The Circulant Matrix Model and the Role of Beam-beam Effects in Coherent Instabilities

The role of beam-beam interactions in coherent instabilities in high energy colliders is discussed with a particular emphasis on the circulant matrix model. This model, based on the development of a one turn matrix including all linearised coherent forces, is particularly suited for the study of the stability of complex configurations involving different forces. Thus it allows for the study of interplays, e.g. between the effect of the beam-beam interactions and the beam coupling impedance. Experimental evidences compatible with this model are reported.