Download Magnetic field calculated using Opera 3D. 2. Tagger optics

Optics and magnetic field
calculation for the Hall D Tagger
Guangliang Yang
Glasgow University
Contents
1. Magnetic field calculated using Opera 3D.
2. Tagger optics calculated using Opera 3D.
3. Tagger optics along the straight line focal
plane.
4. Effects of position and direction errors on
the straight line focal plane optics.
5. Conclusion.
Part 1. 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 checked along various
electron trajectories.
Mesh used by Tosca for magnetic field calculation .
Magnetic field calculated by
using Opera 3D, version 10.025.
TOSCA Magnetic Field Calculation.
Mid-plane magnetic field histogram calculated by
TOSCA.
Magnetic field along a line perpendicular to
the magnet output edge.
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.
Y-component of stray field at focal plane position.
Minimum distance
between focal plane
detector and EFB
Component of stray field normal to y-direction at
focal plane position.
Minimum distance
between focal plane
detector and EFB
Part 2. 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.
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 z direction is along the main beam
direction, the y direction is perpendicular to the mid plane
of the tagger, and the positive x direction is opposite to the
bending direction.
α is the angle between the projected line of the emitted ray
on the x-z plane and the z axis, ψ is the angle between the
projected line of the emitted ray on the y-z plane and the z
axis.
Ray bundle used in the calculation
• By varying x, y, α and ψ, 81 trajectories are defined for each
bundle.
• x=σx or 0 or -σx.
• y=σy or 0 or -σy.
• z=-300 cm (i.e. the radiator position).
• α=4σh or 0 or -4σh.
• ψ=4σv or 0 or -4σv.
• σx and σy 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.
Beam trajectories (1-9 GeV) and the straight line focal plane position
Tosca.
• Electron trajectories have
been calculated using
Opera 3 D post
processor.
• The focal plane position
is determined by using
the calculated electron
trajectories and spot
sizes.
Different colours indicate
different energies
Calculated electron trajectories (81 per ray bundle).
Electron trajectory bundles according to their directions at the object position.
(3 GeV)
(8 GeV)
1
2
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 ).
Sketch showing the two focusing positions
Object
Lens
Image
Position 1
Position 2
From the TOSCA calculation, the best location for a straight line
focal plane is close to position 2 for the lower electron energies.
For high electron energies the best location is close to position 1.
Beam trajectories calculated by TOSCA in a vertical plane
for 3 GeV electrons.
Rays with different
starting points but
with a common angle
Exit
edge
Y position depends on
emission angle of
bremsstrahlung electrons.
Exit
edge
Focal
plane
Without quadrupole
With quadrupole
Focal
plane
TOSCA calculation of the beam spot profile at the focal plane.
For 3 GeV electrons and no quadruople.
(without Quadrupole)
Different lab x co-ords at radiator.
Different
angles ψ at
radiator
different lab y co-ords
at radiator
The nearest three intersections are in the same group. The intersections
in the same group have the same x and y co-ords at the radiator but a
different angle α. They are superimposed together at the precise point to
point focus position.
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 with a quadrupole (81 lines).
With quadrupole
Different lab x co-ords at radiator
Different
angles ψ at
radiator
9 intersections
superimposed together
Two identical dipoles Tagger (with the quadrupole
adjusted to focus at 3 GeV).
Two identical dipoles Tagger (with the quadrupole
adjusted to focus at 4.3 GeV).
Envelopes of electron beam trajectories as they cross the focal
plane– using 81 trajectory ray bundles (without quadrupole).
Electron beam trajectories as they cross the focal plane
- central ray only.
Par 3. Tagger optics along the straight line focal plane.
1. The optical properties have been determined
using Tosca ray tracing .
2. The optical properties meet the requirements of
GlueX.
Straight line focal plane position
Magnet 1
Magnet 1
Straight thin window flange (parallel to
the straight line focal plane determined
by TOSCA ray tracing)
Photon beam
Main beam
Comparison of optical properties along the Straight
Line focal planes (without and with quadrupole).
(quadrupole field optimized for 3 GeV electrons.)
Resolution.
Half vertical height.
Comparison of optical properties along the Straight
Line focal plane (without and with quadrupole).
Dispersion.
Beta.
(Perpendicular to
electron trajectory)
Beta is the angle between an
outgoing electron trajectory
and the focal plane.
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 the
positioning errors.
Conclusions
• The optical properties along the straight line focal plane
of the two identical magnets Tagger meet the GlueX
specifications.
• The Tagger optical properties are insensitive to the
positioning errors investigated.