By Bret Polopolus
Thanks to Itzik Ben-Itzhak and Bishwanath Gaire
J.R. Macdonald Laboratory, Physics Department,
Kansas State University, Manhattan, Kansas 66506
This work was partially funded under NSF grant number PHY-0851599
Supported by the Chemical Sciences, Geosciences, and Biosciences Division,
Office of Basic Energy Sciences, Office of Science, U.S. Department of Energy
Overview
 A 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
Detector
Interaction region
L=64mm
+V
z=668mm
Radius=40mm
d=30mm
-V
l=945mm
Ideal Parallel Plate Deflector
Geometry
Plate Length L = 64 mm
Plate separation d = 30 mm
Detector’s distance from plates z = 668 mm,
Distance from interaction to detection l = 944 mm
Real Parallel Plate Deflector
x
ẑ
ŷ
Without a deflector
Fragments with a low Kinetic Energy Release (KER)
are lost in the faraday cup
Ion Beam is run with an energy of 3-8 keV
O2+ dissociation
40 fs laser
1000
6000
8000
Counts
Counts
6000
4000
500
4000
2000
0
2000
0.075
1
2
3
KER (eV)
0
0
1
2
KER (eV)
3
4
0
0
1
2
KER (eV)
Low KER fragments are lost into the faraday cup
3
4
What is the deflection with yi = 0 and vyi = 0?
Detector
Interaction region
L=64mm
+V
z=668mm
Radius=40mm
d=30mm
-V
l=945mm
 Equation for deflection
 Slope with our geometry
 qV/E is a useful scaling factor between the beam and
the defelctor
x
ẑ
ŷ
90
Chi^2/DoF = 0.00002
R^2
= 1
|yf - yi| = 896.62711x +/- 0.02411
90
80
70
70
60
60
50
50
40
Values above this line miss
the real detector, i.e.,
qV/E < 0.045
30
Deflection (mm)
|yf - yi|
Deflection (mm)
|yf - yi|
80
40
30
20
20
10
10
0
0.00
0.02
0.04
0.06
0.08
0.10
qV/E
V = 30
V = 60
V = 90
V = 120
V = 150
V = 180
0
0.00
0.02
0.04
0.06
0.08
qV/E
Correction factor: ratio of real slope simulated in SIMION to ideal slope
896.63/746.67 = 1.20
What can we conclude?
 Modified ideal equation:
 Correction factor seems independent of detector
position and likely the result of the fringing electric
field:
Effect of varying initial position
y (mm)
Deflection along y
axis by real deflector
with
z = 668 mm simulated
in SIMION
Deflection spread
for qV/E = 0.04
±0.04 mm, which is o.11%
yi = 1
26.925
Deflection (mm)
|yf - yi|
Worst Case Scenario
26.930
26.920
yi = 0.8
26.915
yi = 0.6
yi = 0.4
26.910
yi = 0.2
26.905
yi = 0
26.900
yi = -0.2
26.895
yi = -0.4
26.890
yi = -0.6
26.885
yi = -0.8
26.880
yi = -1
0.02
0.03
qV/E
Resolution requirement
0.1 mm
0.04
Result
 Largest 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
Effect of varying initial transverse
velocity, vyi
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
85
80
75
Worst Case Scenario
Deflection spread about
±40 mm
y = 1.5119*vyi + 26.936
y = 1.4933*vyi + 53.8
70
65
y = 1.2381*vyi + 26.906
60
y (mm)
55
50
y = 1.2439*vyi + 8.9694
45
40
y = 0.8796*vyi + 8.9696
35
30
25
20
15
10
5
0
2
4
6
8
10 12 14 16 18 20 22 24 26 28 30 32 34
vyi (mm/s)
Ideal equation
t is not constant
15
10
5
0
-5
-10
y (mm)
-15
-20
-25
-30
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
-35
-40
-45
-50
-55
-60
-5
0
5
10
15
20
25
30
35
vyi x tsimion (mm)
40
45
50
55
Result
 y 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


The Ideal TOF
Interaction region
L=64mm
+V
Detector
z=668mm
d=30mm
-V
l=945mm
tsimion ≠ tideal
Radius=40mm
x = qV/E
terror = tsimion - tideal (ns)
Intercept set to 0, yi = 0, vyi = 0
4
3
2
R =1
2
0
0.00
Resolution Requirement
25 ps
2
terror = 3092x + 283.74x - 2.1394x
0.02
0.04
0.06
0.08
0.10
0.06
0.08
0.10
terror - tfit (ns)
qV/E
0.010
0.008
0.006
0.004
0.002
0.000
-0.002
-0.004
-0.006
-0.008
-0.010
-0.012
0.00
Residuals
0.02
0.04
qV/E
2.12
yi = 0.6
Spread ≈ ±71 ps
t = tsimion - tideal (ns)
2.10
2.08
yi = 0.4
2.06
yi = 0.2
2.04
yi = 0
2.02
yi = -0.2
2.00
yi = -0.4
1.98
yi = -0.6
1.96
0.030
0.045
qV/E
Resolution Requirement
25 ps
0.060
vyi to -V side of deflector
7.0
6.5
6.0
5.5
terror= tsimion- tideal (ns)
5.0
4.5
4.0
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
3.5
3.0
2.5
2.0
1.5
1.0
0.5
0.0
0.000
0.005
0.010
0.015
0.020
vyi (mm/ns)
0.025
0.030
0.035
y=2.8644x+0.025
y=5.0624x+0.0488
y=10.119x+0.0671
y=7.316x+0.075
y=30.031x+0.6187
y=44.522x+0.758
y=32.93x+1.2212
y=57.711x+2.5192
y=86.754x+3.0805
y=192.08x+4.5642
200
180
m = slope from |TOF vs vyi|
160
140
120
100
80
60
40
20
0
-20
0.00
0.01
0.02
0.03
qV/E
0.04
0.05
0.06
Hold E constant, E=3000 eV
Hold V constant, V = 60
200
60
180
160
2
m = 47803x + 86.468x
m = 989.51x
50
m = slope from |TOF vs vyi|
m = slope from |TOF vs vyi|
140
120
100
80
60
40
30
40
20
20
0
-20
0.00
10
0.01
0.02
0.03
qV/E
0.04
0.05
0.06
0.01
0.02
0.03
0.04
qV/E
0.05
0.06
180000
Scaled slope = slope x E
160000
6
y = 3x10 x
140000
120000
100000
80000
60000
40000
20000
0
0.00
0.01
0.02
0.03
qV/E
0.04
0.05
0.06
qV/E = 90/3000 = 0.03
y = -95.438x + 1.964
t x E/l (ns eV/mm)
t x E/l (ns eV/mm)
2
qV/E = 60/2000 = 0.03
2
0
-2
y = -95.738x + 1.5996
0
-2
0.000
0.005
0.010
0.015
0.020
0.025
0.030
0.035
0.000
0.005
0.010
0.015
0.020
0.025
0.030
0.035
0.030
0.035
Vyi (mm/ns)
Vyi (mm/ns)
Residuals for 60/2000
Residuals for 90/3000
0.015
0.020
0.010
t x E/l - fit (ns eV/mm)
t x E/l - fit (ns eV/mm)
0.015
0.010
0.005
0.000
-0.005
-0.010
0.005
0.000
-0.005
-0.010
-0.015
-0.015
0.000
0.005
0.010
0.015
0.020
0.025
Vyi (mm/ns)
0.030
0.035
0.000
0.005
0.010
0.015
0.020
0.025
Vyi (mm/ns)
Deflection yi = 0
no modification
vyi and time of flight are coupled
Deflection spread
±0.04 mm
vyi ≠ 0, Deflection spread about ±40 mm
TOF correction for yi = 0, vyi = 0
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
Future Directions
Simulations of vyi directed away from the
detector should be run
Imaging
Rewrite equations to reconstruct vyi