Abstract
We consider the calculation of electromagnetic fields generated by an electron bunch passing through an anisotropic transversally non-homogeneous vacuum chamber of round or rectangular cross-section with translational symmetry in the beam direction. The described algorithms are implemented in a numerical code and cross-checked on several examples.
Highlights
Dielectric lined waveguides are under extensive study as accelerating structures excited by charged beams [1]
Several materials used for accelerating structures possess significant anisotropic properties
For example, in [3] that the dielectric anisotropy causes a frequency shift in comparison to dielectric-lined waveguides with isotropic dielectric loadings
Summary
Dielectric lined waveguides are under extensive study as accelerating structures excited by charged beams [1]. Several materials used for accelerating structures (sapphire, ceramic films, etc) possess significant anisotropic properties It is shown, for example, in [3] that the dielectric anisotropy causes a frequency shift in comparison to dielectric-lined waveguides with isotropic dielectric loadings. The rectangular case with one isotropic layer was studied in [10,11,12].The solutions for isotropic structures are obtained in analytical form or a field-matching approach can be used to reduce the problem to a simple matrix equation. With a proper permutation of mesh indexes we reduce a sparse matrix with 7 bands to a pentadiagonal one It allows a fast algorithm of complexity OðNÞ (N-number of mesh steps) for calculation of impedances for non-homogeneous anisotropic materials. For the case when the anisotropic layers are thin we suggest in Sec. V a combination of the field matching and the finite-difference approaches. The algorithms are implemented in numerical code ECHO [13,14]
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