Review of the Magnetohydrodynamic Waves and Their Stability in Solar Spicules and X-Ray Jets

2013

A&A

Context. Tangential velocity discontinuity near the boundaries of solar wind magnetic flux tubes results in Kelvin-Helmholtz instability, which might contribute to solar wind turbulence. While the axial magnetic field stabilizes the instability, a small twist in the magnetic field may allow sub-Alfvénic motions to be unstable. Aims. We aim to study the Kelvin-Helmholtz instability of twisted magnetic flux tubes in the solar wind with different configurations of the external magnetic field. Methods. We use magnetohydrodynamic equations in cylindrical geometry and derive the dispersion equations governing the dynamics of twisted magnetic flux tubes moving along its axis in the cases of untwisted and twisted external fields. Then, we solve the dispersion equations analytically and numerically and find thresholds for Kelvin-Helmholtz instability in both cases of the external field.Results. Both analytical and numerical solutions show that the Kelvin-Helmholtz instability is suppressed in the twisted tube by the external axial magnetic field for sub-Alfvénic motions. However, even a small twist in the external magnetic field allows the Kelvin-Helmholtz instability to be developed for any sub-Alfvénic motion. The unstable harmonics correspond to vortices with high azimuthal mode numbers that are carried by the flow. Conclusions. Twisted magnetic flux tubes can be unstable to Kelvin-Helmholtz instability when they move with small speed relative to the main solar wind stream, then the Kelvin-Helmholtz vortices may significantly contribute to the solar wind turbulence.

Section: Discussionmentioning

confidence: 99%

Kelvin-Helmholtz instability of twisted magnetic flux tubes in the solar wind

Zaqarashvili

Vörös

2013

A&A

“…Vasheghani Farahani et al analyzed analytically, in the limit of thin magnetic flux tube, the dispersion relation of the kink MHD mode and have obtained that this mode is unstable against the KH instability when the critical jet velocity is equal to 4.47V A = 3576 km s −1 (V A = 800 km s −1 is the Alfvén speed inside the jet). Numerical solving of the same dispersion relation when considering the jet and its environment as cold magnetized plasmas, carried out by Zhelyazkov [76,77], yielded a little bit lower critical flow speed for the instability onset; namely, 4.31V A = 3448 km s −1 . The lowest critical jet speed of 4.025V A = 3220 km s −1 was derived by numerically solving the wave dispersion relation without any approximations, that is, treating both media as compressible plasmas.…”

Section: Introductionmentioning

confidence: 99%

Modeling Kelvin–Helmholtz Instability in Soft X-Ray Solar Jets

Chandra

Srivastava

2017

Advances in Astronomy

Self Cite

Development of Kelvin–Helmholtz (KH) instability in solar coronal jets can trigger the wave turbulence considered as one of the main mechanisms of coronal heating. In this review, we have investigated the propagation of normal MHD modes running on three X-ray jets modeling them as untwisted and slightly twisted moving cylindrical flux tubes. The basic physical parameters of the jets are temperatures in the range of 5.2–8.2 MK, particle number densities of the order of 109 cm−3, and speeds of 385, 437, and 532 km s−1, respectively. For small density contrast between the environment and a given jet, as well as at ambient coronal temperature of 2.0 MK and magnetic field around 7 G, we have obtained that the kink (m=1) mode propagating on moving untwisted flux tubes can become unstable in the first and second jets at flow speeds of ≅348 and 429 km s−1, respectively. The KH instability onset in the third jet requires a speed of ≅826 km s−1, higher than the observed one. The same mode, propagating in weakly twisted flux tubes, becomes unstable at flow speeds of ≅361 km s−1 for the first and of 443 km s−1 for the second jet. Except the kink mode, the twisted moving flux tube supports the propagation of higher (m>1) MHD modes that can become unstable at accessible jets’ speeds.

“…All these observations stimulated the modeling of KH instability in moving magnetic flux tubes. Zaqarashvili et al (2010) have studied the KH instability in twisted flux tubes moving in non-magnetic environment, Soler et al (2012) in magnetic tubes of partially ionized plasma, Zaqarashvili (2011), Zhelyazkov (2012a, and Ajabshirizadeh et al (2015) in spicules, Vasheghani Farahani et al (2009 and Zhelyazkov (2012b) in soft X-ray jets, Zhelyazkov & Zaqarashvily (2012) in photospheric tubes, Zhelyazkov et al (2015a,b) in high-temperature and cool surges, Zhelyazkov et al (2015c) in dark mottles, Möstl et al (2013) and Zhelyazkov et al (2015d) at the boundary of rising CMEs, and Zaqarashvili et al (2015) in rotating, tornado-like magnetized jets. A review on modeling the KH instability in solar atmosphere jets (primarily in the limits of homogeneous ideal plasma) the reader can see in Zhelyazkov 2015e and references therein.…”

Section: Introductionmentioning

confidence: 99%

“…We note that in the limit of incompressible plasmas (c si,e → ∞) the wave attenuation coefficients in both media become equal to the axial wavenumber k z and the wave dispersion relation (2) takes the simple form of a quadratic equation, that provides solutions for the real and imaginary part of of the wave phase velocity in closed forms (Zhelyazkov 2012b(Zhelyazkov , 2013:…”

Section: Introductionmentioning

confidence: 99%

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

Chandra

Srivastava

2016

Astrophys Space Sci

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.