Cycle-to-cycle reproducibility and magnet modeling.

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
  http//sma.cern.ch

Cable combinations 02B5 02B8 02C0 02C8 02C9 02D 02G 02K
01B-02X measured 52 4 5 0 NO 2 9 59
01E-02X measured 0 6 0 NO 2 0 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.

• The field

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. Physical
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.

• Procedure
• Quench to erase the memory of previous current
  cycle.
• Ramp up to a flat top current IFT 11850 A for a
  time tFT1000 s.
• Ramp down to 350 A. No pre-injection porch.
• Ramp up to injection current for a time
  tinj1000s
• 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.
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 501792
14
Decay reproducibility (identical cycles).

• Excellent reproducibility.

15
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.

• 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
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.
• Procedure
• 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.

• Cycles with an injection duration of 1000s.

• Injection duration 10000 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 Ift4000 A to 11850 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 tft60 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
Change from tft0 s to 1800s.
b5

• 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 10000 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-back0.16 u/A (LHC)
fsnap-back0.22 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
And snap/back for b1?
ramp
Decay
Too fast phenomena to be measured for the
moment with DAQ _at_10 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 MBs).
• 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.
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-2000-103

35
Annex 2 Modeling Procedure b2
1
2
4
3
5
6
N.Sammut, PAC 2005.
36
Annex 3 Coupling currents.
Calculated field errors based on Rc15 mW and
s30 for 1/Rc R.Wolf (2002).
expected systematic /- 1 s
Units _at_ 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.