Method to compute the longitudinal coupling impedance of an iris in a vacuum chamber

D Davino,G Panariello,G Miano,L Verolino

doi:10.1103/physrevstab.2.044401

Abstract

This paper deals with the evaluation of the longitudinal coupling impedance due to a charged particle traveling along the axis of an iris in a circular waveguide. The solution of the electromagnetic problem is given in terms of a dual series expansion, and some interesting developments of this technique are presented in this paper. [S1098-4402(99)00032-4]

Highlights

Let us consider a charged particle traveling at constant velocity y in the positive direction of the z axis along the symmetry axis of a vacuum chamber, namely a perfectly conducting cylindrical waveguide of radius b
The effects of the field radiated from the iris on the longitudinal motion of the beam can be described in the frequency domain through the longitudinal coupling impedance, a global parameter defined by the integral [1,2]
The aim of this paper is to evaluate the longitudinal coupling impedance of a circular iris for any value of b in a wide range of the aspect ratio w ෇ ab by means of a new technique, based on dual series [7]

Summary

INTRODUCTION

Let us consider a charged particle traveling at constant velocity y in the positive direction of the z axis along the symmetry axis of a vacuum chamber, namely a perfectly conducting cylindrical waveguide (pipe) of radius b. An accurate and robust method able to evaluate the radiated field, and the longitudinal impedance, is needed for any value of b. The aim of this paper is to evaluate the longitudinal coupling impedance of a circular iris for any value of b in a wide range of the aspect ratio w ෇ ab (the ratio between the radius of the iris and the one of the vacuum chamber) by means of a new technique, based on dual series [7]. The solution of our problem is reduced to the solution of a system of complex algebraic equations of low order (typically less than 10) It is given an approximated formula valid for all values of b which reduces the computational load in the high frequency limit

REPRESENTATION OF THE FIELDS

STATEMENT OF THE PROBLEM

SOLUTION OF THE PROBLEM

LONGITUDINAL COUPLING IMPEDANCE

THE HIGH FREQUENCY LIMIT

FINAL REMARKS