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Corrections to H+ deflection and time of flight for an ideal parallel plate deflector using a
real deflector simulated with SIMION
By Bret PolopolusThanks to Itzik Ben-Itzhak and Bishwanath Gaire
Supported by the Chemical Sciences, Geosciences, and Biosciences Division, Office of Basic Energy Sciences, Office of Science, U.S. Department of Energy
J.R. Macdonald Laboratory, Physics Department, Kansas State University, Manhattan, Kansas 66506
This work was partially funded under NSF grant number PHY-0851599
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OverviewA molecular ion beam is sent toward a detector
The laser interacts with the ion beam dissociating
H2+ → H + H+
The particles move through a parallel plate deflector to separate their detection
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+V
-V
z=668mmL=64mm
l=945mm
d=30mm
Radius=40mm
Detector
Interaction region
GeometryPlate Length L = 64 mmPlate separation d = 30 mmDetector’s distance from plates z = 668 mm,Distance from interaction to detection l = 944 mm
Ideal Parallel Plate Deflector
Real Parallel Plate Deflector
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ẑ
ŷ
x
Ion Beam is run with an energy of 3-8 keV
Without a deflectorFragments with a low Kinetic Energy Release (KER)
are lost in the faraday cup
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0 1 2 3 40
2000
4000
6000
Cou
nts
KER (eV)
Low KER fragments are lost into the faraday cup
O2+ dissociation
40 fs laser
0 1 2 3 40
2000
4000
6000
8000
1 2 30
500
1000
Cou
nts
KER (eV)
KER (eV)0.075
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+V
-V
z=668mmL=64mm
l=945mm
d=30mm
Radius=40mm
Detector
Interaction region
What is the deflection with yi = 0 and vyi = 0?
Equation for deflection
Slope with our geometry
qV/E is a useful scaling factor between the beam and the defelctor
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Correction factor: ratio of real slope simulated in SIMION to ideal slope
896.63/746.67 = 1.20
0.00 0.02 0.04 0.06 0.080
10
20
30
40
50
60
70
80
90
0.00 0.02 0.04 0.06 0.08 0.100
10
20
30
40
50
60
70
80
90
V = 30 V = 60 V = 90 V = 120 V = 150 V = 180
Def
lect
ion
(mm
)|y
f - y i|
qV/E
Chi^2/DoF = 0.00002R^2 = 1 |yf - yi| = 896.62711x +/- 0.02411
Def
lect
ion
(mm
)|y
f - y
i|
qV/E
Values above this line miss the real detector, i.e.,qV/E < 0.045
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What can we conclude?Modified ideal equation:
Correction factor seems independent of detector position and likely the result of the fringing electric field:
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Effect of varying initial position
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Deflection along y axis by real deflector with z = 668 mm simulated in SIMION
Worst Case Scenario
Deflection spread for qV/E = 0.04 ±0.04 mm, which is o.11%
0.02 0.03 0.04
26.880
26.885
26.890
26.895
26.900
26.905
26.910
26.915
26.920
26.925
26.930
Def
lect
ion
(mm
)|y
f - y i|
qV/E
yi = 1
yi = 0.8
yi = 0.6
yi = 0
yi = 0.2
yi = 0.4
y (mm)
yi = -1
yi = -0.8
yi = -0.6
yi = -0.2
yi = -0.4
Resolution requirement0.1 mm
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ResultLargest δy was about 0.0408 mm for qV/E = 0.04
Resolution limit on distinguishing deflections:• δy ≥ 0.1 mm
qV/E = 0.0632 → δy = 0.1014• Irrelevant because proton would miss 40 mm detector
Conclusion: no need to modify the ideal equation for initial position nor run SIMION for every variation
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Effect of varying initial transverse velocity, vyi
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Ideal equation
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 345
1015
20
25
30
35
4045
50
55
60
6570
75
80
85 y = 1.4933*vyi + 53.8
y = 1.5119*vyi + 26.936
y = 1.2381*vyi + 26.906
y = 0.8796*vyi + 8.9696
y = 1.2439*vyi + 8.9694
V = 30, qV/E = 0.01 V = 60, qV/E = 0.01 V = 60, qV/E = 0.03 V = 90, qV/E = 0.03 V = 120, qV/E = 0.06
y (m
m)
vyi (mm/s)
Worst Case ScenarioDeflection spread
about ±40 mm
t is not constant
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-5 0 5 10 15 20 25 30 35 40 45 50 55-60
-55
-50
-45
-40
-35
-30
-25
-20
-15
-10
-5
0
5
10
15
vyi x t
simion (mm)
y (m
m)
qV/E = 90/3000 = 0.03, y = 0.9945x - 26.904 qV/E = 60/2000 = 0.03, y = 0.9945x - 26.903 qV/E = 60/1000 = 0.06, y = 0.9776x - 53.793 qV/E = 120/2000 = 0.06, y = 0.9779x - 53.793 qV/E = 180/3000 = 0.06, y = 0.9782x - 53.793
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Resulty intercept is
Expectation: identical slopes for same qV/E
Not the case Explanation → vyi and time of flight are coupled
Time of flight is not constant! Use tsimion instead of tideal
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Time of Flight (TOF) yi = 0 and vyi = 0
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+V
-V
z=668mmL=64mm
l=945mm
d=30mm
Radius=40mm
Detector
Interaction region
The Ideal TOF
tsimion ≠ tideal
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x = qV/E
0.00 0.02 0.04 0.06 0.08 0.10
0
2
4
0.00 0.02 0.04 0.06 0.08 0.10-0.012-0.010-0.008-0.006-0.004-0.0020.0000.0020.0040.0060.0080.010
Intercept set to 0, yi = 0, vyi = 0
terror
= 3092x3 + 283.74x2 - 2.1394x
R2 = 1
t erro
r = t
sim
ion -
t idea
l (ns)
qV/Et er
ror -
tfit (n
s)
qV/E
Residuals
Resolution Requirement25 ps
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TOF dependence on initial position along y-axis, yi
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0.030 0.045 0.060
1.96
1.98
2.00
2.02
2.04
2.06
2.08
2.10
2.12
yi = -0.6
yi = -0.4
yi = -0.2
yi = 0.6
yi = 0.4
yi = 0.2
t =
t sim
ion -
t idea
l (ns)
qV/E
yi = 0
Resolution Requirement25 ps
Spread ≈ ±71 ps
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TOF dependence on initial y-velocity, vyi
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0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.0350.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
6.0
6.5
7.0
vyi to -V side of deflector
qV/E = 0.0075 qV/E = 0.01 qV/E = 0.01 qV/E = 0.012 qV/E = 0.03 qV/E = 0.03 qV/E = 0.045 qV/E = 0.06 qV/E = 0.06 qV/E = 0.06
t erro
r= t
sim
ion- t
idea
l (ns
)
vyi (mm/ns)
y=2.8644x+0.025y=5.0624x+0.0488y=10.119x+0.0671y=7.316x+0.075y=30.031x+0.6187y=44.522x+0.758y=32.93x+1.2212y=57.711x+2.5192y=86.754x+3.0805y=192.08x+4.5642
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0.00 0.01 0.02 0.03 0.04 0.05 0.06-20
0
20
40
60
80
100
120
140
160
180
200
m =
slo
pe fr
om |T
OF
vs v
yi|
qV/E
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0.00 0.01 0.02 0.03 0.04 0.05 0.06-20
0
20
40
60
80
100
120
140
160
180
200
0.01 0.02 0.03 0.04 0.05 0.06
10
20
30
40
50
60
Hold V constant, V = 60
m = 47803x2 + 86.468x
m =
slo
pe fr
om |T
OF
vs v
yi|
qV/E
m = 989.51x
Hold E constant, E=3000 eV
m =
slo
pe fr
om |T
OF
vs v
yi|
qV/E
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0.00 0.01 0.02 0.03 0.04 0.05 0.060
20000
40000
60000
80000
100000
120000
140000
160000
180000
y = 3x106xS
cale
d sl
ope
= sl
ope
x E
qV/E
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0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.035-2
0
2
0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.035-2
0
2
0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.035
-0.015
-0.010
-0.005
0.000
0.005
0.010
0.015
0.020
0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.035
-0.015
-0.010
-0.005
0.000
0.005
0.010
0.015
t x
E/l (
ns e
V/m
m)
Vyi (mm/ns)
y = -95.438x + 1.964
qV/E = 90/3000 = 0.03qV/E = 60/2000 = 0.03
y = -95.738x + 1.5996
t x
E/l (
ns e
V/m
m)
Vyi (mm/ns)
Vyi (mm/ns)
t x
E/l -
fit (
ns e
V/m
m)
Residuals for 90/3000 Residuals for 60/2000
t x
E/l -
fit (
ns e
V/m
m)
Vyi (mm/ns)
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Deflection yi = 0 no modification
vyi and time of flight are coupled
x = qV/E
yi ≠ 0 after y = 0 correction error is reduced to about ± 71 ps
vyi ≠ 0 introduces an error of up to 2 ns
TOF correction for yi = 0, vyi = 0
vyi ≠ 0, Deflection spread about ±40 mm
Deflection spread
±0.04 mm
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Future Directions
ImagingRewrite equations to reconstruct vyi
Simulations of vyi directed away from the detector should be run