Twisted Magnetic Fields in Conducting Fluids

Dungey, J. N.; Loughhead, R. E.

doi:10.1071/ph540005

Cited by 79 publications

(68 citation statements)

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“…The normal mode analysis of twisted magnetic tubes without flow has been performed in early works (Dungey & Loughhead 1954;Roberts 1956;Bennett et al 1999;Carter & Erdélyi 2008), and they show a threshold of the kink instability similar to what is obtained by an energy consideration method (Lundquist 1951). However, a flow along the twisted magnetic tube may decrease the threshold for the kink instability, as recently supposed and tested experimentally (Furno et al 2007).…”

Section: Introductionmentioning

confidence: 62%

Instability of twisted magnetic tubes with axial mass flows

Zaqarashvili

Díaz

Oliver

et al. 2010

A&A

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Context. Recent observations of various kinds of jets in the solar atmosphere motivate studying the influence of mass flow on the stability of solar magnetic structures. Aims. We study the influence of axial mass flows on the stability of twisted magnetic flux tubes. Methods. We use the incompressible magnetohydrodynamic equations to get the dispersion relation governing the behaviour of normal modes in uniformly twisted magnetic tubes with sub-Alfvénic flows. The dispersion relation is then solved analytically and numerically to find stability criteria for twisted tubes with flow. Results. Two main important results are found. First, the axial mass flow reduces the threshold of kink instability in twisted magnetic tubes. Second, the twist of magnetic tubes leads to the Kelvin-Helmholtz instability of sub-Alfvénic flows for the harmonics with a large enough azimuthal wave number −m. Conclusions. The observed mass flow may trigger the kink instability in magnetic configurations that are near their stability threshold, leading to solar flares and coronal mass ejections. The effect is more significant for photospheric magnetic tubes than for coronal ones. Sub-Alfvénic flows undergo the Kelvin-Helmholtz instability in slightly twisted magnetic tubes if the azimuthal wavenumber is big enough.

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Section: Introductionmentioning

confidence: 62%

Instability of twisted magnetic tubes with axial mass flows

Zaqarashvili

Díaz

Oliver

et al. 2010

A&A

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“…Twisted magnetic tubes have been studied for many years in the context of the tube stability (e.g. Dungey & Loughead 1954;Roberts 1956;Shafranov 1957;Kruskal & Tuck 1958;Parker 1974;Browning & Priest 1983). They have also been studied in relation to the magnetohydrodynamic (MHD) wave resonant absorption (e.g.…”

Section: Introductionmentioning

confidence: 99%

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

Ruderman

2015

A&A

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In this paper, we study kink waves in twisted magnetic tubes. In the equilibrium state there is the electrical current with constant density inside the tube directed along the tube axis. This current creates the azimuthal magnetic field with the magnitude proportional to the distance from the tube axis inside the tube and inversely proportional to this distance outside the tube. We derive the dispersion equations for propagating waves and for unstable perturbations in the long wavelength approximation. We show that there are no solutions to the dispersion equation determining the frequencies of unstable perturbations, which implies that there are no unstable long kink modes. We study the dispersion equation for propagating waves both in the case when the plasma density is larger than that in the surrounding plasma as well as when it is smaller. In the first case we obtain that, depending on the wave number, the dispersion equation for propagating waves has either no solutions, or one solution, or two solutions. In the case when there is one solution, in the approximation of very weak twist, the wave mode propagates with the phase speed slightly larger than the kink speed. This wave mode is called the accelerated kink wave. In the case when there are two solutions to the dispersion equation, one of the two solutions gives the frequency of a quasi-mode that is subjected to the Alfvén resonance outside the tube. The other solution gives the frequency of a true eigenmode of linear ideal MHD. In the approximation of very weak twist its phase speed is smaller than the kink speed. This mode is called the decelerated kink wave. In the case of rarefied tube, depending on the wave number, the dispersion equation has either one or three solutions. When there is only one solution, the mode frequency is very close to the Alfvén frequency far from the tube, so the wave mode practically coincides with the Alfvén wave. When there are three solutions, the largest frequency practically coincides with the Alfvén frequency far from the tube. Two other solutions almost coincide. In all cases the wave modes existing in the case of rarefied tube are quasi-modes that are subjected to the Alfvén resonance. A possible application of the obtained results to the solar atmospheric seismology is discussed.

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“…A normal mode analysis (Dungey & Loughhead 1954) and an energy consideration method (calculating the change in magnetic energy per unit length of the cylinder-see Lundquist 1951) yield similar thresholds of the kink instability in twisted magnetic flux tubes in the form B iφ (a) > 2B iz , or in our notation, as ε > 2. In the following, we will consider only weakly twisted tubes, ε 1, and, therefore, only the KH instability may occur in the exploring jet configuration.…”

Section: Now Looking Atmentioning

confidence: 79%

Kelvin–Helmholtz instability in an active region jet observed with Hinode

Zhelyazkov

Chandra

Srivastava

2016

Astrophys Space Sci

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Over past ten years a variety of jet-like phenomena were detected in the solar atmosphere, including plasma ejections over a range of coronal temperatures being observed as extreme ultraviolet (EUV) and X-ray jets. We study the possibility for the development of Kelvin-Helmholtz (KH) instability of transverse magnetohydrodynamic (MHD) waves traveling along an EUV jet situated on the west side of NOAA AR 10938 and observed by three instruments on board Hinode on 2007 January 15/16 (Chifor et al., Astron. Astrophys. 481, L57 (2008)). The jet was observed around Log T e = 6.2 with up-flow velocities exceeded 150 km s −1 . Using Fe XII λ186 and λ195 line ratios, the measured densities were found to be above Log N e = 11. We have modeled that EUV jet as a vertically moving magnetic flux tube (untwisted and weakly twisted) and have studied the propagation characteristics of the kink (m = 1) mode and the higher m modes with azimuthal mode numbers m = 2, 3, 4. It turns out that all these MHD waves can become unstable at flow velocities in the range of 112-114.8 km s −1 . The lowest critical jet velocity of 112 km s −1 is obtained when modeling the jet as compressible plasma contained in an untwisted magnetic flux tube. When the jet and its environments are treated as incompressible media, the critical jet velocity becomes higher, namely 114.8 km s −1 . A weak twist of the equilibrium magnetic field in the same approximation of incompressible plasmas slightly decreases the threshold Alfvén Mach number, M cr A , and consequently the corresponding critical velocities, notably to 114.4 km s −1 for the kink mode and to 112.4 km s −1 for the higher m modes. We have also compared two analytically found criteria for predicting the threshold Alfvén Mach number for the onset of KH instability and have concluded that one of them yields reliable values for M cr A . Our study of the nature of stable and unstable MHD modes propagating on the jet shows that in a stable regime all the modes are pure surface waves, while the unstable kink (m = 1) mode in untwisted compressible plasma flux tube becomes a leaky wave. In the limit of incompressible media (for the jet and its environment) all unstable modes are non-leaky surface waves.

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Twisted Magnetic Fields in Conducting Fluids

Cited by 79 publications

References 1 publication

Instability of twisted magnetic tubes with axial mass flows

Instability of twisted magnetic tubes with axial mass flows

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

Kelvin–Helmholtz instability in an active region jet observed with Hinode

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