Generalized Courant-Snyder Theory for Charged-Particle Dynamics in General Focusing Lattices

Qin, Hong; Davidson, Ronald C.; Chung, М.; Burby, J. W.

doi:10.1103/physrevlett.111.104801

Cited by 21 publications

(29 citation statements)

References 24 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In a recent Letter [20], we reported on the development of a generalized CS theory for focusing lattices with the most general form in Eq. (11), including bending magnets, torsion of the design orbit, and solenoidal magnets, in addition to quadrupole and skew-quadrupole components.…”

Section: Introductionmentioning

confidence: 99%

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

Qin

Davidson

Burby

et al. 2014

Phys. Rev. ST Accel. Beams

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Section: Introductionmentioning

confidence: 99%

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

Qin

Davidson

Burby

et al. 2014

Phys. Rev. ST Accel. Beams

Self Cite

View full text Add to dashboard Cite

show abstract

“…In principle, the beam could be intentionally coupled in the damping rings in order to reduce collective effects, and decoupled in the extraction line, so long as the b-mode emittance is preserved. The decomposition into normal modes has been discussed elsewhere [9][10][11], and therefore will not be covered here.…”

Section: Motivation For Beam-based Emittance Tuningmentioning

confidence: 99%

Low-emittance tuning at the Cornell Electron Storage Ring Test Accelerator

Shanks

Rubin

Sagan

2014

Phys. Rev. ST Accel. Beams

View full text Add to dashboard Cite

In 2008 the Cornell Electron/Positron Storage Ring (CESR) was reconfigured from an electron/positron collider to serve as a test bed for the International Linear Collider damping rings. One of the primary goals of the CESR Test Accelerator (CesrTA) project is to develop a fast low-emittance tuning method which scales well to large rings such as the ILC damping rings, and routinely achieves a vertical emittance of order 10 pm at 2.085 GeV. This paper discusses the tuning methods developed at CesrTA to achieve lowemittance conditions. One iteration of beam-based measurement and correction requires about 10 min. A minimum vertical emittance of 10.3ðþ3.2= − 3.4Þ sys ðAE0.2Þ stat pm has been achieved at 2.085 GeV. In various configurations and beam energies the correction technique routinely achieves vertical emittance around 10 pm after correction, with rms coupling < 0.5%. The measured vertical dispersion is dominated by beam position monitor systematics. The propagation of uncertainties in the emittance measurement is described in detail. Simulations modeling the effects of magnet misalignments, beam position monitor errors, and the emittance correction algorithm suggest the residual vertical emittance measured at the conclusion of the tuning procedure is dominated by sources other than optics errors and misalignments.

show abstract

“…[18][19][20][21][22][23][24][25][26] But none of these schemes is as effective for coupled lattices as the CS theory is for uncoupled lattices. Recently, we have developed a generalized CourantSnyder theory for coupled lattices, 17,[27][28][29][30][31][32][33][34] which generalizes every important aspect of the original CS theory to higher dimensions. Especially, the key components of the original CS theory, i.e., the envelope function (or the b function) and the associated envelope equation are generalized into a matrix envelope function and the associated matrix envelope equation.…”

Section: Introductionmentioning

confidence: 99%

Spectral and structural stability properties of charged particle dynamics in coupled latticesa)

et al. 2015

Self Cite

View full text Add to dashboard Cite

It has been realized in recent years that coupled focusing lattices in accelerators and storage rings have significant advantages over conventional uncoupled focusing lattices, especially for high-intensity charged particle beams. A theoretical framework and associated tools for analyzing the spectral and structural stability properties of coupled lattices are formulated in this paper, based on the recently developed generalized Courant-Snyder theory for coupled lattices. It is shown that for periodic coupled lattices that are spectrally and structurally stable, the matrix envelope equation must admit matched solutions. Using the technique of normal form and pre-Iwasawa decomposition, a new method is developed to replace the (inefficient) shooting method for finding matched solutions for the matrix envelope equation. Stability properties of a continuously rotating quadrupole lattice are investigated. The Krein collision process for destabilization of the lattice is demonstrated. V C 2015 AIP Publishing LLC. [http://dx

show abstract

Generalized Courant-Snyder Theory for Charged-Particle Dynamics in General Focusing Lattices

Cited by 21 publications

References 24 publications

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

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

Low-emittance tuning at the Cornell Electron Storage Ring Test Accelerator

Spectral and structural stability properties of charged particle dynamics in coupled latticesa)

Contact Info

Product

Resources

About