IPAC2021 - List of Keywords (linear-dynamics)

Paper	Title	Other Keywords	Page
MOPAB041	Convergence Map with Action-Angle Variables Based on Square Matrix for Nonlinear Lattice Optimization	lattice, resonance, betatron, GUI	182
	L.H. Yu, Y. Hidaka, F. Plassard, V.V. Smaluk BNL, Upton, New York, USA Y. Hao FRIB, East Lansing, Michigan, USA
	We apply square matrix method to obtain in high speed a "convergence map", which is similar but different from frequency map. The convergence map is obtained from solving nonlinear dynamical equation by iteration of perturbation method and study the convergence. The map provides information about the stability border of dynamical aperture. We compare the map with frequency map from tracking. The result indicates the new method may be applied in nonlinear lattice optimization, taking the advantage of the high speed (about 10~50 times faster) to explore x, y and the off-momentum phase space.
DOI •	reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2021-MOPAB041
About •	paper received ※ 09 May 2021 paper accepted ※ 26 May 2021 issue date ※ 18 August 2021
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MOPAB062	A Single Dipole Source for Broad-Band Soft Photon Beamlines in Diamond-II	lattice, dipole, emittance, dynamic-aperture	261
	M. Apollonio, G. Cinque, H. Ghasem, A.N. Jury, I.P.S. Martin, R. Rambo DLS, Oxfordshire, United Kingdom
	Diamond-II is a project based at Diamond Light Source for an upgrade towards a Storage Ring characterized by a reduction of a factor 20 in its natural emittance and a doubling of the number of straight sections. At Diamond-II the majority of existing beamline capacity should be maintained, while enhancing their performance thanks to the increase in brightness at the source points. The substantial modification of the lattice imposes a likewise re-design of the broad-band sources, presently based on standard dipoles. In this paper we discuss a possible solution for the IR/THz beamline B22 operating within a photon energy range between 1meV and 1eV. This proposal, ideal for low critical energy and single source point sources, entails the insertion of a dipole in one of the newly created mid-cell straights of the machine, while reducing the bending power of the nearby gradient dipoles. After performing the linear matching of the lattice, reproducing a comparable phase advance in the modified cell, we studied the non-linear dynamics of the system. Comparison of the main observables (Dynamic Aperture, Injection Efficiency and Lifetime) with the baseline case is discussed.
DOI •	reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2021-MOPAB062
About •	paper received ※ 18 May 2021 paper accepted ※ 28 May 2021 issue date ※ 12 August 2021
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MOPAB074	Preliminary Study of Design Method for Hybrid MBA Lattice	lattice, resonance, sextupole, emittance	297
	J.J. Tan, Z.H. Bai, Z.L. Ren, J.H. Xu USTC/NSRL, Hefei, Anhui, People’s Republic of China Q. Zhang INEST, Hefei, People’s Republic of China
	Nonlinear optimization of hybrid multi-bend-achromat (HMBA) lattice is a difficult task due to its quite limited variables of multipole magnets. As a result, it is necessary to consider nonlinear potential of the lattice in its linear design. Nonlinear dynamics can be estimated by nonlinear driving terms and detuning terms. In this paper, we propose a design method for HMBA lattice. In this method, objective functions include emittance and two indicators of nonlinear dynamics, which consist of nonlinear driving terms and detuning terms. As an example, an HMBA lattice for a 2.2 GeV storage ring with circumference of 460.8 m was designed to demonstrate the method.
DOI •	reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2021-MOPAB074
About •	paper received ※ 19 May 2021 paper accepted ※ 21 May 2021 issue date ※ 21 August 2021
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MOPAB113	A Low-emittance Booster Lattice Design for the SOLEIL Upgrade	booster, lattice, emittance, storage-ring	410
	M.-A. Tordeux, A. Loulergue, R. Nagaoka SOLEIL, Gif-sur-Yvette, France Z.H. Bai, G. Liu, T. Zhang USTC/NSRL, Hefei, Anhui, People’s Republic of China
	The SOLEIL storage ring upgrade will require an injected beam with small transverse and longitudinal sizes. To meet this requirement, the present booster also needs to be upgraded, aiming to reduce the emittance below 10 nm·rad. A multi-bend achromat lattice is designed in this context for the booster upgrade, which consists of two superperiods to respect the present race-track configuration. The lattice is a 16BA HOA (Higher-Order Achromat) type lattice, composed of 14 unit cells, 2 matching cells and a long straight section, and combined-function bending magnets are used in the unit cells to both save space and reduce the emittance. The natural emittance of the designed booster is 5.2 nm·rad at the final energy of 2.75 GeV. This paper presents the general constraints, linear lattice design and nonlinear dynamics optimization for the booster upgrade.
DOI •	reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2021-MOPAB113
About •	paper received ※ 19 May 2021 paper accepted ※ 28 May 2021 issue date ※ 26 August 2021
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TUPAB136	On Nonlinear Electron Beam Dynamics in a Plasma Environment	plasma, electron, emittance, wakefield	1707
	H.Y. Barminova MEPhI, Moscow, Russia B. Kak RUDN University, Moscow, Russia
	The nonlinear dynamics of an electron beam propagating in a low-density plasma is investigated. The beam envelope equation is obtained analytically for the case of an axisymmetric beam using a model approximation close to the Kapchinsky-Vladimirsky model. Solutions of the envelope equation are presented for various initial conditions (beam current, initial beam radius, transverse beam emittance).
DOI •	reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2021-TUPAB136
About •	paper received ※ 19 May 2021 paper accepted ※ 26 May 2021 issue date ※ 26 August 2021
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WEPAB226	Investigation of Vlasov Systems with a Certain Class of Linearly-Collective Hamiltonians	bunching, simulation, collective-effects, distributed	3157
	Ph. Amstutz, M. Vogt DESY, Hamburg, Germany
	In many cases the Vlasov equation cannot be solved exactly due its inherent non-linearity arising from collective terms in the Hamiltonian. Based on the analysis of the Hamiltonian’s dependence on the phase-space density and the requirement for self-consistency in this contribution a class of Hamiltonians is defined and characterized. For members of this class the corresponding expansion of the Vlasov equation terminates. The new, potentially non-autonomous, Hamiltonian of the resulting Liouville equation depends only on the initial condition of the phase-space density. Prominent members of this class are Poisson-type kick-Hamiltonians, which we show as an example. We expect these investigations to be a potential starting point for the analysis and conception of operator-splitting schemes or splitting-free methods for beam-dynamics simulation codes.
DOI •	reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2021-WEPAB226
About •	paper received ※ 18 May 2021 paper accepted ※ 01 July 2021 issue date ※ 17 August 2021
Export •	reference for this paper using ※ BibTeX, ※ LaTeX, ※ Text/Word, ※ RIS, ※ EndNote (xml)

Paper

Title

Other Keywords

Page

MOPAB041

Convergence Map with Action-Angle Variables Based on Square Matrix for Nonlinear Lattice Optimization

lattice, resonance, betatron, GUI

182

L.H. Yu, Y. Hidaka, F. Plassard, V.V. Smaluk
BNL, Upton, New York, USA
Y. Hao
FRIB, East Lansing, Michigan, USA

We apply square matrix method to obtain in high speed a "convergence map", which is similar but different from frequency map. The convergence map is obtained from solving nonlinear dynamical equation by iteration of perturbation method and study the convergence. The map provides information about the stability border of dynamical aperture. We compare the map with frequency map from tracking. The result indicates the new method may be applied in nonlinear lattice optimization, taking the advantage of the high speed (about 10~50 times faster) to explore x, y and the off-momentum phase space.

DOI •

reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2021-MOPAB041

About •

paper received ※ 09 May 2021 paper accepted ※ 26 May 2021 issue date ※ 18 August 2021

Export •

reference for this paper using ※ BibTeX, ※ LaTeX, ※ Text/Word, ※ RIS, ※ EndNote (xml)

MOPAB062

A Single Dipole Source for Broad-Band Soft Photon Beamlines in Diamond-II

lattice, dipole, emittance, dynamic-aperture

261

M. Apollonio, G. Cinque, H. Ghasem, A.N. Jury, I.P.S. Martin, R. Rambo
DLS, Oxfordshire, United Kingdom

Diamond-II is a project based at Diamond Light Source for an upgrade towards a Storage Ring characterized by a reduction of a factor 20 in its natural emittance and a doubling of the number of straight sections. At Diamond-II the majority of existing beamline capacity should be maintained, while enhancing their performance thanks to the increase in brightness at the source points. The substantial modification of the lattice imposes a likewise re-design of the broad-band sources, presently based on standard dipoles. In this paper we discuss a possible solution for the IR/THz beamline B22 operating within a photon energy range between 1meV and 1eV. This proposal, ideal for low critical energy and single source point sources, entails the insertion of a dipole in one of the newly created mid-cell straights of the machine, while reducing the bending power of the nearby gradient dipoles. After performing the linear matching of the lattice, reproducing a comparable phase advance in the modified cell, we studied the non-linear dynamics of the system. Comparison of the main observables (Dynamic Aperture, Injection Efficiency and Lifetime) with the baseline case is discussed.

DOI •

reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2021-MOPAB062

About •

paper received ※ 18 May 2021 paper accepted ※ 28 May 2021 issue date ※ 12 August 2021

Export •

reference for this paper using ※ BibTeX, ※ LaTeX, ※ Text/Word, ※ RIS, ※ EndNote (xml)

MOPAB074

Preliminary Study of Design Method for Hybrid MBA Lattice

lattice, resonance, sextupole, emittance

297

J.J. Tan, Z.H. Bai, Z.L. Ren, J.H. Xu
USTC/NSRL, Hefei, Anhui, People’s Republic of China
Q. Zhang
INEST, Hefei, People’s Republic of China

Nonlinear optimization of hybrid multi-bend-achromat (HMBA) lattice is a difficult task due to its quite limited variables of multipole magnets. As a result, it is necessary to consider nonlinear potential of the lattice in its linear design. Nonlinear dynamics can be estimated by nonlinear driving terms and detuning terms. In this paper, we propose a design method for HMBA lattice. In this method, objective functions include emittance and two indicators of nonlinear dynamics, which consist of nonlinear driving terms and detuning terms. As an example, an HMBA lattice for a 2.2 GeV storage ring with circumference of 460.8 m was designed to demonstrate the method.

DOI •

reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2021-MOPAB074

About •

paper received ※ 19 May 2021 paper accepted ※ 21 May 2021 issue date ※ 21 August 2021

Export •

reference for this paper using ※ BibTeX, ※ LaTeX, ※ Text/Word, ※ RIS, ※ EndNote (xml)

MOPAB113

A Low-emittance Booster Lattice Design for the SOLEIL Upgrade

booster, lattice, emittance, storage-ring

410

M.-A. Tordeux, A. Loulergue, R. Nagaoka
SOLEIL, Gif-sur-Yvette, France
Z.H. Bai, G. Liu, T. Zhang
USTC/NSRL, Hefei, Anhui, People’s Republic of China

The SOLEIL storage ring upgrade will require an injected beam with small transverse and longitudinal sizes. To meet this requirement, the present booster also needs to be upgraded, aiming to reduce the emittance below 10 nm·rad. A multi-bend achromat lattice is designed in this context for the booster upgrade, which consists of two superperiods to respect the present race-track configuration. The lattice is a 16BA HOA (Higher-Order Achromat) type lattice, composed of 14 unit cells, 2 matching cells and a long straight section, and combined-function bending magnets are used in the unit cells to both save space and reduce the emittance. The natural emittance of the designed booster is 5.2 nm·rad at the final energy of 2.75 GeV. This paper presents the general constraints, linear lattice design and nonlinear dynamics optimization for the booster upgrade.

DOI •

reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2021-MOPAB113

About •

paper received ※ 19 May 2021 paper accepted ※ 28 May 2021 issue date ※ 26 August 2021

Export •

reference for this paper using ※ BibTeX, ※ LaTeX, ※ Text/Word, ※ RIS, ※ EndNote (xml)

TUPAB136

On Nonlinear Electron Beam Dynamics in a Plasma Environment

plasma, electron, emittance, wakefield

1707

H.Y. Barminova
MEPhI, Moscow, Russia
B. Kak
RUDN University, Moscow, Russia

The nonlinear dynamics of an electron beam propagating in a low-density plasma is investigated. The beam envelope equation is obtained analytically for the case of an axisymmetric beam using a model approximation close to the Kapchinsky-Vladimirsky model. Solutions of the envelope equation are presented for various initial conditions (beam current, initial beam radius, transverse beam emittance).

DOI •

reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2021-TUPAB136

About •

paper received ※ 19 May 2021 paper accepted ※ 26 May 2021 issue date ※ 26 August 2021

Export •

reference for this paper using ※ BibTeX, ※ LaTeX, ※ Text/Word, ※ RIS, ※ EndNote (xml)

WEPAB226

Investigation of Vlasov Systems with a Certain Class of Linearly-Collective Hamiltonians

bunching, simulation, collective-effects, distributed

3157

Ph. Amstutz, M. Vogt
DESY, Hamburg, Germany

In many cases the Vlasov equation cannot be solved exactly due its inherent non-linearity arising from collective terms in the Hamiltonian. Based on the analysis of the Hamiltonian’s dependence on the phase-space density and the requirement for self-consistency in this contribution a class of Hamiltonians is defined and characterized. For members of this class the corresponding expansion of the Vlasov equation terminates. The new, potentially non-autonomous, Hamiltonian of the resulting Liouville equation depends only on the initial condition of the phase-space density. Prominent members of this class are Poisson-type kick-Hamiltonians, which we show as an example. We expect these investigations to be a potential starting point for the analysis and conception of operator-splitting schemes or splitting-free methods for beam-dynamics simulation codes.

DOI •

reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2021-WEPAB226

About •

paper received ※ 18 May 2021 paper accepted ※ 01 July 2021 issue date ※ 17 August 2021

Export •

reference for this paper using ※ BibTeX, ※ LaTeX, ※ Text/Word, ※ RIS, ※ EndNote (xml)