SHORT TERM STABILITY

Figure 2 depicts the vertical power spectral densities (PSDs) simultaneously measured on the 40 cm thick concrete slab and a girder mounted quadrupole at the SLS for the spectral range 1-55 Hz.

Figure 2: Vertical PSDs simultaneously measured on the slab and a girder mounted quadrupole at the SLS [3].

The relatively quiet noise floor on the slab with an integrated amplitude of $\approx$20 nm for frequencies $>$4 Hz gets significantly amplified ($\approx$10 times) by magnet girder resonances in the range from 15-50 Hz. On the other hand a pronounced peak at 12.4 Hz induced by a nearby helium-refrigerator is not amplified by the girder [3]. Furthermore the orbit motion is not particularly excited by planar waves at spatial frequencies $<$15 Hz. At higher frequencies horizontal (vertical) orbit response factors of 8(5) at 30 Hz and 25(5) at 60 Hz have been estimated [4] amplifying especially the girder resonances. Consequently these resonances are clearly visible in the orbit PSD measured by an rf beam position monitor (BPM) ($\beta _y$=18 m) for the spectral range 1-60 Hz as shown in Figure 3. The integrated vertical RMS motion without orbit feedback (red curve) is calculated to be $\approx$1.7 $\mu$m. The stray fields of the booster which is mounted to the inner wall of the storage ring tunnel are responsible for a weak 3 Hz component in the PSD which is otherwise dominated by the contribution of the mains at 50 Hz.

Figure 3: Vertical orbit PSD and cumulated spectrum without(red) and with(blue) orbit feedback measured by a BPM ($\beta _y$=18 m) at the SLS [5].

The situation described is typical for modern light sources. Girders are designed to allow grouping and very precise ($\approx$10-20 $\mu$m) pre-alignment of individual magnets. The overall orbit amplification is reduced since the orbit motion is most sensitive to quadrupole-to-quadrupole movement which is strongly suppressed by the rigid girder assembly. In case of SOLEIL [6] the orbit amplification factors are reduced from 30(10) to 16(3) in the horizontal (vertical) plane. Nevertheless mechanical resonances of the girder arrangement can significantly amplify ground motion which is especially dangerous at low frequencies ($<$20 Hz) where the excitation through the ground and the slab tends to be large. At the SOLEIL site a pronounced 2.5 Hz component with an amplitude of $\approx$300 nm was measured. It could be partially traced back to heavy trucks on the nearby roads featuring suspension resonance frequencies close to 2.5 Hz.

Figure 4: Example of a SOLEIL girder assembly. Quadrupoles, sextupoles and BPMs are rigidly mounted on girders. Bending magnets are bridging adjacent girders [6].

Figure 4 depicts the present SOLEIL girder assembly. Quadrupoles, sextupoles and BPMs are rigidly mounted on girders, while bending magnets are bridging adjacent girders. Careful design involving an additional central jack allowed to push the first dangerous eigenmodes of the assembly to frequencies $>$40 Hz. Remotely controlled girder movers which give the option to perform beam-based girder alignment as in the SLS case [7,8] are not foreseen. This suggests that a proper mechanical design can assure short term orbit stability on the micron or even sub-micron level. Thus the operation of the installed IDs becomes the dominant contribution to the short term noise. Since most of the disturbances are of systematic nature and therefore reproducible, feed-forward correction tables can help to minimize the perturbation. Nevertheless the remaining noise is significant and needs to be attenuated by orbit feedback systems featuring large correction bandwidths $>$100 Hz.