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

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

+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

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

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

+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

ẑ

ŷ

x

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

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

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

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

Effect of varying initial transverse velocity, vyi

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

-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

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

Time of Flight (TOF) yi = 0 and vyi = 0

+V

-V

z=668mmL=64mm

l=945mm

d=30mm

Radius=40mm

Detector

Interaction region

The Ideal TOF

tsimion ≠ tideal

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

TOF dependence on initial position along y-axis, yi

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

TOF dependence on initial y-velocity, vyi

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

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

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

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

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)

Summary

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

Future Directions

ImagingRewrite equations to reconstruct vyi

Simulations of vyi directed away from the detector should be run