Optimal Injection Lens Parameters for Improved Energy Resolution

Optimal Injection Lens Parameters for Improved Energy Resolution of a Hemispherical Spectrograph T. J. M. ZOUROS 1, 2, Omer SISE 3, G. MARTÍNEZ 4, A. DIMITRIOU 1, 2, A. LAOUTARIS 1, 2, I. MADESIS 1, 2 1 Dept. of Physics, Univ. of Crete, P. O Box 2208, GR 71003 Heraklion, Greece. E-mail: tzouros@physics. uoc. gr 2 Tandem Accelerator Laboratory, INPP, NCSR Demokritos, GR 15310 Ag Paraskevi, Greece 3 Dept. of Science Education, Faculty of Education, Suleyman Demirel University, 32260 Isparta, Turkey 4 Dept. Física Aplicada III, Facultad de Física, UCM 28040 -Madrid, Spain

What is Spectrograph? (Target area - optics – dispersive element – optics – detector – DAQ unit ) • a spectrograph • a spectrometer Optical spectra dispersion of light Prof. Robert Bunsen What about charged particles? With charged particles, the scenario is practically the same. 24. 08. 2015 BPU 9 - 24 -27 Aug 2015 Istanbul 2

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 Electrostatic field – Ek/q dispersive • Modeling: – Simulation 3 D (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 24. 08. 2015 BPU 9 - 24 -27 Aug 2015 Istanbul E. P. Benis Ph. D thesis 2001 3

The key property: Resolution What is this? The single-humped dromedary camel Singlet Or an unresolved twohumped camel? Doublet Is dromedar an unresolved camel? Bactrian camel With a good resolution there are unlimited If the resolution is good enough, possibilities. we can see more line shapes. 24. 08. 2015 BPU 9 - 24 -27 Aug 2015 Istanbul 4

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

The injection lens r = source radius q = cone semiangle of source E = e- energy at the source rp = source image at the HDA entry a = cone seminagle of image Ep = e- energy at the image An injection lens is to focus beam at the HDA entry. Helmoltz-Lagrange equation Lens magnification Angular magnification Pre-retardation ratio Cone semiangle of image defined by the lens 24. 08. 2015 BPU 9 - 24 -27 Aug 2015 Istanbul 6

Experimental and Simulated Setup APAPES – Atomic Physics with Accelerators; Projectile Electron Spectroscopy http: //apapes. physics. uoc. gr/ Vp or electron gun 24. 08. 2015 BPU 9 - 24 -27 Aug 2015 Istanbul (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 (VL 5) and light green (VL 4). 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). 7

Possible voltage combinations Contour maps of VL 4 vs VL 5 with the z-axis measuring for Δx. B. The black dots represent voltages for the smallest values of Δx. B, while the white dots represent the voltages found empirically. 24. 08. 2015 BPU 9 - 24 -27 Aug 2015 Istanbul 8

Optimal lens voltages 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. F 1 2 4 6 8 10 VL 4 (V) -570 -695 -570 -700 -840 VL 5 (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 24. 08. 2015 BPU 9 - 24 -27 Aug 2015 Istanbul 1262. 74 1577. 42 -0. 51 -0. 55 9

Lineshapes for different F Experimental (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 e. V FWHM) has been taken into account in the simulation. 24. 08. 2015 BPU 9 - 24 -27 Aug 2015 Istanbul 10

Energy Resolution Best energy resolution attained 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. 24. 08. 2015 BPU 9 - 24 -27 Aug 2015 Istanbul 11

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. 24. 08. 2015 BPU 9 - 24 -27 Aug 2015 Istanbul 12

Acknowledgement This research has been co-financed by the European Union and Greek national funds through OP: Education and Lifelong Learning, Research Program: THALES. References 1. 2. 3. 4. 5. 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: http: //simion. com T. J. M. Zouros and E. P. Benis, Applied Physics Letters 86 (2005) 094105. I. Madesis et al, JPCS 583 (2015) 012014. The APAPES collaboration homepage: http: //apapes. physics. uoc. gr/ 24. 08. 2015 BPU 9 - 24 -27 Aug 2015 Istanbul 13