Optimal Injection Lens Parameters for Improved Energy Resolution of a

Hemispherical Spectrograph

T. J. M. ZOUROS1,2, Omer SISE3, G. MARTÍNEZ4, A. DIMITRIOU1,2, A. LAOUTARIS1,2, I. MADESIS1,2

1Dept. of Physics, Univ. of Crete, P.O Box 2208, GR 71003 Heraklion, Greece. E-mail: tzouros@physics.uoc.gr 2Tandem Accelerator Laboratory, INPP, NCSR Demokritos, GR 15310 Ag Paraskevi, Greece

3Dept. of Science Education, Faculty of Education, Suleyman Demirel University, 32260 Isparta, Turkey4Dept. Física Aplicada III, Facultad de Física, UCM 28040-Madrid, Spain

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Prof. Robert Bunsen

dispersion of light

Optical spectra

What is Spectrograph?(Target area - optics – dispersive element – optics – detector – DAQ

unit )

• a spectrograph

• a spectrometer

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With charged particles, the scenario is practically the same.

What about charged particles?

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Hemispherical spectrograph for energy analysis of charged

particles• Principles:– The analyzer disperses

charged particles according to the value of the kinetic energy over charge – Ek/q

– Special arrangement “Biased Paracentric” HDA.

– No additional fringing field corrector electrodes are needed

• Modeling:– Simulation 3D (SIMION, BEM…)

• Simulation:– 2-D image formed at the exit

of the analyzer as a function of the lens voltages and

– compare our results to experimental measurements24.08.2015

Electrostatic field – Ek/q dispersive

E.P. Benis PhD thesis 2001

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The key property: Resolution

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The single-humped dromedary camel

Bactrian camel 

What is this?

Singlet

Or an unresolved two-humped camel?Doublet

Is dromedar an unresolved camel?

With a good resolution there are unlimited possibilities.

If the resolution is good enough, we can see more line shapes.

D

x

D

xx

E

EB

21

The energy resolution of an analyzer depends on many, mainly geometrical, factors. The base energy resolution can be generally expressed as

Energy resolution

Slit Term

Aberration Term

...32221

CBA

D

xx

E

EB

Best (smallest) resolution: large D and small E,Δx, A, B

E

xD

Dispersion

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An injection lens is to focus beam at the HDA entry.

r = source radius q = cone semiangle of sourceE = e- energy at the sourcerp = source image at the HDA entrya = cone seminagle of imageEp = e- energy at the image

Helmoltz-Lagrange equation

Lens magnification

pE

EF Pre-retardation ratio

FMCone semiangle of image defined by the lens

The injection lens

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Angular magnification

...32221

CBA

D

xx

E

EB

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or electron gun

Vp

(a) 3-D rendering of the real HDA with lens and PSD in spectrometer chamber and ion beam line. The two lens electrodes whose voltages are optimized are shown in light blue (VL5) and light green (VL4). The plate electrode which when biased negatively (at VP) is used for pre-retardation is shown in red, while the detection surface of the PSD at the exit of the HDA is shown in purple. (b) Two-dimensional sketch of the simulated experimental setup shown in (a).

Experimental and Simulated Setup

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APAPES – Atomic Physics with Accelerators; Projectile Electron

Spectroscopy http://apapes.physics.uoc.gr/

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Contour maps of VL4 vs VL5 with the z-axis measuring for ΔxB. The black dots represent voltages for the smallest values of ΔxB, while the white dots represent the voltages found empirically.

Possible voltage combinations

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Optimal lens voltages

F 1 2 4 6 8 10

VL4 (V) -570 -695 -570 -700 -840 -840

VL5 (V) 550 200 625 195 -510 -600

D (mm) 159.13 317.29 633.12 948.531262.7

4

1577.4

2

ML -0.24 -0.32 -0.39 -0.41 -0.51 -0.55

Optimal values of the lens voltages giving minimum beam width for different pre-retardation factors F = 1-10. Also listed are the corresponding values of the energy dispersion D and FWHM resolution R, as well as the lens linear magnification ML, for a mm object placed at the center of the electron source.

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Lineshapes for different FExperimental (red circles) and computed (black solid lines) energy spectra for different pre-retardation ratios F = 1-10. The optimizing lens voltages have been found using SIMION. The instrinsic energy resolution of the electron gun (~1.0 eV FWHM) has been taken into account in the simulation.

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Energy Resolution

Relative FWHM Resolution (%) plotted as a function of F: (open triangles) SIMION this work; (Red circles) Recent experimental results using the APAPES setup [5] taken with hot wire e-gun using the lens

voltages.24.08.2015

Best energy resolution attained about 0.1%

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Summary

• We have investigated the voltage settings for the 4-element injection lens of an HDA with virtual entry aperture and 2-D PSD that can lead to improved energy resolution.

• The optimal two lens voltage combinations were found to lie on families of elliptical-like contours.

• As a final test, we also checked our optimal lens voltages on the experimental setup and also measured the FWHM of real electron lines which were in overall good agreement with our simulations.

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AcknowledgementThis research has been co-financed by the European Union and Greek national funds through OP: Education and Lifelong Learning, Research Program: THALES.References1. G. Martínez and M. Sancho, in: P. Hawkes (Ed.), Advances in

Electronics and Electron Physics 81, Academic Press, New York, 1991, pp.1-41.

2. SIMION v.8.1, url: http://simion.com3. T. J. M. Zouros and E. P. Benis, Applied Physics Letters 86 (2005)

094105.4. I. Madesis et al, JPCS 583 (2015) 012014.5. The APAPES collaboration homepage: http://apapes.physics.uoc.gr/

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