STATISTICAL SUMMARY AND INTERPRETATION OF THE TRAINING CAMPAIGNS CERN, 24th January 2017 Chamonix meeting STATISTICAL SUMMARY AND INTERPRETATION OF THE TRAINING CAMPAIGNS E. Todesco CERN, Geneva Switzerland On behalf of the Quench Behaviour Team www.cern.ch/qbt Based on the HC data of 2016, plus 2015 and 2008 and on production data 2001-2006 Thanks to MP3 team and to project engineers of MSC Related presentations from G. Willering and S. Le Naour

CONTENTS 2015 results - LHC at 6.5 TeV Quench distributions Estimates towards 7 TeV and comparison to 2016 results Production homogeneity New estimates and conclusions

TRAINING TO 6.5 TEV RECAP Five important features [see also talk by S. Le Naour] 1. Magnets quench only once (95% of quenches are first quenches) 2. Strong differences between the three manufacturers (80% of quenches are from 3000 series) 3. No correlation in the individual magnet training before and after a thermal cycle 4. Quench probability compatible with Gaussian tails 5. Strong differences along the production of 2000 and 3000 series

in brackets number of second quenches TRAINING TO 6.5 TEV RECAP Five important features First one: 95% of quenches are first quenches (magnets quench only once) Second one: 80% of quenches are from 3000 series (strong differences between the three manufacturers) – sectors with more 3000 series magnets have longer training Both features already seen in 2008 Quenches in 2015 campaign, in brackets number of second quenches [MP3 team] Training in each sector [MP3 team]

2015 RESULTS Third feature (NEW): no correlation in the individual magnet training before and after a thermal cycle This relies on data of one sector (56) trained to 6.6 TeV twice (2008 and 2015) Among the 84 magnets of 3000 series, it took 23 quenches in 2008 and 16 quenches in 2015 – only 3 magnets quenched both in 2008 and in 2015 It will be very interesting to see with sector 12 if this is confirmed For the moment we work on this hypothesis This is a major change of paradigm Training must be described with a statistical approach A magnet series has a probability of quenching to reach XX kA Each time we make a warm up and cool down we throw a dice We have to use probability distributions

DIGRESSION ON BINOMIAL DISTRIBUTIONS If we throw a dice N=60 times, how many times we will get 6? In average 10 times, but what spread? This is the binomial distribution Probability p=1/6, s=p(1-p)N So in our case sigma=0.17*0.83*60 = 2.9 Taking 2s, we will have 10±5.8, so results as low as 5 or as high as 15 If quench is described by a probability distribution, training a sector has a intrinsic variablity due to statistics Typically with 60 magnets of the same manufacturer in a sector, we can have very large spreads due to the low statistics Sector 56 took 23 quenches in 2008, 16 quenches in 2015 to reach 6.6 TeV 62 magnet of 3000 series: 23±8 compared to 16±7 Data are compatible with same performance

CONTENTS 2015 results - LHC at 6.5 TeV Quench distributions Estimates towards 7 TeV and comparison to 2016 results Production homogeneity New estimates and conclusions

DIGRESSION OF DISTRIBUTIONS Case of a flat distribution of quench probability Example: 50 magnets, linear training Instead of using the number of quenches we give the number of quenches/number of magnets (to be able to compare different samples) Typical training curve for a flat distribution of quench probability

DIGRESSION OF DISTRIBUTIONS Gaussian distribution Initial steep slope (gaining a lot) Plateau around the average of the distribution Then it goes fast (if the second quench does not come in the picture) Typical training curve of a sector with infinite number of magnets for a Gaussian distribution of quench probability

DIGRESSION OF DISTRIBUTIONS Gaussian distribution Finite size of the LHC makes training curve wavy Typical training curve of a sector with 50 magnets for a Gaussian distribution of quench probability

DIGRESSION OF DISTRIBUTIONS Gaussian distribution In the following plots, will take two sigma band (approx 95% of the cases) 20 training curves of a sector with 50 magnets for a Gaussian distribution of quench probability

GAUSSIAN TAILS IN THE LHC Fourth feature (NEW): Training of 2015 was found to be compatible with Gaussian tails Remove second quench Remove 1000 series Split 2000 and 3000 series Make a Gaussian fit Gaussian fit of the hardware commissioning data of 2015 (2000 and 3000 series) [E. Todesco, LMC, 20th January 2016]

QUENCH DISTRIBUTIONS IN THE PRODUCTION We have data only up to 11.08 kA To check the upper part of the distribution, we look at SM18 data – these are the training on individual test bench (nearly all magnets quenched twice – all distribution is now accessible) First half of distribution is Gaussian then spread is lower Initially treated with asymmetric Gaussian [LMC, 20th January 2016] Very unelegant, unphysical (discontinuous distribution), but very effective Gaussian Asymmetric Gaussian Gaussian fit of the 1000 series production data, first quench in virgin conditions (left) Asymmetric Gaussian fit of the 1000 series production data, first quench in virgin conditions (right)

QUENCH DISTRIBUTIONS IN THE PRODUCTION Latest results: Gaussian with parabolic cut No inconsistency (is zero for currents larger than m) Good fit at high currents Same Gaussian tail for low currents Gaussian with parabolic cut fit of the 1000 series production data, first quench in virgin conditions [D. Mapelli, QBT January 2017]

CONTENTS 2015 results - LHC at 6.5 TeV Quench distributions Estimates towards 7 TeV and comparison to 2016 results Production homogeneity New estimates and conclusions

THE ~500 QUENCHES ESTIMATE Expectations of first quenches at 7 TeV: 33% of 2000 series ~140 quenches 90% of 3000 series ~370 quenches Gaussian fit (line) of the 2015 training data (dots) for 2000 and 3000 series, first quenches only [E. Todesco, QBT August 2016 and ASC 2016, IEEE TAS in press]

THE ~500 QUENCHES ESTIMATE For the 1000 series, we had no data (5 quenches) Method not available, first guess of 5% (20 quenches) Then base on SM18 data, idea of taking the second virgin quench giving 18% probability (70 quenches) The data after thermal cycle also provide similar number First estimate of 5% revised estimate Gaussian fit (line) of the SM18 training data (dots) for 1000 series, second quenches only [E. Todesco, QBT November 2015 https://indico.cern.ch/event/575912/ ]

Quenches in 2016 campaign (second quenches in brackets) 2016 CAMPAIGN RESULTS We went from ~11.1 kA to ~11.5 kA [see talk by S. Le Naour] A bit less than halfway With 22 first quenches (50 to 80 foreseen for 12 kA) Relevant number of second quenches (10) all in 3000 series 3000 series confirms to account for most of the quenches (72%) Just one 1000 series magnet 2000 series confirms to have an intermediate behaviour between 1000 and 3000 series NO NEW PHYSICS (for magnet training) AT 6.8 TeV Quenches in 2016 campaign (second quenches in brackets) [MP3 team] Magnets installed in sector 34 and 45

[E. Todesco, QBT August 2016 and ASC 2016, IEEE TAS in press] RESULTS VS ESTIMATE We expected 34 first quenches, we had 21 first quenches A bit faster than expected, especially in 2000 in sector 23 and 3000 in sector 45 Gaussian fit (line) of the 2015 training data (dots) for 2000 and 3000 series, first quenches only [E. Todesco, QBT August 2016 and ASC 2016, IEEE TAS in press]

CONTENTS 2015 results - LHC at 6.5 TeV Quench distributions Estimates towards 7 TeV and comparison to 2016 results Production homogeneity New estimates and conclusions

PRODUCTION HOMOGENEITY: 1000 SERIES Overview of quenches along the production: 1000 series Red: first quench (six dot, six quenches, 5 in 2015 and one pushing 34 and 45 towards 6.8 TeV) We had no second quenches Line: max current reached in the LHC (11.08 kA, except 11.55 kA in sector 45 and 11.45 kA in sector 34 No pattern visible Current reached in the LHC Magnets not installed

PRODUCTION HOMOGENEITY: 2000 SERIES Overview of quenches along the production: 2000 series Red: first quench We had no second quenches Line: max current reached in the LHC Clear pattern with more numerous quenches in the 2000-2200 series

PRODUCTION HOMOGENEITY: 3000 SERIES Overview of quenches along the production: 3000 series Red: first quench in the LHC Blue: second quench in the LHC Line: max current reached in the LHC Performance with strong differences along the production Worse batches are 3120-3300 and 3370-3417 Only three magnets not installed, we took 3409 and tested two more times

PRODUCTION HOMOGENEITY: 3000 SERIES Only three magnets from 3000 series are not installed, in 2015 we took 3409 and tested two more times in 2015 and 2016 (see G. Willering talk) Pessimistic view: test failed, the magnet is good Optimistic view: slow trainers improve with time Can we get another one from the critical batch ?

CONTENTS 2015 results - LHC at 6.5 TeV Quench distributions Estimates towards 7 TeV and comparison to 2016 results Production homogeneity New estimates and conclusions

NEW ESTIMATES Data towards 6.8 TeV confirm previous estimates 30% of 2000 series, 75% of 3000 series will have first quenches 400 to 500 first quenches, with respect to 450 to 580 previously reported We have estimate for the second quench 70 to 90 quenches, all in the slow trainer batch of the 3000 series Example: 40% of the batch 3120-3300, 3370-3416 (220 magnets) that makes 90 quenches

NEW ESTIMATES Detail of previous pictures: 2000 series first quench

NEW ESTIMATES Detail of previous pictures: 3000 series first quench

NEW ESTIMATES Detail of previous pictures: 3000 series second quench

NEW ESTIMATES According to the way of splitting the production, we have two estimates, one more optmistic (total 470 quenches), one more pessimistic (total of 600 quenches) Pessimistic – without splitting the production in batches (see plots below), except the second quench case Optimistic – splitting 2000 and 3000 production in two batches each, and taking the more optimistic estimate for 1000 series Note: for 7 TeV we always assume 12.0 kA, i.e. 150 A margin Today we have 100 A margin: we trained at 11080 A to operate at 10980 A

CONCLUSIONS No visible obstacle in training towards 7 TeV Except (1) problem related to short and (2) massive quenches [S. Le Naour, M. Bednarek] 2016 training confirms the ~500 quenches estimate Now it looks a bit better: 500-600 quenches include second quench If done before LS2 The whole LHC to 7 TeV: 300-400 quenches Less than one month per sector Motivation: detect before LS2 if any magnet is blocking If done after LS2 Warming up 8 sectors, the 200 quenches done already are likely to be lost according to our best knowledge 500-600 quenches needed, ~one month per sector Worse sectors (as 45) should start before

CONCLUSIONS Test strategy during the production allowed intercepting magnets blocking the training No magnets have been replaced until now for insufficient quench performance If a sector is kept at 1.9 K, no training is needed to recover previous operational currents If a sector is warmed-up Sector 56 data are compatible with a scenario where one needs the full training (~500 quenches) Note that this is anyway much faster than the virgin training during production (1200 quenches) Sector 56 data are also compatible with an improvement with time (less training required after successive warm-ups) We will look at sector 12 retraining, even though the statistics is very low (only nine 3000 series magnets)

CONCLUSIONS Open points for further discussion in Quench Behaviour Team: Behaviour of 1000 series: will training be negligible ? Why some parts of the 2000 and 3000 production behave differently ? And why this was not visible in the SM18 data? Is there any role of secondary quenches on training ? LHC dipoles at 6.5/7 TeV means operating at 80%/86% of short sample Training phenomenology is different in Nb3Sn and Nb-Ti, but for FCC operating at 86% instead of 80% makes billion(s) difference in the superconductor cost

APPENDIX Detail of the estimates What we expect for sector 12

RECAP OF ESTIMATES Estimate given in January 2009 [A. Verweij, Chamonix 2009] Semi log fit on 2008 data 900-1350 quenches

RECAP OF ESTIMATES Estimate in January 2016 [E. Todesco LMC] Gaussian fit on 2014 data 450 first quenches plus unknown number of second quenches

RECAP OF ESTIMATES Estimate in August 2016 [E. Todesco et al., QBT and ASC, IEEE Trans. Appl. Supercond. in press] Gaussian fit on 2014 data, three estimates with different slicing of the production 530-580 first quenches plus unknown number of second quenches

RECAP OF ESTIMATES Estimate in January 2017, using also 2016 campaign Truncated parabolic Gaussian fit on 2014+2016 data 470-600 quenches including second ones

NEW ESTIMATE: 2000 SERIES Optimistic (splitting the production in 2000-2200 and assuming negligible quench in 2200-2446) 45% probability over the 2000-2200  90 at quenches 7 TeV Pessimistic 30% probability over the whole series  125 quenches at 7 TeV

NEW ESTIMATE: 3000 SERIES Splitting the production (good batch 3000-3120 and 3300-3370) 50% probability over the good batch  90 at quenches 7 TeV 90% probability over the bad batch  200 at quenches 7 TeV No split of production 75% probability over the whole series  310 quenches at 7 TeV

NEW ESTIMATE: 3000 SERIES SECOND QUENCH Pessimistic: we assume this affects only the batch 3120-3300 and 3370-3416 40% probability over this batch  90 quenches at 7 TeV

NEW ESTIMATE: 3000 SERIES SECOND QUENCH Optimistic: we assume this affects only the batch 3150-3230 and 3370-3416 55% probability over this batch  70 quenches at 7 TeV

THE CASE OF SECTOR 12 Sector 12 composition: 95 series 2000 (only 2 from the 2001-2200, so most of them are of the fast trainers) 9 series 3000 (6 from the 3120-3300 or 3370-3416, and 3 from the fast trainers) Sector went to 11.08 kA in 2015 with 7 quenches 2 quenches from 1000 series (1379, 1413) 1 quench from 2000 series (2332) 4 quenches from 3000 series (3325, 3250, and twice 3380) Perhaps the most interesting information will be to see if the same magnet will quench or not

THE CASE OF SECTOR 12 We expect Summary 2000 series: 5% probability, so 5 quenches ± 4 Or no quenches since all the magnets belong to the fast trainers 3000 series: 33% probability, so 3 quenches ± 3 If we split the production, 50% for the long trainers (6 magnets) and 10% for the fast (3 magnets) – same result Summary 5 quenches ± 4 for 2000 series – or 0 quenches 3 quenches ± 3 for 3000 series Plus the 1000 series and the second quenches