1. LHC Closed Orbit For Beam 2
J. Wenninger
December 2008

2. Closed Orbit RMS : 1.6 mm H, 1.3 mm V – with little effort !!!
Sector by sector dp/p offsets
RMS : 1.6 mm H, 1.3 mm V – with little effort !!!
Vertical bare orbit converged well.
Need to be careful when correcting orbits with large initial rms : convergence issues to the non-linearities
>> send in steps (~20% of full correction).
LHC fRF,cap,LHC = 400'788'963 Hz
LHC ‘Theoretical fRF,nom-LHC = 400'788‘734 Hz
Average energy offset of CO : % = -9.4 units.

3. Horizontal Orbit 12th Sept 08
Corrector RMS 10 mrad – with MICADO

4. Vertical Orbit 12th Sept 08
Corrector RMS 8.6 mrad – with MICADO

5. Bare Orbits
Bare orbits after [linear] unfolding of all corrector kicks.
Similar quality H & V : 12 mm rms H, 11 mm rms in V – peaks ~ 30 mm

6. Alignment
The bare orbit rms is related to the misalignment through an optics sensitivity factor k :
RMSorbit = k RMSalignment
R. Steinhagen, S. Redaelli, J. Wenninger, CERN-AB
An estimate for the rms alignment error is therefore given by
rms orbit/30 = (V) to 0.4 (H) mm

7. ‘Ultimate’ Correction - H
Corrected orbit with SVD 240 eigenvalues (~ limit)
H rms value dominated by dp/p offset, rms 0.52 mm without dp/p contribution.
No excessive kick (but some ‘larger’ kicks around IR6 and IR8).
Typical max. 7 TeV is ~ 80 mrad.

8. ‘Ultimate’ Correction - V
Corrected orbit with SVD 240 eigenvalues (~ limit).
V rms value down to 0.35 mm (rejecting some more or less obvious outliers).
Max offset of ‘good’ (green) BPMs is +-1 mm !
The corrector settings reflect the systematic V offsets in S23, S34 and S45.
No excessive kick (but some ‘larger’ kicks around IR2).
Typical max. 7 TeV is ~ 80 mrad.

9. Conclusions
The BPM system performance was great (at least for this stage).
Orbit corrections worked well and converged : optics ‘reasonable’.
Bare orbits indicate good alignment of ~0.35 to 0.4 mm.
We have to understand the funny vertical offsets in sectors 23, 34, and 45. Can be partly, but apparently not fully, explained by BPM offsets.
We can potentially achieve a very good orbit rms (<< 1 mm) in both planes with reasonable kick strengths : could can 1-2 sigma of aperture at 450 GeV !