1. 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 Heraklion, Greece.
2Tandem Accelerator Laboratory, INPP, NCSR Demokritos, GR Ag Paraskevi, Greece
3Dept. of Science Education, Faculty of Education, Suleyman Demirel University, Isparta, Turkey
4Dept. Física Aplicada III, Facultad de Física, UCM Madrid, Spain
Good afternoon ladies and gentlemen.
First of all, let me thank you all for coming here today.
Allow me to introduce myself. My name is Omer Sise and I’m an assistant prof in Suleyman Demirel University.
I’m doing research into charged particle optics and electron spectroscopy and collaborating with Prof. Theo Zouros and his group in Greece.
My talk is about how to improve the energy resolution of a hemispherical spectrograph by an electrostatic injection lens.
My presentation will be of special interest to those of you who are involved in collision physics.

2. What is Spectrograph? a spectrograph a spectrometer
(Target area - optics – dispersive element – optics – detector – DAQ unit )
a spectrograph
a spectrometer
Prof. Robert Bunsen
dispersion of light
Optical spectra
Let’s start with the definition of spectrograph.
In 1860s, Robert Bunsen, a German chemist, investigated emission spectra of heated elements with the physicist Gustav Kirchhoff. They had invented an appropriate instrument, a prototype spectroscope or spectrograph.
Basicaly, It consists of target area, optics, dispersive element, optics, detector, and DAQ unit. In this mode, there is a fixed film like a position sensitve detector.
In the spectrometric mode, the detector is scanned. Simple counter type detector utilized.
These systems are for the detection of photon or light. This brings us to the next question. What about the energy analysis of charged particles?
With charged particles, the scenario is practically the same.
What about charged particles?
With charged particles, the scenario is practically the same.
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3. 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 measurements
Electrostatic field – Ek/q dispersive
The hemispherical analyzer is one of the most widely used electrostatic dispersive element in low energy atomic collision physics as it can combine high energy resolution with good counting rates.
A special arrangement has come to be known as the “biased paracentric” HDA.
No additional fringing field corrector electrodes are needed which is the big advantage of this arrangement.
In this work, we extend our simulations to the study of the 2-D image formed at the exit of the analyzer as a function of the lens voltages and compare our results to experimental measurements.
E.P. Benis
PhD thesis 2001
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4. The key property: Resolution
What is this?
The single-humped dromedary camel
Singlet
Or an unresolved two-humped camel?
Doublet
Is dromedar an unresolved camel?
This is a single-humped dromedary camel.
One can say that this might be an unresolved two-humped camel.
The question is that Is dromedar an unresolved camel?
With good resolution there are unlimited possibilities.
In electron spectroscopy applications, we can see more line profiles if the resolution is good enough.
The energy resolution measures the ability to distinguish particles with close energies. The better the energy resolution, the better it can separate two adjacent energy peaks.
Bactrian camel 
With a good resolution there are unlimited possibilities.
If the resolution is good enough, we can see more line shapes.
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5. Energy resolution Slit Term Aberration Term
The energy resolution of an analyzer depends on many, mainly geometrical, factors. The base energy resolution can be generally expressed as
Dispersion
Slit Term
Aberration Term
So energy resolution is one of the most important features of an analyzer.
For the ideal HDA, assuming uniform entry illumination, the base energy resolution is given by the well-known formula.
where alpha and beta are the maximum input half-angles in the dispersion and non-dispersion directions, and D is the dispersion. Note that the energy resolution is directly related to dispersion feature (chromatic aberration) of the analyzer. 
A,B,C are tabulated for most known electrostatic analyzers.
Best (smallest) resolution: large D and small E,Δx, A, B

6. The injection lens
An injection lens is to focus beam at the HDA entry.
r = source radius
= cone semiangle of source
E = e- energy at the source
rp = source image at the HDA entry
= cone seminagle of image
Ep = e- energy at the image
Helmoltz-Lagrange equation
Lens magnification
Angular magnification
Here's the most important slide in this talk.
Electrostatic lenses can guide charged particles emitted from a sample to an energy analyzer, analogous to the way an optical lens assists in the transport of light in an optical instrument.
The Helmholtz-Lagrange Law relates the linear magnification and angular magnification to the ratio of initial-to-final electron energy F. Linear magnification is M = Dxp/Dx, where Dx and Dxp are the displacements from the axis of the object and image locations. Angular magnification m = alpha/theta, where theta and alpha are the pencil angles of the object and image points.
The pencil angle and the size of the beam at the exit of the lens are controlled by the lens.
The lens provides a virtual aperture and therefore its settings (particularly its magnification) will be crucial in obtaining high resolution.
Pre-retardation ratio
Cone semiangle of image defined by the lens
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7. Experimental and Simulated Setup
APAPES – Atomic Physics with Accelerators; Projectile Electron Spectroscopy
(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).
or electron gun Vp
Here we will explore the influence of injection lens voltages on the resolution both in experiment and simulation.
A 3-D drawing of the complete analyzer system is shown in Fig. (a). It consists of an injection lens, two hemispheres forming the analyzer and a detector placed at the exit of the analyzer.
Fig. (b) shows a sketch of the full experimental setup modeled in SIMION program.
Concerning the excitation of the lens, the first electrode is fixed at ground; voltages applied to the second and third electrodes, VL5 and VL4, will be free parameters to be varied in the optimization process. The lens exit apertures VP are used for controlling the beam retardation F.
Values of F=1, 2, 4, 6, 8 and 10 have been simulated in the present study.
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8. Possible voltage combinations
This figure represents the beam widths at the detector as a function of the two lens voltages for all possible voltage polarity (positive or negative) combinations for F=1, 2, 4, 6, 8 and 10.
We observe that in each case the voltages giving rise to the smallest values of ΔxB lie along elliptical-like curves.
The smallest values obtained for each polarity combination are shown as black dots in this figure together with the corresponding optimal experimental values shown as white dots.
Once the optimizing lens voltages VL4 and VL5 have been found and set, it is possible to obtain the two parameters that characterize the system: the energy dispersion D and the FWHM energy resolution.
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.
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9. Optimal lens voltages F 1 2 4 6 8 10 VL4 (V) -570 -695 -700 -840
Optimal values of the lens voltages giving minimum beam width for different pre-retardation factors F = 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. F 1 2 4 6 8 10
VL4 (V)
-570
-695
-700
-840
VL5 (V)
550
200
625
195
-510
-600
D (mm)
159.13
317.29
633.12
948.53 ML
-0.24
-0.32
-0.39
-0.41
-0.51
-0.55
In this table we list the optimal values of the lens voltages giving minimum beam width at the detector in each case, together with the linear magnification and the corresponding energy dispersion D.
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10. Lineshapes for different F
Experimental (red circles) and computed (black solid lines) energy spectra for different pre-retardation ratios F = 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.
This figure shows the line profile resulting from vertical projections of the electron distributions on to the dispersion direction.
It is seen that resolution improves as F increases as expected.
The F=4 is in excellent agreement.
The simulation underestimates the width of the peak for F=1, and overestimate for F=10. 
Currently we are working towards in this direction.
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11. Energy Resolution Best energy resolution attained about 0.1%
This brings me to the end of my presentation.
The resolution is plotted as a function of F.
The best energy resolution attained is about 0.1%.
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.
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12. 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.
This is the summary of my talk.
We have simulated electron trajectories in a hemispherical spectrograph [with 4-element injection lens and 2-dimensional position sensitive detector (PSD)] modeling existing apparatus.
Optimal lens voltages were found by minimizing the measured beam widths on the PSD plane leading to optimal energy resolution.
Overall a good agreement was observed between experiment and simulation.
We expect this approach to be helpful to experimenters in determining the lens voltages for best energy resolution, which can be done in simulation with substantial savings in overall effort.
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13. Acknowledgement References
This research has been co-financed by the European Union and Greek national funds through OP: Education and Lifelong Learning, Research Program: THALES.
References
G. Martínez and M. Sancho, in: P. Hawkes (Ed.), Advances in Electronics and Electron Physics 81, Academic Press, New York, 1991, pp.1-41.
SIMION v.8.1, url:
T. J. M. Zouros and E. P. Benis, Applied Physics Letters 86 (2005)
I. Madesis et al, JPCS 583 (2015)
The APAPES collaboration homepage:
Thank you. Your questions are welcome.
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