John J. LeRoseTechnical Review of the Super BigBite Project
January 22, 2010
SBS Magnet, Optics, and Spin Transport
SBS: a “large” acceptance, small angle, moderate resolution device
48D48 Basic Geometry
The magnet is “available”.
To guarantee that it’s ours we need to formally
transfer ownership.
Needed Modifications to the Magnet
• For small angles at short distance– Cut opening in Yoke– Modify coils
• For Polarized Target & background control– Add field clamp to reduce field at target
• For beam transport to the dump– Field clamp (again)– Add magnetically shielded beam pipe– Add solenoid
Shielded Beam pipe
Field Clamp
Layout of system with part of yoke removed
Modified Coils
B at target < 2 Gauss
With magnetically shielded pipe with 1kA/cm current density solenoid
Calculations by Stepan MikhailovUsing “Mermaid” (units are kG, cm)
Nice clean magnetic field
5105.369.360013.0
69.3611
B
Bdl
mTBcGeVP
mTdlBy3
' 103.1
yy’
x
x’
θ
1 mm @ 30mEffect on beamline by transverse field is effectively eliminated
Various Views of the Modified Magnet
Optics
It’s really very simple!
This is what it looks like to me!
x
y
0
Reference Trajectory
Arbitrary Trajectory
Magnetic Midplane
y
x
z
TRANSPORT formalism
References:
K.L. Brown, D.C. Carey, C. Iselin and F. Rothacker, Designing Charged Particle Beam Transport Systems, CERN 80-04 (1980)
K.L. Brown, SLAC Report-75 (http://www.slac.stanford.edu/cgi-wrap/getdoc/slac-r-075.pdf)
…...
All trajectories are characterized by their difference from a reference trajectory*
l
y
x
Xx
zx
z
y
zy
z
*”The Central Trajectory”
zx
xx
l = length difference between trajectory and the reference trajectory
TRANSPORT formalism cont’d
yxz
0
0
ppp
Relative change in momentum
General Solution of the equation of motion:
000000
),,,,(),,,,(),,,,(),,,,(),,,,(
),,,,(
0,000
0,000
0,000
0,000
0,000
0,000raycentral
yxzlyxzyxzyyxzyxzx
yxzF
Each component can be expressed as a Taylor series around the Central Ray:
......
......),,,,(
......),,,,(
......),,,,(
......),,,,(
)(0
)(00
)(00
)(00
)(00
)(00,000
)(0
)(00
)(00
)(00
)(00
)(00,000
)(0
)(00
)(00
)(00
)(00
)(00,000
)(0
)(00
)(00
)(00
)(00
)(00,000
zzzzzz
zzzzzz
zzzzzz
zzzzzz
ll
yy
xx
yxz
yllyyy
yyyx
xyyxzy
ll
yy
xx
yxz
xllxxy
yxxx
xxyxzx
TRANSPORT formalism cont’d
The first order transfer matrix:
f
f
f
f
f
f
XXMor
l
y
x
l
y
x
lyxllllyllxl
lyxylyyyyyxy
lyxxlxxyxxxx
0
0
0
0
0
0
00000
00000
00000
00000
00000
00000
||||||||||||||||||||||||||||||||||||
For static magnetic systems with midplane symmetry:
f
f
f
f
f
l
y
x
l
y
x
llxllylyyyylx
xlxxxx
0
0
0
0
0
00
000
000
000
000
100000|100||0|||000|||00||00||||00||
1|| M
0
0
00
00
||||
yyyyy
y
f
f
01 XXM f
eg.0
0 xxxx
TRANSPORT formalism cont’d
If you know how well you can measure x, θ, y, and φ, you know how well you can determine the target parameters.
Projected Errorsbased on projected detector performance and general setup
mradP(GeV/c)
mrad
mm36.114.0
07.0
yx
1st orderResolution
1st OrderP = 8 GeV/c
δ (%) (Momentum) 0.03P+0.29 0.53
θtar (mrad) 0.09 + 0.59/P 0.16
ytar (mm) 0.53 + 4.49/P 1.09
φtar (mrad) 0.14+1.34/P 0.31
Higher Order Effects?
Strategy:Use SNAKE to create a database of trajectories and then fit the reconstruction
tensor. (higher order terms)Use the reconstruction tensor in a Monte-Carlo fashion to evaluate the errors.
δ0-δmeas θ0-θmeas
φ0-φmeasy0-ymeas
δ0-δmeas θ0-θmeas
φ0-φmeasy0-ymeas
1st Orderresolution
1st OrderP = 8 GeV/c
SNAKE P = 7-9 GeV/c
δ (%) (Momentum) 0.03P+0.29 0.53 0.48
θtar (mrad) 0.09 + 0.59/P 0.16 0.16
ytar (mm) 0.53 + 4.49/P 1.09 0.9
φtar (mrad) 0.14+1.34/P 0.31 0.30
Higher order terms, while necessary to accurately reconstruct the target variables, don’t contribute to the uncertainties in the measurements. i.e. They’re small corrections!
Momentum Dependence of ΔΩ
0 2 4 6 8 10 120
0.2
0.4
0.6
0.8
1
1.2
Super BigBite Relative Acceptance
P (GeV/c)
8 GeV/c
1 GeV/c
Spin Transport )1(Non-dispersive precessionDispersive precession )1(
to Reaction Plane Reaction Plane
2tan
2)( e
p
ebeam
l
t
Mp
Ep
MEE
PP
GG
PP
PP
t
l
tfp
nfp s in
)1(sin
2tan
2)(
fpl
fpte
p
ebeam
Mp
Ep
PP
MEE
GG
TargetTarget
outin
Spin Transport
Because of Pl - Pt mixing, the non-dispersive bend angle contributes by a factor of ~100 to the FF ratio systematic error.However, it is very small: ±1.1 mrad (FWHM) and can be reconstructed with high precision (~0.1mrad).
-0.0025 -0.002 -0.0015 -0.001 -0.0005 0 0.0005 0.001 0.0015 0.002 0.00250
20
40
60
80
100
120
140
160
SBS Δφ σ = 0.00046
Systematic error is 10% of projected statistical error
Calibration Scheme
Will need to:• Calibrate Momentum (P0 and δ)
• Calibrate Angle reconstruction (θ0 & φ0)• Calibrate Vertex reconstruction (y0)
Calibration scheme cont’d
• Do a series of elastic scattering runs (H2(e,e’p))– δ scans (P0 and δ)– with and without sieve slit (θ0 & φ0)– Requires a proton arm in coincidence
• Segmented extended target (y0)– i.e. a series of thin targets along the beamline
• Has been very successfully done with BigBite• Compare to Magnet off
– straight throughs
Conclusion
• Magnet exists and is available• Magnet will work nicely
–with proposed modifications• Optics are very simple
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