Model for the Evaluation of an Angular Slot’s Coupling Impedance

Abstract

In high energy particle accelerators, a careful modeling of the electromagnetic interaction between the particle beam and the structure is essential to ensure the performance of the experiments. Particular interest arises in the presence of angular discontinuities of the structure, due to the asymmetrical behavior. In this case, semi-analytical models allow one to reduce the computational effort and to better understand the physics of the phenomena, with respect to purely numerical models. In the paper, a model for analyzing the electromagnetic interaction between a traveling charge particle and a perfectly conducting angular slot of a negligible thickness is discussed. The particle travels at a constant velocity along a straight line parallel to the axis of symmetry of the strip. The longitudinal and transverse coupling impedances are therefore evaluated for a wide range of parameters.

Coupling impedance of a PEC angular strip in a vacuum pipe

“…with r 1 ≤ r 2 , it is easy to verify that Equation ( 13) is a generalisation of Equation ( 10) in [19]. However, the present work in not just a generalisation of [19].…”

“…with r 1 ≤ r 2 , it is easy to verify that Equation ( 13) is a generalisation of Equation ( 10) in [19]. However, the present work in not just a generalisation of [19]. In the previous study, the adopted project scheme did not benefit from the possible expansion of the potentials and fields in cylindrical harmonics.…”

“…Instead, in this study, the adoption of the projection scheme based on Equation (17), allows to fully take advantage of the Neumann series expansion, leading to a more efficient and more accurate calculation of the coefficients of the linear system Equation (21). It is trivial to verify that in the actual formulation, in the case b → ∞, adopting the same projection scheme of [19], the same expression of A and b would have been found.…”

“…RELATION WITH PREVIOUS WORKS Some of the authors have already discussed in [19] the problem of a particle travelling parallel to an angular strip in the free space that is in the absence of the pipe. In this section, we show how the previous work can be considered a special case of the present formulation and the improvements in the present formulation.…”

“…On the other hand, analytical or semi-analytical methods, although suitable for more canonical geometries, still play a valuable role in this field allowing a better understanding of the physics of some phenomena [14,15]. Modal analyses are often adopted for closed structures [16], diffractive methods for high-frequency solutions and integral formulations for open geometries or in presence of edges [16][17][18][19]. Validation methods are based on the measurement of the coupling impedance using a wire as a source current instead of a travelling charge [20][21][22].…”