  Transverse mode-coupling instability (TMCI) with a high-frequency resonator
wake is examined by the Nested Head-Tail Vlasov solver (NHT), where a Gaussian
bunch in a parabolic potential (GP model) is represented by concentric rings in
the longitudinal phase space. It is shown that multiple mode couplings and
decouplings make impossible an unambiguous definition of the threshold, unless
Landau damping is taken into account. To address this problem, instead of a
single instability threshold, an interval of thresholds is suggested, bounded
by the low and high intensity ones. For the broadband impedance model, the high
intensity threshold is shown to follow Zotter's scaling, but smaller by about a
factor of two. The same scaling, this time smaller than Zotter's by a factor of
four, is found for the ABS model (Air Bag Square well).
