Fast-slow mode coupling instability for coasting beams in the presence of detuning impedance

A destabilizing effect of the detuning impedance has been recently observed in simulations of the CERN Proton Synchrotron (PS) at the injection energy: while without the detuning impedance the instability is faster in the vertical plane as expected (due to the elliptical shape of the vacuum chamber), with detuning impedance the instability appears to be faster in the horizontal plane. In order to understand the detuning impedance destabilizing effect, we study the collective behavior for the simpler case of a coasting beam with PS-like parameters and a simplified impedance model. The analysis, carried out from both numerical and theoretical points of view, highlights a new destabilizing mechanism related to the coupling of slow and fast waves.