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Title: Analytical methods for describing charged particle dynamics in general focusing lattices using generalized Courant-Snyder theory

Abstract

The dynamics of charged particles in general linear focusing lattices with quadrupole, skew-quadrupole, dipole, and solenoidal components, as well as torsion of the fiducial orbit and variation of beam energy is parametrized using a generalized Courant-Snyder (CS) theory, which extends the original CS theory for one degree of freedom to higher dimensions. The envelope function is generalized into an envelope matrix, and the phase advance is generalized into a 4D symplectic rotation, or a Uð2Þ element. The 1D envelope equation, also known as the Ermakov-Milne-Pinney equation in quantum mechanics, is generalized to an envelope matrix equation in higher dimensions. Other components of the original CS theory, such as the transfer matrix, Twiss functions, and CS invariant (also known as the Lewis invariant) all have their counterparts, with remarkably similar expressions, in the generalized theory. The gauge group structure of the generalized theory is analyzed. By fixing the gauge freedom with a desired symmetry, the generalized CS parametrization assumes the form of the modified Iwasawa decomposition, whose importance in phase space optics and phase space quantum mechanics has been recently realized. This gauge fixing also symmetrizes the generalized envelope equation and expresses the theory using only the generalized Twiss function β.more » The generalized phase advance completely determines the spectral and structural stability properties of a general focusing lattice. For structural stability, the generalized CS theory enables application of the Krein-Moser theory to greatly simplify the stability analysis. The generalized CS theory provides an effective tool to study coupled dynamics and to discover more optimized lattice designs in the larger parameter space of general focusing lattices.« less

Authors:
; ; ;
Publication Date:
Research Org.:
Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)
Sponsoring Org.:
USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)
OSTI Identifier:
1151738
Report Number(s):
FERMILAB-PUB-14-092-APC
Journal ID: ISSN 1098-4402; PRABFM; ArticleNumber: 044001
DOE Contract Number:  
AC02-07CH11359
Resource Type:
Journal Article
Journal Name:
Physical Review Special Topics - Accelerators and Beams
Additional Journal Information:
Journal Volume: 17; Journal Issue: 4; Journal ID: ISSN 1098-4402
Country of Publication:
United States
Language:
English

Citation Formats

Qin, Hong, Davidson, Ronald C., Burby, Joshua W., and Chung, Moses. Analytical methods for describing charged particle dynamics in general focusing lattices using generalized Courant-Snyder theory. United States: N. p., 2014. Web. doi:10.1103/PhysRevSTAB.17.044001.
Qin, Hong, Davidson, Ronald C., Burby, Joshua W., & Chung, Moses. Analytical methods for describing charged particle dynamics in general focusing lattices using generalized Courant-Snyder theory. United States. doi:10.1103/PhysRevSTAB.17.044001.
Qin, Hong, Davidson, Ronald C., Burby, Joshua W., and Chung, Moses. Tue . "Analytical methods for describing charged particle dynamics in general focusing lattices using generalized Courant-Snyder theory". United States. doi:10.1103/PhysRevSTAB.17.044001. https://www.osti.gov/servlets/purl/1151738.
@article{osti_1151738,
title = {Analytical methods for describing charged particle dynamics in general focusing lattices using generalized Courant-Snyder theory},
author = {Qin, Hong and Davidson, Ronald C. and Burby, Joshua W. and Chung, Moses},
abstractNote = {The dynamics of charged particles in general linear focusing lattices with quadrupole, skew-quadrupole, dipole, and solenoidal components, as well as torsion of the fiducial orbit and variation of beam energy is parametrized using a generalized Courant-Snyder (CS) theory, which extends the original CS theory for one degree of freedom to higher dimensions. The envelope function is generalized into an envelope matrix, and the phase advance is generalized into a 4D symplectic rotation, or a Uð2Þ element. The 1D envelope equation, also known as the Ermakov-Milne-Pinney equation in quantum mechanics, is generalized to an envelope matrix equation in higher dimensions. Other components of the original CS theory, such as the transfer matrix, Twiss functions, and CS invariant (also known as the Lewis invariant) all have their counterparts, with remarkably similar expressions, in the generalized theory. The gauge group structure of the generalized theory is analyzed. By fixing the gauge freedom with a desired symmetry, the generalized CS parametrization assumes the form of the modified Iwasawa decomposition, whose importance in phase space optics and phase space quantum mechanics has been recently realized. This gauge fixing also symmetrizes the generalized envelope equation and expresses the theory using only the generalized Twiss function β. The generalized phase advance completely determines the spectral and structural stability properties of a general focusing lattice. For structural stability, the generalized CS theory enables application of the Krein-Moser theory to greatly simplify the stability analysis. The generalized CS theory provides an effective tool to study coupled dynamics and to discover more optimized lattice designs in the larger parameter space of general focusing lattices.},
doi = {10.1103/PhysRevSTAB.17.044001},
journal = {Physical Review Special Topics - Accelerators and Beams},
issn = {1098-4402},
number = 4,
volume = 17,
place = {United States},
year = {2014},
month = {4}
}

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