Resonant damping and instability of propagating kink waves in flowing and twisted magnetic flux tubes
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ABSTRACT We study the propagation and stability of kink waves in a twisted magnetic tube with the flow. The flow velocity is assumed to be parallel to the magnetic field, and the magnetic field lines are straight outside the tube. The density is constant inside and outside of the tube, and it monotonically decreases from its value inside the tube to that outside in the transitional or boundary layer. The flow speed and magnetic twist monotonically decrease in the transitional layer from their values inside the tube to zero outside. Using the thin tube and thin boundary layer (TTTB) approximation, we derived the dispersion equation determining the dependence of the wave frequency and decrement/increment on the wavenumber. When the kink wave frequency coincides with the local Alfvén frequency at a resonant surface inside the transitional layer, the kink wave is subjected to either resonant damping or resonant instability. We study the properties of kink waves in a particular unperturbed state where there is no flow and magnetic twist in the transitional layer. It is shown that in a tube with flow, the kink waves can propagate without damping for particular values of the flow speed. Kink waves propagating in the flow direction either damp or propagate without damping. Waves propagating in the opposite direction can either propagate without damping, or damp, or become unstable. The theoretical results are applied to the problem of excitation of kink waves in spicules and filaments in the solar atmosphere.Keywords:
Flux tube
Magnetic damping
Dispersion relation
Wavenumber
Kink instability
Kink instability
Coronal loop
Solar flare
Flux tube
Photosphere
Solar prominence
Nanoflares
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Kink instability
Flux tube
Solar prominence
Ribbon
Flare
Solar flare
Coronal loop
Field line
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The development of kink instability in a flux tube is investigated numerically, by solving the resistive MHD equations in three dimensions for a setup where a flux tube is stressed by rotating both ends in opposite directions. Two cases are investigated: one where the tube is initially isolated and in pressure equilibrium with surrounding plasma (external kink) and another with an initially uniform magnetic field, where only a smaller part of the boundaries are used to twist the field (internal kink). The twist angle at the onset of the kink instability depends on several parameters, such as rotation velocity, tube diameter, field strength, and magnetic resistivity, but is generally in the range 4π–8π. Both sets of experiments are followed beyond the point where they become kink unstable into the regime of nonlinear evolution. Of particular interest is the topological evolution. As magnetic dissipation becomes significant, the connectivity between the two boundaries changes from ordered to chaotic, and small‐scale current sheets develop. Even though the gross features of the external kink appear to saturate, the total magnetic energy continues to grow, by a steady increase of the free energy in the chaotic region that develops as a result of the kink and by a secular spreading of the magnetic field into the initially field‐free region. The internal kink is confined to the cylinder defined by the boundary driving and has only limited influence on the external magnetic field. After the kink, the twist of the magnetic field is reduced, and the internal kink settles into a quasi‐steady state where the dissipation on the average balances the Poynting flux input. The average Poynting flux is similar in the external and internal kinks, with a magnitude that corresponds to local winding numbers of the order of unity. Scaling of these results to values characteristic of the solar corona indicate that systematic rotation or shear of the endpoints could be a source of quasi‐steady heating in coronal loops.
Kink instability
Flux tube
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