Bimurzaev, S.; Sautbekov, S.; Sautbekova, Z. Calculation of the Electrostatic Field of a Circular Cylinder with a Slot by the Wiener–Hopf Method. Mathematics2023, 11, 2933.
Bimurzaev, S.; Sautbekov, S.; Sautbekova, Z. Calculation of the Electrostatic Field of a Circular Cylinder with a Slot by the Wiener–Hopf Method. Mathematics 2023, 11, 2933.
Bimurzaev, S.; Sautbekov, S.; Sautbekova, Z. Calculation of the Electrostatic Field of a Circular Cylinder with a Slot by the Wiener–Hopf Method. Mathematics2023, 11, 2933.
Bimurzaev, S.; Sautbekov, S.; Sautbekova, Z. Calculation of the Electrostatic Field of a Circular Cylinder with a Slot by the Wiener–Hopf Method. Mathematics 2023, 11, 2933.
Abstract
The article considers an internal boundary value problem of the distribution of an electrostatic field in a lens formed by two identical semi-infinite circular cylinders coaxially located inside an infinite external cylinder. The problem is reduced to solving 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.
Keywords
time-of-flight mass spectrometer; electron microscope; electrostatic lens; electrostatic mirror; relativistic effect; system of singular integral equations; factorized functions; eigenfunctions; eigenvalues.
Subject
Physical Sciences, Particle and Field Physics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
