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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.
Transverse beam stability is strongly affected by the beam space charge. Usually it is analyzed with the rigid-beam model. However this model is only valid when a bare (not affected by the space charge) tune spread is small compared to the space char
A brief historical review is presented of progressing understanding of transverse coherent instabilities of charged particles beams in circular machines when both Coulomb and wake fields are important. The paper relates to a talk given at ICFA Worksh
For a single hadron bunch in a circular accelerator at zero chromaticity, without multi-turn wakes and without electron clouds and other beams, only one transverse collective instability is possible, the mode-coupling instability, or TMCI. For suffic
To understand and control the dynamics in the longitudinal phase space, time-resolved measurements of different bunch parameters are required. For a reconstruction of this phase space, the detector systems have to be synchronized. This reconstruction
Coulomb fields of charged particle beams in circular machines determine, together with wake fields, modes of the collective beam oscillations, both for transverse and longitudinal degrees of freedom. Recent progress in these two areas of beam dynamics is discussed.