Kelvin–Helmholtz instability of magnetohydrodynamic waves propagating on solar surges

In the present paper, we study the evolutionary conditions for Kelvin–Helmholtz (KH) instability in a high-temperature solar surge observed in NOAA AR 11271 using the Solar Dynamics Observatory data on 2011 August 25. The jet with speed of ≈100 km s−1, width of 7 Mm, and electron number density of 4.17×109 cm−3 is assumed to be confined in an untwisted/twisted magnetic flux tube with magnetic field of 10 G. The temperature of the plasma flow is 2×106 K while that of its environment, according to the observational data, is of the order of 106 K. The electron number density of surrounding magnetized plasma is evaluated to be equal to 1.15×109 cm−3. Under these conditions, the Alfvén speed inside the flux tube is 337.6 km s−1, the sound speed is around 166 km s−1, while these characteristic speeds of the environment are ≅719 km s−1 and ≅117 km s−1, respectively. We study the propagation of normal MHD modes in the flux tube considering the two cases, notably of untwisted magnetic flux tube and the twisted one. The numerical solution to the dispersion relation shows that the kink (m=1) wave traveling in an untwisted flux tube becomes unstable if the jet speed exceeds 1060 km s−1—a speed which is inaccessible for solar surges. A weak twist (the ratio of azimuthal to longitudinal magnetic field component) of the internal magnetic field in the range of 0.025–0.2 does not change substantially the critical flow velocity. Thus, one implies that, in general, the kink mode is stable against the KH instability. It turns out, however, that the m=−2 and m=−3 MHD modes can become unstable when the twist parameter has values between 0.2 and 0.4. Therefore, the corresponding critical jet speed for instability onset lies in the range of 93.5–99.3 km s−1. The instability wave growth rate, depending on the value of the wavelength, is of the order of several dozen inverse milliseconds. It remains to be seen whether these predictions will be observationally validated in future in the coronal jet-like structures in abundant measure.