Effect of Reactive Feedback on the Transverse Mode Coupling Instability Using the Few-Particles Model and Simulation

For short bunches in electron storage rings the onset of the transverse mode coupling instability usually occurs when the frequency shift of the coherent dipole mode (mode zero) equals around three quarters of the synchrotron frequency. A reactive feedback system has been proposed which maintains the coherent dipole frequency constant and may thereby delay the onset of instability. The influence of this feedback system on the threshold of instability is studied using matrix eigenvalue analysis (few particles model) and a computer simulation code. This analysis shows that for a single localised transverse impedance, the reactive feedback system increases significantly the threshold for instability, provided the betatron phase shift between the kicker and the impedance is properly chosen. Results are also shown for the more realistic case of many localised sources of transverse impedance.