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

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 GeV electron energy. Length ~4m. Upper part from GeV electron energy. Length: ~6 m. Edge angles: At first magnet, entrance edge: 5.9 degrees. At second magnet, exit edge ~ 6.6 degrees. Quadrupole magnet: Length 0.5m. Field gradient: KGs/cm. Red – without quad. Blue – with quad. 12 GeV Tagger Design - 2 identical magnets. Transport result

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

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

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

2 D magnetic field histogram calculated by TOSCA. Magnetic field along a line perpendicular to the magnet output edge. TOSCA Magnetic Field Calculation.

Magnetic field along electron beam trajectory (1GeV).

Magnetic field along electron beam trajectory (8 GeV).

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

Electron beam trajectories – using 81 trajectory ray bundles.

Electron beam trajectories - central ray only.

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

Object Image Sketch showing the two focusing positions Position 1 Position 2 Lens

Beam trajectories calculated by TOSCA in a vertical plane for 3 GeV electron beam. Exit edge Focal plane Without quadrupole With quadrupole

The intersections of the beam trajectories with the plane through the focusing point and perpendicular to the beam, the red line shows the beam spot profile. TOSCA calculation of the beam spot profile at the focal plane.

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. Comparison of focal planes calculated using Transport and Tosca – results are almost identical. Tosca.

Comparison of optical properties calculated using Transport and Tosca. Resolution.Half vertical height.

Detector positions Red line indicates the focal plane position calculated by using Transport. (From 1 GeV to 9 GeV) Main beam Magnet 1 Photon beam Straight thin window flange

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

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

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

Effects of the second magnet positioning error on the tagger optical properties.

Electron beam trajectories – using 81 trajectory ray bundles. Electron trajectories from 4.1 to 4.8 GeV (Red line shows the straight line focal plane position.) (T +2mm)

Z-component of stray field at focal plane position.

Component of stray field normal to z-direction at focal plane position.