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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. Juchno July 4th, 2014. Thanks to all people involved in the continuous improvement of the PS machine for many discussions. Introduction. Proton synchrotron: >50 years of operation and no end in sight!

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

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  1. The status of the magnetic model of the CERN PS.A snapshot! D. Schoerling, M. Juchno July4th, 2014 Thanks to all people involved in the continuous improvement of the PS machine for many discussions

  2. Introduction • 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

  3. CERN Proton Synchrotron • 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

  4. CERN Proton Synchrotron • 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

  5. PS main magnetic unit • Saturation of iron magnetization • Complex geometry of coils system Combined-function magnet with hyperbolic pole shape (4 types)

  6. Coil system Narrow circuit B I8L B Wide circuit 7 November, 2013 Mariusz Juchno – Magnetic Model of the CERN Proton Synchrotron

  7. Coil system contributions • Main coil and figure-of eight loop • Hyperbolic pole shape • Only dipolar and quadrupolar field at low field level • Iron saturation • Sextupolar and higher order components at high field level • Pole-face windings • 3-Current Mode • 5-Current Mode I8L I8L IFN=IFW IFN IDW IFW IDN=IDW IDN • Un-balanced N and W circuit current generated octupolar and higher components • Working point non-linearities! • Non-linearities at high field (iron saturation) • Conductors configuration designed to produce only up to sextupolar component • Affects tune and linear chromaticity • Non-linearities at high field (iron saturation)

  8. Effect on the yoke magnetization Main coil Figure-of-eight loop IMC = 2500 A I8L = -600 A 0.16 T 0.0 T 1.45 T 1.45 T 0.0 T 0.0 T Focusing Narrow PFW IFW = 100 A Focusing Wide PFW IFN = 100 A 0.016 T 0.041 T 0.0 T 0.0 T

  9. Numerical analysis • Currents set for 2D analysis • Currents set for 3D analysis • 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

  10. Field decomposition & circuit efficiency • 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 g Bgap

  11. Efficiency functions • Main Coil Main coil circuit Auxiliary circuits • Figure-of-eight loop • Focusing Narrow Pole-face windings affecting their own function magnitude • Focusing Wide Shift in the current space due to figure-of-eight loop contribution • Focusing Narrow • Focusing Wide

  12. Validation of the model formulas • B-train system • Peaking strips (“Marker) • Search coils • History dependent effects in the machine • Quasi-static analysis • Virgin magnetization curve • Equivalent packing factor scaling (laminations, block gaps) • No history dependenteffects • Pre-excitation during measurements

  13. “Recent” magnetic measurements Asklöv, A.Magnetic measurement on the CERN proton synchrotron, Master’s Thesis, LITHIFM- EX-05/1463-SE, Linköpingsuniversitet, Linköping, 2005. B. Kuiper & G. Plass, Measurementson the prototype magnet unit, PS/Int MM 59-5, Geneve 1959 Cornuet D. and SharifullinZ.Magnetic measurements on the PS magnet unit 17 with Hall probes, Technical Report AT-MA Note 92-93, CERN, Geneva, 1992 • 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!

  14. Validation of the model formulas • Current configurations • Model validation (2D) • Measurement errors

  15. Analysis of effective magnetic length and field integral corrections • Integration regions • Magnet ends • Junction • Block gaps Multipolar field distribution along the beam trajectory

  16. Effective magnetic length corrections • 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 Bending length correction Gradient length correction Beam based

  17. Effective field integral corrections • Sextupolar correction Beam based • Sextupolar correction • Higher field region – significant 3D effects • Beam based adjustment required • Octupolar correction • Low field region – linear bare machine working point • High field region – significant 3D effects • F and D not cancelled at high field

  18. Auxiliary coils corrections • 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

  19. Magnet representation in the optical model • “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)

  20. Magnet representation in the optical model • 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 adjustmentof the reference working point • Only quadrupolar and sextupolar component • Unused elements were remove • Two equivalent models tested (MADX and MADX+PTC)

  21. Non-linear chromaticity analysis 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

  22. Nonlinear chromaticity (3.5 GeV/c) • FN • DN ΔQ Magnetic center offset? • 8L • FW • DW Δξ Feed-down Constant magnetic lengths

  23. Nonlinear chromaticity (14 GeV/c) • DN • FN Over-/under estimatedtune offset -> sensitivity to radial position • DW • 8L • FW

  24. 14 GeV/c Transfer Matrices • Reproduced with the model • Mcj = Δc/ΔIj • c = Qx, Qy, ξx, ξy • I = FN, DN, FW, DW, 8L • 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

  25. 14 GeV/c Transfer Matrices • Reproduced with the model (dp/p= -1.9x10-3) • Mcj= Δc/ΔIj • c = Qx, Qy, ξx, ξy • I = FN, DN, FW, DW, 8L • Matrix measured in 2008 • 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

  26. Element sensitivity to the beam radial position Quadrupole contribution ΔG [Tm-1/A] • FN and DN tune elements – 3.5GeV/c cycle Focusing 2008 2012 Model Defocusing • 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)

  27. Nonlinear chromaticity (26 GeV/c) • DN • FN Similar observations -3.63±0.14mm offset • DW • 8L • FW

  28. Nonlinear chromaticity (2 GeV) From study on PFW correction during injection [measurement: A. Huschauer] Unbalanced PFW Strong nonlinearities • DN Linear coupling • FN Non-linear chromaticity within 18% No octu-/decapolar correction • DW • 8L • FW

  29. 2 GeV Transfer Matrices • Tune elements • No significant offset • Linear chromaticity elements • Discrepancies for FW and DW elements • Non-linear chromaticity elements • Significant inconsistencies • Matrix measured in 2012 • Matrix calculated with the new model Focusing Defocusing Sextupole Contribution ΔS/I [Tm-2/A]

  30. 2 GeV Linearization • Horizontal Linearization – target:Qx’’ = 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 • Vertical Linearization – target: Qy’’ = 0

  31. 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

  32. Whydoingevenmore? • 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… See H. Damerau et al., TUXA02, IPAC’12, New Orleans

  33. Methodology

  34. Structuralanalysis UY • 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

  35. Vacuumchamberinfluence • PS spare vacuum chambers stored in building 169 • Permeability measurements withDr.FoersterMagnetoscop 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 Introducedwelding seams (in red) • Limitations • Usually thick samples required but permeability is very small and therefore, the influence on the magnetic field is also small.

  36. 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’smodel for measured magnet (limited improvement)

  37. 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

  38. 2D magneto-staticsimulations • 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 2.14 GeV/c Coils can be displaced, no rotation: Main coils (2 x 4 DOFs),  = 3 mm F8 (2 x 4 DOFs),  = 1 mm PFW (2 x 2 DOFs),  = 0.7 mm Iron is displaced in y-direction,  = 0.02/3 mm Reference radius r = 10 mm

  39. 3D magneto-staticsimulations • 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

  40. 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 MADthe main magnets are divided in 4 half units 2D & 2F  400 elements F F D D Half unit Half unit Half unit Half unit • 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

  41. Resonance compensation (R. Wasef) C • In the 80’s several compensation schemes using normal and skew sextupolesin 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

  42. Resonance compensation (A. Huschauer) Scan Direction Compensated resonance 2qx+qy=1 Scan Direction

  43. Resonance compensation (A. Huschauer) Scan Direction Compensated resonance 3qy=1 Scan Direction

  44. 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.

  45. Conclusionandoutlook • 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

  46. Appendix: 14 GeV/c Transfer Matrices • Reproduced with the model • Mcj= Δc/ΔIj • c = Qx, Qy, ξx, ξy • I = FN, DN, FW, DW, 8L • Matrix predictedin 1974 • Corresponding FN and DN tune elements • Both predictions idealized • Chromaticity elements • FW and DW - magnetic lengths

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