Transverse Oscillations Damping with Wide-Band Feedback on Spear II

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Abstract
With its high peak currents, SPEAR II is likely to show transverse coherent oscillations. A closed loop system using the beams as a signal path detects the bunches' center-of-mass motion and reacts on the beams after one machine period with a set of traveling wave electrodes. The detector senses oscillations at the betatron frequency and rejects signals due to equilibrium orbit shifts. The amplifier output is solely determined by the desired gain and the detector noise. Since, for a given machine tune, the system's phase margin can be made 90° by selecting the respective location of the pickup and feedback electrodes, stability is secured for all values of gain. However, one shows that critical damping cannot be obtained except with infinite gain, and that the system's damping rate is strictly equal to the gain per turn. Measurements of the loop gain have been carried out and agree with the observed damping. To date the system has been successful in dealing with injection oscillations and headtail instabilities.

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