LHC Closed Orbit For Beam 2 J. Wenninger December 2008

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 : -0.094% = -9.4 units.

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

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

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

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-2005-087 An estimate for the rms alignment error is therefore given by rms orbit/30 = 0.36 (V) to 0.4 (H) mm

‘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. kick @ 7 TeV is ~ 80 mrad.

‘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. kick @ 7 TeV is ~ 80 mrad.

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 !