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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
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.
Workshop Chamonix XV - 23-27 January 2006, L'Esplanade du Lac, Divonne-les-Bains 3 / 23S. Sanfilippo
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.
Workshop Chamonix XV - 23-27 January 2006, L'Esplanade du Lac, Divonne-les-Bains 4 / 23S. Sanfilippo
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
Workshop Chamonix XV - 23-27 January 2006, L'Esplanade du Lac, Divonne-les-Bains 5 / 23S. Sanfilippo
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.
Workshop Chamonix XV - 23-27 January 2006, L'Esplanade du Lac, Divonne-les-Bains 6 / 23S. Sanfilippo
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.
Workshop Chamonix XV - 23-27 January 2006, L'Esplanade du Lac, Divonne-les-Bains 7 / 23S. Sanfilippo
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 .
Workshop Chamonix XV - 23-27 January 2006, L'Esplanade du Lac, Divonne-les-Bains 8 / 23S. Sanfilippo
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
Workshop Chamonix XV - 23-27 January 2006, L'Esplanade du Lac, Divonne-les-Bains 9 / 23S. Sanfilippo
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.
Workshop Chamonix XV - 23-27 January 2006, L'Esplanade du Lac, Divonne-les-Bains 10 / 23S. Sanfilippo
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
Workshop Chamonix XV - 23-27 January 2006, L'Esplanade du Lac, Divonne-les-Bains 11 / 23S. Sanfilippo
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
Workshop Chamonix XV - 23-27 January 2006, L'Esplanade du Lac, Divonne-les-Bains 12 / 23S. Sanfilippo
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).
Workshop Chamonix XV - 23-27 January 2006, L'Esplanade du Lac, Divonne-les-Bains 13 / 23S. Sanfilippo
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.
Workshop Chamonix XV - 23-27 January 2006, L'Esplanade du Lac, Divonne-les-Bains 14 / 23S. Sanfilippo
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
Workshop Chamonix XV - 23-27 January 2006, L'Esplanade du Lac, Divonne-les-Bains 15 / 23S. Sanfilippo
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
Workshop Chamonix XV - 23-27 January 2006, L'Esplanade du Lac, Divonne-les-Bains 16 / 23S. Sanfilippo
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).
Workshop Chamonix XV - 23-27 January 2006, L'Esplanade du Lac, Divonne-les-Bains 17 / 23S. Sanfilippo
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 140 A, min cur 10 A
LHC-Cycle-injection 120 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).
Workshop Chamonix XV - 23-27 January 2006, L'Esplanade du Lac, Divonne-les-Bains 18 / 23S. Sanfilippo
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.
Workshop Chamonix XV - 23-27 January 2006, L'Esplanade du Lac, Divonne-les-Bains 19 / 23S. Sanfilippo
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
Workshop Chamonix XV - 23-27 January 2006, L'Esplanade du Lac, Divonne-les-Bains 20 / 23S. Sanfilippo
-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.
Workshop Chamonix XV - 23-27 January 2006, L'Esplanade du Lac, Divonne-les-Bains 21 / 23S. Sanfilippo
-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.
Workshop Chamonix XV - 23-27 January 2006, L'Esplanade du Lac, Divonne-les-Bains 22 / 23S. Sanfilippo
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.
Workshop Chamonix XV - 23-27 January 2006, L'Esplanade du Lac, Divonne-les-Bains 23 / 23S. Sanfilippo
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.