Optics and magnetic field calculation for the Hall D Tagger

1. Optics and magnetic field calculation for the Hall D Tagger Guangliang Yang Glasgow University

2. Contents 1. Tagger optics calculated using Transport. 2. Magnetic field calculated using Opera 3D. 3. Tagger optics calculated using Opera 3D. 4. Tagger optics along the straight line focal plane. 5. Effects of position and direction errors on the straight line focal plane optics. 6. Conclusion.

3. Part 1. Optics calculated using Transport. • Two identical dipole magnets were used. • A quadrupole magnet can be included. • Each dipole has its own focal plane; these two focal • planesjoin together, with no overlap. • The optical properties (with and without a quadrupole) • meet the GlueX requirements.

4. 12 GeV Tagger Design - 2 identical magnets. Main beam energy: 12 GeV. Bending angle: 13.4 degrees. Object distance: 3 m. Total focal plane length: 10.3 m. Two identical dipole magnets: Magnet length : 3.11 m. Field: 1.5 T. Focal plane (Red: without quadrupole, Blue: with a quadrupole.) Lower part from 1-4.3 GeV electron energy. Length ~4m. Upper part from 4.3-9 GeV electron energy. Length: ~6 m. Edge angles (for main beam): At first magnet, entrance edge: 5.9 degrees. At second magnet, exit edge ~ 6.6 degrees. Quadrupole magnet: Length 0.5m. Field gradient: -0.47 KGs/cm. Red – without quad. Blue – with quad. Transport result

5. Two identical magnets tagger with and without quadrupole (Transport calculation). Resolution Dispersion

6. Two identical magnets tagger with and without quadrupole (Transport calculation). Beta Vertical height Beta is the angle between an outgoing electron trajectory and the focal plane.

7. Part 2: Magnetic field calculation. The magnetic field of the Hall D Tagger is calculated by using a finite element software- Opera 3D, version 10.025 Two identical dipoles and one quadupole are included in the same mesh model. More than 2 million elements and 1.5 million nodes have been used in the calculation. The magnetic fields have been shown along various electron trajectories.

8. Mesh used by Tosca for magnetic field calculation . Magnetic field calculated by using Opera 3D, version 10.025.

9. TOSCA Magnetic Field Calculation. Magnetic field along a line perpendicular to the magnet output edge. Mid-plane magnetic field histogram calculated by TOSCA.

10. Magnetic field along electron beam trajectory (1GeV).

11. Magnetic field along electron beam trajectory (8 GeV).

12. Magnetic field along electron beam trajectories between 3.9 and 5.0 GeV.

13. Z-component of stray field at focal plane position. Minimum distance between focal plane detector and EFB

14. Component of stray field normal to z-direction at focal plane position. Minimum distance between focal plane detector and EFB

15. Part 3. Optics calculated using Opera 3D. The electron trajectories of various energies have been evaluated using the calculated magnetic field. By using the calculated electron trajectories, optical properties of the Tagger are determined. The optical properties calculated by using Tosca are almost identical to the results from Transport.

16. Starting position and direction of an electron trajectory. We use (x, y, z) to describe the starting position of an electron trajectory and use α and ψto determine its direction. (x, y, z) are the co-ordinates of a point in a Cartesian system. The positive y direction is along the main beam direction, the z direction is perpendicular to the mid plane of the tagger, and the positive x direction points to the bending direction. α is the angle between the projected line of the emitted ray on the x-y plane and the y axis, ψ is the angle between the projected line of the emitted ray on the y-z plane and the y axis.

17. Ray bundle used in the calculation • By varying x, z, α and ψ, 81 trajectories are defined for each bundle. x=σx or 0 or -σx. y=-300 cm (i.e. the radiator position). z=σz or 0 or -σz. α=4σh or 0 or -4σh. ψ=4σv or 0 or -4σv. • σx andσz are the standard deviations for the main beam in the horizontal or vertical directions. • σhandσv are the energy degraded electron characteristic angles in the horizontal or vertical directions.

18. Calculated electron trajectories (81 per ray bundle). Electron trajectory bundles according to their directions at the object position. (3 GeV) (8 GeV) 2 1 2 1 Beam trajectories calculated from TOSCA in the mid plane for 3 GeV and 8 GeV.Those trajectories having the same directionfocus on position 1, and those trajectories having the same starting position focuson position 2.( Electrons travelling in the direction shown by the top arrow ).

19. Sketch showing the two focusing positions Object Lens Image Position 1 Position 2 From the TOSCA calculations, the best location for a straight line focal plane is close to position 2 for the lower electron energies. For the higher electron energies the best location is close to position 1.

20. Beam trajectories calculated by TOSCA in a vertical plane for 3 GeV electrons. Rays with different starting points but with a common angle Z position depends on emission angle of the bremsstrahlung electrons. Exit edge Exit edge Focal plane Focal plane Without quadrupole With quadrupole

21. TOSCA calculation of the beam spot profile at the focal plane. For 3 GeV electrons and no quadruople. Different x co-ords for different columns (without Quadrupole) Different ψ for different rows different y co-ords for different rows Three intersections are displayed. Each of them has the same x and y co-ords and the same ψ but a different angle α. The intersections of the beam trajectories with the plane through thefocusing point for the central line energy and perpendicular to the beam.

22. TOSCA calculation of the beam spot profile at the focal plane for 3 GeV electrons and with a quadrupole (81 lines). With quadrupole Different x co-ords for different columns Different ψ for different rows 9 intersections displayed, they have the same x and ψ, but different y and α.

23. Beam spot profiles at the focal plane for the two identical dipoles tagger (with the quadrupole adjusted to focus at 3 GeV). (for each energy, 81 trajectories have been used).

24. Beam spot profiles at the focal plane for the two identical dipoles tagger (with the quadrupole adjusted to focus at 4.3 GeV). (for each energy, 81 trajectories have been used).

25. Comparison of focal planes calculated using Transport and Tosca – results are almost identical (without quadrupole). Different colours indicate different energies • Electron trajectories have been calculated using Opera 3 D post processor. • By using the calculated electron trajectories, beam spot size, and focal plane position have been determined. Tosca.

26. Comparison of optical properties calculated using Transport and Tosca (without quadrupole). Resolution. Half vertical height.

27. Electron beam trajectories – using 81 trajectory ray bundles (without quadrupole).

28. Electron beam trajectories - central ray only.

29. A straight line focal plane is proposed as described in the previous section. The optical properties along the straight line focal plane have been determined using Tosca ray tracing . The optical properties along the straight line focal plane meet the requirement of GlueX. Part 4. Tagger optics along the straight line focal plane.

30. Straight line focal plane position Magnet 1 Magnet 2 Photon beam Main beam Straight thin window flange (parallel to the straight line focal plane determined by TOSCA ray tracing) Red line indicates the point to point focal plane position.(From 1 GeV to 9 GeV.)

31. Comparison of optical properties along the Point to Point and the Straight Line focal planes (without quadrupole). Resolution. Half vertical height.

32. Comparison of optical properties along the Point to Point and the Straight Line focal planes (without quadrupole). Dispersion. Beta. Discontinuity disappears for the straight line focal plane

33. Comparison of optical properties along the Point to Point and the Straight Line focal planes (with quadrupole). Resolution. Half vertical height.

34. Comparison of optical properties along the Point to Point and the Straight Line focal planes (with quadrupole). Dispersion. Beta. Including a quadrupole does not affect the result

35. Part 5. Effects of positioning errors. • The effects of positioning errors on the Tagger optics are simulated by using Opera 3 D. In these calculations, the second magnet is intentionally put in the wrong position. • Various positioning errors have been investigated: 1.the second magnet is moved longitudinally +-2 mm along a straight line parallel to the long exit edge of the first magnet. 2.the second magnet is moved right or left 2 mm along a straight line perpendicular to the long exit edge of the first magnet. 3. the second magnet is rotated around the bottom right corner of the second magnet by an angle of 0.1 degree or -0.1degree. • It has been found that the Tagger optical properties are insensitive to these positioning errors.

36. Effects of the second magnet positioning errors on the tagger optical properties.

37. Effects of the second magnet positioning errors on the tagger optical properties.

38. Effects of the second magnet positioning errors on the tagger optical properties.

39. Effects of the second magnet positioning errors on the tagger optical properties. Specified energy resolution is 0.5%E0.

40. Conclusions • The Transport results show that the optical properties of the two identical magnets Tagger meet the GlueX specifications. • The optical properties calculated using Tosca ray tracing are almost identical to the Transport results. • A straight line focal plane improves the Tagger performance. • The Tagger optical properties are insensitive to the positioning errors investigated.

41. Single Magnet Tagger

42. Single Magnet Tagger

43. Single Magnet Tagger

44. Single Magnet Tagger

45. Comparison of optical properties between a single dipole tagger and a two dipoles tagger.

46. Comparison of optical properties between a single dipole tagger and a two dipoles tagger.

47. Comparison of optical properties between a single dipole tagger and a two dipoles tagger.

48. Comparison of optical properties between a single dipole tagger and a two dipoles tagger.