Proposal of highresolution eA collider spectrometer

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Proposal of high-resolution eA collider
spectrometer
Seigo Kato
Yamagata University
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Contents

• Requirements
• Case 1
• Principle
• Magnetic field
• Expected performances
• Case 2
• Expected performances
• Comparison

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Requirements
4 m available
1 m available
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Case 1 --- Q-magnet-based spectrometer
4 m available
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Principle of Q-based spectrometer

• Electron and RI beams collide each other along
  the symmetry axis of the quadrupole magnet of the
  spectrometer.
• Intact beams go straight along the field-free,
  symmetrical axis of the quadrupole magnet.
• Scattered electron are focused vertically,
  magnifying the acceptance.
• They are horizontally defocused, magnifying the
  angle of exit.
• Electrons are extracted from the side face of the
  quadrupole magnet.

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• Electrons scattered to extreme forward angles can
  be analyzed.
• They are then analyzed by a dipole magnet.
• The exit angle from the quadrupole magnet is
  almost constant.
• (demerit) We lose significant part of the
  information on scattering angles.
• (merit) The scattering angle can be changed
  without rotating the dipole magnet if we adjust
  the strength of the quadrupole magnet and/or the
  collision position of the beams.

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The proposal to RIKEN

• Interference to the cooler ring
• Too big

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Quadrupole magnet with and without magnetic shield
proposed to RIKEN
present proposal
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Comparison of the size
RIKEN 900 MeV/c
present 600 MeV/c
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Detail of the quadrupole magnet
field strength in detail (log scale)
dipole gap 10 cm shield inner diameter 10 cm
field line
field strength
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Precise description of the fringing field
The magnetic field distribution is much different
from the conventional quadrupole magnet. We have
to describe it precisely improving the
traditional method of describing two-dimensional
fringing field which has been found to be
reliable only in a very narrow region around the
symmetry plane.
reference
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Traditional method
(J.E.Spencer H.A.Enge NIM 49(1967)181) 1.
Define x in unit of the gap and fit By along
x-axis by
2. Extend to two-dimensional space
model geometry
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Field strength distribution had never been
displayed.
summation up to 4-th derivative
The field is not uniform at deep inside the gap.
summation up to 24-th derivative
Singular behavior grows as we take the higher
order terms into account.
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Summation up to infinity is possible!
There is no reason to terminate the summation at
a finite order while the exact summation is
possible.
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Singularities in two-dimensional space

We cannot avoid the singularities because any
solution of Laplace equation has singularities
unless it is zero everywhere.
For complex z, h(x) can diverge. The location of
singularities can be obtained by solving
following equation
(algebraically unsolvable)
We have to replace h(z) by a new one whose
singularities can be easily controlled.
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Trial functions
Enge function
original field distribution
singularities in the region of interest
modified Fermi function
proposed function
vertically cyclic
singularities at (a,b) and (c,d)
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Field distribution of the quadrupole magnet
left fringe
right fringe
The singularities are located at (a1,b1),(c1,d1),
(a2,b2), and (c2,d2).
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Extension to 2-dimensional space
Original distribution
Reproduced distribution 4 singularities are seen.
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Proposed spectrometer
acceptance 300400 mr
acceptance 100 mr suitable for forward angles
available 100 950 mr best 200 -300 mr
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Changing the detection angle without rotation
most forward (limited by collision position)
optimaized
most backward (limited by Q strength)
zero Q field
Measuring angle can be changed by changing the
quadrupole field and the collision position, The
latter can be fixed with some loss of the
performance.
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Resolutions
counter resolution 0.2 mm multiple scattering
0.5 mr
counter resolution 0.1 mm multiple scattering
0.2 mr
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Dependence on the colliding length
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Why the colliding length acceptance is so
large It is because (xy) is very small at the
focal plane (y means the source position along
the beam direction).
dy 30 cm dq 0
dy 0 dq 100 mr
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Smaller radius of the shield
r 0 cm (RIKEN) quadrupole field
r 3 cm better performance
r 5 cm
The smaller radius, the better performance at
forward angle can be obtained. How small the
radius can be made?
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Case 2 ---- big solid angle spectrometer
1 m available
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QQD spectrometer with big f acceptance
same scale for three directions
acceptance 600 mr
acceptance 100 mr suitable for 90 deg
60 msr
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Quadrupole magnet with bigger width than bore
diameter
Q2 of HKS at Jlab
assembled in May, 2005
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Increasing the angular acceptance
1000 mr
1200 mr
200 mr (unnecessary if rotatable)
100 mr
240 msr
100 msr
RD on Q1 superconducting or tapered-bore
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Superconducting Panovsky Q magnet
7.50 T/m _at_ 30 A/mm2 gap 69 cm field
width 24 cm field height 80 cm magnet
width 70 cm magnet height 110 cm
3D calculation of the fringing field is necessary.
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Tapered-bore quadrupole magnet
Tapered-bore quadrupole magnet
3D calculation
parametrization
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Realistic width of the first quadrupole magnet
60 deg from the beam (50 deg by SC Panovsky?)
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Effect of the collision length
beam length 5 cm
An upstream position counter is necessary in
order to determine the collision point (between
Q2 and D). We have to make the initial direction
dependent of the collision point so that
particles go through the central region of
magnets.
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Comparison
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Appendix
The following panels show the revised contents
from the original proposal together with the
newly added ones.
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Quadrupole magnet with and without magnetic shield
proposed to RIKEN
present proposal
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Detail of the quadrupole magnet
field strength in detail (log scale)
dipole gap 10 cm shield inner diameter 6 cm
field line
field strength
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Field distribution of the quadrupole magnet
left fringe
right fringe
The singularities are located at (a1,b1),(c1,d1),
(a2,b2), and (c2,d2).
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Extension to 2-dimensional space
Original distribution
This figure corresponds to 10 cm of diameter.
Reproduced distribution 4 singularities are seen.
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Length requirement of the Q magnet
length 100 cm
Although this figure shows the case of 10 cm
shield diameter which was changed to 6 cm, we can
see that we need almost no margin of length for
the collision point and the exit point. The left
figure shows the structure. Left half of the
right figure shows the field strength on the iron
surface, the right half on the median plane.
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Solution for fixed collision point
short Q magnet
no possibility of extending the angular range out
of 15 52 deg
Because of the tight spacing, we have to fix the
collision point losing performances, mainly the
azimuthal angle acceptance.
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Total system
Even if we fix the collision point, the spacing
is still tight. If the collision point is fixed
at the center of the straight section, its length
has to be more than 5.5 m.
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Dimensions
Q magnet length 1 m mass 5 ton D
magnet gap 16 cm mass 74 ton counter
length counter-1 70 cm counter-2 150 cm
counter-3 200 cm
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Resolutions
assumption counter resolution (FWHM) 0.2 mm,
multiple scattering (sigma) 0.2 mr
Above resolutions are presented by FWHM. From
the simulations, effect of the multiple
scattering is found to be much severe than that
of counter resolution. If it is bigger than 0.2
mr, resolution of 10-4 cannot be obtained even
with the infinite counter resolution.
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Comparison (revised)
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To do
Improve the azimuthal angle acceptance which was
lost by fixing the collision point. By
making the dipole gap wider? By rotating or
horizontally shifting the dipole? By taking
the upstream margin of quadrupole
length? Replace the panels which correspond to 5
cm radius of the shielding radius by 3 cm
version. Minimize the size in the downstream
direction. By C-type dipole? By
superconducting window frame?