Compensation for the effect of vacuum chamber eddy current by digital signal processing for closed orbit feedback

The Advanced Photon Source (APS) will implement both global and local beam position feedback systems to stabilize the particle and X-ray beams. The relatively thick (1/2") aluminum storage ring vacuum chamber at corrector magnet locations for the local feedback systems will induce significant eddy current. This will reduce the correction bandwidth and could potentially destabilize the feedback systems. This paper describes measurement of the effect of the eddy current induced in the APS storage ring vacuum chamber by a horizontal/vertical corrector magnet and its compensation using digital signal processing at 4 kHz sampling frequency with proportional, integral, and derivative (PID) control algorithm for closed orbit feedback. A theory of digital feedback to obtain the linear system responses and the conditions for optimal control will also be presented. The magnet field in the vacuum chamber shows strong quadrupole and sextupole components varying with frequency, in addition to significant attenuation and phase shift with bandwidth (-3 dB) of 20 Hz for horizontal and 4 Hz for vertical fields relative to the magnet current. Large changes in the magnet resistance and inductance were also observed, as the result of reduced total magnetic energy and increased Ohmic heat loss