TMCI, why is the horizontal plane so different from the vertical one?

Based on the recent work of R. Lindberg on transverse collective instabilities it was observed that if the ratio of quadrupolar to dipolar impedance ρ is equal to -1, there is no TMC-instability. This relationship is actually fulfilled by resistive wall (RW)-impedance on the horizontal plane in case of a flat vacuum chamber. HEADTAIL simulations were carried out to check if this observation can be con- firmed. Additionally the eect of radial modes on the TMC- instability was studied.