REVIEW OF ESTIMATES OF RANDOM COMPONENTS IN THE INNER TRIPLET HI LUMI and LARP collaboration meeting CERN, 7th June 2012 REVIEW OF ESTIMATES OF RANDOM COMPONENTS IN THE INNER TRIPLET E. Todesco CERN, Geneva Switzerland Based on the Phase-I work by F. Borgnolutti, P. Fessia, on HQ estimates by X. Wang, and tracking presented by Y. Cai in LARP CM May 2012

METHODS Random movements of coil blocks due to tolerances Note: Amplitudes of the order of 0.025 to 0.1 mm - Rref=40 mm Estimate given for the Phase I [P. Fessia, et al., SLHC PR 45 (2010) IEEE Trans. Appl. Supercond. 20 (2010) 140 ] Note: Random b6 estimated with 4 times larger movements, based on experience Uncertainty=random with exception of a6 and b6 This is the best estimate we have today

METHODS Extrapolation to higher orders Scaling with Biot Savart

and HQ measurements (spread along the axis) METHODS Comaprison with HQ estimates Calculation by X. Wang on HQ cross-section, 0.025 mm standard deviation of movements Very similar results Also in this case we take 4 times larger movement for b6 Measurements are not so far from this estimate Comparison between estimates with s=25 mm movement (solid line) and HQ measurements (spread along the axis)

DEPENDENCE ON AMPLITUDE For a fixed aperture radius and Rref= 2/3 of the aperture, random components scale with inverse of aperture This is due to the hypothesis that tolerances do not increase with larger aperture – i.e., they are absolute and not relative Hypothesis suggested by analysis of built magnets [B. Bellesia et al, Phys. Rev. STAB 10 (2007) 062401] Therefore for the 150 mm we assume a reduction of 20%

COMPARISON WITH WHAT PRESENTED IN LAST LARP CM Random components of a6 and a10 look pretty pessimist Other components (b4, b6) very optimist

COMPARISON WITH WHAT PRESENTED IN LAST LARP CM Random components of a6 and a10 look pretty pessimist They looked critical in Cai presentation We suggest to have a second run with these new tables Some dependence of random on the specific cross-section (up to 50%) – I would assume the same as MQXC for the moment

CONCLUSION First version of error tables We always give errors at 2/3 of reference radius I propose to just take phase I estimates and scale with inverse of the aperture