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Magnetic Model of the CERN PS Accelerator

Magnetic Model of the CERN PS Accelerator. ECOLE DOCTORALE DOCTORAL SCHOOL PROGRAMME DOCTORAL EN PHYSIQUE DOCTORAL PROGRAM IN PHYSICS. Mariusz Juchno. Miniworkshop on PS Main Magnet field issues. Objectives.

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Magnetic Model of the CERN PS Accelerator

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  1. Magnetic Model of the CERN PS Accelerator ECOLE DOCTORALE DOCTORAL SCHOOL PROGRAMME DOCTORAL EN PHYSIQUE DOCTORAL PROGRAM IN PHYSICS Mariusz Juchno Miniworkshop on PS Main Magnet field issues

  2. Objectives • To develop a model of the magnetic field inside the PS magnets, capable of accurately recreating the magnetic field along the beam trajectory. • Implement and validate the magnetic model inside existing optical model of the PS accelerator. Miniworkshop on PS Main Magnet field issues

  3. Methodology • Investigation of the field development inside the PS magnet • Broad numerical analysis in 2D and 3D • Magnetic measurements • Derivation of quasi-static formulas of the field components. • Implementation of the magnetic model in existing optical model the PS accelerator. • Simulation of the optical parameters with MAD-X model. • Beam-based measurements (tune and chromaticity). • Verification and calibration of the magnetic model. • Optical model enhancements. Miniworkshop on PS Main Magnet field issues

  4. Proton Synchrotron main magnetic unit • Combined-function magnet with hyperbolic pole shape • Dipole field – guiding • Quadrupole field – focusing • Higher component are also present due to saturation • Focusing and defocusing half (alternating-gradient focusing) • 5 C-shaped block in each half • Wedge shaped air gaps between blocks • Complex geometry of coils system • In total 100+1 main units of four different types. Miniworkshop on PS Main Magnet field issues

  5. Coils of the PS magnet • Main coil • Dipole and quadrupole field mostly • Figure-of-eight loop • Adjusts quadrupole field but also contributes to dipole field • Pole-face windings (PFW) • Separately for focusing and defocusing half • Each winding has narrow and wide circuit • Corrects higher components of the field • PFW Powering upgrade • Five currents (If8, IpfwFN, IpfwFW, IpfwDN, IpfwDW) insted of three (If8, IpfwF, IpfwD) • Control of the four beam parameters Qh, Qv, ξh, ξv • One current remains free for controlling an additional physical parameter • Possibility of exploring new working points • Debalancing PFW narrow and wide circuits leads to strong nonlinearities !!! Miniworkshop on PS Main Magnet field issues

  6. Investigating contributions of separate circuits • 2D quasi-static numerical analysis (OPERA) of the magnetic field inside the PS magnet. • Range of operations: • Injection pinj = 2.12 GeV/c • Extraction pextr = 26 GeV/c • Current range: • Main coil Imc = 400-5500 A (ΔImc = 250 & 500 A) • Figure-of-eight loop If8 = ±1200 A (ΔIf8 = 600 A) • Pole-face windings Ipfw = ±200 A (Δ Ipfw = 100 A) Miniworkshop on PS Main Magnet field issues

  7. Contribution of auxiliary circuits Focusing Defocusing Dipole Contribution ΔB [T/A] Quadrupole Contribution ΔG [Tm-1/A] Miniworkshop on PS Main Magnet field issues

  8. Contribution of auxiliary circuits Focusing Defocusing Sextupole Contribution ΔS [Tm-2/A] Octupole Contribution ΔO [Tm-3/A] Miniworkshop on PS Main Magnet field issues

  9. Formulas of the field model • Field multipoles in the Taylor coefficients [T/mn-1] • Main and auxiliary field multipoles • Total multipole component Linear field transfer function Equivalent magnetomotiveforce Miniworkshop on PS Main Magnet field issues

  10. Formulas of the field model • Circuit efficiency function [1/mn-1] • Main circuit efficiency • Circuit saturation Efficiency functions example (dipole component) Miniworkshop on PS Main Magnet field issues

  11. Effective magnetic length corrections • 3D numerical analysis Miniworkshop on PS Main Magnet field issues

  12. Effective magnetic length corrections • 3D numerical analysis Miniworkshop on PS Main Magnet field issues

  13. Effective magnetic length corrections • 3D numerical analysis • Correction components • Magnet ends • Junction • Block gaps • Contain the pole-face angle effect • High variation of the sextupolar distribution • Octupolar component ? Miniworkshop on PS Main Magnet field issues

  14. Effective magnetic length corrections • Bare machine corrections Miniworkshop on PS Main Magnet field issues

  15. Effective magnetic length corrections • Bare machine corrections Miniworkshop on PS Main Magnet field issues

  16. Effective magnetic length corrections • Bare machine corrections • Validation with beam-based measurements • Quadrupolar correction discrepancy (JUNCTION) • Strong sextupolar correction • Radial position dependency! • Auxiliary coils! • Octupolar component? Miniworkshop on PS Main Magnet field issues

  17. Magnet representation in the optical model • Official optics • Static elements length • SBEND • Bare machine 14 GeV/c quadrupolar component • No pole-face angle • MULTIPOLE • Beam-based fit • JUNCTION=DRIFT • Model optics • Dynamic elements length – effective length correction • SBEND • Up to K2 from the model • Integrated pole-face angle effect • MULTIPOLES • K3 (and higher?) • No JUNCTION element • Beam-based matched effective lengths corrections? Defocusing Half-unit (SBEND) Focusing Half-unit (SBEND) Drift space (DRIFT) Drift space (DRIFT) Defocusing higher order components (MULTIPOLE) Defocusing higher order components (MULTIPOLE) Junction (SBEND) Defocusing Half-unit (SBEND) Focusing Half-unit (SBEND) Drift space (DRIFT) Drift space (DRIFT) Defocusing higher order components (MULTIPOLE) Defocusing higher order components (MULTIPOLE) Miniworkshop on PS Main Magnet field issues

  18. Flowchart: corrections for the basic case Field control loop Magnetic model +Optimisation Btr(Imc,Iaux)= (1.091 BF+0.909 BD)/2 Iaux ΔIaux=0 Btr Required Imc Magnetic model K0, K1, K2, K3 for T, U, R and S magnets Measured Q and ξ for ΔIaux=0 and Δp/p=0 MAD-X +MATCHING Effective length correction for K1 and K2 Miniworkshop on PS Main Magnet field issues

  19. Flowchart: chromaticity analysis for ΔIaux Field control loop Magnetic model +Optimisation Btr(Imc,Iaux)= (1.091 BF+0.909 BD)/2 Iaux ΔIaux Btr Required Imc Magnetic model K0, K1, K2, K3 for ΔIaux Δp/p, corrections for ΔIaux=0 MAD-X (PTC) Q and ξ as function of Δp/p, Imc and Iaux+ΔIaux Miniworkshop on PS Main Magnet field issues

  20. Nonlinear chromaticity (14 GeV) • Narrow focusing PFW variation • Narrow defocusing PFW variation ΔIaux=5A ΔIaux=5A • Figure-of-eight variation • Wide focusing PFW variation • Wide defocusing PFW variation ΔIaux=50A ΔIaux=5A ΔIaux=5A If8=543.3A If=43.5A Id=-52.56A Measurement data: matrix measurement campaing Miniworkshop on PS Main Magnet field issues

  21. 14 GeV Transfer Matrices • Reproduced with the model • Predicted in 1974 • Reproduced with the modelfor dp/p= -0.002 • Measured matrix • In the model MRP=0for dp/p=0 BUT in reality MRP≠0 for dp/p=0 Miniworkshop on PS Main Magnet field issues

  22. Nonlinear chromaticity (2 GeV) • Narrow focusing PFW variation • Narrow defocusing PFW variation ΔIaux=2A ΔIaux=2A • Figure-of-eight variation • Wide focusing PFW variation • Wide defocusing PFW variation ΔIaux=5A ΔIaux=2A ΔIaux=2A If8=-0.018 A Ifn=-0.015A Ifw=-14.545A Idn=-4.669A Idw=-8.235A Measurement data: A. Huschauer Miniworkshop on PS Main Magnet field issues

  23. Nonlinear chromaticity (3.5 GeV) • Narrow focusing PFW variation • Narrow defocusing PFW variation ΔIaux=1.5A ΔIaux=2A • Figure-of-eight variation • Wide focusing PFW variation • Wide defocusing PFW variation ΔIaux=7A ΔIaux=2A ΔIaux=2A Iaux=0A Measurement data: matrix measurement campaing Miniworkshop on PS Main Magnet field issues

  24. Nonlinear chromaticity (26 GeV) • Narrow focusing PFW variation • Narrow defocusing PFW variation ΔIaux=20A ΔIaux=15A • Figure-of-eight variation • Wide focusing PFW variation • Wide defocusing PFW variation ΔIaux=20A ΔIaux=20A ΔIaux=140A If8=1370.8A If=205.1A Id=80.4A Measurement data: matrix measurement campaing Miniworkshop on PS Main Magnet field issues

  25. What next? • Further validation with the beam-based measurements • Real-time magnetic measurements with a prototype coil • Effective length corrections • Understanding discrepancies • Investigating radial position dependency • Implementing auxiliary coils dependency • Detailed nonlinear chromaticity analysis • Consolidation with the up to date (official) optics model Miniworkshop on PS Main Magnet field issues

  26. Possible error sources • Random errors • Manufacturing tolerances • Numerical estimation by introducing random displacements within manufacturing tolerances (Monte-Carlo) • Coils position • Pole shape • Blocks alignement • Systematic errors • Magnetic field related displacement • Poles atractiontion • (Th. Zickler, Deformation Measurements on the PS Main Magnets) • Lorentz forces (coils, eddy currents) • Main coil terminals Miniworkshop on PS Main Magnet field issues

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