1. Design Study of the PRISM-FFAG Magnet with inter- pole S. Nakaoka Osaka Univ.

2. Contents Outline of PRISM-FFAG Magnet Principle of Anisotropic inter-pole Effects of Anisotropic inter-pole Prototype test of inter-pole Summary

3. Outline of PRISM Magnet Aperture size : 110 cm (horizontal) 30 cm (vertical) Gradient of magnetic field is produced by main pole Anisotropic inter pole is used r θ z

4. What is Anisotropic Inter-Pole? Structure Layers of ferromagnetic and paramagnetic material Advantage Fringe field distribution become uniform at different r-position. Smoothing of fluctuation for field distribution caused by trim coil

5. Why is “Anisotropic” Inter-Pole? Boundary condition of surface in magnetic material Vertical Horizontal μ1μ1 μ2μ2 θ1θ1 θ2θ2 z r divB=0Bz 1 =Bz 2 (B 1 cosθ 1 =B 2 cosθ 2 ) rotH=0Hr 1 =Hr 2 (H 1 sinθ 1 =H 2 sinθ 2 ) Br 2 =(μ 2 /μ 1 )Br 1 μ 2r ： small μ 2r : large If μ 2 is large,magnetic flux which is produced by main pole flows rapidly and magnetic field in gap becomes flat. So to reflect gradient of magnetic field produced by main pole, μ 2r 〜 μ 1r in horizontal direction.

6. Why is “Anisotropic” Inter-Pole? And more… In vertical Bz 1 =Bz 2,so magnetomotive force is not loss. And horizontal permeability is not unity, so magnetic flux is slightly flowed and fluctuation of magnetic field which is caused by trim coil or pole becomes smooth. μ1μ1 μ2μ2 θ1θ1 θ2θ2 z r μ 2 ： small μ 2 : large

7. Effect of inter-pole 1 Uniform fringing magnetic field distribution in different r Without inter-pole With inter-pole 3D Calculation by TOSCA

8. Effect of inter-pole 2 Improvement of field fluctuation of local k caused by trim coils Without inter-pole With inter-pole 2D Calculation by PANDIRA

9. Prototype test of Inter-Pole Purpose To check 3D TOSCA simulation for magnetic design To confirm effects of inter-pole Detail Using Ushiwaka magnet (at KEK). Do 3d mapping of magnetic field. Preparing additional pole, by which gradient of magnetic field is produced. Preparing several pitch which is thickness of a layer of inter-pole.

10. Prototype Inter-Pole with Ushiwaka

14. Summary Anisotropic inter-pole is used, which have following merits Make uniform magnetic field distribution at fringe Damp the undulation of local k due to trim coils Now we are preparing prototype test of inter- pole

15. Calculation Results Magnetic field distribution

16. Estimate of accuracy 1 Comparing irregular magnetic field with normal magnetic field In case of lowering inter-pole 1cm all over

17. Estimate of accuracy 2 Comparing irregular magnetic field with normal magnetic field In case of extended inter- pole 1cm in vertical direction

18. Estimate of accuracy 3 Comparing irregular magnetic field with normal magnetic field In case of deviated 1 cm in horizontal direction

19. Estimate of accuracy 4 Comparing irregular magnetic field with normal magnetic field In case of B-H curve of inter- pole uneven