  Transverse instability of a bunched beam is investigated with synchrotron
oscillations, space charge, and resistive wall wakefield taken into account.
Boxcar model is used for all-round analysis, and Gaussian distribution is
invoked for details. The beam spectrum, instability growth rate and effects of
chromaticity are studied in a wide range of parameters, both with head-tail and
collective bunch interactions included. Effects of the internal bunch
oscillations on the of collective instabilities is investigated thoroughly.
Landau damping caused by the space charge tune spread is discussed, and the
instability thresholds of different modes of Gaussian bunch are estimated.
