1. Proposal of high-resolution eA collider spectrometer Seigo Kato Yamagata University

2. Requirements Case 1 Principle Magnetic field Expected performances Case 2 Expected performances Comparison Contents

3. Requirements 4 m available 1 m available

4. Case 1 --- Q-magnet-based spectrometer 4 m available

5. Principle of Q-based spectrometer Electron and RI beams collide each other along the symmetry axis of the quadrupole magnet of the spectrometer. Intact beams go straight along the field-free, symmetrical axis of the quadrupole magnet. Scattered electron are focused vertically, magnifying the acceptance. They are horizontally defocused, magnifying the angle of exit. Electrons are extracted from the side face of the quadrupole magnet.

6. Electrons scattered to extreme forward angles can be analyzed. They are then analyzed by a dipole magnet. The exit angle from the quadrupole magnet is almost constant. (demerit) We lose significant part of the information on scattering angles. (merit) The scattering angle can be changed without rotating the dipole magnet if we adjust the strength of the quadrupole magnet and/or the collision position of the beams.

7. The proposal to RIKEN 1.Interference to the cooler ring 2.Too big

8. Quadrupole magnet with and without magnetic shield proposed to RIKEN present proposal

9. RIKEN 900 MeV/c present 600 MeV/c Comparison of the size

10. field line field strength field strength in detail (log scale) dipole gap: 10 cm shield inner diameter: 10 cm Detail of the quadrupole magnet

11. Precise description of the fringing field The magnetic field distribution is much different from the conventional quadrupole magnet. We have to describe it precisely improving the traditional method of describing two-dimensional fringing field which has been found to be reliable only in a very narrow region around the symmetry plane. reference

12. Traditional method (J.E.Spencer & H.A.Enge: NIM 49(1967)181) 1. Define x in unit of the gap and fit B y along x-axis by 2. Extend to two-dimensional space: model geometry

13. Field strength distribution had never been displayed. summation up to 4-th derivative summation up to 24-th derivative Singular behavior grows as we take the higher order terms into account. The field is not uniform at deep inside the gap.

14. Summation up to infinity is possible! There is no reason to terminate the summation at a finite order while the exact summation is possible.

15. Singularities in two-dimensional space For complex z, h(x) can diverge. The location of singularities can be obtained by solving following equation: (algebraically unsolvable) We cannot avoid the singularities because any solution of Laplace equation has singularities unless it is zero everywhere. We have to replace h(z) by a new one whose singularities can be easily controlled.

16. original field distribution Enge function modified Fermi function proposed function vertically cyclicsingularities at (a,b) and (c,d) singularities in the region of interest Trial functions

17. The singularities are located at (a 1,b 1 ),(c 1,d 1 ), (a 2,b 2 ), and (c 2,d 2 ). left fringe right fringe Field distribution of the quadrupole magnet

18. Extension to 2-dimensional space Original distribution Reproduced distribution 4 singularities are seen.

19. acceptance: 300~400 mr acceptance: 100 mr suitable for forward angles available: 100 – 950 mr best: 200 -300 mr Proposed spectrometer

20. Changing the detection angle without rotation most forward (limited by collision position) most backward (limited by Q strength) optimaized zero Q field Measuring angle can be changed by changing the quadrupole field and the collision position, The latter can be fixed with some loss of the performance.

21. counter resolution 0.2 mm multiple scattering 0.5 mr counter resolution 0.1 mm multiple scattering 0.2 mr Resolutions

22. Dependence on the colliding length

23. Why the colliding length acceptance is so large It is because (x|y) is very small at the focal plane (y means the source position along the beam direction).  y = 30 cm  = 0  y = 0  = 100 mr

24. Smaller radius of the shield r = 5 cm r = 3 cm better performance r = 0 cm (RIKEN) quadrupole field The smaller radius, the better performance at forward angle can be obtained. How small the radius can be made?

25. Case 2 ---- big solid angle spectrometer 1 m available

26. QQD spectrometer with big  acceptance acceptance: 600 mr acceptance: 100 mr suitable for 90 deg 60 msr same scale for three directions

27. Quadrupole magnet with bigger width than bore diameter Q2 of HKS at Jlab assembled in May, 2005

28. Increasing the angular acceptance R&D on Q1: superconducting or tapered-bore 1000 mr 1200 mr 100 mr 200 mr (unnecessary if rotatable) 100 msr 240 msr

29. Superconducting Panovsky Q magnet 7.50 T/m @ 30 A/mm2 gap = 69 cm field width = 24 cm field height = 80 cm magnet width = 70 cm magnet height = 110 cm 3D calculation of the fringing field is necessary.

30. Tapered-bore quadrupole magnet 3D calculation parametrization

31. Realistic width of the first quadrupole magnet 60 deg from the beam (50 deg by SC Panovsky?)

32. Effect of the collision length beam length = 5 cm An upstream position counter is necessary in order to determine the collision point (between Q2 and D). We have to make the initial direction dependent of the collision point so that particles go through the central region of magnets.

33. Type proposed byI. A. KoopS. Kato  acceptance 300 mr280 ~ 440 mr1000 ~ 1200 mr  acceptance ?100 mr  min ~  max (40 O ~ 80 O) ?6 O ~ 55 O (60 O ~ 120 O) collision length?30 cm5~? cm momentum bite25 %20 % Q magnetsuper-conductingnormal conducting tapered-bore or SC Panovsky D gap25 cm16 cm30 cm median planeverticalhorizontal Comparison

34. Appendix The following panels show the revised contents from the original proposal together with the newly added ones.

35. Quadrupole magnet with and without magnetic shield proposed to RIKEN present proposal

36. field line field strength field strength in detail (log scale) dipole gap: 10 cm shield inner diameter: 6 cm Detail of the quadrupole magnet

37. The singularities are located at (a 1,b 1 ),(c 1,d 1 ), (a 2,b 2 ), and (c 2,d 2 ). left fringe right fringe Field distribution of the quadrupole magnet

38. Extension to 2-dimensional space Original distribution Reproduced distribution 4 singularities are seen. This figure corresponds to 10 cm of diameter.

39. length = 100 cm Length requirement of the Q magnet Although this figure shows the case of 10 cm shield diameter which was changed to 6 cm, we can see that we need almost no margin of length for the collision point and the exit point. The left figure shows the structure. Left half of the right figure shows the field strength on the iron surface, the right half on the median plane.

40. no possibility of extending the angular range out of 15 ~ 52 deg Solution for fixed collision point short Q magnet Because of the tight spacing, we have to fix the collision point losing performances, mainly the azimuthal angle acceptance.

41. Total system Even if we fix the collision point, the spacing is still tight. If the collision point is fixed at the center of the straight section, its length has to be more than 5.5 m.

42. Q magnet length: 1 m mass: 5 ton D magnet gap: 16 cm mass: 74 ton counter length counter-1: 70 cm counter-2: 150 cm counter-3: 200 cm Dimensions

43. Resolutions assumption: counter resolution (FWHM) 0.2 mm, multiple scattering (sigma) 0.2 mr Above resolutions are presented by FWHM. From the simulations, effect of the multiple scattering is found to be much severe than that of counter resolution. If it is bigger than 0.2 mr, resolution of 10^-4 cannot be obtained even with the infinite counter resolution.

44. Type proposed byI. A. KoopS. Kato  acceptance 300 mr250 mr1000 ~ 1200 mr  acceptance ?100 mr  min ~  max (40 O ~ 80 O) ?15 O ~ 52 O (60 O ~ 120 O ) collision length?30 cm5~? cm momentum bite25 %20 % Q magnetsuper-conductingnormal conducting tapered-bore or SC Panovsky D gap25 cm16 cm30 cm median planeverticalHorizontalhorizontal Comparison (revised)

45. To do Improve the azimuthal angle acceptance which was lost by fixing the collision point. By making the dipole gap wider? By rotating or horizontally shifting the dipole? By taking the upstream margin of quadrupole length? Replace the panels which correspond to 5 cm radius of the shielding radius by 3 cm version. Minimize the size in the downstream direction. By C-type dipole? By superconducting window frame?