GROUND WAVES

The magnets of the SLS storage ring are mounted onto 48 girders with the 36 bending magnets of the 12 TBAs sitting on the ends of two adjacent girders [7]. The amplitude of stored beam orbit oscillation excited by groundwaves is calculated by convolution of the seismic spectrum on site, damping by the concrete slab of the hall, girder mechanical amplification factors, closed orbit distortion amplification factors and attenuation factors of the fast feedback system [4].

For a rough worst case estimate the following assumptions are made:

• The largest ground noise observed was recorded while a heavy truck was passing by on the nearby road. Peaks of 300 nm at 30 Hz and 30 nm at 60 Hz [8] were found. Continuos ground noise however is at least one order of magnitude lower.

• Within the worst case estimate the damping effect of the hall's 40 cm concrete slab are neglected.

• The mechanical amplification factors of the girder were measured to be $\leq 10$ on resonance horizontally and vertically over a frequency range from 0...50 Hz [9].

• Amplification factors for the closed orbit with and without girders are shown in Fig. 5. With girders one sees horizontal [vertical] amplification factors of 8 [5] at 30 Hz and 25 [5] at 60 Hz.

• The attenuation provided by the fast feedback system is about -55 dB at 30 Hz and -35 dB at 60 Hz (assuming that there is only one dominant peak) [4].

  

Figure: Amplification factors defined as ratio of closed orbit (averaged over ground wave incident angle and phase) to ground wave amplitude for single elements (dotted) and elements mounted on girders (solid). For high frequency the factors approach the values from random magnet misalignments which are for single elements, girder to girder and girder absolute alignment given by 58, 22, 6 horizontally and 25, 4, 3 vertically. An increase of the factors is observed where $\lambda$ equals the betatron wavelength, which occurs at 36 Hz for the horizontal and at 14 Hz for the vertical. Speed of sound was assumed to be 500 m/s (soft ground).

Multiplying these numbers one arrives at rms average orbit distortions of 25 [15] $\mu$m horizontally [vertically] at 30 Hz and 7.5 [1.5] $\mu$m at 60 Hz without feedback. Including the feedback the orbit distortions are well below 1 $\mu$m over the whole frequency range.

With this as the result of a worst case estimate we are looking forward to achieve a rather quiet beam at SLS.