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EMMA MAGNETS - CONTENTS

The document explores the advanced design and functionality of EMMA magnets focusing on key parameters, combining dipole and quadrupole fields, and the impact of moving magnets during operations. It provides insights into resulting magnet parameters, gradient quality in linear and non-linear steel, and the geometrical configurations of ‘BF’ and ‘BD’ magnets. The content includes future design considerations, including end effects and magnetic interactions, emphasizing the necessity of 3D finite element analysis and prototype measurements.

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EMMA MAGNETS - CONTENTS

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  1. EMMA MAGNETS - CONTENTS • Basic Parameters. • Combining dipole and quadrupole fields. • Moving magnets during operation. • Before and after. • Resulting magnet parameters. • ‘BF’ magnet f.e.a. geometry • ‘BF gradient quality, linear steel; • ‘BF’ gradient quality, non-linear steel; • Resulting ‘BF’ design; • ‘BD’ magnet f.e.a. geometry; • ‘BD’ gradient quality – linear steel; • Half ‘BD’ magnet with mirror plate; • Half ‘BD’ gradient quality on y = 0 axis; • Half ‘BD’ gradient quality on x = 0 axis; • Resulting ‘BD’ design; • Cell layout geometry; • Injection/extraction path; • Significant issues for the future. EMMA Hardware Meeting 1/7/06

  2. BASIC PARAMETERS At ‘reference’ orbit (10 MeV?) EMMA Hardware Meeting 1/7/06

  3. COMBINING DIPOLE & QUAD FIELD • from experience, combining variable dipole and quadrupole field in the same magnet is difficult and expensive; • the series of ‘allowed’ harmonics in dipoles is n = 1, 3, 5, etc; ie dipoles are quadrupoles are ‘chalk and cheese’; • the parameters given above show that the EMMA magnets are substantially quadrupole magnets with low dipole components; SOLUTION: • build the EMMA magnets as pure quadrupoles; • position them off-centre to provide the dipole component; • when the ratio dipole/quadrupole needs to be varied, adjust the quad field and move the magnets radially to retain to correct dipole field. EMMA Hardware Meeting 1/7/06

  4. MOVING MAGNETS DURING OPERATION IS NOT NEW! • In HERA (DESY), e- spin transfer into the longitudinal plane requires a horizontal and vertical bump to be applied after vertical polarisation has been achieved – • horizontal is applied first; • then the vertical bump is applied and magnet positions changed to keep beam inside the vacuum vessel. With thanks to Prof. Des Barber, DESY and U. of Liverpool. – see http://www.lancs.ac.uk/cockcroft-institute/education/Barber_spin_June06.ppt EMMA Hardware Meeting 1/7/06

  5. BEFORE AND AFTER Before vertical bump is applied. After vertical bump is applied. With thanks to Prof. Des Barber, DESY and U. of Liverpool. – see http://www.lancs.ac.uk/cockcroft-institute/education/Barber_spin_June06.ppt EMMA Hardware Meeting 1/7/06

  6. RESULTING MAGNET PARAMETERS EMMA Hardware Meeting 1/7/06

  7. ‘BF’ MAGNET FEA GEOMETRY One eighth cross section used for 2D f.e.a of BF magnet. EMMA Hardware Meeting 1/7/06

  8. ‘BF’ GRADIENT QUALITY (LINEAR STEEL) Expressed as: D(dBy/dx (x,0))/By/dx (0,0); Gradient: 10.1 T./m at J = 3.2 A/mm2; Gradient quality: + 0.25% at x = 34 mm; -0.35% at x = 39 mm; Max induction in pole root: 1.24 T. EMMA Hardware Meeting 1/7/06

  9. ‘BF’ GRADIENT QUALITY (NON-LINEAR STEEL) Identical quality to linear steel case. Gradient: 9.96 T; Hence, amplitude linearity: 98.6 %. EMMA Hardware Meeting 1/7/06

  10. RESULTING ‘BF’DESIGN EMMA Hardware Meeting 1/7/06

  11. ‘BD’ MAGNET FEA GEOMETRY One eighth cross section used for 2D f.e.a of BD magnet; half-magnet geometry and mirror plate ignored (for the moment). EMMA Hardware Meeting 1/7/06

  12. ‘BD’ GRADIENT QUALITY (LINEAR STEEL) Expressed as: D(dBy/dx (x,0))/By/dx (0,0); Gradient: 6.19 T/m at J = 3.2 A/mm2; Gradient quality: + 0.04% at x = 45 mm; -0.28% at x = 59 mm; Max induction in pole root: < 1.0 T. EMMA Hardware Meeting 1/7/06

  13. HALF ‘BD’ MAGNET WITH MIRROR PLATE EMMA Hardware Meeting 1/7/06

  14. HALF ‘BD’ GRADIENT QUALITY (LINEAR STEEL) on y = 0 axis Expressed as: D(By/dx (x,0))/By/dx (0,0);between x = 5 and x = 60; (steel at x = 0 gives singularity in dBy/dx); Gradient quality: + 0.1% at x = 55 mm; - 0.25% at x = 59 mm. EMMA Hardware Meeting 1/7/06

  15. HALF ‘BD’ GRADIENT QUALITY (LINEAR STEEL) on x = 0 axis Expressed as: D(Bx/dy (0,y))/Bx/dy (0,0); between y = 0 and y = 30; Gradient quality: + 0.03% at y = 30 mm; EMMA Hardware Meeting 1/7/06

  16. RESULTING ‘BD’ DESIGN EMMA Hardware Meeting 1/7/06

  17. CELL LAYOUT GEOMETRY NOTE MAGNET PROXIMITY EMMA Hardware Meeting 1/7/06

  18. INJECTION/EXTRACTION PATH Note injection line cutting through mirror plate on median plane EMMA Hardware Meeting 1/7/06

  19. SIGNIFICANT ISSUES FOR THE FUTURE • The magnets are so thin that end effects will dominate and there will be no uniform central field. • Magnets are so close that magnetic interaction will be inevitable. • 3D f.e.a. work will be necessary but insufficient. • Prototypes will need to be built and measured! EMMA Hardware Meeting 1/7/06

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