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Dynamic kink instability and transverse motions of solar spicules

Hydrodynamic jets are unstable to the kink instability (m=1 mode in cylindrical geometry) owing to the centripetal force, which increases the transverse displacement of the jet. When the jet moves along a magnetic field, then the Lorentz force tries to decrease the displacement and stabilises the instability of sub-Alfvenic flows. The threshold of the instability depends on the Alfven Mach number (the ratio of Alfven and jet speeds). We suggest that the dynamic kink instability may be of importance to explain observed transverse motions of type II spicules in the solar atmosphere. We show that the instability may start for spicules which rise up at the peripheries of vertically expanding magnetic flux tubes owing to the decrease of the Alfven speed in both, the vertical and the radial directions. Therefore, inclined spicules may be more unstable and have more higher transverse speeds. Periods and growth times of unstable modes in the conditions of type II spicules have the values of 30 s and 25-100 s, respectively, which are comparable to the life time of the structures. This may indicate to the interconnection between high speed flow and rapid disappearance of type II spicules in chromospheric spectral lines.