Magnetohydrodynamic waves and their stability status in solar spicules

Zhelyazkov, I.

doi:10.1051/0004-6361/201117780

Cited by 24 publications

(24 citation statements)

References 33 publications

(42 reference statements)

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“…To evaluate the effect of the adopted magnetic field twist, ε, on the kink-speed wave dispersion curves and chiefly on the value of the critical Alfvén-Mach number that determines that flow speed that ensures the onset of an instability of the Kelvin-Helmholtz type, we compared the wave dispersion diagrams in twisted tubes with those in untwisted magnetic tubes. It is well established that in untwisted magnetic tubes the kink waves are subject to the Kelvin-Helmholtz instability when M A exceeds a certain critical value, depending upon the density contrast, η, and on the ratio of the background magnetic fields, b, in both media (see Vasheghani Farahani et al 2009;Zhelyazkov 2010Zhelyazkov , 2012a. For an isolated magnetic tube, b = 0, and, hence, the threshold value of the Alfvén-Mach number depends only on the density contrast, η.…”

Section: Resultsmentioning

confidence: 99%

Kelvin-Helmholtz instability of kink waves in photospheric twisted flux tubes

Zhelyazkov

Zaqarashvili

2012

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Aims. We investigate conditions under which kink magnetohydrodynamic waves propagating along photospheric uniformly twisted flux tubes with axial mass flows become unstable as a consequence of the Kelvin-Helmholtz instability. Methods. We employed the dispersion relations of kink waves derived from the linearised magnetohydrodynamic equations. We assumed real wave numbers and complex angular wave frequencies, namely complex wave phase velocities. The dispersion relations were solved numerically at fixed input parameters and several mass flow velocities. Results. We show that the stability of the waves depends upon four parameters, the density contrast between the flux tube and its environment, the ratio of the background magnetic fields in the two media, the twist of the magnetic field lines inside the tube, and the value of the Alfvén-Mach number (the ratio of the jet velocity to Alfvén speed inside the flux tube). We assume that the azimuthal component of the magnetic field in the tube is proportional to the distance from the tube axis and that the tube is only weakly twisted (i.e., the ratio of the azimuthal and axial components of the magnetic field is low). At certain densities and magnetic field twists, an instability of the Kelvin-Helmholtz type of kink (m = 1) mode can arise if the Alfvén-Mach number exceeds a critical value. In particular, for an isolated twisted magnetic flux tube (magnetically free environment) at a density contrast (the ratio of the mass density of the environment to that of the tube itself) equal to 2 and a magnetic field twist (defined as the ratio of azimuthal magnetic field component at the inner surface of the tube to the background magnetic field strength) equal to 0.4, the threshold Alfvén-Mach number has a magnitude of 1.250075, which means that for an Alfvén speed inside the tube of 10 km s −1 the jet velocity should be higher than 12.5 km s −1 to ensure the onset of the Kelvin-Helmholtz instability of the kink (m = 1) mode. Speeds of that order can be detected in photospheric tubes. Conclusions. The observed mass flows may trigger the Kelvin-Helmholtz instability of the kink (m = 1) mode in weakly twisted photospheric magnetic flux tubes at critical Alfvén-Mach numbers lower that those in untwisted tubes if the magnetic field twist lies in the range 0.36−0.4 and the flow speed exceeds a critical value. A weak external magnetic field (with a ratio to the magnetic field inside the tube in the range 0.1−0.5) slightly increases that critical value.

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Section: Resultsmentioning

confidence: 99%

Kelvin-Helmholtz instability of kink waves in photospheric twisted flux tubes

Zhelyazkov

Zaqarashvili

2012

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“…We start with the simplest magnetic fields configuration pictured by the left column in Figure 4. Dispersion relation of normal MHD modes propagating in a flowing compressible jet surrounded by a static compressible plasma reads (Terra-Homem et al, 2003;Nakariakov, 2007;Zhelyazkov, 2012)…”

Section: Dispersion Relation In Untwisted Moving Flux Tubementioning

confidence: 99%

Solar jet on 2014 April 16 modeled by Kelvin–Helmholtz instability

et al. 2018

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We study here the arising of Kelvin-Helmholtz Instability (KHI) in one fast jet of 2014 April 16 observed by the Atmospheric Imaging Assembly (AIA) on board Solar Dynamics Observatory (SDO) in different UV and EUV wavelengths. The evolution of jet indicates the blob like structure at its boundary which could be the observational evidence of the KHI. We model the jet as a moving cylindrical magnetic flux tube of radius a embedded in a magnetic field B i and surrounded by rest magnetized plasma with magnetic field B e . We explore the propagation of the kink MHD mode along the jet that can become unstable against the KHI if its speed exceeds a critical value.Concerning magnetic fields topology we consider three different configurations, notably of (i) spatially homogeneous magnetic fields (untwisted magnetic flux tube), (ii) internal (label 'i') twisted magnetic field and external homogeneous one (label 'e') (single-twisted flux tube), and (iii) both internal and external twisted magnetic fields (double-twisted magnetic flux tube). Plasma densities in the two media ρ i and ρ e are assumed to be homogeneous. The density contrast is defined in two ways: first as ρ e /ρ i and second as ρ e /(ρ i + ρ e ). Computations show that the KHI can occur at accessible flow velocities in all the cases of untwisted and single-twisted flux tubes. It turns out, however, that in the case of a double-twisted flux tube the KHI can merge at an accessible jet speed only when the density contrast is calculated from the ratio ρ e /(ρ i + ρ e ).Evaluated KHI developing times and kink mode wave phase velocities at wavelength of 4 Mm lie in the ranges of 1-6.2 min and 202-271 km s −1 , respectively-all being reasonable for the modeled jet.

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“…Our frame of reference is attached to the TR/coronal plasma that implies that v 0 is the relative jet velocity with respect to its environment. We must mention that because the density contrast, η, is relatively high, in such a case, like in spicules, the occurrence of a KH instability, for instance of kink (m = 1) waves, becomes possible at generally high Alfvén Mach numbers (the Alfvén Mach number is defined as the ratio of jet velocity to Alfvén speed inside the jet, M A = v 0 /v Ai ) and correspondingly at high critical flow velocities being far beyond the speeds accessible for surges/spicules in the solar atmosphere (Zhelyazkov, 2012;Zhelyazkov and Zaqarashvili, 2012). This circumstance implies that the only possible way for emerging a KH instability in surges is the excitation of higher MHD harmonics that can become unstable at sub-Alfvénic flow velocities in twisted tubes (Zaqarashvili et al, 2010).…”

Section: Surge Models Basic Parameters and Governing Equationsmentioning

confidence: 99%

Kelvin–Helmholtz instability in solar cool surges

Zhelyazkov

Zaqarashvili

Chandra

et al. 2015

Advances in Space Research

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We study the evolutionary conditions for Kelvin-Helmholtz (KH) instability in a Hα solar surge observed in NOAA AR 8227 on 1998 May 30. The jet with speeds in the range of 45-50 km s −1 , width of 7 Mm, and electron number density of 3.83 × 10 10 cm −3 is assumed to be confined in a twisted magnetic flux tube embedded in a magnetic field of 7 G. The temperature of the plasma flow is of the order of 10 5 K while that of its environment is taken to be 2 × 10 6 K. The electron number density of surrounding magnetized plasma has a typical for the TR/lower corona region value of 2 × 10 9 cm −3 . Under these conditions, the Alfvén speed inside the jet is equal to 78.3 km s −1 . We model the surge as a moving magnetic flux tube for two magnetic field configurations: (i) a twisted tube surrounded by plasma with homogeneous background magnetic field, and (ii) a twisted tube which environment is plasma with also twisted magnetic field. The magnetic field twist in given region is characterized by the ratio of azimuthal to the axial magnetic field components evaluated at the flux tube radius. The numerical studies of appropriate dispersion relations of MHD modes supported by the plasma flow in both magnetic field configurations show that unstable against Kelvin-Helmholtz instability can only be the MHD waves with high negative mode numbers and the instability occurs at sub-Alfvénic critical flow velocities in the range of 25-50 km s −1 .

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Magnetohydrodynamic waves and their stability status in solar spicules

Cited by 24 publications

References 33 publications

Kelvin-Helmholtz instability of kink waves in photospheric twisted flux tubes

Kelvin-Helmholtz instability of kink waves in photospheric twisted flux tubes

Solar jet on 2014 April 16 modeled by Kelvin–Helmholtz instability

Kelvin–Helmholtz instability in solar cool surges

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