Transverse mode-coupling instability in the presence of detuning impedance

In non-axisymmetric beam pipes, a detuning impedance is present in addition to the usual driving impedance. The impact of this additional impedance contribution on the Transverse Mode-Coupling Instability (TMCI) has been re-examined in detail, comparing four different approaches: the two-particle model solved analytically; the circulant-matrix formalism with two (or many) azimuthal modes but only one radial mode solved semi-analytically; the circulant-matrix formalism with many azimuthal and radial modes solved numerically and HEADTAIL macroparticle tracking simulations. The results of the several benchmarks performed are discussed and the possible next steps are outlined.