1. Magnetic Field Design of a Superconducting Magnet for the FFAG Accelerator T.Obana, T.Ogitsu A,T.Nakamoto A,K.Sasaki A A.Yamamoto A, M.Yoshimoto A, Y.Mori A,T.Orikasa B The Graduate University for Advanced Studies High Energy Accelerator Research Organization A Toshiba Corporation B

2. Contents 1.Background & Purpose 2.2D Coil Design 3.3D Coil Design 4.Tracking 5.Conclusion

3. Contents 1.Background & Purpose 2.2D Coil Design 3.3D Coil Design 4.Tracking 5.Conclusion

4. Why’s SC magnet required? Superconducting magnet is proposed for the FFAG accelerator. Medical applications In some cases, compactness of the accelerator is important. Required magnetic field… - High magnetic field - Static magnetic field

5. 150MeV FFAG accelerator at KEK The purpose of this study is to develop a superconducting magnet for the FFAG accelerator. Purpose

6. Contents 1.Background & Purpose 2.2D Coil Design 3.3D Coil Design 4.Tracking 5.Conclusion

7. How to generate the FFAG Field! Dipole Quadrupole Sextupole FFAG field can be realized with a multipole combination!

8. Current distribution Magnetic forces on the coil are complex and are difficult to support ! Up to n=8 ++ – – X Y + + + – – – X +– Y X Y n=3 n=2 n=1 I=I 0 cos(nθ) Multi-layer coil

9. Current distribution – ＋ X Y Simplify! – ＋ X Y Left-Right asymmetry & Ellipse Downsize! With single layer Left-Right asymmetry ++ – – X Y + + + – – – X + – Y X Y Up to n=8 n=1 n=2 n=3

10. FFAG FFAG for Medical applications Extraction beam Cross-Section Injection beam Excursion Extraction energy~200 MeV Beam currentSeveral 100 μA Major axis of the beam pipe0.8 m Minor axis of the beam pipe0.6 m Geometrical field index, k10 Ro5 m Excursion0.4 m Turn number120 Bo1.0 T Parameters of the FFAG Accelerator

11. Local k value & Field distribution @ 2D Local k is used to evaluate the magnetic field closely. Positions of the conductor can be optimized in 2D! Excursion

12. Contents 1.Background & Purpose 2.2D Coil Design 3.3D Coil Design 4.Tracking 5.Conclusion

13. 3D Design The 3D coil is designed so that the design requirement can be satisfied in terms of integral magnetic field. “Single winding coil” is proposed ! The coil end greatly influences the field distribution, because the ratio of the physical length of the coil end to that of the straight section is large. It is difficult to meet the design requirement locally.

14. Single winding coil @ 3D Design X Z Y Y Z X The odd layer The even layer

15. Single Winding coil @ 3D Design Z X Y 2 layers with 2 coils - The difference of the straight length of the coil in each turn can be minimized when the number of the coil layers is even. The characteristic of the single winding coil

16. Superconducting wire 0.9 mm Superconducting wire Diameter (mm) NbTi 0.9 Cu/NbTi ratio4.0 Parameters

17. Winding Technique Direct Winding technique Superconducting wire can be directly adhered to the base. Reference http://www.bnl.gov/magnets/BioMed/BioMed.asp

18. Local k value at each angle@3D It is difficult to meet the design requirement at each angle! 0.0 5.8° 4°4° 0° 2° X [ m] 0.4 -0.4 o Calculated area on the top view Beam trajectory Coil Accelerator center

19. Local K+1 value by BL at each radius @3D Local K+1 value by BL at each radius @3D “ BL= ” It is possible to meet the design requirement for the integrated magnetic field along the trajectory. Calculated area on the top view 0.0 5.8 ° 0° 15° X [ m] 0.4 -0.4 o Beam trajectory Accelerator center Coil

20. Contents 1.Background & Purpose 2.2D Coil Design 3.3D Coil Design 4.Tracking 5.Conclusion

21. Tracking Particles will circulate stably in the accelerator at each beam orbit if the integral magnetic field comes close to satisfying the design requirement. Layout of the FFAG accelerator with some closed orbits Beam energy at each radius Tracking a particle in the FFAG accelerator with the magnetic field which almost meets the design requirement by BL

22. Tune Tune at each energy Tune diagram Tune shifts and crosses some resonance lines because of the beam acceleration.

23. Contents 1.Background & Purpose 2.2D Coil Design 3.3D Coil Design 4.Tracking 5.Conclusion

24. Conclusion A superconducting magnet design is proposed which is suitable for an FFAG. The cross section of the coil is optimized by a computer program that we have developed. The 3D coil configuration is designed to satisfy the design requirement in terms of the integral field. Particles are transported stably in the field for which the local k+1 meets the design requirement.

25. Future plan Development of a multi-layer coil with “Single winding” is in progress, and a full scale model coil is to be made and tested.

26. Practical single winding coil X X X Z Z Y Y Type of the magnetRadial sector Major axis of the beam pipe0.8 m Major axis of the beam pipe0.6 m Coil Length1.06m Turn number Layer number 120 30

27. Peak field B 0 @x =0 mPeak field 1.0 T4.1 T Current = 360A Parameters are adjusted to reduce the peak field. - Turn number - Distance between conductors at the coil end - Ratio of the major axis of the aperture to the minor of the aperture

28. How to optimize the position of the conductor Obtain the current distribution. Divide the portion with the same area. Arrange the conductor with same current. Current angle 180° SS S S S S Current distribution Conductor

29. Extraction beam Injection beam Excursion Acceptance 5.0 4.8 5.2 radius [m]

30. How to adjust the design requirement! X[m] K+1 value X[m] K+1 value Adjust the 2D design requirement so that the local k+1 value can reach 3D design requirement. Difference Design requirement Adjust the design requirement! Calculation Design requirement

31. Single winding @ 3D In single winding, one coil makes one layer. Y X Z X Z Y Z Y Z-Y plane Z Y Straight section Superconducting wire

32. Conventional winding @ 3D In conventional winding, two coils make one layer. X X Z Z Y Y Z X X Z Y Z Y Z-Y plane Straight section Superconducting wire

33. Magnetic Field for FFAG 0 Beam tube Beam area Magnet center Accelerator center r : Distance from the accelerator center [m] R 0 : Distance between the accelerator center and the magnet center [m] B o : Magnetic field at the magnet center [T] k : k value ( Geometrical field index)

34. Various Accelerators FieldFixRampFix Closed Orbit Large MoveFixSmall Move FocusingWeakStrong Duty Factor LargeSmallLarge

35. Local k value at each angle Local k values don’t meet the design requirement, even the angle is 0°.

36. Expansion plane @ Single winding Expansion plane @ Single winding ・・・ Overlapped part 0° 90°180°-90° -180° ・・・ the odd layer ・・・ the even layer

37. Accelerator Driven System (ADS) FFAG Proton Reactor Core neutron Target (Uranium )

38. How to evaluate K value Roughly evaluation Locally evaluation

39. Straight length with 2 layers Single winding Z Y Z Y Odd layer Even layer Odd layer Even layer Z-Y plane Z Y Y Z Straight length with 2layers Conventional winding

40. 0° 90° 180° -90° -180° (-90°) (90°) θ Single winding & Conventional winding Conventional winding Single winding

41. How to obtain K+1 value BL= X=0.0 m θ = 0° Coil Center of accelerator θ r

42. K value & K+1 value Z B Z X X-Z plane Local evaluation of the field Beam traveling direction K value K+1 value by BL Total evaluation of the field