  Transverse mode-coupling instability (TMCI) is known to limit bunch
intensity. Since space charge (SC) changes the spectra of the collective modes,
it affects the TMCI threshold as well. In agreement with results of M.
Blaskiewicz and V. Balbekov, we found that, when the wake is negative or it
essentially negative, the instability threshold increases as fast as the space
charge tune shift when the latter is large enough. In contrast, for oscillating
wakes, when the oscillations are sufficiently pronounced, the threshold
dependence on SC is non-monotonic; at sufficiently high SC tune shift the
threshold goes inversely proportional to that.
