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PS magnetic & optical model: Preliminary results, status & plans

PS magnetic & optical model: Preliminary results, status & plans. A . Huschauer, M. Juchno, D. Schoerling, R. Wasef October 3 , 2012. Thanks to all people involved in the continuous improvement of the PS machine for many discussions . Overview.

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PS magnetic & optical model: Preliminary results, status & plans

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  1. PS magnetic & optical model: Preliminary results, status & plans A. Huschauer, M. Juchno, D. Schoerling, R. Wasef October3, 2012 Thanks to all people involved in the continuous improvement of the PS machine for many discussions

  2. Overview Study of the field distribution in the PS main magnets • Introduction • 2D structural analysis (ANSYS) • 2D magnetic including Gaussian distribution of the position of the coils and the shape of the iron with up to 22 DOFs per magnet (OPERA) • 3D magnetic study (OPERA) • Permeability of welds in vacuum chambers • BH curve optimization in Opera Implementation in the optical model of PS • Including errors in MAD lattice • Verification and calibration of the magnetic model • Optical model enhancements A B

  3. PART A Study of the field distribution in the PS main magnets • Introduction • 2D structural analysis (ANSYS) • 2D magnetic including Gaussian distribution of the position of the coils and the shape of the iron with up to 22 DOFs per magnet (OPERA) • 3D magnetic study (OPERA) • Permeability of welds in vacuum chambers • BH curve optimization in Opera Implementation in the optical model of PS • Including errors in MAD lattice • Verification and calibration of the magnetic model • Optical model enhancements A B

  4. A. I. PS mainmagnets Dipole: B1 Quadrupole: B2 Sextupole: B3 y + + … = + x z y=  r 2xy=  r2 3x2y - y3 =  r3 Taylor decomposition of field (26 GeV/c) • Normal field components (B1, B2, B3,…) are normal on xz-plane • Skew components (A1, A2, A3, …) are normal on yz-plane • 5+1 independent currents allow for many different settings of multipoles • Due to symmetry constraints no skew components allowed in perfect PS main magnets Main coils W + N PFW Figure-of-eight

  5. A. I. PS mainmagnets • Open and closed block of the main magnet units + different current modes (effects PFW + F8) • 5+1 independent currents available to control the field components and therewith the beam properties (underactuated system): • Momentum p • Tune Qx, Qy • Linear chromaticity x, y • Non-linear chromaticity Qx’’, Qy’’ Open Closed Closed Open Closed Open Open Closed Open Closed TE-MSC-MNC

  6. A. I. PS mainmagnets DipoleContribution ΔB [T/A] Defocusing Focusing • Fits from simulation exist for multipoles up to octupole • Influence of currents on field components varies strongly with position and has to be taken therefore into account • Is the pick-up system center aligned with the magnet model’s center? See also A. Huschauer, 2012 x x QuadrupoleContribution ΔG [Tm-1/A] x x TE-MSC-MNC

  7. A. I. Motivation ofmagneticstudy Working point control Skew sextupole components Calculated 5-current modematrixgivesgoodpredictionsformachinetunes but needspolishingfor linear andsecondorderchromaticities. Oneofthemajorproblemsturned out tobethesmallvalidityofthematrix, moremeasurementsareeitherchallenging due to beam instabilityor time consuming, a precisemagneticmodelisrequired. Skewsextupolar component Losses New reference working point with PFWs (constant beam intensity) A. Huschauer, Diplomarbeit, Working pointandresonancestudiesatthe CERN Proton Synhrotron, 2012 Identification of resonances A magnetic model with 10-4 precision for the whole machine at all currents including all alignment errors would allow for answering the above questions • Reasons for resonances: • magnet alignment errors • magnet manufacturing errors TE-MSC-MNC

  8. A. II. Structuralanalysis (ANSYS) • 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 measured skew components at low energy UY [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 TE-MSC-MNC

  9. A. III. 2D statisticalanalysis (Opera) • 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 • 26 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 • 26 GeV/c TE-MSC-MNC

  10. A. IV. Magnetic model (3D Opera) • Advanced 3D magnetic model available, so far only static solution performed. • Transient solutions are possible but will require long calculation times (several weeks per model). • All coils are implemented, auxiliary coils are approximated by linear pieces. 1 2 3 4 5 6 7 8 9 10 TE-MSC-MNC

  11. A. IV. Magnetic model • Magnetic model on the ideal beam trajectory (from OPERA calculation) • Variants of the PS magnet representation in the ring lattice: Drift space (DRIFT) Defocusing Half-unit (SBEND) Focusing Half-unit (SBEND) Drift space (DRIFT) Pure MAD-X (8 elements) MAD-X+PTC (4 elements) Defocusing higher order (B4,…) components (MULTIPOLE) Defocusing higher order (B4,…) components (MULTIPOLE) Drift space (DRIFT) Defocusing Half-unit (SBEND) Focusing Half-unit (SBEND) Drift space (DRIFT) • Constraints • Using only field integrals from magnetic simulations does not give useful results yet • Prediction of tune & chromaticity variation with respect to the reference working point gives much better results • Adjustment of 4 parameters (2 x gradient length, 2 x sextupolar integral) is required to meet measured tune/chromaticity of the reference working point • Future calibration and validation with beam-based + magnetic measurements (array of fluxmetersin the referencemagnet) Defocusing higher order (B4,…) components (PTC MULTIPOLE) Defocusing higher order (B4,…) components (PTC MULTIPOLE) TE-MSC-MNC

  12. A. IV. Magnetic model Reference working point Conclusion: Excellent prediction around p/p = 0 • Model is tuned relative to measured tune and linear chromaticity because 3D model does not capture all higher order multipoles • Magnetic center has to be investigated Multipoles up to decapoles are included in the simulation and p/p =  0.05 TE-MSC-MNC

  13. A. IV. Magneticmodel • Target working point • Qx’’ = 0, all other parameters unchanged: 5CM matrix with Qy’’ as free parameter used • Achieved working point • (difference to targeted WP) Conclusion: Relative good prediction around p/p  0 TE-MSC-MNC

  14. A. IV. Magneticmodel • Target working point: • Qy’’ = 0, all other parameters unchanged: 5CM matrix with Qx’’ as free parameter used • Achieved working point (difference to targeted WP) Conclusion: Relative good prediction around p/p  0, poor prediction of chromaticities TE-MSC-MNC

  15. A. IV. Magneticmodel • Target working point: • Qx= 6.2, Qy = 6.3, all other parameters unchanged: 5CM matrix with Qy’’ as free parameter used • Achieved working point (difference to targeted WP) Smaller difference between FN & FW and DN & DW Poor prediction TE-MSC-MNC

  16. A. IV. Magneticmodel • Target working point • y = -0.03, all other parameters unchanged: 5CM matrix with Qx’’ as free parameter used • Achieved working point (difference to targeted WP) Conclusion: Good prediction in vicinity of p/p = 0 TE-MSC-MNC

  17. A. V. Permeabilitymeasurement • 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 Limitations Usually the sample thickness has to be at least some centimetres to perform precise measurements. However, these measurements tell us already that the permeability of the spare PS vacuum chamber is very small and therefore, the influence on the magnetic field will be also small. Introducedwelding seams (in red) TE-MSC-MNC

  18. A. VI. BH curve optimization in Opera • Up to now measured BH curve diluted with packing factor λ=0.925 for simulation • Optimization of BH curve by using reverse engineering: • Input: F and D field measurement of cycle C (‘92 campaign) with constraints on errors : 10-4 T and 80  10-4 T/m • Wlodarski’smaterial model of BH curve (4 independent parameters): • Output: Gives two different BH curves for F and D magnets • Dilution with packing factor λ=0.925 • One single BH curve with two different packing factors, might be more physical • Improvement of B1 accuracy for all cases with optimized BH curve • Significant improvement of B2 only for cycle C as measured in ‘92 TE-MSC-MNC

  19. Conclusion & Outlook: Part A • Fits for fields of machine are well established. • Precise 2D models of the main magnets exist. • Structural calculations were performed and give similar results like measurements; however, the effect on the skew component from magnetic simulations is smaller as expected from beam based measurements. • Many multipole calculations were performed and results given to BE. • Mechanical errors are investigated by using a statistical approach. The implementation in MAD-X is on-going. The results will be compared with beam based measurements to verify the assumptions taken for the magnetic simulations. After verification 5CM matrices can be calculated for an extended operation range. • Magnetic model exists and implementation in MAD-X seems to be quite successful around p/p = 0. Further studies will be required to extend the validity of the model. • BH curve limited for high field, feed-back from B-train measurements yields good results. TE-MSC-MNC

  20. PART B Study of the field distribution in the PS main magnets • Introduction • 2D structural analysis (ANSYS) • 2D magnetic including Gaussian distribution of the position of the coils and the shape of the iron with up to 22 DOFs per magnet (OPERA) • 3D magnetic study (OPERA) • Permeability of welds in vacuum chambers • BH curve optimization in Opera Implementation in the optical model of PS • Including errors in MAD lattice • Verification and calibration of the magnetic model • Optical model enhancements A B

  21. B. I. Including errors in MAD lattice • Magnetic & alignment 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 • Main magnetic errors have been implemented in MAD and alignment errors will be implemented soon • For each half unit one set of multipolar field errors is created, i.e., 400 numbers per multipolar field error have to be generated TE-MSC-MNC

  22. B. II. Verification and calibration • Benchmark between lattice with errors and experimental data: • Loss due to skew sextupole resonance over 25ms (MD 06/08/2012), Ramp Qy= 6.24; Qx= [6.34 : 6.38] • PTC-ORBIT simulation using the lattice with magnetic errors (~12 days run-time) • Resonance Driving Terms measurement: • Still optimizing the measurement conditions (reduce chromaticity, use feedback kicker,…) to reduce the noise • Validate the numerical calculated error distribution TE-MSC-MNC

  23. B. III. Optical model/machineenhancements • In 80’s (or maybe even earlier) there was a compensation scheme using normal and skew sextupoles in the PS (sections 2, 52, 14, 64). • The air-cooled sextupolemagnets (11 x 601,  160 mm; 4 x 602,  240 mm) will be certified. If they are certified, they can be installed in the winter shutdown and used in beginning 2013. • If our current estimation of the magnetic errors is correct, installing these sextupoles in sections 2, 52, 14, 72 and operating with currents less than 5 A (air-cooled, estimated with PTC and a PTC-ORBIT simulation is running). 601 602 TE-MSC-MNC

  24. Conclusion & Outlook: Part B • Implement the alignment errors in the lattice • Continue PTC-Orbit simulations for the tune ramp scanning the skew sextupole resonance, and compare it to MD data.  Verify/improve the error estimation • Check the possibility of installing the skew sextupoles in the ring and the compensation scheme • Continue the Resonance Driving Terms measurements TE-MSC-MNC

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