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

Author

Listed:
  • Seitkerim Bimurzaev

    (Department of Science and Commercialization, G. Daukeev Almaty University of Power Engineering and Telecommunication, Almaty 050013, Kazakhstan
    These authors contributed equally to this work.)

  • Seil Sautbekov

    (Department of Physics and Technology, Al-Farabi Kazakh National University, Almaty 050040, Kazakhstan
    These authors contributed equally to this work.)

  • Zerde Sautbekova

    (Department of Science and Commercialization, G. Daukeev Almaty University of Power Engineering and Telecommunication, Almaty 050013, Kazakhstan
    These authors contributed equally to this work.)

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.

Suggested Citation

  • Seitkerim Bimurzaev & Seil Sautbekov & Zerde Sautbekova, 2023. "Calculation of the Electrostatic Field of a Circular Cylinder with a Slot by the Wiener–Hopf Method," Mathematics, MDPI, vol. 11(13), pages 1-11, June.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:13:p:2933-:d:1183908
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