1. Practical aspects of small aperture quadrupoles Dr Ben Leigh Tesla Engineering Ltd

2. Content Overview of magnet design choices Critical yoke and pole dimensions Tolerances and issues with tolerances Problems specific to laminated yokes Solutions Measurement BeMa20142

3. Practical design decisions Solid or laminated yoke Air or water cooled coils Number of yoke segments Accuracy and location of pole profile Fitting of coils and assembly of yoke Physical measurements BeMa20143

4. Example - PSI QFD Quadrupole > 100 magnets built and shipped 20T/m gradient 22mm aperture 150mm long yoke 10A air cooled coils Additional steering function BeMa20144

5. Complete magnet BeMa20145

6. CAD model BeMa20146

7. Assembly drawing BeMa20147

8. Critical yoke region Pole tip shape derived from required field Actual field dictated by the real pole tip Geometry here must be controlled tightly Effect of errors scale with aperture Smaller aperture means tighter absolute physical control required BeMa20148

9. Yoke scheme determination Freedom to choose yoke shape within constraints Sufficient iron to carry return flux Space to accommodate the coils Provision for mounting to the beamline (girder) BeMa20149

10. Yoke segmentation 1 piece yoke – best mechanical stability and control, but impossible to fit coils around poles! Also impossible to fit the magnet around the beam pipe! BeMa201410

11. Yoke segmentation 2 piece yoke – good stability and control, but awkward coil fitting since coils must pass between the poles Limits coil size, or dictates multipart coils BeMa201411

12. Coil fitting complexity BeMa201412

13. Yoke segmentation 4 piece yoke – least good stability and control, but easy to fit coils Most common design for quadrupole magnets BeMa201413

14. Yoke quadrant BeMa201414

15. Lamination detail BeMa201415

16. Pole tip detail BeMa201416

17. Pole profile tolerance BeMa201417

18. Implications for mating surfaces BeMa201418 0.020mm 0.014mm 1:4  0.014/4 = 0.004mm

19. Laminated yoke Real laminated yokes contain many laminations Further complexity to maintain tolerances along the magnet length Choice of constraint important BeMa201419

20. Solution for ultimate accuracy Mechanical fixation of poles Machining after assembly [LAC quad 7mm aperture] Adjustment after assembly [DLS quad] BeMa201420

21. Symmetry measurement Inscribed radius by bore gauge (4-point custom) Alternatively by go-nogo gauge Symmetry by pole gaps – small flat surfaces enable accurate measurement (can’t measure between corners) Note – issues with measurement along the length of the magnet BeMa201421

22. Profile measurement How to measure and verify the pole profile? CMM measures points on surfaces  either need lots of points or else accept approximation Particularly relevant to mating surfaces BeMa201422

23. Measurement for mating surfaces BeMa201423

24. Lamination punching BeMa201424

25. Laminated surface measurement Bore or surface established high points CMM (two point) can establish erroneous surface Actual assembly position can be influenced by lamination edge profile BeMa201425

26. Laminated surface measurement Bore or surface established high points CMM (two point) can establish erroneous surface Actual assembly position can be influenced by lamination edge profile BeMa201426

27. Measurement mitigation Rely on magnetic field measurements for acceptance – Field mapping – Rotating coil measurement – Stretched wire measurement etc Mechanical measurements as a guide only BeMa201427

28. Summary Many factors affect the accuracy of the physical shape of the yoke Practically, tolerances of 0.020mm in pole profile and location are very difficult to achieve For ultimate accuracy, pole profiles can be machined after assembly Magnetic field quality should be used as the primary measure of magnet performance, not mechanical measurements BeMa201428

29. Thank you for your attention Dr Ben Leigh Tesla Engineering Ltd