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Title: Betatron motion with coupling of horizontal and vertical degrees of freedom

Abstract

The Courant-Snyder parameterization of one-dimensional linear betatron motion is generalized to two-dimensional coupled linear motion. To represent the 4 x 4 symplectic transfer matrix the following ten parameters were chosen: four beta-function, four alpha-functions and two betatron phase advances. The beta-functions have a meaning similar to the Courant-Snyder parameterization, and the definition of alpha-functions coincides with the standard one at regions with zero longitudinal magnetic field, where they are equal to negative half-derivatives of the beta-functions. Such a parameterization can be useful for analysis of coupled betatron motion in circular machines and transfer lines.

Authors:
;
Publication Date:
Research Org.:
Thomas Jefferson National Accelerator Facility, Newport News, VA (US)
Sponsoring Org.:
USDOE Office of Energy Research (ER) (US)
OSTI Identifier:
754650
Report Number(s):
DOE/ER/40150-1275; JLAB-ACC-99-19
TRN: US0002259
DOE Contract Number:  
AC05-84ER40150
Resource Type:
Journal Article
Resource Relation:
Other Information: PBD: 1 Oct 1999
Country of Publication:
United States
Language:
English
Subject:
43 PARTICLE ACCELERATORS; BETATRON OSCILLATIONS; ACCELERATORS; BEAM TRANSPORT; TRANSFER FUNCTIONS; MATRICES; ACCELERATOR

Citation Formats

Lebedev, V A, and Bogacz, S A. Betatron motion with coupling of horizontal and vertical degrees of freedom. United States: N. p., 1999. Web.
Lebedev, V A, & Bogacz, S A. Betatron motion with coupling of horizontal and vertical degrees of freedom. United States.
Lebedev, V A, and Bogacz, S A. Fri . "Betatron motion with coupling of horizontal and vertical degrees of freedom". United States. https://www.osti.gov/servlets/purl/754650.
@article{osti_754650,
title = {Betatron motion with coupling of horizontal and vertical degrees of freedom},
author = {Lebedev, V A and Bogacz, S A},
abstractNote = {The Courant-Snyder parameterization of one-dimensional linear betatron motion is generalized to two-dimensional coupled linear motion. To represent the 4 x 4 symplectic transfer matrix the following ten parameters were chosen: four beta-function, four alpha-functions and two betatron phase advances. The beta-functions have a meaning similar to the Courant-Snyder parameterization, and the definition of alpha-functions coincides with the standard one at regions with zero longitudinal magnetic field, where they are equal to negative half-derivatives of the beta-functions. Such a parameterization can be useful for analysis of coupled betatron motion in circular machines and transfer lines.},
doi = {},
journal = {},
number = ,
volume = ,
place = {United States},
year = {1999},
month = {10}
}