Submitted:
29 April 2023
Posted:
30 April 2023
You are already at the latest version
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.
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