Calculation of the Electrostatic Field of a Circular Cylinder with a Slot by the Wiener–Hopf Method
Bimurzaev S. Sautbekov S. Sautbekova Z.
July 2023Multidisciplinary Digital Publishing Institute (MDPI)
Mathematics
2023#11Issue 13
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.
eigenfunctions , eigenvalues , electron microscope , electrostatic lens , electrostatic mirror , factorized functions , relativistic effect , system of singular integral equations , time-of-flight mass spectrometer
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Department of Science and Commercialization, G. Daukeev Almaty University of Power Engineering and Telecommunication, Almaty, 050013, Kazakhstan
Department of Physics and Technology, Al-Farabi Kazakh National University, Almaty, 050040, Kazakhstan
Department of Science and Commercialization
Department of Physics and Technology
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