The status of the magnetic model of the CERN PS. A snapshot!

The status of the magnetic model of the CERN PS.A snapshot!

D. Schoerling, M. JuchnoJuly 4th, 2014

Thanks to all people involved in the continuous improvement of the PS machine for many discussions

Daniel Schoerling TE-MSC-MNC

Introduction

2

• Proton synchrotron: >50 years of operation and no end in sight!

• PS optics model– Field coefficients derived from beam-based measurements– No link between powering currents and WP parameters– Can model but not predict non-linear chromaticity

• Magnetic model (static)– Numerical analysis– Integration with the optics model– Validation with beam-based measurements

• Systematic and random effects


CERN Proton Synchrotron

3

• Built in 1959• Today: key element of the

LHC injector system• Tunnel: 200 m in diameter• Main magnets: 100 (+1)

combined function units– Bending – Focusing

• Compact but complex design– Focusing and defocusing

half-unit powered with the same main coil


CERN Proton Synchrotron

4

• Built in 1959• Today: key element of the

LHC injector system• Tunnel: 200 m in diameter• Main magnets: 100 (+1)

combined function units– Bending – Focusing

• Compact but complex design– Focusing and defocusing

half-unit powered with the same main coil


PS main magnetic unit

5

• Combined-function magnet with hyperbolic pole shape (4 types)

• Saturation of iron magnetization • Complex geometry of coils system


Coil system

6Mariusz Juchno – Magnetic Model of the CERN Proton Synchrotron 7 November, 2013

Narrow circuit

B

B

Wide circuit

I8L


Coil system contributions

7

– 3-Current Mode – 5-Current Mode

IFWIDN

IFNIDW

I8L

IFN=IFW

IDN=IDW

I8L

– Hyperbolic pole shape– Only dipolar and quadrupolar

field at low field level

– Iron saturation– Sextupolar and higher order

components at high field level

• Main coil and figure-of eight loop

• Pole-face windings

– Conductors configuration designed to produce only up to sextupolar component

– Affects tune and linear chromaticity– Non-linearities at high field (iron saturation)

– Un-balanced N and W circuit current generated octupolar and higher components

– Working point non-linearities!– Non-linearities at high field (iron

saturation)


Effect on the yoke magnetization

8

Main coil Figure-of-eight loopIMC = 2500 A I8L = -600 A

Focusing Narrow PFW Focusing Wide PFWIFN = 100 A IFW = 100 A

1.45 T0.0 T 1.45 T0.0 T 0.16 T0.0 T

0.041 T0.0 T 0.016 T0.0 T


Numerical analysis

9

• Quasi-static numerical analysis (OPERA)• Top-down symmetry (only normal field components analysed)• Magnetization curve

– Wlodarski model (extrapolation)

• Packing factor scaling– λ2D = 0.925 – λ3D = 0.9424

Circuit type Current range [A] Current step [A]

Main coil [500, 5500] 250, 500

Figure-of-eight loop [-1200, 1200] 600

Pole-face windings [-200, 200] 100

Circuit type Current values [A]Main coil 1000, 3000, 4500, 5500

Figure-of-eight loop -1200, 0 , 1200

Pole-face windings -200, 0, 200

• Currents set for 2D analysis • Currents set for 3D analysis

Ha

aH

aHL

bHL

bH

MaHLMHM ba

coth

tanh)(

0)1( lnnlnl

Fe

Fe


Field decomposition & circuit efficiency

10

• Decomposition assumptions Main coil contribution not affected by other circuits All auxiliary circuits depend on the main coil and the

figure-of-eight contribution (magnetization of the whole yoke)

Pole-face winding circuits depend on their own contribution (magnetization of the pole tip)

Alteration of MC contribution due to other circuits included in that circuit contribution

• Concept of circuit efficiency

gapcore

gap

gap

RRRg

NIB

0

Bgapg


Efficiency functions

11

aux auxnMCntotn BBB ,,,

MCMCnfMCMCMCn INTINB ,

auxauxnfauxauxauxn IFTInB ,*, gT f 0

2

10 tanh1

21

M

i nom

isnMCMCinnMCMCn NI

NIININ

2

1

*

0* tanh1

2)1(

1,M

i sni

isnauxauxininnauxauxn NI

NIFIIF

MCLLauxMCMCaux NInfINF /88*

LLaux Inf 88LLaux Inf 88

LLaux Inf 88

)1( auxinin I )1( auxinin I Pole-face windingsaffecting their own function magnitude

Shift in the current space due to figure-of-eight loop contribution

Main coil circuit

Auxiliary circuits

Figure-of-eight loop

Main Coil

Focusing Wide

Focusing Wide

Focusing Narrow

Focusing Narrow


Validation of the model formulas

12

Cycle stepMeasuredBtr [10-4 T]

Alone in S.C.Imc [A]

Full S.C.Imc [A]

Estimated|ΔBtr| [10-4 T]

Injection 1013.7 ± 0.03 404.9 ±0.03 404.5 ±0.03 1Extraction 6665.84 ± 0.04 2667.94 ± 0.05 2665.89 ±0.05 5

• Quasi-static analysis Virgin magnetization curve Equivalent packing factor

scaling (laminations, block gaps)

No history dependenteffects

• Pre-excitation during measurements

2909.0091.1 DF

trBBB

• B-train system Peaking strips (“Marker) Search coils

• History dependent effects in the machine

Daniel Schoerling TE-MSC-MNC 13

Cornuet D. and Sharifullin Z.Magnetic measurements on the PS magnet unit 17 with Hall probes, Technical Report AT-MA Note 92-93, CERN, Geneva, 1992

“Recent” magnetic measurements

Asklöv, A.Magnetic measurement on the CERN proton synchrotron, Master’s Thesis, LITHIFM-EX-05/1463-SE, Linköpings universitet, Linköping, 2005.

B. Kuiper & G. Plass, Measurements on the prototype magnet unit, PS/Int MM 59-5, Geneve 1959

• Summary Extensive measurements performed in 1959 including dynamic effects Hall probe measurements performed in 1992 and 2005

• Planned: Rotating coil measurement at DC to check also higher order multipoles• What was done from our side: Comparison with simulations!


Validation of the model formulas

14

Cycle |Bmag. model – Bmeas.|[10-4 T]

|Gmag. model – Gmeas.|[10-4 T/m]

Direct Opt. Direct Opt.E 2 2 17 17A 9 6 76 64B 35 3 120 40C 80 6 320 99

LHC 59 3 220 160

Cycle εB [%]

Berr. [10-4 T]

εG [%]

Gerr. [10-4 T/m]

E ±0.20 ±4 ±0.25 ±17 A ±0.13 ±8 ±0.18 ±49 B ±0.08 ±10 ±0.15 ±71 C ±0.08 ±10 ±0.15 ±78

LHC ±0.05 ±6 ±3 ±157

Cycle p0 [GeV/c] Bavg [T] IMC [A] I8L [A] IFN/FW [A] IDN/DW [A]

E 3.5 0.167 669.2 0.0 0.0 0.0A 14.0 0.667 2677.5 450.4 39.5 -45.1B 24.0 1.149 4732.0 0.0 77.0 88.0C 26.0 1.257 5413.2 1257.9 200.7 99.8

LHC 26.0 1.257 5400.7 1452.8 206.7 86.9

• Current configurations

• Measurement errors• Model validation (2D)


Analysis of effective magnetic length and field integral corrections

• Multipolar field distribution along the beam trajectory

• Integration regions Magnet ends Junction Block gaps

15


Effective magnetic length corrections

16

• Bending length correction Very good agreement Data processing differences

• Gradient length correction Offset – junction correction Processed measurement data – no contribution

of the junction region Beam-based correction

Beam based

Bending length correction

Gradient length correction


Effective field integral corrections

17

• Sextupolar correction Higher field region –

significant 3D effects Beam based

adjustment required

Sextupolar correction

• Octupolar correction Low field region – linear bare machine

working point High field region – significant 3D effects F and D not cancelled at high field

Beam based


Auxiliary coils corrections

18

• Figure-of-eight loop corrections Approximated with the bare machine field corrections

• Pole-face windings corrections Difference in magnetic lengths of F and D circuits

remain close to physical length difference of these circuits (8 mm)

Difference in magnetic lengths of N and W circuits up to 8 cm for octupolar component indicates that even in 3CM contributions of N and W circuits do not cancel one another completely

8L

PFW


Magnet representation in the optical model

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• “Official” optics– Magnetic parameters – beam based measurements– No link between currents and field parameters– Other elements fixed (SBEND) or unused (some

MULTIPOLE elements, junction SBEND element)


Magnet representation in the optical model

20

• Modified optics– Input from new magnetic model– 3D effects correction – numerical

analysis– Link between currents and coefficients– Main coil current value optimized in

the field-control loop manner– Beam-based adjustment of the

reference working point• Only quadrupolar and sextupolar

component– Unused elements were remove– Two equivalent models tested (MADX

and MADX+PTC)


Non-linear chromaticity analysis

21

Initial optimization of the main coil current

Field correction adjustments based on beam measurements

Final optimization of the main coil current

Non-linear chromaticity analysis


Nonlinear chromaticity (3.5 GeV/c)

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FN

FW

DN

DW8L

ΔQ

Δξ

Magnetic center offset?

Feed-down

Constant magnetic lengths


Nonlinear chromaticity (14 GeV/c)

23

FN

FW

DN

DW8L

Over-/under estimatedtune offset -> sensitivity to radial position


14 GeV/c Transfer Matrices

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Δ IFN Δ IFW Δ IDN Δ IDW Δ I8L

Δ Qx 0.0028 0.0046 -0.0031 -0.0027 -0.0012

Δ Qy -0.0013 -0.0032 0.0051 0.0041 0.0012

Δ ξx 0.1122 -0.0115 0.0770 -0.0167 0.0008

Δ ξy -0.0736 0.0077 -0.1060 0.0223 -0.0003

• Matrix measured in 2008• Corresponding FN and DN tune elements Numerical matrix – similar Measured matrix – factor 2

difference Numerical model idealized

• Chromaticity elements Magnetic lengths


Δ Qx 0.0044 0.0045 -0.0022 -0.0028 -0.0013

Δ Qy -0.0021 -0.0028 0.0043 0.0045 0.0013

Δ ξx 0.1412 -0.0382 0.0777 -0.0169 0.0008Δ ξy -0.0919 0.0209 -0.1135 0.0281 0.0002

• Reproduced with the model• Mcj = Δc/ΔIj

c = Qx, Qy, ξx, ξy I = FN, DN, FW, DW, 8L



Δ Qx 0.0028 0.0049 -0.0032 -0.0026 -0.0013

Δ Qy -0.0011 -0.0030 0.0057 0.0041 0.0013

Δ ξx 0.1259 -0.0223 0.0855 -0.0242 0.0006

Δ ξy -0.0813 0.0108 -0.1249 0.0385 0.0003

14 GeV/c Transfer Matrices

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Δ Qx 0.0028 0.0046 -0.0031 -0.0027 -0.0012

Δ Qy -0.0013 -0.0032 0.0051 0.0041 0.0012

Δ ξx 0.1122 -0.0115 0.0770 -0.0167 0.0008

Δ ξy -0.0736 0.0077 -0.1060 0.0223 -0.0003

• Reproduced with the model (dp/p= -1.9x10-3)

• Corresponding FN and DN tune elements Both predictions idealized dp/p= -1.9x10-3 offset Sensitive to radial loop

(-3.67±0.35mm with respect to geometrical center)

• Chromaticity elements FW and DW – sensitive to radial

position Magnetic lengths

• Matrix measured in 2008

• Mcj = Δc/ΔIj c = Qx, Qy, ξx, ξy I = FN, DN, FW, DW, 8L


Element sensitivity to the beam radial position

26

Focusing

Defocusing

Quadrupole contribution ΔG [Tm-1/A]

2008 2012

Model

• Matrix measurement (2008)• Radial loop pickups adjustment (2009)

3.5mm deviation of the radial beam position• Sensitivity measurement (2012)• 2008 elements consistent with 3.5mm offset (RL

2.5mm)• Magnetic model – still 2.5mm offset (RL 1.6mm)

• FN and DN tune elements – 3.5GeV/c cycle


Nonlinear chromaticity (26 GeV/c)

27

FN

FW

DN

DW8L

Similar observations -3.63±0.14mm offset


Nonlinear chromaticity (2 GeV)

28

FN

FW

DN

DW8L

Linear coupling

Unbalanced PFWStrong nonlinearities

From study on PFW correction during injection [measurement: A. Huschauer]

Non-linear chromaticity within 18%No octu-/decapolar correction


Defocusing

2 GeV Transfer Matrices

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Δ Qx 0.0223 0.0231 -0.0115 -0.0145 -0.0064Δ Qy -0.0108 -0.0142 0.0217 0.0228 0.0066Δ ξx 0.7438 -0.2102 0.4209 -0.0879 0.0059Δ ξy -0.4869 0.1169 -0.6026 0.1538 0.0012

Δ Q’’x 110.3123 -167.4144 -47.5570 81.4052 9.4781Δ Q’’y -86.9241 102.1239 92.1193 -95.9876 -3.1709


Δ Qx 0.0219 0.0213 -0.0116 -0.0142 -0.0061Δ Qy -0.0094 -0.0131 0.0230 0.0207 0.0061Δ ξx 0.8569 -0.0890 0.4671 -0.1353 -0.0196Δ ξy -0.4396 0.0380 -0.5422 0.1746 0.0212

Δ Q’’x 207.9130 4.6475 -218.1390 -105.7302 17.2275Δ Q’’y -115.9633 1.9839 36.2483 -9.2980 9.8931

• Matrix calculated with the new model

• Matrix measured in 2012

Sextupole Contribution ΔS/I [Tm-2/A]

Focusing

• Tune elements No significant offset

• Linear chromaticity elements Discrepancies for FW and DW elements

• Non-linear chromaticity elements Significant inconsistencies


2 GeV Linearization

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Initial WP Meas. pred. Model predMeas. Model Meas. Model Meas. Model.

Qx 6.105 6.105 6.102 6.106 6.11 6.105Qy 6.205 6.205 6.207 6.205 6.201 6.205ξx 0.72 0.69 0.67 0.71 0.67 0.72ξy -1.03 -0.98 -0.81 -0.74 -1.55 -1.03

Q’’x 2105 1845 3418 2920 -253 0Q’’y -874 -1007 -1537 -2037 756 1129

• Horizontal Linearization – target: Qx’’ = 0

Initial WP Meas. pred. Model predMeas. Model Meas. Model Meas. Model.

Qx 6.105 6.105 6.111 6.102 6.111 6.105Qy 6.205 6.205 6.199 6.205 6.202 6.205ξx 0.72 0.69 0.74 0.63 0.63 0.72ξy -1.03 -0.98 -2.24 -1.59 -1.22 -1.03

Q’’x 2105 1845 -569 -767 956 1187Q’’y -874 -1007 1206 1487 -240 0

• Vertical Linearization – target: Qy’’ = 0

• Minimization of non-linear chromaticity Measurement matrix prediction

ineffective Numerical matrix prediction

significantly reduces non-linear chromaticity

• Other test cases Linear chromaticity – FW & DW

elements Discrepancies close to 3CM Initial matching validity


Summary Part I

• A detailed magneto-static model for almost all combinations of currents was developed.

• By linking this magnetic model to the optics model it become possible to: Reconstruct the working point transfer matrices for any energy. Predict for the first time in the history of the PS the higher-order chromaticity

function among other working point parameters. Analyze the transfer matrix sensitivity to the radial beam position.

• No means of predicting resonances

Further reading: M. Juchno, Magnetic Model of the CERN Proton Synchrotron, PhD thesis, EPFL, 2013


Why doing even more?

See H. Damerau et al., TUXA02, IPAC’12, New Orleans

• Higher brightness/intensity beams are required for the LHC to achieve its high luminosity objective

Consolidating and upgrading PSB, PS, SPS and using the newly built LINAC4 PS’ injection energy will be increased from 1.4 to 2 GeV to reduce space charged

induced tune shift• Working point control (under good control)

• Resonance compensation scheme required

• Upgrade program for hardware in the PS machine

• Much more activities outside our group…


Methodology


Structural analysis

• The simulation and measurement [1] of the deformation of the magnet are similar

• The magnetic field is used to derive the normal and skew components of the magnetic fields in Taylor series

• The effect on the optics of the machine were calculated with MAD-X and PTC

• The effect of the deformation is especially visible for 26 GeV/c, because F B2

• The mechanical deformations cannot explain the resonances at low energy

[1] M. Buzio, M. Tortrat, Deformation of the PS reference magnet U101 during operation: geometrical survey and impact on B-train magnetic field measurements, April 2010

Qx Qy x y

14 GeV/c, normal components (negligible difference between magnetic and structural) 6.2058 6.3032 0.2023 0.6837

14 GeV/c, normal & skew com. 6.2058 6.3032 0.2022 0.683926 GeV/c, no deformation, only normal components 6.2686 6.2219 0.0381 0.4770

26 GeV/c, with deformation, only normal components 6.2647 6.2179 0.1196 0.396126 GeV/c, with deformation, normal & skew components 6.2647 6.2179 0.1646 0.3506

UY


Vacuum chamber influence

Dipole [T]

Quadrupole [T/m]

Sextupole [T/m2]

Octupole [T/m3]

Permeability Weld 1.0000 1.2364 5.2327 2.7668 -36.3321

Permeability Weld 1.0030 1.2364 5.2327 2.7483 -36.5692

Difference 1.56 10-05 5.67 10-05 0.0185 0.2371

• PS spare vacuum chambers stored in building 169

• Permeability measurements with Dr. Foerster Magnetoscop 1.069

• Pre-measurements have shown that the permeability is very small

• Calibration with a relative permeability of 1.0037

• Largest measured relative permeability was on a long vacuum chamber with around 1.002

Limitations• Usually thick samples required but

permeability is very small and therefore, the influence on the magnetic field is also small.

Introduced welding seams

(in red)


Material uncertainty

• Shuffling was performed Reduction of the spread per yoke Minimization of uncertainties in the

magnetic field• Epstein-frame measurement of

electrical steel 2-5% anisotropy in steel Good correlation to split-coil

measurements• Fit with Wlodarski’s model for

measured magnet (limited improvement)


Geometrical measurement

• Unit 17 was measured with a laser tracker with 19.05 mm offset to the plane• Fitting by rotating and translating the measurement data to nominal surface was

applied (normally offset by 19.05 mm)• Standard deviation from this nominal surface was calculated

D. Schoerling, Analysis of PS main magnet geometrical measurements, Unit 17, EDMS 1336186, 2013


2D magneto-static simulations

• 2D calculation including Gaussian distribution of the position of the coils and the shape of the iron with up to 22 DOFs per magnet (OPERA)

• 1000 models per magnet type and current level have to be calculated (<1 d with advanced and additional licenses, before 10 d)

• Performed for momentum of 2.14 GeV/c, 2.78 GeV/c, 14 GeV/c, 26 GeV/c

Coils can be displaced, no rotation:Main coils (2 x 4 DOFs), = 3 mmF8 (2 x 4 DOFs), = 1 mmPFW (2 x 2 DOFs), = 0.7 mm

Iron is displaced in y-direction, = 0.02/3 mm

2.14 GeV/c

Reference radius r = 10 mm


3D magneto-static simulations

• Time consuming Monte-Carlo study performed.• New features were implemented together with Vectorfields (deforming of

mesh).• Each block was shifted, the pole face and coils were altered to simulate the

effect on the magnetic field


Resonance compensation (R. Wasef)

• Magnetic & alignment ( = 200 m) errors are essential for space charge studies because at low energy (bare machine) they are the main cause of resonance excitation, and cause therefore losses and emittance growth

• PS is implemented in MAD with ideal lattice • In MAD the main magnets are divided in

4 half units 2D & 2F 400 elements

• Magnetic errors (Systematic & Gaussian distribution , ) can be implemented for each element in the lattice up to the normal & skew octupolar component.

• For each half unit one set of multipolar field errors is created, i.e., 400 numbers per multipolar field error have to be generated

F F D DHalf unit Half unit Half unit Half unit


Resonance compensation (R. Wasef)

• In the 80’s several compensation schemes using normal and skew sextupoles in the PS (sections 2, 52, 14, 64) were applied: Y. Baconnier, Tune shifts and stop bands at injection in the CERN proton synchrotron, CERN/PS 87-89 (PSR), 1987

• The air-cooled sextupole magnets have been installed in the winter shutdown in sections 2, 52, 14, 72 (instead of 64)

• A compensation scheme for each of the resonances 2Qx+Qy=19 and 3Qy=19 was implemented, using the new locations and the magnetic field error distribution

• Compensating both resonances requires larger skew sextupole fields, which cannot be generated with the currently installed magnet-power supply installation

601

602

C


Resonance compensation (A. Huschauer)

Scan Direction

Scan Direction

Compensated resonance 2q

x +qy =1


Resonance compensation (A. Huschauer)

Scan Direction

Scan Direction

Compensated resonance 3q

y =1


Summary Part II

• Deforming the magnet due to magnetic forces is a systematic effect that has a large impact on the field distribution at high field and only a negligible influence at low field.

• Estimating the permeability of the beam pipe and calculating the influence on the field distribution, it could be shown that this systematic effect is negligible.

• The influence of anisotropy in the steel of the magnets is negligible. • The random effects were investigated by performing Monte Carlo simulations with 2D

and 3D finite element models. • The 2D simulations showed that skew components can be neglected and the standard

deviation is small. • The 3D simulations showed larger skew components but also a small standard

deviation. Therefore, the field distribution variation from magnet to magnet is expected to be small in PS.

• The presented data will be used to enhance the resonance compensation scheme after re-start of the CERN injector complex and beam-based measurements will be performed.

Further reading: D. Schoerling, Prediction of the field distribution in CERN-PS magnets, TUPRO107, IPAC 2014.


Conclusion and outlook

• Very precise systematic and random model of the PS magnet available!• What is next?

Magnetic measurements with rotating coils More geometrical measurements of magnets to understand better the mechanical errors More 3D simulations (cross-check with other mesh, update with other mechanical errors,

improving the precession by setting the potential manually, etc.) Measurements in the machine.

• What could be in the far-future? Hysteresis effects Eddy current effects including vacuum chamber effects*

*B. Auchmann, Compensation of Eddy-Current Effects in PS Vacuum Chambers by Pole-Face Windings, 2007, EDMS #973216


Appendix: 14 GeV/c Transfer Matrices

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• Reproduced with the model

• Matrix predicted in 1974• Corresponding FN and DN

tune elements Both predictions idealized

• Chromaticity elements FW and DW - magnetic lengths

• Mcj = Δc/ΔIj c = Qx, Qy, ξx, ξy

I = FN, DN, FW, DW, 8L


Δ Qx 0.0044 0.0045 -0.0022 -0.0028 -0.0013

Δ Qy -0.0021 -0.0028 0.0043 0.0045 0.0013

Δ ξx 0.1412 -0.0382 0.0777 -0.0169 0.0008Δ ξy -0.0919 0.0209 -0.1135 0.0281 0.0002


Δ Qx 0.0046 0.0047 -0.0025 -0.0031 -0.0018

Δ Qy -0.0025 -0.0032 0.0046 0.0048 0.0019

Δ ξx 0.1279 -0.0222 0.0744 -0.0144 0.0000

Δ ξy -0.0873 0.0130 -0.1062 0.0219 0.0000

The status of the magnetic model of the CERN PS. A snapshot!

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