Tracking through Measured
Misalignments
Chris Rogers,
ASTeC,
Rutherford Appleton Laboratory
1
Three Questions





Can we observe measured misalignments using a beam based
alignment technique, with only one module at a time powered?
Can we observe measured misalignments using a beam-based
alignment technique, with all modules powered?
Can we tolerate measured misalignments and still observe
cooling
First study
No material or detectors...


Probably given sufficient statistics, we can untangle these effects
No thought given to proper magnet currents...

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We can at least change FC, M1, M2 currents
We can probably change E1, CC, E2 currents

I do not intend to use momentum reconstruction in any analysis
2
Geometry as per 2015-04-22
SSU
Z
Z
x0
(local)
(global)
Upstream Flange
-3256
-3956
0.09
Centre Centre coil
-1750
-2450 0.317856
Downstream Flange
247
-453
0.62
y0
theta_x [rad]
theta_y [rad]
-0.36
-0.8974
-1.61
0.0001512989
-0.000356837
-0.730
-0.3385
0.053
-0.0003720379
0.0009277249
453
0.8
-3.9
2450 0.609693 -8.64541 -9.529664896E-005
3706
0.49
-11.63
-0.0023762636
FC
Upstream
Centre
Downstream
-422
0
422
Upstream Flange
Centre centre coil
Downstream Flange
853
2850
4106
-422
0
422
0.588
0.431
0.274
SSD


Blue numbers are Rogers calculated position/alignment
I insert test volumes, at the flange position, into my geometry
and check that they return appropriate position rotation
3
MAUS Coil Geometry
Name
FocusCoil_US
FocusCoil_DS
MatchCoil1_DS
MatchCoil2_DS
EndCoil1_DS
CenterCoil_DS
EndCoil2_DS
MatchCoil1_US
MatchCoil2_US
EndCoil1_US
CenterCoil_US
EndCoil2_US
Current Density
60
60
129
120
124.512
144.896
133.877
129
120
124.512
144.896
133.877
Position
(0,0,-202.75)
(0,0,202.75)
(0,0,861)
(0,0,1300)
(0,0,1700)
(0,0,2450)
(0,0,3200)
(0,0,-861)
(0,0,-1300)
(0,0,-1700)
(0,0,-2450)
(0,0,-3200)
Rotation Vector
(0,0,1)
(0,0,1)
(0,0,1)
(0,0,1)
(0,0,1)
(0,0,1)
(0,0,1)
(0,0,1)
(0,0,1)
(0,0,1)
(0,0,1)
(0,0,1)
Angle
Name
FocusCoil_US
FocusCoil_DS
MatchCoil1_DS
MatchCoil2_DS
EndCoil1_DS
CenterCoil_DS
EndCoil2_DS
MatchCoil1_US
MatchCoil2_US
EndCoil1_US
CenterCoil_US
EndCoil2_US
Current Density
60
60
129
120
124.512
144.896
133.877
129
120
124.512
144.896
133.877
Position
(0.506431,-0.526596,-202.75)
(0.355569,-0.150404,202.75)
(0.761119,-4.86953,861.004)
(0.719283,-5.91271,1300)
(0.681165,-6.86321,1700)
(0.609693,-8.64541,2450)
(0.53822,-10.4276,3200)
(0.55827,-1.46441,-861)
(0.49185,-1.30776,-1300)
(0.43133,-1.16502,-1700)
(0.317856,-0.897397,-2450)
(0.204382,-0.629769,-3200)
Rotation Vector
(-0.928149,-0.372208,-0.000172653)
(-0.928149,-0.372208,-0.000172653)
(0.999197,-0.0400713,4.76101e-05)
(0.999197,-0.0400713,4.76101e-05)
(0.999197,-0.0400713,4.76101e-05)
(0.999197,-0.0400713,4.76101e-05)
(0.999197,-0.0400713,4.76101e-05)
(0.920662,0.390361,-6.96476e-05)
(0.920662,0.390361,-6.96476e-05)
(0.920662,0.390361,-6.96476e-05)
(0.920662,0.390361,-6.96476e-05)
(0.920662,0.390361,-6.96476e-05)
Angle
0.0572696
0.0572696
0.136259
0.136259
0.136259
0.136259
0.136259
0.0222071
0.0222071
0.0222071
0.0222071
0.0222071
0
0
0
0
0
0
0
0
0
0
0
0
4
All Modules Powered

Tracking, shell of particles



8 mm amplitude
Typical of low emittance beamline
Beam is basically well behaved
5
All Modules Powered

Transverse displacement of the particles (dx, dy), following
misaligment, at downstream tracker planes is readily observable

No guarantee that we can untangle the different magnet
misalignments from each other
6
SSU Powered, reference currents

Tracking, shell of particles



8 mm amplitude
Typical of low emittance beamline
Straight tracks downstream
7
SSU Powered

Transverse offset at downstream tracker planes is readily
observable
8
AFC Powered, reference currents

Tracking, shell of particles



8 mm amplitude
Typical of low emittance beamline
Where SSU is not powered, I insert
beam with unrealistic 333 mm beta
but not angular momentum
9
AFC Powered

Transverse offset at downstream tracker planes is readily
observable


Note, no tracks at z = 2918.5
Transmission can be improved by tuning down the AFC current
10
SSD Powered, reference currents

Tracking, shell of particles



8 mm amplitude
Typical of low emittance beamline
Where SSU is not powered, I insert
beam with unrealistic 333 mm beta
but not angular momentum
11
SSD Powered

Transverse offset at downstream tracker planes is readily
observable

Note displacements ~ 100 mm
12
Beam centroid
10k muons

Now track sample of particles through the cooling channel
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10k muons
All magnets powered
Random seed = initial emittance
BLACK: magnets with perfect alignment (3, 6, 12 mm emittance)
BLUE: magnets with measured alignment (3, 6, 12 mm
emittance)
X-z: no observation outside of statistics – sample too small?
Y-z: observe systematic displacement of beam mean
13
Beam emittance
1k muons
1k muons
1k muons

How does the emittance respond?
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
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BLACK: magnets with perfect
alignment
BLUE: magnets with measured
alignment
Small increase in emittance
14
From the Beam's Perspective

The measured misalignments are expected to induce a
transverse kick to individual particles >> tracker resolution
i.e. can be observed



The measured misalignments are expected to induce a
transverse kick to the beam >> tracker resolution i.e. can be
observed
The number of particles and analysis required to make these
observations are not determined
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
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Number of particles => how much noise in the system?
Analysis => fit to position data through misaligned fields...
The beam emittance does not appear to be perturbed by the
misalignment


Both for individual modules and the fully powered assembly
Something of a surprise, could do with a cross-check here
Should choose magnet currents to catch more particles
Show that it is within the possibility of the detectors

Now need to develop an analysis to show it works
15