Statistics of the half-integer stopband

Author

Dutt, S. ; Chantard, F. ; Gerig, R. ; Kauffmann, S.

Author_Institution

SSC Lab., Dallas, TX, USA

fYear

1993

fDate

17-20 May 1993

Firstpage

267

Abstract

We consider the statistical nature of the stopband set up in the vicinity of a half-integer tune when a linear lattice is subjected to quadrupole errors distributed according to gaussians. The probability density function of the stopband, treated as a complex number, is found to be a correlated bivariate gaussian in the real and imaginary parts. The mean magnitude of the stopband is calculated in terms of the complete elliptic integral of the first kind, and the conditional probability density of its magnitude is obtained in closed form. A number of limiting conditions are studied. Finally, we estimate the requirements on a correction system for neutralizing the stopband with a given probability of success

Keywords

beam handling equipment; beam handling techniques; probability; tuning; closed form; complex number; conditional probability density; correction system; correlated bivariate gaussian; elliptic integral; half-integer stopband; half-integer tune; limiting conditions; linear lattice; mean magnitude; probability density function; quadrupole errors; statistical nature; Displays; Educational institutions; Eigenvalues and eigenfunctions; Gaussian distribution; Gaussian processes; Laboratories; Lattices; Physics; Probability density function; Statistics;

fLanguage

English

Publisher

ieee

Conference_Titel

Particle Accelerator Conference, 1993., Proceedings of the 1993

Conference_Location

Washington, DC

Print_ISBN

0-7803-1203-1

Type

conf

DOI

10.1109/PAC.1993.308944

Filename

308944