Download Magnetic field calculations

Optics and magnetic field
calculation for the Hall D Tagger
Guangliang Yang
Glasgow University
Contents
1.
2.
3.
4.
Tagger optics calculated using Transport.
Magnetic field calculated using Opera 3D.
Tagger optics calculated using Opera 3D.
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.
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.
Red – without quad.
12
Blue – with quad.
10
Two identical dipole magnets:
Magnet length : 3.11 m.
Field: 1.5 T.
8
Focal plane
(Red: without quadrupole,
Blue: with a quadrupole.)
Lower part from 1-4.3 GeV electron energy.
Length ~4m.
Y (m)
6
4
Upper part from 4.3-9 GeV electron energy.
Length: ~6 m.
2
Edge angles (for main beam):
At first magnet, entrance edge: 5.9 degrees.
At second magnet, exit edge ~ 6.6 degrees.
0
-2
Transport result
-4
-5
-3
-1
1
X (m)
3
5
Quadrupole magnet:
Length 0.5m.
Field gradient: -0.47 KGs/cm.
Two identical magnets tagger with and without
quadrupole (Transport calculation).
8
Resolution
0.07
7
0.06
6
Dispersion (cm/%E0)
Resolution (%)
0.08
0.05
0.04
0.03
Dispersion
5
4
3
2
0.02
0.01
1
without quadruple
with quadrupole
w ithout quadrupole
w ith quadrupole
0
0
0
2
4
6
Electron enregy (GeV)
8
10
0
2
4
6
Electron energy (GeV)
8
10
Two identical magnets tagger with and without
quadrupole (Transport calculation).
25
Beta
Vertical height
without quadrupole
with quadrupole
Beta (degrees)
20
15
10
5
Beta is the angle between an
outgoing electron trajectory
and the focal plane.
0
0
2
4
6
Electron Energy (GeV)
8
10
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.
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.
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).
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 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.
Rays with different
starting points but
with a common angle
Exit
edge
Z position depends on
emission angle of the
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 x co-ords
for different columns
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 coords and the same ψ but a different angle α.
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 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.
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).
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.
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
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.)
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)
500
L -2mm
L +2mm
R -0.1 degree
R +0.1degree
T -2mm
T +2mm
450
400
Dispersion (mm/%E0)
350
300
250
200
150
100
50
0
0
1
2
3
4
5
Electron energy (GeV)
6
7
8
9
10
Effects of the second magnet positioning errors on
the tagger optical properties.
Energy calibration error( relative to the properly positioned Tagger)
0.4
L -2mm
L +2mm
R -0.1 degree
R +0.1degree
T -2mm
T +2mm
0.3
0.2
Specified energy resolution is 0.5%E0.
Error %E0
0.1
0
-0.1
-0.2
-0.3
-0.4
0
1
2
3
4
5
6
Electron enrgy (GeV)
7
8
9
10
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.