Ground motion induced beam movements at the CNGS target

1. Ground motion induced beam movements at the CNGS target J. Wenninger AB-OP-SPS Estimates for beam movements @ CNGS target based on LEP orbit drift data. CNGS Comm. Comm. / J. Wenninger

2. Ground motion • The effect of ground motion on the beam is in principle easy to evaluate … provide you know how ground and girders (!) move. • Both amplitude and correlations of the ground movement over the ring/line are important. • For rings resonances may occur when ground motion wavelengths become comparable to or smaller than betatron wavelengths. At the LHC amplification factors ~ 10-100 are possible at higher frequencies ( 5-10 Hz). Amplification = orbit amplitude/GM amplitude. • For slow movements (time  10-60 seconds) a conservative estimate can be obtained assuming that the movement of the quadrupoles are un-correlated. CNGS Comm. Comm. / J. Wenninger

3. Ground motion effects • Assumption : • The ground movement is characterized by an r.m.s. motion sG. • Every quadrupole is subject to the same motion. • Quadrupole movements are NOT correlated. • It is possible to estimate analytically the resulting orbit r.m.s. for a ring and the resulting r.m.s. beam movement at a ‘target’ location in a line CNGS Comm. Comm. / J. Wenninger

4. LEP orbits A large data sample of LEP orbits from 1997 to 2000 is available to estimate long(er) term ground motion effects (time  30 seconds). The LEP orbit data sample was analyzed in the following way : • For every fill the first orbit with stable colliding beams is taken as reference. • The r.m.s. drift (normalized by b) with respect to the reference is reconstructed for each fill. Orbit corrections are unfolded. • For the vertical plane, anomalous drifts from the low-beta quadrupoles are removed. • The data of all fills of a given run is averaged in time bins (from start of fill time):  typical sample size ~ 30’000 orbits. • The ground motion rms sG is obtained from the drifts by correcting for kR. Data from different years is very consistent. CNGS Comm. Comm. / J. Wenninger

5. LEP Data / 1 H plane : sG versus time from start of fill rms spread The LEP data is ~ consisted with : mean C  50-60 nm/s½ V plane : sG versus time from start of fill sG2 versus time

6. LEP Data / 2 • The time dependence of the LEP orbit data is consistent with a random walk (Brownian motion) of the quadrupoles. • It is also consistent with the ‘T’ (but not necessarily the ‘L’) of the ATL law that postulates that the relative movement D between 2 points depends on time T, on the distance between the points L and on a constant A A depends on the ground structure. • Strictly speaking the LEP data is only valid over ~ 10-12 hours, but it is likely that it can be extended to longer time periods. • Extrapolated to 1 year : sG ~ 0.3 mm • Observed (~ 1 year) : sG ~ 0.1 mm • SPS estimates (<< statistics) yield C values that are ~ factor 3-4 smaller. CNGS Comm. Comm. / J. Wenninger The r.m.s. drift (normalized by b) with respect to the start of the fill was reconstructed for each LEP fill. Orbit corrections were unfolded. For the vertical plane, anomalous drifts from the low-beta quadrupoles were removed. The data of all fills of a given run were averaged in time bins (from start of fill time):  typical sample size ~ 30’000 orbits. The ground motion rms sG is obtained from the drifts

7. CNGS Target • At the CNGS target, the effect of the TT40 & TT41 transfer lines is kL = 5-6 for H & V plane • The estimated beam position drift due to the TL (using LEP numbers) :  takes ~ 30 days to reach 0.5 mm. • The effect of the ground motion on the SPS orbit and the resulting ‘imported’ drift on the target is ~ factor 2 larger. But the position interlock in the SPS will trigger first (± 0.5 mm @ b = 100 m). • It should be noted that the fluctuations around the average drift are very large (> 30%)  the time span gives ~ order of magnitude ! CNGS Comm. Comm. / J. Wenninger

8. Summary • An estimate of the beam movement at the CNGS target due to ground motion based on LEP data implies that the interlock limit of ~ 0.5 mm is reached on the time scale of ~ week ! • This estimate does not include ground settlement after civil engineering work. • The short time beam movements (cycle to cycle) will probably be dominated by PC ripple (dominated by extraction septum, see TI8). • Additional ‘warm/cold’ effects (after access, MD…) must be evaluated experimentally. • For the commissioning I propose to perform stability runs of  1 shift with low or moderate intensity (criterion is good BPM data quality) to obtain more information on ripple(s) and ground motion  see TI8 stability analysis based on MIA techniques (Model Independent Analysis). CNGS Comm. Comm. / J. Wenninger