Review of longitudinal perturbation formalism

Author

Zhang, S.Y.

Author_Institution

Brookhaven Nat. Lab., Upton, NY, USA

Volume

5

fYear

1995

fDate

1-5 May 1995

Firstpage

3214

Abstract

The foundation of the beam perturbation formalism was established on the Sacherer integral equation. The original solution was obtained by using simplified radial functions, and the results can be used to explain several important beam instability problems. To solve the instabilities caused by high beam intensities calls for more complete solution and the extension to the formalism as well. For the non-coupled perturbation problem without frequency spread, two different eigenvalue type solutions were proposed. The formalism is also modified to solve the azimuthal mode coupling instability and the beam instability with synchrotron frequency spread, where both dispersion type and eigenvalue type solutions were proposed. In this article, a brief review of longitudinal perturbation formalism based on Sacherer integral equation is given. Some perspectives will also be discussed

Keywords

eigenvalues and eigenfunctions; integral equations; particle beam stability; perturbation theory; synchrotrons; Sacherer integral equation; azimuthal mode coupling instability; beam instability; beam perturbation formalism; dispersion type solutions; high beam intensities; longitudinal perturbation formalism; noncoupled perturbation problem; radial functions; synchrotron frequency spread; Eigenvalues and eigenfunctions; Impedance; Integral equations; Laboratories; Optical coupling; Polynomials; Radio frequency; Sampling methods; Synchrotrons; Voltage;

fLanguage

English

Publisher

ieee

Conference_Titel

Particle Accelerator Conference, 1995., Proceedings of the 1995

Conference_Location

Dallas, TX

Print_ISBN

0-7803-2934-1

Type

conf

DOI

10.1109/PAC.1995.505833

Filename

505833