Optics and magnetic field calculation for the Hall D Tagger

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Optics and magnetic field calculation for the
Hall D Tagger

• Guangliang Yang
• Glasgow University

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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.

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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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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
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Two identical magnets tagger with and without
quadrupole (Transport calculation).
Dispersion
Resolution
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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.
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• 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.
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Mesh used by Tosca for magnetic field calculation
.
Magnetic field calculated by using Opera 3D,
version 10.025.
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TOSCA Magnetic Field Calculation.
Magnetic field along a line perpendicular to the
magnet output edge.
Mid-plane magnetic field histogram calculated by
TOSCA.
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Magnetic field along electron beam trajectory
(1GeV).
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Magnetic field along electron beam trajectory (8
GeV).
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Magnetic field along electron beam trajectories
between 3.9 and 5.0 GeV.
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Z-component of stray field at focal plane
position.
Minimum distance between focal plane detector and
EFB
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Component of stray field normal to z-direction at
focal plane position.
Minimum distance between focal plane detector and
EFB
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• 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.
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Starting position and direction of an electron
trajectory.

• We use (x, y, z) to describe the starting
  position of an electron trajectory and use a and
  ? 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.
• a is the angle between the projected line of
  the emitted ray on the x-y plane and the y axis,
  ? is the angle between the projected line of the
  emitted ray on the y-z plane and the y axis.

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Ray bundle used in the calculation

• By varying x, z, a and ?, 81 trajectories are
  defined for each bundle.
• xsx or 0 or -sx.
• y-300 cm (i.e. the radiator position).
• zsz or 0 or -sz.
• a4sh or 0 or -4sh.
• ?4sv or 0 or -4sv.
• sx and sz are the standard deviations for the
  main beam in the horizontal or vertical
  directions.
• sh and sv are the energy degraded electron
  characteristic angles in the horizontal or
  vertical directions.

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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 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 ).
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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.
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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
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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 ? 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 ? but a
different angle a.
The intersections of the beam trajectories with
the plane through the focusing point for the
central line energy and perpendicular to the beam.
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TOSCA calculation of the beam spot profile at the
focal plane for 3 GeV electrons and with a
quadrupole (81 lines).
Different x co-ords for different columns
With quadrupole
Different ? for different rows
9 intersections displayed, they have the same x
and ?, but different y and a.
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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).
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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).
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Comparison of focal planes calculated using
Transport and Tosca results are almost
identical (without quadrupole).
Different colours indicate different energies

Tosca.

• 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.

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Comparison of optical properties calculated using
Transport and Tosca (without quadrupole).
Resolution.
Half vertical height.
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Electron beam trajectories using 81 trajectory
ray bundles (without quadrupole).
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Electron beam trajectories - central ray only.
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• 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.
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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.)
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Comparison of optical properties along the Point
to Point and the Straight Line focal planes
(without quadrupole).
Resolution.
Half vertical height.
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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
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Comparison of optical properties along the Point
to Point and the Straight Line focal planes (with
quadrupole).
Resolution.
Half vertical height.
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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
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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.

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

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