1. Cycle-to-cycle reproducibility and magnet modeling.
L. Bottura, N.Sammut, S.Sanfilippo.
presentation to the 17th LHC Machine Advisory Committee
June 10th, 2005

2. Outline Magnetic measurements at 1.9 K and magnetic model.
Status of magnetic measurements.
Magnetic model-generalities.
Modeling static components.
The Decay at injection field: cycle to cycle reproducibility.
Results at 1.9 K and modeling.
Powering history dependence.
The snap-back phase.
Modeling the snap/back.
Scaling law.
Conclusions and outlook.

3. Outline Magnetic measurements at 1.9 K and magnetic model.
Status of magnetic measurements.
Magnetic model-generalities.
Modeling static components.
The Decay at injection field: cycle to cycle reproducibility.
Results at 1.9 K and modeling.
Powering history dependence.
The snap-back phase.
Modeling the snap/back.
Scaling law.
Conclusions and outlook.

4. Status of magnetic measurements at 1.9 K.
Status in June 2005
Magnetically cold tested : Dipoles (165), SSS (21) special SSS (5) .
Fair mix of (MB)
3 producers.
three X-sections.
10 cable combinations (over 14).
you can have access to the data through
Cable combinations
02B5
02B8
02C0
02C8
02C9
02D
02G
02K
01B-02X measured 52 4 5 NO 2 9 59
01E-02X measured 6 3 10
Foreseen up to the end of 2006 a total amount of:
- MB (250), SSS (50), special SSS (10-20) in standard conditions (load line , LHC cycle) which include:
24 special tests to study the powering history effect and the snap-back wave form.
- sampling : 5-10 samples for each cable combination (MB).
Knowledge at cold :MB (20%), SSS (15%), SSSS (15%).

5. Information from 1.9 K measurements.
Information obtained:
-warm/cold correlation at injection and nominal
model the different field error components.
Uncertainty coming from:
-Warm/cold correlation.
Measurements errors.
L.Bottura,MAC-16
Friday, December 10th, 2004
Forecast field strength and multipoles by octant :
Modelling the errors + beam based measurements.

6. The field model. + + + + linear composition of contributions:
Dependence of : time (t), current (I),
ramp rate dI/dt, Temperature (T)
powering history I(-t).
The field errors are composed of:
Dynamic Long Term Effects +
Dynamic Short Term Effects + +
Steady State Effects +
Geometric
Coupling Currents
Decay
DC Magnetisation
Snap-Back
Iron Saturation
Coil Displacement
Residual Magnetisation
linear composition of contributions:

7. Characteristics of the field model.
Field and field errors are assumed to have different origins (components) that have a physical origin (e.g.geometric, persistent, saturation, …).
General functions for each component are obtained fitting cold data as a function of current or time, using functional dependencies that are “expected” from theory, or “practical” in describing data.
Scaling parameters are applied to the general functions to model single magnets.
The scaling parameters are either:
-measured (injection, mid-field, flat-top), or
-extrapolated from warm conditions (geometric), or
-extrapolated from averages measured (persistent currents for the same cable combination).
set of 17 parameters/property/aperture/magnet
includes modeling of static variations
Same behavior for different geometries, e.g. Xs
includes modeling of dynamic effects
Predict the Snap back from the previous Decay
handles powering history changes (Decay)
simple to update (recalibration).
Courtesy L.Bottura.

8. Steady state effects. Geometric Physical Empirical Persistent Current.
Residual
Magnetization.
Physical/
empirical
Iron
Saturation
L.Bottura, N.Sammut: “ The Use of magnetic measurements for LHC Operation” Chamonix Workshop 2005

9. Error from the model (steady state).
Behaviour of the magnet well described at any current level (static).
But only 80% of the MB not measured at cold.
For these magnets : knowledge of the geometric (from warm/cold correlation) and of the hysteresis amplitude at injection are required.
Information from beam-based measurements needed
(chromaticity, tune, …)
Study performed on 60 magnets of the sector 7/8.
N.Sammut, L. Bottura, J. Micallef, ‘The LHC Magnetic Field Model’, PAC 2005

10. Outline Magnetic measurements at 1.9 K and magnetic model.
Status of magnetic measurements.
Magnetic model-generalities.
Modeling static components.
The Decay at injection field: cycle to cycle reproducibility.
Results at 1.9 K and modeling.
Powering history dependence.
The snap-back phase.
Modeling the snap/back.
Scaling law.
Conclusions and outlook.

11. Decay : Reference machine cycle.
1000s
time I
760 A
Quench
Procedure:
Quench to erase the memory of previous current cycle.
Ramp up to a flat top current IFT =11850 A for a time tFT=1000 s.
Ramp down to 350 A. No pre-injection porch.
Ramp up to injection current for a time tinj=1000s
Measurement of the decay and snap back during the ramp with rotating coil (1Hz) or Hall plates (10Hz). ,

12. Decay at injection field (b3, b5).
Amplitude of the decay/snap back for b3,b5 (reference cycle).
Same variation with time for b3, b5. No dependence of the cable type.
Expected amplitudes but large spread measured among the magnets.

13. Case of b1. Feeble effect (1-2 units)
Family 1 : Magnets with 01B- 02X combination
Family 2 : Magnets with 01E-02X combination.
ex : 01 E-02 K
ex : 01 B-02 B
Average
Average
ex : 01B-02 K
Feeble effect (1-2 units)
But : Not all the cable combinations seen for the moment!
N.Sammut and L.Bottura, “Classification of LHC dipole at injection”, EDMS

14. Decay reproducibility (identical cycles).
Excellent reproducibility.

15. current redistribution  local field  magnetization  bore field
Modeling the Decay.
appears during constant current excitation.
associated with current redistribution in the superconducting cables.
result of a complex interaction:
current redistribution  local field  magnetization  bore field
assume that the dynamics follows that of current diffusion:
Powering history dependence
L.Bottura, M.Breschi, M.Fabbri:
“Analytical calculation of current redistribution in multi strand superconducting cables.” ASC 2002.
Modelling the decay of b1, b3, b5 on 30 dipoles.

16. Using the Decay Model. scale f3,i(s) = Predictability
Population average
Sample measured
Scaled decay
How to represent the average behavior of the population using the model and the measured magnets?
Answer.
Fit Cmeas,idecay(t) with the (average) measured magnets of the sector, i.
Obtain the decay amplitude for ex at the end of injection of the population from the model-calibration run
Use of the scaling law:
Predictability
scale f3,i(s) =
L.Bottura, T.Pieloni, N.Sammut: “ Scaling laws for the Field Quality at Injection in the LHC Dipoles” LHC Project Note 361

17. Pre-cycling condition dependence.
main parameters:
flat-top current IFT
flat-top duration tFT
waiting time before injection tpre-injection
Injection duration.
Scaling for decay amplitude:
Decay amplitude

18. Test procedure. Influence of the parameters studied one by one.
Quench to erase the memory of previous current cycle.
Ramp up to a flat top current IFT for a time tFT.
Ramp down to 350 A. Wait during a pre-injection time tpre-injection.
Ramp up to injection current for a time tinj.
Measurement of the decay and snap back during the ramp. ,

19. Test Program. Reference cycle. Injection duration : 10000 s.
Cycles with an injection duration of 1000s.
Injection duration : s.
So far only on Dipole Magnets (~9), no test on MQ.

20. Influence of the flat-Top Current
average is straight b3
Statistic based on 9 magnets.
Change from Ift=4000 A to A. b5
The decay of b3 (b5) increases (decreases) proportionally to the energy of the previous run.

21. Influence of the flat-Top Duration.b3
average can be fitted with exponential. b5
Change from tft=60 s to 3600 s.
The decay saturates for cost times
of the order of 30 mm
or more. Similar behaviors observed.

22. Influence of the pre-injection time.b3 b5
Change from tft=0 s to 1800s.
Strong reduction of the decay for b3 by
30%. No effect on b5.
Preliminary results. More points between 300s and 1800s are needed.

23. Influence of a longer injection.
Small change after 2000s
Decay for an injection of s.
Increase of the decay by about 25 %
(for b3) w.r.t the reference cycle.
small change after 2000s

24. Parameterization procedure.
Example for 2 parameters, tft, Ift.
Assumption: dynamic remains the same.
Standard cycle : reference point Dstd.
Data is normalized with a linear scaling w.r.t the standard cy
Surface fit built using the average curves fitted with the scaling law Dn (Ift,Tft,..).
Prediction of the decay
Amplitude.
Courtesy, N.Sammut.

25. Uncertainty for powering history prediction.
the empirical model (data fits) has a typical error that can amount to up to 20 % of the effect.
add uncertainty on average due to limited sample.
so far 1 % of the population has been characterized.
assume 20 magnets till the end of the production.

26. Outline Magnetic measurements at 1.9 K and magnetic model.
Status of magnetic measurements.
Magnetic model-generalities.
Modeling static components.
The Decay at injection field: cycle to cycle reproducibility.
Results at 1.9 K and modeling.
Powering history dependence.
The snap-back phase.
Modeling the snap/back.
Scaling law.
Conclusions and outlook.

27. Snap-back phase.
first few tens of mT in the acceleration ramp, after injection
pendant to decay: magnetization changes are swept away by background field
result of a complex interaction:
current ramp  background field  magnetization  bore field
Amplitude changed with the pre-cycling conditions.
Model proposed :
DI : current needed during the ramp to resolve the snapback.
G. Ambrosio, P. Bauer, L. Bottura, M. Haverkamp, T. Pieloni, S. Sanfilippo, G. Velev
“ A scaling law for the snap back in Superconducting Accelerator Magnets” ASC 2004

28. Modeling the snap-back (sextupole).
exponential fit
hysteresis baseline subtracted
b3 snap-back singled out
fit of the b3 hysteresis baseline
Model tested on 8 dipoles for b3, (b5).

29. Snap back scaling law for b3.
Test on 9 magnets, changing also the powering cycle.
Db3 and DI change
for different cycles:
b3 and I are correlated.
linear behavior.
Error on b3 ~ 0.3 units (but only 9
magnets tested.).
Identical correlation for b5
needs to be confirmed.
fsnap-back~0.16 u/A (LHC)
fsnap-back~0.22 u/A (Tev)
The correlation plot holds for magnets of the same family.
G. Ambrosio, P. Bauer, L. Bottura, M. Haverkamp, T. Pieloni, S. Sanfilippo, G. Velev
“ A scaling law for the snap back in Superconducting Accelerator Magnets” ASC 2004.

30. Too fast phenomena to be measured for the moment
And snap/back for b1?
ramp
Decay
Too fast phenomena to be measured for the moment
with Hz.

31. Snap-back compensation.
During the decay ….
Extract sextupole change in dipoles from slow Q’ measurements during the decay (or predict the decay amplitude Db3 at snap-back using the b3(t) fit formula.)
Predict the DI (correlation).
Just before ramping ….
Extract total b3 correction.
Db3 and DI used to forecast the sextupole correction using the exponential fit.
Convert to current for b3 spool pieces
Incorporate into ramp functions and download.
Andy Butterworth, M.Lamont, Chamonix XIV.

32. Conclusions and outlook.
Robust established modelling functions for the current and the time
behaviour of each field error component (for the MB’s).
The model will be refined (in its dynamic part) using the other MB
special tests that will be performed up to 2006:
- to continue the study of the influence of the powering history ( in particular the effect of the pre-injection time and the long time injection).
- to improve the b3/b5 snap/back knowledge using a detector with an upgrade hardware (resolution better than 0.1 unit).
Coefficients of the model not frozen but can be adapted based on
results of beam measurements or special measurement campaigns
on spare and left over magnets on the cryogenic benches.
Extension of the modelling to magnets other than dipoles is foreseen.
Improvement of the physical description of the magnetic field
and of the errors is required.

33. Acknowledgements. Dr. Valeria Granata. Dr. Laurent Deniau.
Tatiana Pieloni.
Ovidiu Achim.
Alessandro Masi.
Gabriele Greco.

34. Annex 1: Snap-back measurements.
b3 sensors
b5 sensors
Electrical connection card
64 pin connector
inclinometer
Hall-probe device for 10 Hz b3 (and b5) measurement.
Sum  B1 – B1/2 – B1/2 = 0 dipole is bucked-out
Sum  – B3 – B3 – B3 = -3B3
Resolve the snap/back wave form.
Software and hardware have been upgraded recently
M. Breschi, L. Bottura, ‘Fast Measurement of Field Harmonics through a set of Hall Probes’, LHC-MTA-IN

35. Annex 2 :Modeling Procedure – b21 2 3 4 5 6
N.Sammut, PAC 2005.

36. Annex 3: Coupling currents.
Calculated field errors based on Rc~15 mW and s~30% for 1/Rc: R.Wolf (2002).
expected systematic +/- 1 s
Units @ 17 mm
expected values at 10 A/s, referred to injection field
Statistic on 50 magnets tested.
Small effect, below 0.1 unit at the limit of the measurement accuracy.
Effect not considered in the field model.