RESULTS

Up to now, the FOFB was operated only during machine development shifts. The tune BPM has been chosen for monitoring the FOFB performance since it is not part of the feedback loop and therefore allows a more objective analysis of beam oscillations. Although the observed orbit excitations vary over time, Tab. 1 gives an overview of the main beam noise sources and their typical contributions to the position RMS value at the location of the tune BPM. Note, the beta functions at this BPM amount to $\beta_x \simeq$ 11 m and $\beta_y \simeq$ 18 m while the average machine beta values are $\beta_{x/y}$ $\approx$ 10 m at the location of the BPMs. The measured power spectral densities of both planes (see Fig. 2) show snapshots of the orbit excitations at the tune BPM with and without feedback.

Figure 2: Snapshots of the horizontal and vertical power spectral densities measured with the digital BPM system at the location of the tune BPM.

The dominant noise sources in the frequency range up to 100 Hz as indicated in Tab. 1 could be suppressed from 1.7 $\mu$m to 1.4 $\mu$m horizontally and from 1.5 $\mu$m to 0.9 $\mu$m vertically. Fig. 3 shows the measured vertical closed loop transfer function for non-optimized PI start parameters.

Figure 3: Measured vertical closed loop transfer function with moderate PI parameter settings. The amplitude curve shows the maximal suppression of orbit perturbations at the locations of the BPMs.

The differential control has not been applied so far. According to the transfer function unity gain is reached at 80 Hz and moderate amplifications can be observed up to 400 Hz. The integrated RMS orbit motions were enlarged from 0.95 $\mu$m to 1.1 $\mu$m horizontally and from 0.95 $\mu$m to 1.2 $\mu$m vertically.

Two excitation of the electron beam at frequencies of 76 and 95 Hz are most likely due to numerical rounding errors in the digital receivers. This effect can be eliminated by adjusting the internal gain settings in the DBPM system. The integrated position RMS values with and without feedback are summarized in Tab. 2.

	horizontal		vertical
FOFB	off	on	off	on
0.5-100 Hz$^{*}$	1.7 $\mu$m	1.4 $\mu$m	1.5 $\mu$m	0.9 $\mu$m
100-400 Hz$^{*}$	0.95 $\mu$m	1.1 $\mu$m	0.95 $\mu$m	1.2 $\mu$m

Table 2: Integrated position RMS values at the location of the tune BPM ( $\beta _x\simeq 11$ m, $\beta _y\simeq 18$ m).
$^{*}$These figures still contain the sensor noise contribution which is not clearly quantified yet.