On reproducibility From several inputs of N. Sammut, S. Sanfilippo, W. Venturini Presented by L. Bottura LHCCWG - 4.10.2006

Components & reproducibility Geometric Proportional to conductor and iron positions and shapes May change from cycle to cycle (powering and thermal) due to conductor displacement because of the effect of Lorentz and thermal stresses Persistent currents Depends on the integral of the magnetic moments of each strand in the coil (including iron contribution) May change from cycle to cycle (powering) due to the hysteretic nature of the magnetic moments Saturation Depends on the shape and characteristics of the iron yoke There is no physical mechanism that could produce a relevant change during the magnet lifetime Decay & Snapback Depends on the powering history and on the cable characteristics Different magnet to magnet Changes from cycle to cycle

Geometry Effect of repeated cycles Data courtesy of N. Sammut Geometry Effect of repeated cycles Six loadline measurements separated by 100 cycles Static – nominal current Standard deviation for both cycles is below 0.01 units for b3 which is lower than the measurement repeatability 55

Geometry Changes over the magnet life Data courtesy of N. Sammut Geometry Changes over the magnet life MB1017 - magnetic measurement in April 2003 - magnetic measurement in September 2005 Static – nominal current Effect is small within measurement uncertainty but still larger than measurement repeatability 55

Geometry Summary of uncertainty uncertainty estimated as 3  of multipoles repeatedly measured on the same magnet (few magnets tested) after powering after training u(b1)=2.8 units u(b3)=0.3 units @ 17 mm

Persistent currents Effect of precycle - MB - 1 Data courtesy of N. Sammut, S. Sanfilippo Persistent currents Effect of precycle - MB - 1 55

Persistent currents Effect of precycle - MB - 2 Data courtesy of N. Sammut, S. Sanfilippo Persistent currents Effect of precycle - MB - 2 Differences in TF up to ≈ 1.5 units, on b3 up to ≈ 1 unit 55

Persistent currents Effect of precycle - MQY Data courtesy of W. Venturini Persistent currents Effect of precycle - MQY Differences in TF in the range of 10 units 55

Persistent currents Summary of uncertainty The effects are large (of the order of 10 units) The variability associated with powering cycles is very large MB (IFT 2 kA vs. nominal) u(b1) ≈ 1.5 units u(b3) ≈ 1 units @ 17 mm MQY (Imin 50 vs. 200 A) u(b2) ≈ 10 units @ 17 mm These values are relevant only if the pre-cycle is changed from run to run

Decay Effect of powering cycle Data courtesy of N. Sammut Decay Effect of powering cycle Large effects observed on harmonics Main field dependency has larger random Also because it is more difficult to measure (range 1…2 units) 55

Decay Model of powering cycle Courtesy of N. Sammut Decay Model of powering cycle Median of the model error b1 b3 b5 IFT 0.835 0.03 0.016 tFT - 0.02 tpreparation 0.07 55

Decay Aperture difference - 1 Standard cycle (30’ flat-top), 1000 s injection Negligible systematic difference 57

Decay Aperture difference - 2 Influence of flat-top current, 1000 s injection 57

Decay Aperture difference - 3 Influence of flat-top time, 1000 s injection Influence of wiaiting time, 1000 s injection 57

Decay Effect of repeated cycles Error is small and comparable to median of max scaling error for powering history b3  0.05 units b5  0.004 units 57

Decay Changes over the magnet life MB1017 - magnetic measurement in April 2003 - magnetic measurement in September 2005 Dynamic – decay amplitude Change is comparable to the static and dynamic model error 55

Decay Summary of uncertainty Although we have seen (much) better, we maintain that the empirical model (data fits) has a typical error that can amount to up to 20 % of the effect Main source of uncertainty is from the modelling of powering history, all other effects (aperture differences, cycle details, ageing) are small and have negligible systematic Why so cautious ? The sample of magnets used for the data-fitting is limited (10 magnets) This adds an uncertainty in the projection of the average

Uncertainty after correction Values estimated for MB’s in July 2004, RMS rview NOTE: variations of pre-cycle from the nominal one (e.g. due to limitations during commissioning or changes in optics) will cause an additional uncertainty that can be much larger than the above values

Open issues think we think we We know what we know and we know how well we know what we know but we do not know what we do not know nor do we know how badly we do not know what we do not know I think we I think

Examples a2 anomaly in Ansaldo-2 (2002) The shape of the a2(I) has a strong anomaly in one aperture of on Ansaldo-2 (2002) reassembled This data is real ! not a cable hysteresis measurements are OK as far as we can tell a magnetic piece (protection layer, shim,…) in the collared coils? Observed in few other magnets Depends linearly on maximum current reached

Examples Effect of precycle - MQT Data courtesy of W. Venturini Examples Effect of precycle - MQT The effect low current cycling can be massive 55