Single feedback systems for simultaneous damping of horizontal and longitudinal coherent oscillations

A complete analysis of the Type (x, delta) feedback system is presented using a matrix method. The analyses of other types are similar to that of Type (x, delta) and only the results are included. Some comparisons of these types of feedback schemes in terms of power consumptions and the effectiveness in damping the horizontal-betatron and synchrotron oscillations are included. Some effects of position measuring errors on the performance of the feedback systems are also discussed