1. 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
Based on the HC data of 2016, plus 2015 and 2008
and on production data
Thanks to MP3 team and to project engineers of MSC
Related presentations from G. Willering and S. Le Naour

2. 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

3. 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

4. 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]

5. 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

6. 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

7. 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

8. 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

9. 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

10. 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

11. 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

12. 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]

13. QUENCH DISTRIBUTIONS IN THE PRODUCTION
We have data only up to 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)

14. 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]

15. 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

16. 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]

17. 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 ]

18. 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

19. [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]

20. 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

21. 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 kA in sector 45 and kA in sector 34
No pattern visible
Current reached in the LHC
Magnets not installed

22. 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 series

23. 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 and
Only three magnets not installed, we took 3409 and tested two more times

24. 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 ?

25. 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

26. 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 , (220 magnets) that makes 90 quenches

27. NEW ESTIMATES
Detail of previous pictures: 2000 series first quench

28. NEW ESTIMATES
Detail of previous pictures: 3000 series first quench

29. NEW ESTIMATES
Detail of previous pictures: 3000 series second quench

30. 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 A to operate at A

31. 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: quenches include second quench
If done before LS2
The whole LHC to 7 TeV: 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
quenches needed, ~one month per sector
Worse sectors (as 45) should start before

32. 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)

33. 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

34. APPENDIX
Detail of the estimates
What we expect for sector 12

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

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

37. 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
first quenches plus unknown number of second quenches

38. RECAP OF ESTIMATES Estimate in January 2017, using also 2016 campaign
Truncated parabolic Gaussian fit on data
quenches including
second ones

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

40. NEW ESTIMATE: 3000 SERIES
Splitting the production (good batch and )
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

41. NEW ESTIMATE: 3000 SERIES SECOND QUENCH
Pessimistic: we assume this affects only the batch and
40% probability over this batch  90 quenches at 7 TeV

42. NEW ESTIMATE: 3000 SERIES SECOND QUENCH
Optimistic: we assume this affects only the batch and
55% probability over this batch  70 quenches at 7 TeV

43. THE CASE OF SECTOR 12 Sector 12 composition:
95 series 2000 (only 2 from the , so most of them are of the fast trainers)
9 series 3000 (6 from the or , and 3 from the fast trainers)
Sector went to 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

44. 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