1. #1 Energy matching It is observed that the orbit of an injected proton beam is horizontally displaced towards the outside of the ring, by about  x~1 mm. Assume that  C =0.001,  =40, average dispersion at BPMs D x = 1 m, dipole field 0.5 T. To center the beam, should the magnetic dipole field of the ring be increased or decreased if the observation was made (a) on the first turn, and (b) for the stored beam? How large is the field change required in the two cases? #2 Injection oscillation When a beam is injected horizontally into a storage ring, the horizontal oscillation amplitude seen to be modulated. Separating the vertical and horizontal tune decreases the modulation depth (x max 2 -x min 2 ). What is the most likely source of the modulation? If this is true, should the modulation period T decrease or increase after the tune separation? Homework for Friday June 19, 2015 #3 Phase-space correlations Consider a distribution with some y-x correlation not equal to zero. Show that removing this correlation and transforming y into y- x/  x 2 decreases the spot size 1/2. #4 Beam profile from a collimator In the LHC the beam tails and beam shape can be measured by slowly moving a collimator (as “scraper”) into the beam. Assume that the transverse beam profile is Gaussian and derive an expression describing the fraction of surviving beam as a function of beam closed orbit x 0, the scraper position x s and the horizontal beam size  x.

2. The 2nd order polynomial fit gave an effective beam size of σ ≈ 760µ m. Assuming a dispersion of 3.2 m, and an rms momentum spread of 1.15x10 -4, the expected rms beam size at the collimator F49H due to the dispersive component alone is σ ≈ 373 µ m. Subtracting this in quadrature quadrature from the fitted value of σ, the effective transverse beam size becomes σ ≈ 662 µ m. With a beta function of about 200 m, we obtain a 6σ2 normalized transverse emittance of 14 µm. Without subtracting the dispersive part, it would be 18 µm. measuring Tevatron pbar emittance by scraping CERN AB-Note-2003-007 (MD)

3. Beam tail population calculated from the BLM signals at the TCPs, during the scan on May 15th, 2012. Expected populations for two emittance values are given. measuring beam tails at the LHC It was found that on average up to 1% of the beam is found in the beam tails between 5.7 and 6.6 σreal in the ramp, with peaks up to a few per-cent. Tails are dynamically populated in the ramp, as no improvements were observed after cleaning the tails at injection. In the squeeze, up to several percent of beam is found above 5.2 σreal and lost at the TCPs due to orbit drifts. The induced loss spikes can become a concern at higher energies… S. Redaelli et al., IPAC’13 Shanghai

4. measuring beam tails at the LHC - II Comparison of the normalized integrated lost beam intensity, I tot,lost /I total, versus jaw position in units of measured beam sigma, σ meas, during slow (black) and fast (purple) vertical scrapings (left: B1, right: B2).

5. The lower and upper betatron tune sidebands. The span is 12 kHz. The difference in width and height between the sidebands comes from chromaticity. The average width yields the momentum spread. Chromaticity from difference in sideband width on Schottky pick up Tevatron, 2004 P. Lebrun, A. Jansson

6. tidal effect at LEP  C/C ~4x10 -8 associated with gravitation variation  g/g 0 ~2.5x10 -7 ; 1 mm change in circumference (C 0 =26.7 km) caused energy variation of 220 pm 1 gal = 0.01 m/s 2

8. more data on LEP tidal effects

9. LEP circumference was also correlated with the water level of Lake Geneva

10. NMR puzzle

12. cartoon explaining the TGV effect om LEP beam energy

13. Italy earthquake – effect on LHC?  Two consecutive earthquakes struck Northern Italy during fill 2646. The earthquakes with magnitude 6 caused important damage in Italy.  UTC time of the earthquakes:  20/05/201202:01:10  20/05/201202:03:20  Losses, luminosity and orbit were impacted but not noticed at the time... J. Wenninger et al.

14. Italy earthquake – LHC beam losses A series of large loss spikes occurred at 02:05 during an interval of ~2 mins Losses at TCPs in IR7 The peak losses reached ~10% of the BLM dump threshold of the TCPs Earthquakes BLM loss/threshold J. Wenninger et al.

15. Italy earthquake – LHC orbit response  The orbit turns out to be a very sensitive measurement of the Earthquakes.  There is a strong radial and a significant transverse response.  Radial activity is visible a long time after the main perturbation. Radial change Transverse change RMS drift due to temperature (BPM electronics), ground motion, BPM noise… J. Wenninger et al.

16. Costa Rica earthquake  By scanning the logging data M. Fitterer found another candidate earthquake of magnitude 7.6 that occurred in Costa Rica during fill 3032.  UTC time of the earthquake :  05/09/201214:42:10  Arrival of the first waves at CERN ~15:06 UTC. J. Wenninger et al.

17. Costa Rica earthquake - intensity and luminosity  Clear dips, but smaller than for Italy event.  The intensity loss corresponds to ~5x10 11 protons per beam (factor 10 less). J. Wenninger et al.

18. Costa Rica earthquake – orbit response 1 hour !  Earthquake visible on the ring radius for over 1 hour.  The first waves (6 km/s) seemed to affect the LHC mainly radially – but it is also weaker.  The second type of waves (4 km/s) is visible in radial and transverse.  Radial amplitude is larger than for Italy Earthquake, equivalent to strongest tides. .. J. Wenninger et al.