Transverse Feedback Research Articles

The Transverse Feedback System in Desy

To overcome single bunch instabilities at high intensities, a transverse feedback in DESY was necessary. A position-monitor detecting the coherent betatron oscillations delivers a signal which is amplified, matched in phase and used to power a kicker magnet. The latter consists of a two turn air coil which - with additional capacitors - has been made resonant in the betatron frequency range. Fine tuning of the system is effected by a ferrite loaded inductance in series with the kicker coil and biased by a variable magnetic field. The frequency range can be changed by switching capacitors. Appropriate triggering of the amplifiers and phase shifters allows the use of the same system for both electrons and positrons which are accelerated in different cycles.

Operation of the PEP Transverse Beam Feedback

The PEP Storage Ring has been equipped with a wide band beam feedback system capable of damping the vertical and horizontal motion of six bunches. The oscillation detection is done at a symmetry point on the Storage Ring and feedback is applied at the same location one orbital period later. The signal is synchronously gated and the system appears as twelve independent feedback loops, operating on the two coordinates of each of the six bunches. Two beam deflection electrodes are driven each by a low-Q push-pull amplifier which is tuned at the 72nd harmonic of the revolution frequency and suppressed-carrier modulation is generated by a sequence of the detected bunch oscillations. The design parameters are reviewed as well as the salient features of the hardware, and the impact of this system on the machine operation is evaluated in the light of experimental results.

Theoretical Treatment of Transverse Feedback Systems with Memory

The differential equation of the dipole moment of coherent oscillations in the presence of a feedback system is derived. The analysis, which starts in the time domain, is extended to the frequency domain; this allows a straightforward derivation of the damping rate for both coasting and bunched beams. The damping rate is expressed in terms of the transfer function of the feedback system and in a general form which takes into account the ..beta..-function and betatron phase modulation along the beam trajectory, the effect of memory arising from the finiteness of the system bandwidth, the effect of the time delay and of the betatron phase advance between detector and kicker. Some examples of the dependence of the damping rate on the feedback parameters are given.