The physical presence of vacuum structures can be expressed in terms of a coupling impedance experienced by the beam. The beam environment considered here consist of parasitic higher order modes of the r.f. cavities. These resonances may have high enough Q's to allow consecutive bunches to interact through mutually induced fields. The cumulative effect of such fields as the particles pass through the cavity may be to induce a coherent buildup in synchrotron motion of the bunches, i.e., a longitudinal coupled-bunch instability. The colliding mode operation of the present generation of high energy synchrotrons and the accompanying r.f. manipulations, make considerations of individual bunch area of paramount importance. Thus, a longitudinal instability in one of a chain of accelerators, while not leading to any immediate reduction in the intensity of the beam in that accelerator, may cause such a reduction of beam quality that later operations are inhibited (resulting in a degradation performance). In this paper we employ a longitudinal phase-space tracking code (ESME) as an effective tool to simulate specific coupled bunch modes arising in a circular accelerator. One of the obvious advantages of the simulation compared to existing analytic formalisms, e.g., based on the Vlasov equation, is that it allows consideration of the instability in a self-consistent manner with respect to the changing accelerating conditions. Furthermore this scheme allows to model nonlinearities of the longitudinal beam dynamics, which are usually not tractable analytically. 5 refs., 3 figs
