Theory and calculations of synchrotron instabilities and feedback-mechanism

The properties of the phenomenon synchrotron radiation are given with general theory on the basic processes and betatron and synchrotron oscillations. A more extended theoretical view at transverse instabilities and the influence of a damping feedback system are discussed. The longitudinal case is covered. For the calculations on the longitudinal case with M equally spaced pointbunches, with N electrons each, in the storage ring, the parasitic modes of the radio-frequency cavity were measured. A description of this is given. The values of damping rates of the longitudinal feedback system found, are as expected, but too low to damp the longitudinal instabilities calculated. This might be caused by the input data. The calculated growth rates are very sensitive to changes in frequency and width of the parasitic modes, which were measured under conditions differing slightly from the operating conditions