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Kelvin-Helmholtz instability in solar H-alpha surges

We study the evolutionary conditions for Kelvin-Helmholtz (KH) instability in a H-alpha solar surge observed in NOAA AR 8227 on 1998 May 30. The jet with speeds in the range of 45-50 km/s, width of 7 Mm, and electron number density of 3.83 x 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 x 10^6 K. The electron number density of surrounding magnetized plasma has a typical for the TR/lower corona region value of 2 x 10^{9} cm^{-3}. Under these conditions, the Alfven speed inside the jet is equal to 78.3 km/s. 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-Alfvenic critical flow velocities in the range of 25-50 km/s.