1. EMMA Magnet Design Ben Shepherd Magnetics and Radiation Sources Group ASTeC STFC Daresbury Laboratory

2. EMMA Magnet Design – Ben ShepherdFFAG 2007 - Grenoble, April 12-17 2007 Overview Introduction – the EMMA lattice EMMA magnets – ‘interesting’ aspects 3D modelling Current status Next steps

3. EMMA Magnet Design – Ben ShepherdFFAG 2007 - Grenoble, April 12-17 2007 ERLP and EMMA EMMA will be an FFAG addon to the Energy Recovery Linac Prototype (ERLP) project at Daresbury EMMA: 10MeV  20MeV ERLP is in the early stages of commissioning – the photoinjector gun is being commissioned and the booster linac is about to be installed Ready by the end of 2007…?

4. EMMA Magnet Design – Ben ShepherdFFAG 2007 - Grenoble, April 12-17 2007 The EMMA Ring 21 cells, each has: 2x D magnet 2x F magnet  84 magnets in main ring + injection + extraction 6m

5. EMMA Magnet Design – Ben ShepherdFFAG 2007 - Grenoble, April 12-17 2007 EMMA Cell Layout F D D Cavity 15 MeV Reference orbit centreline Clockwise Beam Inside of ring Outside of ring Magnet Reference Offsets D = 34.048 mm F = 7.514 mm Geometry consisting of 42 identical(ish) straight line segments of length 394.481 mm Long drift210.000 mm F Quad58.782 mm Short drift50.000 mm D Quad75.699 mm Magnet Yoke Lengths D = 65 mm F = 55 mm Circumference = 16.568m

6. EMMA Magnet Design – Ben ShepherdFFAG 2007 - Grenoble, April 12-17 2007 Magnet Challenges ‘Combined function’ magnets Dipole and quadrupole fields Independent field and gradient adjustment Movable off-centre quads used Very thin magnets Yoke length of same order as inscribed radius ‘End effects’ dominate the field distribution Full 3D modelling required from the outset Large aperture + offset Good field region (0.1%) must be very wide Close to other components Field leakage into long straight should be minimised Close to each other Extremely small gap between magnets F & D fields interact  Full 3D modelling and prototyping essential!

7. EMMA Magnet Design – Ben ShepherdFFAG 2007 - Grenoble, April 12-17 2007 F magnet D magnet http://www.cst.com/ Modelling carried out using CST EM Studio Combined model with ‘realistic’ steel – B-H curve provided by Tesla also produce Microwave Studio

8. EMMA Magnet Design – Ben ShepherdFFAG 2007 - Grenoble, April 12-17 2007 F Magnet

9. EMMA Magnet Design – Ben ShepherdFFAG 2007 - Grenoble, April 12-17 2007 D Magnet Smaller horizontal aperture – but further out – so more challenging!

10. EMMA Magnet Design – Ben ShepherdFFAG 2007 - Grenoble, April 12-17 2007 Reduction of gradient with yoke length (F) 2D model gradient only reached by extending the magnet longitudinally by a factor of 3. However, end effects are dominant, and the integrated gradient is larger than in the hard-edge model.

11. EMMA Magnet Design – Ben ShepherdFFAG 2007 - Grenoble, April 12-17 2007 Field Clamps Tracking studies suggest that field clamps are needed Reduce the amount of field leaking into the long straight Symmetric or asymmetric? Occupy space and increase power demand

12. EMMA Magnet Design – Ben ShepherdFFAG 2007 - Grenoble, April 12-17 2007 Field Clamps F magnet D magnet Field at clamp reduced by ~80% in each case Difference between asymmetric and symmetric windows is negligible

13. EMMA Magnet Design – Ben ShepherdFFAG 2007 - Grenoble, April 12-17 2007 — QBD — QBF — added — combined max difference ~0.25T/m (5%) Plot of absolute x gradient Differences between separate and combined models F D

14. EMMA Magnet Design – Ben ShepherdFFAG 2007 - Grenoble, April 12-17 2007 Shape Optimisation Two variables tangent point chamfer size Optimise in terms of normalised integrated gradient quality integrate vertical field along z differentiate w.r.t x normalise to value at centre of vac chamber 0.1% region 

15. EMMA Magnet Design – Ben ShepherdFFAG 2007 - Grenoble, April 12-17 2007 Tangent point variation QBD – tangent point 10mm tangent point 48mm hyperbolic region tangent region pole profile inscribed radius

16. EMMA Magnet Design – Ben ShepherdFFAG 2007 - Grenoble, April 12-17 2007 No chamfer 10mm chamfer size of chamfer Variation of chamfer on pole ends Angle can be adjusted too – 45° used up to now OPERA-3D results suggest that a chamfer of up to 5mm has negligible effect on field quality

17. EMMA Magnet Design – Ben ShepherdFFAG 2007 - Grenoble, April 12-17 2007 Magnet Apertures F magnetD magnet Beam stay clear apertures highlighted F: -28.2…13.8mm (42 mm) D: -41.6…-17.3mm (24.3 mm)

18. EMMA Magnet Design – Ben ShepherdFFAG 2007 - Grenoble, April 12-17 2007 2D Modelling of F Magnet Using OPERA 2D (Neil Marks): 0.02% over required good gradient region

19. EMMA Magnet Design – Ben ShepherdFFAG 2007 - Grenoble, April 12-17 2007 3D Modelling In OPERA 3D (Takeichiro Yokoi)

20. EMMA Magnet Design – Ben ShepherdFFAG 2007 - Grenoble, April 12-17 2007 Tangent point variation 11mm pole shape gradient quality +5% -5%

21. EMMA Magnet Design – Ben ShepherdFFAG 2007 - Grenoble, April 12-17 2007 Tangent point variation 14mm pole shape gradient quality +5% -5%

22. EMMA Magnet Design – Ben ShepherdFFAG 2007 - Grenoble, April 12-17 2007 Tangent point variation 15mm pole shape gradient quality +5% -5%

23. EMMA Magnet Design – Ben ShepherdFFAG 2007 - Grenoble, April 12-17 2007 Tangent point variation 16mm pole shape gradient quality +5% -5%

24. EMMA Magnet Design – Ben ShepherdFFAG 2007 - Grenoble, April 12-17 2007 Tangent point variation 20mm pole shape gradient quality +5% -5%

25. EMMA Magnet Design – Ben ShepherdFFAG 2007 - Grenoble, April 12-17 2007 Tangent point variation 28mm pole shape gradient quality +5% -5%

26. EMMA Magnet Design – Ben ShepherdFFAG 2007 - Grenoble, April 12-17 2007 Optimal result (OPERA-3D) Tangent point at 11mm Good field region: ±26mm

27. EMMA Magnet Design – Ben ShepherdFFAG 2007 - Grenoble, April 12-17 2007 3D Field Effects Transverse gradient strength changes as the integration region is expanded ‘End effects’ are dominant over full range z

28. EMMA Magnet Design – Ben ShepherdFFAG 2007 - Grenoble, April 12-17 2007 Pole Shape - Alternatives Optimisation done so far in terms of ‘hyperbolic section’ and ‘tangent section’ ‘End effects’ mean that the field profile is different to a long magnet Maybe try a slightly different pole shape? Difficult to set parameters for a ‘free’ curve Quadratic section? Polynomial approximation of hyperbola? Try to guess optimal shape from ‘constant integrated gradient’ contours What tweaks to the pole shape are required to make the gradient more uniform?

29. EMMA Magnet Design – Ben ShepherdFFAG 2007 - Grenoble, April 12-17 2007 Future Work Complete yoke shape optimisation Include field clamp plates Model both magnets together Finalise current-turns in combined model Build and test prototypes Requests for quotes were sent out last week Comparison of codes CST & OPERA results must agree Interface: magnet codes  tracking codes

30. EMMA Magnet Design – Ben ShepherdFFAG 2007 - Grenoble, April 12-17 2007 Conclusions EMMA Magnets: design is “nearly finished” Good gradient region should be improved Pole shapes could be tweaked further Prototypes are in the process of being ordered Tests from these will validate 3D codes Acknowledgements: Takeichiro Yokoi Neil Marks Neil Bliss