Optics and magnetic field calculation for the Hall D Tagger

Guangliang YangGlasgow University

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.

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

planes join together, with no overlap.

• The optical properties (with and without a quadrupole)

meet the GlueX requirements.

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X (m)

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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.

12 GeV Tagger Design - 2 identical magnets.

Transport result

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Dispersion Resolution

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

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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.

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.

Magnetic field calculated by using Opera 3D, version 10.025.

Mesh used by Tosca for magnetic field calculation .

Mid-plane 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.

Z-component of stray field at focal plane position.

Minimum distance between focal plane detector and EFB

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

Minimum distance between focal plane detector and EFB

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.

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 ψ to 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.

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 and σz are the standard deviations for the main beam in

the horizontal or vertical directions.• σh and σv are the energy degraded electron characteristic

angles in the horizontal or vertical directions.

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)

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ObjectImage

Sketch showing the two focusing positions

Position 1

Position 2

Lens

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.

Beam trajectories calculated by TOSCA in a vertical plane for 3 GeV electrons.

Exit edge

Exit edge

Focal plane

Focal plane

Without quadrupole With quadrupole

Rays with different starting points but with a common angle

Z position depends on emission angle of the bremsstrahlung electrons.

The intersections of the beam trajectories with the plane through the focusing point for the central line energy and perpendicular to the beam.

TOSCA calculation of the beam spot profile at the focal plane. For 3 GeV electrons and no quadruople.

Three intersections are displayed. Each of them has the same x and y co-ords and the same ψ but a different angle α.

different y co-ords for different rows

Different ψ for different rows

Different x co-ords for different columns(without Quadrupole)

TOSCA calculation of the beam spot profile at the focal plane

for 3 GeV electrons and with a quadrupole (81 lines).

9 intersections displayed, they have the same x and ψ, but different y and α.

Different x co-ords for different columnsWith quadrupole

Different ψ for different rows

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).

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).

• 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 (without quadrupole).

Tosca.

Different colours indicate

different energies

Comparison of optical properties calculated using Transport and Tosca (without quadrupole).

Resolution. Half vertical height.

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

Electron beam trajectories - central ray only.

Part 4. Tagger optics along the straight line focal plane.

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.

Straight line focal plane position

Red line indicates the point to point focal plane position.(From 1 GeV to 9 GeV.)

Main beam

Magnet 1Magnet 2

Photon beam

Straight thin window flange (parallel to the straight line focal plane determined by TOSCA ray tracing)

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 (without quadrupole).

Dispersion. Beta.

Discontinuity disappears for the straight line focal plane

Comparison of optical properties along the Point to Point and the Straight Line focal planes (with quadrupole).

Resolution. Half vertical height.

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

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.

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

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

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

Dispersion along the straight line focal plane (caculated by using Tosca)

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

Energy calibration error( relative to the properly positioned Tagger)

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Specified energy resolution is 0.5%E0.

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.

Single Magnet Tagger

Single Magnet Tagger

Single Magnet Tagger

Single Magnet Tagger

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

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

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

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