Refinements to longitudinal, single bunch, coherent instability theory

Author

Koscielniak, S.R.

Author_Institution

TRIUMF, Vancouver, BC, Canada

Volume

5

fYear

1995

fDate

1-5 May 1995

Firstpage

3115

Abstract

For the case of a bunched beam confined to a quadratic potential well, we demonstrate the necessity for considering mode-coupling to correctly obtain the threshold current for the d.c. instability. Further we find the effect upon growth rate and coherent tune shift of evaluating the impedance at a complex frequency. For the case of a bunched beam confined to a cosine potential well, we give an exact analytic expression for the dispersion integral, and calculate (with no approximations), the stability diagram for the Robinson instability taking into account Landau damping. This paper comprises extracts from a lengthy internal report

Keywords

beam handling techniques; particle beam stability; DC instability; Landau damping; Robinson instability; bunched beam; coherent instability; coherent tune shift; complex frequency; cosine potential well; dispersion integral; growth rate; impedance; longitudinal instability; mode-coupling; quadratic potential well; single bunch instability; stability diagram; threshold current; Damping; Frequency; Impedance; Integral equations; Narrowband; Optical coupling; Oscillators; Potential well; Stability; Threshold current;

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.1995.505802

Filename

505802