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