1. E. Todesco for the QBT CERN, Geneva Switzerland
CERN, 20th January 2016
LMC
SECOND UPDATE ON QUENCH BEHAVIOUR TEAM ACTIVITIES AND STRATEGIES TOWARDS 7 TeV
E. Todesco for the QBT
CERN, Geneva Switzerland

2. RECENT ACTIVITIES Recent work www.cern.ch/qbt
7 meetings in July-December 2015
Average partecipation: 8, total number of colleagues: 17
Recent work
Investigation on the difference between firms
Recall of the features of the 3000 production and main events
Shape of distributions and strategy for having more information at 7 TeV
SM18 test
Flattop quenches

3. COMPOSITION B. Auchmann M. Bajko G. De Rijk P. Fessia P. Ferracin
P. Hagen
S. Le Naour
J. C. Perez
M. Modena
F. Savary
R. Schmidt
J. Ph. Tock
E. Todesco
D. Tommasini
A. Verweij
G. Willering

4. BRIEF RECALL OF RESULTS
Result I:
2015 confirmed that 3000 series magnets quench more than 2000/1000 series:
140 quenches of 3000 series, 27 of 2000 series and 5 of 1000 series
Result II:
In the 3000 series, the production is not homogeneous
Differences are statistically significant
Degradation at (that went on 45)
Number of quenches per magnet in 3000 series with statistical error

5. 2008 VS 2015 What can we expect for the future?
Two sectors can be compared: apparent paradox
S56 powered at A
23 quenches in 2008, 16 quenches in 2015
S45 powered to A
3 quenches in 2008, 10 quenches in 2015
Adding statistical error with two sigma
S56: 23±8 in 2008 versus 16±7 in 2015
S34: 3±6 in 2008 versus 10±6 in 2015
Result III: Data are compatible with a scenario where at each warm up we start in the same condition as at the beginning of the previous training

6. 2015 VS VIRGIN TRAINING Did 3000 series totally lost memory?
In virgin condition: 46% of 3000 series, i.e. 191±20 quenches
In 2015: 34% of 3000 series, i.e. 142±19 quenches
Result IV: data compatible with a partial but small preservation of memory for 3000 series
HC «a bit better» than virgin training
Training of virgin magnets during production

7. WHICH MAGNETS ARE BAD IN 56?
Two extreme situations can be imagined:
In 56 there are some bad magnets, always quenching, and other good magnets, never quenching
In this case, all magnet quenching in 2008 will quench in 2015
In 56 all magnets are belonging to the same distribution, with a probability p of quenching
In this case, the probability of having magnet quenching in 2008 and in 2015 will be p2(0.25)2=6%
So it is enough to count how many magnet quenched both in 2008 and in 2015
3 magnets quenched in 2008 and 2015:
3358, 3330 and 3336 out of 84, ie 3%
Result V: S56 data compatible with magnets belonging to the same distribution (no bad or good magnets)
No evidence of magnets to be removed in LS2

8. SHAPE OF DISTRIBUTIONS
We test the hypothesis of a Gaussian quench probability for the lower part of the quench spectrum

9. SHAPE OF DISTRIBUTIONS
Integral of the distribution is the training curve, an erf function

10. SHAPE OF DISTRIBUTIONS
Interesting result: HC data of 3000 except 45 are compatible with a Gaussian
Statistical error (2s) is associated to having 350 magnets
Gaussian parameters: m=11.6 kA s=0.73 kA

11. SHAPE OF DISTRIBUTIONS
For 45, we quenched 75% of the magnets
Erf fit does not look so nice …

12. SHAPE OF DISTRIBUTIONS
For 45, we quenched 75% of the magnets
Erf fit does not look so nice …
But since the sample is 62 magnets only, statistical error is larger, and it fits within 2 sigma
Gaussian parameters: m=10.75 kA s=0.45 kA

13. SHAPE OF DISTRIBUTIONS
It does not look gaussian, the beginning is too steep
First quenches are too low
Tentative parameters: m=12.3 kA s=0.75 kA
This is a shaky fit, we do not have enough data

14. FIRST RESULT
The apparently chaotic training of the LHC can be seen in terms of three Gaussian distributions
Where the 2000 series part has some discrepancies in the initial part

15. SHAPE OF DISTRIBUTIONS
A good fraction of HC data are compatible with Gaussian distribution for the first quench
We now that
extrapolation is a dangerous exercice
the whole distribution cannot be Gaussian (some asymmetry should be on the short sample side)
Let’s go back to the production data where we have access to the whole distribution for the first and second quench

16. PRODUCTION DATA
1000 case: first half gaussian, second half a bit slower as expected
Distribution falls faster on the short sample side as expected from the physics

17. PRODUCTION DATA A very effective and very inelegant patch
Using two Gaussian distribution with the same average and two different sigma, very good agreeement
Sigma on the upper part 30% smaller than in the lower part
Gaussian parameters: m=12.0 kA s1=0.70 kA s2=0.45 kA

18. PRODUCTION DATA The same approach works for the 2000 case
Sigma on the upper part 30% smaller than in the lower part
Gaussian parameters: m=11.35 kA s1=0.90 kA s2=0.60 kA
We know that this fit has a dark side, there is work in progress on fit with asymmetric distributions xn exp –x2

19. PRODUCTION DATA The same approach works for the 2000 case
Sigma on the upper part 30% smaller than in the lower part
Gaussian parameters: m=11.35 kA s1=0.90 kA s2=0.60 kA
We know this fit has a dark side, we are working on asymmetric distributions xn exp –x2

20. PRODUCTION DATA
3000 case
Does not fit Gaussian - another sign that something went wrong in 3000 production?
But we will see that the second quench fits

21. A TENTATIVE EXTRAPOLATION
Accouting for the asymmetry observed in production
Assuming the shaky fit for the 2000 series
Assuming an a priori 5% 1000 series magnets quenching to reach 7 TeV
We end up with 450 quenches to 7 TeV
Plus the second quench – for which very little data are available on HC

22. SECOND QUENCH IN PRODUCTION DATA
In virgin condition, 30% of 3000 series magnet had a second quench below 7 TeV
Asssuming that it cannot go worse , we have to add a most 140 quenches

23. A TENTATIVE EXTRAPOLATION
So our best estimate with available data is 450 first quenches plus at most 150 second quenches
Estimate is rather linear in the TeV range so for pushing the LHC today towards 7 TeV is about 50 quenches per 100 GeV, plus the second quench
If we consider case after a thermal cycle, we have to add the 170 quenches to go to 6.5 TeV

24. A TENTATIVE STRATEGY
Possible strategy: push S12 and S45 to 7 TeV before LS2
45 – to see the 3000 series second quench (we already quenched 75% of 3000 magnets,)
12 – to see the 1000 and 2000 behaviour (there are only series magnets)
These two sectors are also requiring the lower number of quenches, so we maximize information and minimize the risk

25. SUMMARY
The HC training curves are compatible with an erf fit, with the physical meaning that the lowest part of the quench distribution is Gaussian-like
We have to separate 2000 from 3000, and 45 from the 3000 set
The production data support this statement, showing Gaussian shape over half of the distribution
Work to fit with asymmetric distribution is ongoing
An extrapolation to 7 TeV gives 450 first quenches
Plus the second quench, for which an upper bound of 150 can be given
To have a more solid extrapolation a possible strategy is to push S12 and S45 to 7 TeV
This should cost about 50 first quenches