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Transverse mode coupling instability of bunched beam is investigated in thepaper at different form of the bunches with space charge included. Equation oftransverse motion of the bunch in parabolic potential well of synchrotronoscillations is derived and analysed. The bunch of constant density (flatbunch) is examined in detail to make comparison with the square well model. Itis shown that both models result in very close instability thresholds of theflat bunch. Then different form bunches are investigated in the parabolicpotential well. It is shown that decrease of the bunch r.m.s length leads tothe growth of its threshold, that is the flat bunch model gives only a minimalestimation of the threshold. The results are treated in terms of Landau dampingdue to spread of the space charge tune shift.

Effect of bunch shape on its TMCI spectrum and threshold with high space charge