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.
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