Open AccessNONLOCAL EQUATIONS FOR THE ELECTROMAGNETIC FIELD IN THE INHOMOGENEOUS ACCELERATING STRUCTURES
Author(s) -
M. I. Ayzatsky
Publication year - 2019
Publication title -
problems of atomic science and technology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.216
H-Index - 17
eISSN - 1562-6016
pISSN - 1682-9344
DOI - 10.46813/2019-124-071
Subject(s) - electric field integral equation , boundary value problem , electric field , electromagnetic field , physics , field (mathematics) , mathematical analysis , boundary (topology) , wave equation , electromagnetic wave equation , mathematics , optical field , partial differential equation , quantum mechanics , pure mathematics
The procedure for obtaining a difference equation, the solution of which is the components of the electric (or magnetic) field at the chosen set of points in the volume of the resonator chain, was developed. We started with the wave equation with boundary conditions and obtained the difference equation without boundary conditions. Boundary conditions were included into the coefficients of the difference equation for the electric field. As the obtained equation connects the field values in different points (in general case, on an infinite set of points), the proposed procedure represents a nonlocal model for field description. Solutions of the difference equation for the electric field were analyzed. It was shown that they coincide with good accuracy with the ones that were obtained by direct summing of relevant series.