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Transverse mode coupling instability of a single bunch caused by oscillatingwake field is considered in the paper. The instability threshold is found atdifferent frequencies of the wake with space charge tune shift taken intoaccount. The wake phase advance in the bunch length from 0 up to $4\pi$ isinvestigated. It is shown that the space charge can push the instabilitythreshold up or down dependent on the phase advance. Transition region isinvestigated thoroughly, and simple asymptotic formulas for the threshold arerepresented.

Transverse mode coupling instability of the bunch with oscillating wake field and space charge