COLLIMATOR AND TELESCOPIC MODES OF A CATHODE LENS
DOI:
https://doi.org/10.31489/2025N4/123-131Keywords:
electron optics, electrostatic lens, paraxial optics, potential distributionAbstract
One way to improve the performance of emission systems (electron microscopes, microfocus X-ray tubes, etc.) is to reduce cathode lens aberrations. Such a reduction is only possible through a thorough theoretical analysis of their electron-optical schemes. This research attempts to develop tools for modeling a cathode lens with a virtually arbitrary electrode configuration in the paraxial approximation, and the conditions for implementing the collimator and telescopic modes have been determined. The relationship between the parameters that provide the specified operating modes of the lens has been studied. Electron-optical schemes have been developed that guarantee collimator and telescopic modes of a cathode lens of a real (non-idealized) design.
References
Guo X. (2024) The Schottky emitter as a source for multi-electron-beam instruments. Dissertation (TU Delft), Delft University of Technology. doi.org/10.4233/uuid:304cdd73-083a-4f89-ad47- f192e84a5313
Ohsawa S., Ikeda M., Sugimura T., Tawada M., Hozumi Y. and Kanno K. (2005) High Brightness Electron Gun for X-Ray Source. Proceedings of the 2005 Particle Accelerator Conference, Knoxville, TN, USA. 1488-1490. doi: 10.1109/PAC.2005.1590809. DOI: https://doi.org/10.1109/PAC.2005.1590809
Hideo Morishita, Takashi Ohshima, Kazuo Otsuga, Makoto Kuwahara, Toshihide Agemura, Yoichi Ose (2021) Brightness evaluation of pulsed electron gun using negative electron affinity photocathode developed for time-resolved measurement using scanning electron microscope. Ultramicroscopy, 230, 113386. doi.org/10.1016/j.ultramic.2021.113386. DOI: https://doi.org/10.1016/j.ultramic.2021.113386
Bronsgeest M. S., Barth J. E., Swanson L. W., Kruit P. (2008) Probe current, probe size, and the practical brightness for probe forming systems. Journal of Vacuum Science & Technology B. 26 (3), 949-955. doi: 10.1116/1.2907780 DOI: https://doi.org/10.1116/1.2907780
Han C, Sul I, Cho B. (2017) Edge shadow projection method for measuring the brightness of electron guns. Rev Sci Instrum, 88(2), 023302. doi: 10.1063/1.4974956. DOI: https://doi.org/10.1063/1.4974956
Lauer R. (2020) Characteristics of triode electron guns. In P. W. Hawkes (Ed.), Advances in imaging and electron physics, 215. 195–266. Academic Press, London. doi.org/10.1016/bs.aiep.2020.06.007. DOI: https://doi.org/10.1016/bs.aiep.2020.06.007
Kuriki M. (2022) Theoretical limit of electron beam brightness generated from electron guns. Proceedings of the 19th Annual Meeting of Particle Accelerator Society of Japan, October 18 – 21, Kyushu University, 1065-1069.
Fujita S, Shimoyama H. (2005) A new evaluation method of electron optical performance of high beam current probe forming systems. J Electron Microsc (Tokyo). 54(5), 413-427. doi: 10.1093/jmicro/dfi063. DOI: https://doi.org/10.1093/jmicro/dfi063
Cardona J. D., DietrichIsh k., Mukul M. et al. (2022) Simulations of a new electron gun for the TITAN EBIT. Journal of Physics: Conference Series 2244, 012075. doi:10.1088/1742-6596/2244/1/012075. DOI: https://doi.org/10.1088/1742-6596/2244/1/012075
Wang RC., Jiao JQ., Zang K. et al. (2025) Development of pulsed electron gun based on PIC simulation. Radiat Detect Technol Methods. https://doi.org/10.1007/s41605-025-00591-z. DOI: https://doi.org/10.1007/s41605-025-00591-z
Sushkov A.D. (2022) Vacuum Electronics. Physical and Technical Foundations. Lan, St. Petersburg. 464. [in Russian]. Available at: https://lanbook.com/catalog/inzhenerno-tekhnicheskie-nauki/vakuumnaya-elektronika-fiziko-tehnicheskie-osnovy-3883606/?utm_source
Hawkes P.W. (1972) Electron Optics and Electron Microscopy. Taylor & Francis Ltd., London, 244. https://doi.org/10.1002/crat.19720071212 DOI: https://doi.org/10.1002/crat.19720071212
Smirnov V.I. (1974) Course of Higher Mathematics, Vol. 3, Part 2. Nauka, Moscow, 672. [in Russian] Available at: https://www.litres.ru/book/vladimir-smirnov-3/kurs-vysshey-matematiki-tom-iii-chast-2-6988781/ ?utm_source
Yakushev E.M. (2013) Theory and Computation of Electron Mirrors: The Central Particle Method. In P. W. Hawkes (Ed.), Advances in imaging and electron physics, 178. 147–247. Academic Press, London. https://doi.org/10.1016/B978-0-12-407701-0.00003-0 DOI: https://doi.org/10.1016/B978-0-12-407701-0.00003-0
Yakushev E.M., Bimurzaev S.B., & Kholodov M.A. (2016) To Determine the Cardinal Elements and Angular Characteristics of Cathode Lenses with Rotational Symmetry. Bulletin of the Aktobe Regional State University named after K. Zhubanov, 44(2), 32 – 40. [in Russian] Available at: https://vestnik.arsu.kz/ index.php/hab/issue/view/12/18
Trubitsyn A.A., Grachev E.Yu., &Kochergin E.G. (2024) Focus CL Program for Modeling Cathode Lenses. Certificate of State Registration of Computer Program No. 2024680471. [in Russian]
Brebbia C.A., Telles J.C.F., Wroubel L.C. (2012) Boundary Element Techniques: Theory and Applications in Engineering. Springer Berlin Heidelberg, 464. https://doi.org/10.1007/978-3-642-48860-3 DOI: https://doi.org/10.1007/978-3-642-48860-3
Korn G.A., Korn T.M. (2013) Mathematical Handbook for Scientists and Engineers. Dover Publications Inc, NY. 1152. Available at: https://www.scribd.com/document/530807645/Mathematics-Handbook-for-Scientists-and-Engineers?utm_source=chatgpt.com
Abramovits M., Stigan I.A. (1965) Handbook of Special Functions with Formulas, Graphs, and Mathematical Tables. Dover Publications Inc, NY. 1046. Available at: https://personal.math.ubc.ca/~cbm/aands/abramowitz _and_stegun.pdf
Trubitsyn A.A., Grachev E.Yu., & Kochergin E.G. (2025) Telescopic Mode of a Cathode Lens. Pis'ma v zhurnal tekhnicheskoy fiziki, 51 (13), 32 – 36. [in Russian]. https://doi.org/10.61011/PJTF.2025.13.60701.20284 [in Russian]
Gurov V.S., Saulebekov A.O., & Trubitsyn A.A. (2015) Analytical, Approximate-Analytical and Numerical Methods in the Design of Energy Analyzers. In P. W. Hawkes (Ed.), Advances in Imaging and Electron Physics, 192. Academic Press, London, 212. https://doi.org/10.1016/S1076-5670(15)00103-2 DOI: https://doi.org/10.1016/S1076-5670(15)00103-2
Trubitsyn A.A. (2001) A Correlation Method of Search for Higher-Order Angular Focusing. Technical Physics, 46 (5), 630-631. https://doi.org/10.1134/1.1372960 DOI: https://doi.org/10.1134/1.1372960
Downloads
Published online
How to Cite
Issue
Section
License

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.





