1 / 23 Workshop Chamonix XV 23-27 January 2006, L'Esplanade du Lac, Divonne-les-Bains S. Sanfilippo...

Workshop Chamonix XV 23-27 January 2006,

L'Esplanade du Lac, Divonne-les-Bains 1 / 23S. Sanfilippo [email protected]

Transfer Function of the Quadrupoles

And Expected -Beating at injection.

S. Sanfilippo

and

P. Hagen, J.-P. Koutchouk, M. Giovannozzi, T. Risselada

Acknowledgments: S. Fartoukh, A. Lombardi, Y. Papaphilippou

Workshop Chamonix XV - 23-27 January 2006, L'Esplanade du Lac, Divonne-les-Bains 2 / 23S. Sanfilippo

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Special thanks to :

L.Bottura, N. Smirnov, M. Buzio, M.Calvi, N.Sammut, G.Deferne, M.Gateau, W. Venturini-Delsolaro & his team, O.Dunkel, J.Garcia.Perez & his team, D.Cornuet and his team (AT-MTM), E.Todesco (AT-MAS) for calibration measurements and analysis, follow-up, general information and feed-back.

R. Ostojic & his team, N. Catalan-Lasheras, S. Ramberger (AT-MEL), J.Di-Marco (FNAL) for the follow-up of the measurement results and feed-back on the instrument performance.


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Outline Motivations. Sources of gradient errors. Study of the gradient errors coming from the measurements:

Uncertainty of the measurement systems. Cross-calibration results and estimate of the absolute accuracy.

Analytical estimate of the impact of the gradient errors on the -beating (static case): Arc quadrupole. Stand alone magnets- impact of the magnetic history.

MAD Computation of the -beating. -beating results versus targets. Conclusions.


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Motivations

Target : the aperture budget being tight, try as much as possible to minimize the gradient uncertainties.

Budget: (S.Fartoukh, O.Brüning, LPR 501) Overall budget of ()peak=21% (i.e. 10% of r.m.s beam size) Off momentum -beating (~7% for H and 5% for V) Gradient errors: (x/x)peak<14%, (y/y)peak<16%

Method: analytical estimate and numerical computations (MAD-X)C (L,N,K,x,y)

]unit)[b(C]unit)[b(Q2sin22

K2NL

10~[%])( 2Y,X2

Y,X

22QF2rms

Y,X

Y,X

Example for MQs


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Sources of gradient errors

“Static” error sources : Knowledge of the transfer function (uncertainty, random) of the

quadrupoles (MQ, MQM, MQY, MQX, MQW, MQTL). Systematic and random of b2 in dipoles (MB). Precision of the power converters. Transfer function dependence on the magnetic field history. Mismatch of the MQT’s when performing a tune shift Q~ ± 0.1. Feed-downs from lattice and spool-piece sextupoles.

“Dynamic” error sources : Variation of MQ’s transfer functions during the decay, snap-back. PC tracking errors on B2(MQ)/B1(MB). Chromaticity correction during the decay/snap-back.


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Break-down of uncertainties in the transfer function (static)

Quadrupoles measured at cold. Precision of the measurement system (resolution, reproducibility,

calibration uncertainty). Uncertainty on the cold magnet state (history dependence).

Quadrupoles measured at warm (or partially at cold). Precision of the measurement system (resolution, reproducibility,

calibration uncertainty). Uncertainty on the magnet state (history dependence). Precision of the warm-to-cold correlation and uncertainty on the

extrapolation.

Quadrupoles powered in series: Spread of the transfer function due to manufacturing tolerances.


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Break-down of the errors coming from the measurement systems

Resolution: Smallest variation that the system can measure. For all the systems used resolution is better that 1 unit.

( not discussed in the following)

Reproducibility: Random coming from 10 consecutive measurements under the same conditions.

Uncertainty: Absolute accuracy of the system. Errors coming from the calibration of the systems. The systematic part is removed using cross-calibration between systems.

All measurement errors are supposed to be normally distributed. The uncertainty and the reproducibility will be given at 1 .

All measurement errors are supposed to be normally distributed. The uncertainty and the reproducibility will be given at 1 .


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Measurement systems of transfer function at cold (SM18)

1) Long rotating coils (7 pairs for MB, 2 - for SSS) Uncertainty (Gdl)~ 10-15 units, reproducibility <1 unit.

2) Automated scanner (2 heads) Used for SSS & special SSSs of variable lengths One 600/700mm-long rotating coil, longitudinal scanning

over magnet length. Uncertainty (Gdl)~ 10 units, reproducibility ~0.2 unit.

3) Single Stretched Wire (SSW) (3 systems) 1 wire loop over any total magnet length. Integrated strength of quadrupoles and dipoles.

Uncertainty (Gdl): ~5 units, reproducibility ~1 units at high field but ~10 units low field (for quads).

Superconducting dipole on the cold test bench in SM18 equipped

with rotating coil system

SSW for special SSS measurement


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Measurements at cold (block 4) and industry (warm)

4)Rotating coils in vertical facility (2 pairs) Used for MQMC, MQM, MQY Test in a vertical cryostat with no anti-cryostat: higher

uncertainty on absolute value of Gdl (but relative value between two currents is reliable).

Uncertainty (Gdl):~40 units, reproducibility ~ 1 unit.

5) Industry moles (300 K) :QIMM(2 pairs) Used for MQ, MQMC, MQM, MQY,MQW and dipoles. Uncertainty (Gdl) ~ 20 units Reproducibility ~ 0.2-3 units depending on the mole.

QIMM

Vertical test facility.


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1

10

100

indu

stry

mole

verti

cal t

est f

acility

long

sha

ft

scan

ner

Single

Stretc

hed

Wire

unce

rtain

ty(u

nit

s@1

7 m

m)

B1B2

Uncertainty and reproducibility for cold measurements systems

Reproducibility for all systems is excellent (<1 unit) except the SSW at low current (1 kA).

Uncertainty on the quadrupole of 5 (SSW) to 30 units (coils) has a large variability from system to system: Calibration errors: Rotation

radius reproducible only to 5-30 m

Mechanics: Uncertainty on the coil rotation axis position during real measurement.

low field

Improvement of the calibration procedure (scanner, long shaft) already started.A plan of cross calibration between systems is on going to reduce the uncertainty.

Improvement of the calibration procedure (scanner, long shaft) already started.A plan of cross calibration between systems is on going to reduce the uncertainty.

Courtesy L.Bottura

reproducibility


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magnet class Numbertest

conditiontest (%)

industry mole

warm corrector bench

long shaft vertical test facility

long shaft (SM18)

scanner

Single Stretched Wire

1232warm 100main

bending dipoles

Bdl X X (1)

Bdl X X (1)

Gdl X

Gdl X X (3) X

Gdl X X (2) X XGdl X (2) X X

Gdl X

Gdl X (4) X (4) X (4)

Gdl X

1232warm 100

cold 20

362warm 100

cold 15

114 warm 100cold 65

warm 100

cold 1.5

48 warm 100

main bending dipoles

main arc quadrupoles

DS and MS quadrupoles

corrector magnets

resistive quadrupoles

Low Quad 24

7500

cold 100 Gdl X

Measurement and cross-calibration test plan

The original idea (100% of cold tests) had to be adapted as we went along and: ~15% of the MBs, MQs, will be

tested at cold: we will rely on warm data and established the warm to cold correlation.

Cross-calibration with 3 systems: rotating coils/SSW/scanner for

stand-alone magnets.

Special tests are planned have started in block 4 to study the impact of the magnetic history.

(1) type test to establish in-situ calibration of long shaft rotating coil system and verify field direction in cold conditions(2) absolute calibration of the system is missing (random error of the order of 1 %)(3) the scanner was used for main quadrupoles tests only during the initial tests on prototypes and pre-series magnets(4) type test performed on few units in the assembled cryomagnets (bending dipoles, arc quadrupoles, DS and MS quadrupoles)

Courtesy L.Bottura


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Gdl measurements at cold with two systems for arc MQs.

58.1

58.15

58.2

58.25

58.3

58.35

58.4

58.45

58.5

58.55

58.6

58 58.1 58.2 58.3 58.4 58.5

Transfer function_room temperature (T / kA)

Tra

nsfe

r fu

nctio

n at

1.9

K (

T /

kA)

rotating coil (scanner)SSW system

17 units

After new calibration procedure . Before calibration of the scanner. SSW system (1.9 K) / scanner (1.9 K).

Significant improvement : values from the two systems within 5 units (rms).Significant improvement : values from the two systems within 5 units (rms).


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Quadrupoles (B2) cross-calibrationSSW/rotating coil

SSW system (1.9 K) / rotating coil measurements (1.9 K).

Goal: To guarantee a maximal uncertainty of the transfer function measured with any system (including the vertical facility) of Umeas. syst ~10 units (rms).

Goal: To guarantee a maximal uncertainty of the transfer function measured with any system (including the vertical facility) of Umeas. syst ~10 units (rms).

Rotating coils (#35,#36,#37,#38) versus SSW

58.0

58.1

58.2

58.3

58.4

58.5

58.0 58.1 58.2 58.3 58.4 58.5

Gdl, SSW (T/kA)

Gd

l, R

ota

ting

co

il (T

/kA

)

#35

#36

#37

#38

~17 units

Courtesy M.Calvi

Shafts offset sigmaunits units

#35 -1.24 4.14#36 -16.52 1.58#37 -19.49 9.69#38 1.2 4.47

Calibration has to be improved.All the shafts have to be calibrated.


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Dipole (B1) cross-calibration

SSW system (1.9 K) / 15-m long rotating coil (1.9 K).

Uncertainty for MB transfer function measurement at cold Umeas. syst~ 3 units (rms). Uncertainty for MB transfer function measurement at cold Umeas. syst~ 3 units (rms).

10.045

10.050

10.055

10.060

10.065

10.070

10.075

10.045 10.050 10.055 10.060 10.065 10.070 10.075T.F. from SSW [Tm/kA]

T.F

. fr

om L

ong

Shaf

ts [

Tm

/kA]

5 u

nit

s

TFshafts = TF SSW - 1.41 units

RMS = 3 units

Courtesy M.Buzio


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Impact of the b2 errors on the beating: Arc quadrupoles

unitswarmproduction 13~

58.1

58.15

58.2

58.25

58.3

58.35

58.4

58.45

58.5

58.55

58.6

58 58.1 58.2 58.3 58.4 58.5

Transfer function_room temperature (T / kA)

Tra

nsfe

r fun

ctio

n at

1.9

K (T

/ kA

)

17 units

units4~MQcold/warm

Courtesy E.Todesco

Uncertainty

production

effective after (2n+1) pairing(warm/cold) in units

U meas system (rms) due to the impact of magnetic history

b

x/ Ky 0.76 0.78

x y peak 9 9 x,y [%] peak= Cx,y. b2

20 MQs measuredSSW used for the W/C

quadratic sum

FQWG March 2005

Comments

85% of MQ measuredreduction by ~30% (Y.Papaphilippou)

11

units

45

913

2

after sorting Courtesy Y. PapaphilippouCourtesy Y. Papaphilippou


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Impact of the random b2 for stand alone magnets

Magnets measured fully at cold (MQY, MQX) or fully at warm (MQW): Uncertainty coming from the measurement system.

MQM(C,L), MQTL measured partially at cold: uncertainty from the warm to cold correlation to be added.

Analytical estimate of [%] peak for stand alone quadrupoles.

Contribution of the magnetic history significant (working current between 100-300 A) to be added for all.

This class of magnets gives total contribution of about 13 % (peak at 3). This class of magnets gives total contribution of about 13 % (peak at 3).


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Influence of the magnetic history on the b2 knowledge

MQY , machine cyles with various injection currents and pre-cycles

2.595

2.600

2.605

2.610

2.615

2.620

2.625

0 50 100 150 200 250 300 350 400

Current (A)T

F (

Tm

@1

7mm

/kA

)

LHC-Cycle-injection and min curr at 100 A

LHC-Cycle-injection and min curr at 140 A

LHC-Cycle-injection 176 A, min cur 100 A



LHC-Cycle-injection 200A, min cur 100 A

Hysteresis loop min current 0 A

T=4.4 K

20 units

Courtesy W.Venturini.

First experiment on MQY: Measurements with different

minimum current of pre-cycle. Change of TF values up to 60

units at injection current ~100 A!

ref. cycle

25 special tests foreseen in Block 4 on MQM(C), MQY in 2006.

Magnetic modeling will follow.

Rough estimate of the uncertainty coming from the modeling ~ 10 units (rms).

Rough estimate of the uncertainty coming from the modeling ~ 10 units (rms).


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Simulation model of the -beating

Installation databaseLayout + MEB slot allocation

Database of warm magnetic measurements

Database of cold magnetic measurements

Generator of magnetic

imperfections

Configurable options:(class of magnets, random

sampling…

MAD-XLHC machine calculations

Nominal LHC sequence and optics definitions.

β-beat calculations

NB: Simulation carried out with nominal optics V6.5 at injection energy.Correctors and MQT for tune shift are set to 0.


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Measurements at cold are used for cryo-magnets whenever available. Magnets not yet built are drawn from a Gaussian distribution matching

observed production spread in warm measurements. Cryo-magnets with warm measurements are then extrapolated to cold

by a warm-cold correlation (systematic and Gaussian random). Allocation of magnets to slots not yet defined by MEB are drawn

randomly. The simulations assume that the power supplies are re-calibrated to

provide the nominal average gradient when there is a chain of magnets. For the power supplies the reproducibility chosen is that for one day and

originate from the values of the design report. The statistics are based on 30 seeds.

Simulation model: details and assumptions


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-distributions

0.0

0.1

-15 -10 -5 0 5 10 15xxgiven by all Q

No

rma

lize

d f

req

ue

nc

y

Simulated

Gaussian

Distribution of the / sampling in the machine circumference for MQs (1 seed).

Distributions are not Gaussian (Kolmogorov-Smirnov test).The ratio ()peak/()rms is found to be about 2.2.

Distributions are not Gaussian (Kolmogorov-Smirnov test).The ratio ()peak/()rms is found to be about 2.2.


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-beating targets/simulations

Estimations from the FQWG (March 2005)

Not re-computed with MAD but initial targets re-scaled.

Re-computed with MAD Not re-computed with MAD, identical targets.


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Conclusions and issues (1)

Good agreement between the targets/analytical estimates and the results obtained from a model based on actual magnetic errors and slot allocation. Checks are going on for the case of stand alone magnets.

At injection the static -beating budget will be respected however: The error on the b2 knowledge due to the magnetic history

dependence is assumed to be at level of 10 units (r.m.s). The special magnetic measurement program planned in block

4 for 2006 (25 tests)+ modeling have to be carried out.


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Conclusions and issues (2)

Next issue : The knowledge of the transfer function in dynamic state (snap back/squeeze). A dedicated magnetic measurement program with the

appropriate cycles has to be performed.

Additional numerical simulations using the MAD-X model will be carried out to: Investigate the -beating values during snap/back and squeeze. Evaluate the feed-down effects from sextupoles using the information from the

geometry database and cross-check with targets/analytical calculations.

1 / 23 Workshop Chamonix XV 23-27 January 2006, L'Esplanade du Lac, Divonne-les-Bains S. Sanfilippo...

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Transcript of 1 / 23 Workshop Chamonix XV 23-27 January 2006, L'Esplanade du Lac, Divonne-les-Bains S. Sanfilippo...