Simulation of longitudinal coupled-bunch instabilities

The purpose of this note is to document some work done as part of the effort directed at designing and simulating a bunch-by-bunch feedback system to control longitudinal coupled bunch instabilities in the B-factory. In particular, I discuss the ring model used in the simulation program developed to study this feedback system. Basically the simulation is a simple tracking program in which the rf drive voltage, the wakefields due to all the bunches, the synchrotron radiation losses, and the kicks applied to the bunches by the bunch-by-bunch feedback are all modelled as voltages applied at a single, discrete point in the ring. The computation of the bunch-by-bunch feedback voltages may of course be done by any desired algorithms. An example and discussion of the general behavior without bunch-by-bunch feedback is given at the end of this report