisted nonuniform coronal flux tube in the limit of long wavelengths. Our results show that a twisted magnetic field can enhance or diminish the rate of phase-mixing of the Alfvén continuum modes and the decay rate of the global kink oscillation depending on the twist model and the sign of the longitudinal (k z ) and azimuthal (m) wavenumbers. Also our results confirm that in the presence of a twisted magnetic field, when the sign of one of the two wavenumbers m and k z is changed, the symmetry with respect to the propagation direction is broken. Even a small amount of twist can have an important impact on the process of energy cascade to small scales.

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Propagating kink waves in thin twisted magnetic tubes with continuous equilibrium magnetic field

Cited by 37 publications

References 41 publications

Resonant absorption of kink magnetohydrodynamic waves by a magnetic twist in coronal loops

Resonant absorption of kink magnetohydrodynamic waves by a magnetic twist in coronal loops

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

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

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