IES Calibration Modeling

Phil Valek and Roman GomezMay 29, 2013

Outline

• Summary of testing• Recent Modeling and Analysis Results• Remaining Work

IES in Calibration Chamber

Calibration notes

• Calibration performed over 3 different time periods, with the last occurring as part of a refurbishment– Oct 1999– Sept 2001– July 2003 (15 keV and 2 keV)

• Calibration perform primarily with positive ions and some tests with negative ions

• Records of most of the facility states (i.e. incident beam flux) have been lost– Beam position and energy information is known

Overall Goals

• Use a pre-existing SIMION simulation model to determine transmission characteristics of the IES electron ESA

• Compare simulation and calibration results to arrive at reasonable Geometric Factor (G) values for all 16 azimuth anodes

• Apply these findings to in-flight instrument data (forthcoming)

Simulation Technique: Reverse-fly

• Particles are started from the detector and flown out of the ESA

• Position, angle, energy, and velocity values are recorded for particles exiting the analyzer

• Particle trajectories are reversed (velocity vectors in particular) and the inverted quantities are used to determine the ESA transmission characteristics

Simulation Geometry

• Acquired from Greg Miller• Rotated for ease of simulating Electron ESA• 1:1 dimensional correspondence with flight model• SIMION model includes potential arrays for individual

ESA plates, detectors and deflection electrodes• All potential array are programmatically adjustableSide View: Electron ESA Bottom

IES: Iso-view

Electron ESA

Ion ESA

Electron DEF

Ion DEF

IonDef: 0 V ElecDef: 0V

Reverse Fly of IES• Four Energies Chosen: 17.26 eV, 172.60

eV, 1756.23 eV, and 17670 eV.• Preliminary: Particles gridded in energy,

angles, and position systematically flown from the detector to define the edges of the ESA’s transmission envelope

• Once found, the limiting trajectories are used to “bracket” the values of a randomized distribution at the detector.

• Transmission envelope at 17.26 eV shown in three views: ESA Voltage = 1.628 V

Side View

Top View Edge-on View

Flyback Checks

Side View

Top View

Edge-on View

Edge-on View w/2500 V on MCP

17.26 eV Flyback Results

Energy-Impact Differences

• The impact positions of lower energy particles spread out because of the field between the ESA exit and the detector at 2500 V

17.26 eV hit positions w/2500 V on MCP

17.67 keV hit positions w/2500 V on MCP

Simulation Results

13 14 15 16 17 18 19 20 21 220.0

0.2

0.4

0.6

0.8

1.0

IES-electrons Energy Response-17.26 eV

Norm

aliz

ed R

esp

onse

Energy (eV)

Model Extreme

Equation double z = (x-xc)/w;y = y0+A*exp(-exp(-z)-z+1);

Reduced Chi-Sqr 1.26872E-4

Adj. R-Square 0.99878

Value Standard Error

Normalized Response y0 -0.00596 0.0019

Normalized Response xc 17.0297 0.00295

Normalized Response w 0.585 0.0035

Normalized Response A 1.00011 0.00446

140 150 160 170 180 190 200 2100.0

0.2

0.4

0.6

0.8

1.0

IES-electrons Energy Response-172.60 eV

Norm

aliz

ed R

esp

onse

Energy (eV)

1500 1600 1700 1800 1900 2000 21000.0

0.2

0.4

0.6

0.8

1.0

Norm

aliz

ed R

esp

onse

Energy (eV)

Normalized Response

16000 17000 18000 19000 20000 210000.0

0.2

0.4

0.6

0.8

1.0

Norm

aliz

ed R

esp

onse

Energy (eV)

Model Extreme

Equation double z = (x-xc)/w;y = y0+A*exp(-exp(-z)-z+1);

Reduced Chi-Sqr

3.77517E-4

Adj. R-Square 0.99659

Value Standard Error

Normalized Response

y0 -0.01073 0.0024

Normalized Response

xc 17769.36958 2.45794

Normalized Response

w 627.19612 3.43772

Normalized Response

A 0.9707 0.0036

17.26 eV 172.60 eV 1756.23 eV 17670.20 eV

Energy

-6 -4 -2 0 2 4 60.0

0.2

0.4

0.6

0.8

1.0

IES-electrons Azimuth Response-17.26 eV

Norm

aliz

ed R

esp

onse

Azimuth (degrees)

-6 -4 -2 0 2 4 60.0

0.2

0.4

0.6

0.8

1.0

IES-electrons Azimuth Response-172.60 eV

Norm

aliz

ed R

esp

onse

Azimuth (degrees)

-6 -4 -2 0 2 4 60.0

0.2

0.4

0.6

0.8

1.0

Norm

aliz

ed R

esp

onse

Alpha (degrees)

Normalized Response

-6 -4 -2 0 2 4 60.0

0.2

0.4

0.6

0.8

1.0

Norm

aliz

ed R

esp

onse

Alpha (degrees)

Alpha-Elevation

14

Simulation Results

-10 -5 0 5 100.0

0.2

0.4

0.6

0.8

1.0

IES-electrons Elevation Response 5 degree detector section-17.26 eV

Norm

aliz

ed R

esp

onse

Elevation (degrees)

Model Asym2Sig

Equation y =y0+ A*(1/(1+exp(-(x-xc+w1/2)/w2)))*(1-1/(1+exp(-(x-xc-w1/2)/w3)))

Reduced Chi-Sqr 2.39317E-4

Adj. R-Square 0.99812

Value Standard Error

Normalized Response y0 -7.14467E-4 0.00131

Normalized Response xc 0.00662 0.00566

Normalized Response A 0.95802 0.00385

Normalized Response w1 4.98099 0.01459

Normalized Response w2 0.41196 0.00806

Normalized Response w3 0.40656 0.00799

-15 -10 -5 0 5 10 150.0

0.2

0.4

0.6

0.8

1.0

IES-electrons Elevation Response-172.60 eV

Norm

aliz

ed R

esp

onse

Elevation (degrees)

-5 0 50.0

0.2

0.4

0.6

0.8

1.0

Norm

aliz

ed R

esp

onse

Beta (degrees)

Normalize to [0, 1] of "Count"

-10 -5 0 5 100.0

0.2

0.4

0.6

0.8

1.0

Norm

aliz

ed R

esp

onse

Beta (degrees)

Normalize to [0, 1] of "Count"

14 15 16 17 18 19 20 21

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

Energy (eV)

Azi

mu

th (

de

gre

es)

0.000

0.1000

0.2000

0.3000

0.4000

0.5000

0.6000

0.7000

0.8000

0.9000

1.000Energy-Alpha Response (17.26 eV)

150 160 170 180 190 200 210

-6

-4

-2

0

2

4

6

Energy (eV)

Azi

mu

th (

de

gre

es)

0.000

0.1000

0.2000

0.3000

0.4000

0.5000

0.6000

0.7000

0.8000

0.9000

1.000Energy-Alpha Response (172.60 eV)

Beta-Azimuth

Integrated Response

15

Tabulated ResultsEnergy (eV) <dE/E d(Alpha)>

(eV/eV*rad)A(eff) (squ. cm) d(Beta) (rad) G(pixel)( squ

cm*sr*eV/eV)17.26 2.67e-3 0.11 0.393 1.15e-4172.60 2.60e-3 0.11 0.393 1.12e-41756.23 2.64e-3 0.11 0.393 1.14e-417670.6 2.44e-3 0.11 0.393 1.05e-4

Geometric Factors are determined with Gosling’s formula:

E

EAG eff

Where:• Aeff is determined by flying a normal incidence beam

from a set area and then computingflown

flown

transeff A

N

NA

• <E/E α> is determined by flying a normal incidence beam from a set area and then computing:

ji

jij

i N

N

E

E

E

E,

max

,

• And is the coverage of one azimuth anode 22.5°= 0.393 radians.

Ion: 21 V Elec: -21 V Ion: -21 V Elec: 21 V

Ion: 55 V Elec: -55 V Ion: -55 V Elec: 55 V

17

150 155 160 165 170 175 180 185 190 195 200

-56

-54

-52

-50

-48

-46

Ion Def = -55 V; Electron Def = 55 V; ESA = 16.283 V

Energy (eV)

Alp

ha (

degre

es)

0.000

0.1000

0.2000

0.3000

0.4000

0.5000

0.6000

0.7000

0.8000

0.9000

1.000

Ion Def = 63 V; Electron Def = -63 V;

18

150 160 170 180 190 200

-56

-54

-52

-50

-48

-46

-44

-42

-40

-38Ion Def = 55 V; Electron Def = -55 V; ESA = 16.283 V

Energy (eV)

Alp

ha (

degre

es)

0.000

0.1000

0.2000

0.3000

0.4000

0.5000

0.6000

0.7000

0.8000

0.9000

1.000

19

150 155 160 165 170 175 180 185 190 195 200-48

-46

-44

-42

-40

-38

-36

Ion Def = 47 V; Electron Def = -47 V; ESA = 16.283 V

Energy (eV)

Alp

ha (

degre

es)

0.000

0.1000

0.2000

0.3000

0.4000

0.5000

0.6000

0.7000

0.8000

0.9000

1.000

20

150 155 160 165 170 175 180 185 190 195 200

-36

-34

-32

-30

Ion Def = 38 V; Electron Def = -38 V; ESA = 16.283 V

Energy (eV)

Alp

ha (

degre

es)

0.000

0.1000

0.2000

0.3000

0.4000

0.5000

0.6000

0.7000

0.8000

0.9000

1.000

21

150 155 160 165 170 175 180 185 190 195 200-30

-28

-26

-24

-22Ion Def = 30 V; Electron Def = -30 V; ESA = 16.283 V

Energy (eV)

Alp

ha (

degre

es)

0.000

0.1000

0.2000

0.3000

0.4000

0.5000

0.6000

0.7000

0.8000

0.9000

1.000

22

150 155 160 165 170 175 180 185 190 195 200

-22

-20

-18

-16

Ion Def = 21 V; Electron Def = -21 V; ESA = 16.283 V

Energy (eV)

Alp

ha (

degre

es)

0.000

0.1000

0.2000

0.3000

0.4000

0.5000

0.6000

0.7000

0.8000

0.9000

1.000

23

150 155 160 165 170 175 180 185 190 195 200

-16

-14

-12

-10

Ion Def = 13 V; Electron Def = -13 V; ESA = 16.283 V

Energy (eV)

Alp

ha (

degre

es)

0.000

0.1000

0.2000

0.3000

0.4000

0.5000

0.6000

0.7000

0.8000

0.9000

1.000

24

150 155 160 165 170 175 180 185 190 195 200

-8

-6

-4

-2

Energy (eV)

Alp

ha (

degre

es)

0.000

0.1000

0.2000

0.3000

0.4000

0.5000

0.6000

0.7000

0.8000

0.9000

1.000Ion Def = 4 V; Electron Def = -4 V; ESA = 16.283 V

25

150 155 160 165 170 175 180 185 190 195 200-6

-4

-2

0

2Ion Def = 0V; Electron Def = 0V; ESA = 16.283 V

Energy (eV)

Alp

ha (

degre

es)

0.000

0.1000

0.2000

0.3000

0.4000

0.5000

0.6000

0.7000

0.8000

0.9000

1.000

26

150 155 160 165 170 175 180 185 190 195 200-2

0

2

4

6Ion Def = -4 V; Electron Def = 4 V; ESA = 16.283 V

Energy (eV)

Alp

ha (

degre

es)

0.000

0.1000

0.2000

0.3000

0.4000

0.5000

0.6000

0.7000

0.8000

0.9000

1.000

27

150 155 160 165 170 175 180 185 190 195 200

6

8

10

12

Ion Def = -13 V; Electron Def = 13 V; ESA = 16.283 V

Energy (eV)

Alp

ha (

degre

es)

0.000

0.1000

0.2000

0.3000

0.4000

0.5000

0.6000

0.7000

0.8000

0.9000

1.000

28

150 155 160 165 170 175 180 185 190 195 20012

14

16

18

20Ion Def = -21 V; Electron Def = 21 V; ESA = 16.283 V

Energy (eV)

Alp

ha (

degre

es)

0.000

0.1000

0.2000

0.3000

0.4000

0.5000

0.6000

0.7000

0.8000

0.9000

1.000

29

150 155 160 165 170 175 180 185 190 195 20018

20

22

24

26Ion Def = -30 V; Electron Def = 30 V; ESA = 16.283 V

Energy (eV)

Alp

ha (

degre

es)

0.000

0.1000

0.2000

0.3000

0.4000

0.5000

0.6000

0.7000

0.8000

0.9000

1.000

30

150 155 160 165 170 175 180 185 190 195 200

24

26

28

30

32

Ion Def = -38 V; Electron Def = 38 V; ESA = 16.283 V

Energy (eV)

Alp

ha (

degre

es)

0.000

0.1000

0.2000

0.3000

0.4000

0.5000

0.6000

0.7000

0.8000

0.9000

1.000

31

150 155 160 165 170 175 180 185 190 195 200

30

32

34

36

38

40

42

44

Ion Def = -47 V; Electron Def = 47 V; ESA = 16.283 V

Energy (eV)

Alp

ha (

degre

es)

0.000

0.1000

0.2000

0.3000

0.4000

0.5000

0.6000

0.7000

0.8000

0.9000

1.000

32

150 155 160 165 170 175 180 185 190 195 20034

36

38

40

42

44

46

48

50

52

54Ion Def = -55 V; Electron Def = 55 V; ESA = 16.283 V

Energy (eV)

Alp

ha (

degre

es)

0.000

0.1000

0.2000

0.3000

0.4000

0.5000

0.6000

0.7000

0.8000

0.9000

1.000

33

150 155 160 165 170 175 180 185 190 195 200

40

50

60

Ion Def = -63 V; Electron Def = 63 V; ESA = 16.283 V

Energy (eV)

Alp

ha (

degre

es)

0.000

0.1000

0.2000

0.3000

0.4000

0.5000

0.6000

0.7000

0.8000

0.9000

1.000

Remaining analysis

• Scale simulation results to match calibration values– The simulation generally agrees with the calibration results with

small differences– Example: Analyzer constant- simulated 10.6 vs calibration 10.8

• Determine Geometric factor for each IES energy / angle step– Simulation values assume 100% grid transmission and 100%

detector efficiency– Using 2003 calibration data, we can determine the scaling factor

for 2 and 15 keV– Published MCP efficiencies will be used to fill in the remaining

energies• Produce an analytical model of the IES response