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Abstract

Abstract. Calculations of Harmonics of Quadrupole Magnets  Rybitskaya Tatyana, Budker Institute of Nuclear Physics, Russia

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Abstract

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  1. Abstract • Calculations of Harmonics of Quadrupole Magnets •  Rybitskaya Tatyana, Budker Institute of Nuclear Physics, Russia • Design of pole profile and chamfers of NSLSII quadrupole magnets manufactured at BINP are presented. Calculations of dependence skew-sextupole harmonic of current are shown. Way for correction the dependence is described. Calculations of harmonics correction by bronze bars, nose pieces and modified nose pieces are presented.

  2. Calculations of harmonics of quadrupole magnets Budker Institute of Nuclear Physics Rybitskaya Tatyana

  3. Plan of presentation Calculations of: • Allowed harmonics • Dependence of skew-sextupole harmonic of current • Harmonics correction by bronze bars • Harmonics correction by nose pieces • Nose pieces with modified profile

  4. Software used for calculations • MERMAID • Mermaid applies first order Finite Elements Method on the mesh consisted of triangle prisms for field computation. Created at Budker Institute of Nuclear physics. • OPERA • A finite element environment for the complete analysis and design of electromagnetic applications in 3 dimensions. Product of company COBHAM

  5. Magnetic field expansion r φ z On radius r0 = 2.5 cm Skew harmonics Normal harmonics

  6. Profile features of magnets calculated chamfer L L magnetic axis 45° • Flat parts of shims (necessary for stacking and gluing magnets with high precision). • Long (9804/9807) and middle (9810/9813) length magnets have nose pieces. • Chamfers are flat 45°. chamfer Pole/ nose piece Flat part

  7. Calculations of allowed harmonics 2D or magnetic field in magnet centre plane Allowed harmonics in magnet center were minimized 3D without chamfer 120 A Yoke edges in 3D provide big b6 3D with chamfer 120 A Chamfers decrease b6 but at the same time increase b10 MERMAID

  8. Shimming of magnet K.Halbach First order perturbation effect in iron-dominated two dimensional symmetric multipoles // NIM vol.74, 1969. β Relative changing of harmonic volume. Bumps along profile has the same area.

  9. Calculations of chamfers of long magnets chamfer H L magnetic axis α α - angle between magnetic axis and chamfer plane nose piece • Nose pieces size: • 15 mm along magnetic axis • 34.45 mm perpendicular magnetic axis • The sizes limit size of chamfer

  10. Calculations of chamfers of long magnets Current 125 A Without chamfer MERMAID

  11. Sextupole harmonics of current • First measurements of sextupole harmonics of first long magnet 9807-0001 measurements a3 current dependence was quite big

  12. Possible reasons of a3 current dependence • Different permeability of halves. Two samples were cut from steel roll – one from beginning, another from middle of roll. Steel properties measured at DESY • Different packing factor of halves. Measurements shown maximum difference 0.25% • Different halves lengths. Measurements shown maximum difference 0.2 mm.

  13. Calculations of a3 current dependence for long magnets Δ=1.1 Δ=1.5 If the worst case variation of a3 can be 2.5 units. MERMAID

  14. Corrections of harmonic a3 dependence of current • The most effective way for correction is special shuffling. • Additional way for correction : Face of nose piece Δ=1.94 Shift need additional correction OPERA

  15. Harmonics correction by bronze bars One bar width is increased Two bars widths are increased simultaneously + ∆l + ∆l - ∆l - ∆l - ∆l/2 - ∆l/2 + ∆l Calculations∆l = 20 µm Widths of two insertions can correct a3 and b4 OPERA

  16. Harmonics correction by nose pieces + ∆l + ∆l + ∆l Calculations∆l = 150µm + ∆l Each nose pieces can be shifted independently. Advantage: In principal many harmonics can be corrected. Disadvantage: Nose pieces should be installed carefully not to reduce field quality. OPERA

  17. Correction of allowed harmonics on ready magnet Nose pieces with modified profile

  18. Calculations of magnetic field of middle length magnets (9810 and 9813) Chamfer 12.8 mm Chamfer 9.6 mm MERMAID

  19. Measurements of magnetic field of magnet 9813-0001 modified profile Chamfer 13mm Chamfer 10mm

  20. Summary • 2D profile was chosen with allowed harmonics less then 0.7 units, as result chamfering increase b10 up to 2.5 units for short magnets. • Material properties can increase a3 dependence of current up to 2.5 units. • Bronze bars provide corrections of a3 and b4. • Nose pieces provide correction of b3 and additional correction of a3 and b4. • Using nose pieces with modified profile make integral fields and fields in the magnet center “good” at the same time.

  21. THE END

  22. Comparison measurements and calculations of long magnets without nose pieces and chamfers

  23. Question • Why calculations and measurements has deviations? • Different magnetic steel properties in program and in reality? • Changes of permeability at the age of plates cause of stamping? • Something else?

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