Calculation of the Electrostatic Field of a Circular Cylinder with a Slot by the Wiener–Hopf Method

Seitkerim Bimurzaev, Seil Sautbekov () and Zerde Sautbekova
Additional contact information
Seitkerim Bimurzaev: Department of Science and Commercialization, G. Daukeev Almaty University of Power Engineering and Telecommunication, Almaty 050013, Kazakhstan
Seil Sautbekov: Department of Physics and Technology, Al-Farabi Kazakh National University, Almaty 050040, Kazakhstan
Zerde Sautbekova: Department of Science and Commercialization, G. Daukeev Almaty University of Power Engineering and Telecommunication, Almaty 050013, Kazakhstan

Mathematics, 2023, vol. 11, issue 13, 1-11

Abstract: The paper presents an exact solution to the internal boundary value problem of the field distribution in an electrostatic lens formed by two identical semi-infinite coaxially located round cylinders separated by a slit of finite width and located inside an infinite outer cylinder. The problem is reduced to a system of singular Wiener–Hopf integral equations, which is further solved by the Wiener–Hopf method using factorized Bessel functions. Solutions to the problem for each region inside the infinite outer cylinder are presented as exponentially converging series in terms of eigenfunctions and eigenvalues. Using the obtained formulas, a numerical calculation of the axial distribution of the potential of a two-electrode lens was made for various values of the radii of the outer and inner cylinders.

Keywords: time-of-flight mass spectrometer; electron microscope; electrostatic lens; electrostatic mirror; relativistic effect; system of singular integral equations; factorized functions; eigenfunctions; eigenvalues (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/11/13/2933/pdf (application/pdf)
https://www.mdpi.com/2227-7390/11/13/2933/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:11:y:2023:i:13:p:2933-:d:1183908

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().