  The transverse instability of a bunch in a circular accelerator is elaborated
in this paper. A new tree-modes model is proposed and developed to describe the
most unstable modes of the bunch. This simple and flexible model includes
chromaticity and space charge, and can be used with any bunch and wake forms.
The dispersion equation for the bunch eigentunes is obtained in form of a
third-order algebraic equation. The known head-tail and TMCI modes appear as
the limiting cases which are distinctly bounded at zero chromaticity only. It
is shown that the instability parameters depend only slightlyon the bunch model
but they are rather sensitive to the wake shape. In particular, space charge
effects are investigated in the paper and it is shown that their influence
depends on sign of wake field enhancing the bunch stability if the wake is
negative. The resistive wall wake is considered in detail including a
comparison of single and collective effects. A comparison of the results with
earlier publications is carried out.
