  When a resistive feedback and single-bunch wake act together, it is known
that some head-tail modes may become unstable even without space charge. This
feedback-wake instability, FWI, modified by space charge to a certain degree,
is shown to have a special single-maximum increasing- dropping pattern with
respect to the gain. Also, at sufficiently large Coulomb and wake fields, as
well as the feedback gain, a new type of transverse mode-coupling instability
is shown to take place, 3FMCI, when head-to-tail amplified positive modes
couple and the growth rate saturates with the gain.
