U.S. Particle Accelerator School

Analytic Methods for Impedance Calculations course

Sponsoring University:

Indiana University
held in Tucson, Arizona


Analytic Methods for Impedance Calculations


Robert Gluckstern, University of Maryland and Sergei Kurennoy, Los Alamos National Lab

The interaction of an intense beam with its environment in a beam pipe generates electromagnetic wakefields, which may cause instabilities whose effects on a beam bunch can be analyzed by using coupling impedances. In this course we present the definitions of the longitudinal and transverse impedances and discuss a variety of analytic techniques to calculate them. We will focus particularly on the frequency dependence of the following sources of impedance in beam pipes of circular, elliptical and rectangular cross section: space charge, small obstacle, hole in a beam shield (using the electric polarizability and magnetic susceptibility, and techniques to calculate them), cavity in a beam pipe, periodic obstacles and irises in a beam pipe. Many accelerator structures involve long chains of electromagnetically-coupled cavities. We will outline the analysis of such structures by means of coupled circuits when the structures are almost periodic. In particular, we will explore the unique and useful detuned and damped cavity structures. Prerequisites: accelerator physics.