IPAC2022 - Classification: MC5: Beam Dynamics and EM Fields / D02:Non-linear Single Particle Dynamics - Resonances,Tracking,Higher Order,Dynamic Aperture,Code Dev

Paper	Title	Page
MOPOST003	BBQ and Doughnut Beams: A Tasty Recipe for Measuring Amplitude Dependence of the Closest Tune Approach	42
	E.H. Maclean, F.S. Carlier, T.H.B. Persson, R. Tomás García CERN, Meyrin, Switzerland
	Beam-based observations and theoretical studies have demonstrated the existence of a significant amplitude dependence of the closest tune approach (ADECTA) in the LHC. This effect has the potential to generate significant distortion of the tune footprint and thus is of interest in regard to Landau damping. Conventionally ADECTA has been studied through saturation of tune separation with action during amplitude-detuning type measurements. In this paper, an alternative measurement technique is proposed and results of initial tests with beam are presented. The novel technique attempts to measure ADECTA by performing a classical closest approach tune scan, using proton beams in the LHC, which have been kicked and allowed to decohere, effectively giving a large action doughnut beam. It is shown that the tune and closest approach of the doughnut beams can be measured using the existing LHC Base-Band tune (BBQ) measurement system, and an amplitude dependence can be observed.
DOI •	reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2022-MOPOST003
About •	Received ※ 08 June 2022 — Revised ※ 20 June 2022 — Accepted ※ 12 July 2022 — Issue date ※ 22 June 2022
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MOPOST038	Excitation of the σ_l_l = 90° Resonance by the Cavity RF Accelerating Fields	152
	J.-M. Lagniel GANIL, Caen, France
	In RF linacs the longitudinal focusing is done by nonlinear forces and at high accelerating fields the zero-current longitudinal phase advance per longitudinal focusing period σ₀l_l can be high. The nonlinear components of the RF field (sextupolar, octupolar and higher order components) can then excite parametric resonances, including the 4th-order resonance (σ_l_l = 90°) when σ₀l_l is higher than 90°, inducing strong longitudinal emittance growths and acceptance reductions. The longitudinal beam dynamics is therefore complex, even when the nonlinear space-charge forces are ignored. The parametric resonance excitation by the RF field is analyzed before discussing the additional effect of the nonlinear space-charge forces, in particular to explain why the zero-current longitudinal phase advance per transverse focusing period σ₀l_t is not a relevant parameter. Examples are given in the SPIRAL2 linac case.
DOI •	reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2022-MOPOST038
About •	Received ※ 16 May 2022 — Accepted ※ 17 June 2022 — Issue date ※ 22 June 2022
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MOPOST040	On a Framework to Analyze Single-Particle Non-Linear Beam Dynamics: Normal Form on a Critical Point	160
	M. Titze HZB, Berlin, Germany
	Funding: Work supported by German Bundesministerium für Bildung und Forschung, Land Berlin, and grants of Helmholtz Association. Normal form analysis around a stable fixed point is a well-established tool in accelerator physics and has proven to be invaluable for an understanding of non-linear beam dynamics. In this work we present progress in developing a modular Python framework to analyze some of the non-linear aspects of a storage ring, by directly operating with the given Hamiltonians. Hereby we have implemented Birkhoff’s normal form and Magnus expansion. This leads to a flexible framework to perform calculations to high order and, moreover, to relax the constraint of stability to also include certain unstable fixed points in the analysis.
DOI •	reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2022-MOPOST040
About •	Received ※ 31 May 2022 — Revised ※ 13 June 2022 — Accepted ※ 14 June 2022 — Issue date ※ 25 June 2022
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MOPOST041	Dynamic Aperture Studies for the Transfer Line From FLUTE to cSTART	164
SUSPMF062	use link to see paper's listing under its alternate paper code
	J. Schäfer, B. Härer, A.-S. Müller, A.I. Papash, R. Ruprecht, M. Schuh KIT, Karlsruhe, Germany
	Funding: J. Schäfer acknowledges the support by the DFG- funded Doctoral School "Karlsruhe School of Elementary and Astroparticle Physics: Science and Technology". The compact STorage ring for Accelerator Research and Technology cSTART project will deliver a new KIT accelerator test facility for the application of novel acceleration techniques and diagnostics. The goal is to demonstrate storing an electron beam of a Laser Plasma Accelerator (LPA) in a compact circular accelerator for the first time. Before installing an LPA, the Far-Infrared Linac and Test Experiment (FLUTE) will serve as a full energy injector for the compact storage ring, providing stable bunches with a length down to a few femtoseconds. The transport of the bunches from FLUTE to the cSTART storage ring requires a transfer line which includes horizontal, vertical and coupled deflections which leads to coupling of the dynamics in the two transverse planes. In order to realize ultra-short bunch lengths at the end of the transport line, it relies on special optics which invokes high and negative dispersion. This contribution presents dynamic aperture studies based on six-dimensional tracking through the lattice of the transfer line.
DOI •	reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2022-MOPOST041
About •	Received ※ 08 June 2022 — Revised ※ 09 June 2022 — Accepted ※ 17 June 2022 — Issue date ※ 24 June 2022
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MOPOST042	Using Dynamic Indicators for Probing Single-Particle Stability in Circular Accelerators	168
	C.E. Montanari, A. Bazzani, G. Turchetti Bologna University, Bologna, Italy M. Giovannozzi, C.E. Montanari CERN, Meyrin, Switzerland
	Computing the long-term behaviour of single-particle motion is a numerically intensive process, as it requires a large number of initial conditions to be tracked for a large number of turns to probe their stability. A possibility to reduce the computational resources required is to provide indicators that can efficiently detect chaotic motion, which are considered precursors to unbounded motion. These indicators could allow skilful selection of a set of initial conditions that could then be considered for long-term tracking. The chaotic nature of each orbit can be assessed by using fast-converging dynamic indicators, such as the Fast Lyapunov Indicator (FLI), the Reversibility Error Method (REM), and the Smallest and Global Alignment Index (SALI and GALI). These indicators are widely used in the field of Celestial Mechanics, but not so widespread in Accelerator Physics. They have been applied both to a modulated Hénon map, as a toy model, as well as to realistic lattices of the High-Luminosity LHC. In this paper, we discuss the results of detailed numerical studies, focusing on their performance in detecting chaotic motions.
DOI •	reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2022-MOPOST042
About •	Received ※ 07 June 2022 — Accepted ※ 17 June 2022 — Issue date ※ 02 July 2022
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MOPOST043	Testing the Global Diffusive Behaviour of Beam-Halo Dynamics at the CERN LHC Using Collimator Scans	172
SUSPMF063	use link to see paper's listing under its alternate paper code
	C.E. Montanari, A. Bazzani Bologna University, Bologna, Italy M. Giovannozzi, C.E. Montanari, S. Redaelli CERN, Meyrin, Switzerland A.A. Gorzawski University of Malta, Information and Communication Technology, Msida, Malta
	In superconducting circular particle accelerators, controlling beam losses is of paramount importance for ensuring optimal machine performance and an efficient operation. To achieve the required level of understanding of the mechanisms underlying beam losses, models based on global diffusion processes have recently been studied and proposed to investigate the beam-halo dynamics. In these models, the building block of the analytical form of the diffusion coefficient is the stability-time estimate of the Nekhoroshev theorem. In this paper, the developed models are applied to data acquired during collimation scans at the CERN LHC. In these measurements, the collimators are moved in steps and the tail population is re-constructed from the observed losses. This allows an estimate of the diffusion coefficient. The results of the analyses performed are presented and discussed in detail.
DOI •	reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2022-MOPOST043
About •	Received ※ 07 June 2022 — Revised ※ 10 June 2022 — Accepted ※ 16 June 2022 — Issue date ※ 17 June 2022
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MOPOST045	A Novel Tool for Beam Dynamics Studies with Hollow Electron Lenses	176
	P.D. Hermes, R. Bruce, R. De Maria, M. Giovannozzi, G. Iadarola, D. Mirarchi, S. Redaelli CERN, Meyrin, Switzerland
	Hollow Electron Lenses (HELs) are crucial components of the CERN LHC High Luminosity Upgrade (HL-LHC), serving the purpose of actively controlling the population of the transverse beam halo to reduce particle losses on the collimation system. Symplectic particle tracking simulations are required to optimize the efficiency and study potentially undesired beam dynamics effects with the HELs. With the relevant time scales in the collider in the order of several minutes, tracking simulations require considerable computing resources. A new tracking tool, Xsuite, developed at CERN since 2021, offers the possibility of performing such tracking simulations using graphics processing units (GPUs), with promising perspectives for the simulation of hadron beam dynamics with HELs. In this contribution, we present the implementation of HEL physics effects in the new tracking framework. We compare the performance with previous tools and show simulation results obtained using known and newly established simulation setups.
DOI •	reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2022-MOPOST045
About •	Received ※ 08 June 2022 — Revised ※ 13 June 2022 — Accepted ※ 22 June 2022 — Issue date ※ 08 July 2022
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MOPOST046	Enforcing the Convergence of Longitudinal Bunch Density Calculation in the Presence of a Harmonic Cavity Through Anderson Acceleration Method	180
	I. Carvalho de Almeida CNPEM, Campinas, SP, Brazil M. Hoffmann Wallner, A.P.B. Lima LNLS, Campinas, Brazil
	Sirius is a 4th generation synchrotron light source at the Brazilian Center for Research in Energy and Materials in Campinas, Brazil. A passive superconducting third harmonic cavity is planned to be installed in the storage ring in order to lengthen the bunches and increase beam lifetime by reducing Touschek scattering while keeping its high brightness. This paper presents the results obtained in applying Anderson acceleration method to enforce the convergence of the self-consistent algorithm used for calculation of the equilibrium longitudinal bunch density in the presence of a harmonic cavity.
DOI •	reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2022-MOPOST046
About •	Received ※ 08 June 2022 — Accepted ※ 16 June 2022 — Issue date ※ 18 June 2022
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MOPOST047	Determination of the Phase-Space Stability Border with Machine Learning Techniques	183
	F.F. Van der Veken, R. Akbari, M.P. Bogaert, E. Fol, M. Giovannozzi, A.L. Lowyck, C.E. Montanari, W. Van Goethem CERN, Meyrin, Switzerland
	The dynamic aperture (DA) of a hadron accelerator is represented by the volume in phase space that exhibits bounded motion, where we disregard any disconnected parts that could be due to stable islands. To estimate DA in numerical simulations, it is customary to sample a set of initial conditions using a polar grid in the transverse planes, featuring a limited number of angles and using evenly distributed radial amplitudes. This method becomes very CPU intensive when detailed scans in 4D, and even more in higher dimensions, are used to compute the dynamic aperture. In this paper, a new method is presented, in which the border of the phase-space stable region is identified using a machine learning (ML) model. This allows one to optimise the computational time by taking the complex geometry of the phase space into account, using adaptive sampling to increase the density of initial conditions along the border of stability.
DOI •	reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2022-MOPOST047
About •	Received ※ 06 June 2022 — Accepted ※ 17 June 2022 — Issue date ※ 20 June 2022
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MOPOST048	Efficient Representation of Realistic 3D Static Magnetic Fields for Symplectic Tracking and First Applications for Frequency Analysis and Dynamic Aperture Studies in ELENA	187
	L. Bojtár CERN, Meyrin, Switzerland
	The algorithm called SIMPA has a new and unique approach to long-term 4D tracking of charged particles in arbitrary static electromagnetic fields. Field values given on the boundary of the region of interest are reproduced by an arrangement of hypothetical magnetic or electric point sources surrounding the boundary surface. The vector and scalar potentials are obtained by summing the contributions of each source. The second step of the method improves the evaluation speed of the potentials and their derivatives by orders of magnitude. This comprises covering the region of interest by overlapping spheres, then calculating the spherical harmonic expansion of the potentials on each sphere. During tracking, field values are evaluated by calculating the solid harmonics and their derivatives inside a sphere containing the particle. Frequency analysis and dynamic aperture studies in ELENA is presented. The effect of the end fields and the perturbation introduced by the magnetic system of the electron cooler on dynamic aperture is shown. The dynamic aperture calculated is the direct consequence of the geometry of the magnetic elements, no multipole errors have been added to the model.
DOI •	reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2022-MOPOST048
About •	Received ※ 08 June 2022 — Revised ※ 15 June 2022 — Accepted ※ 17 June 2022 — Issue date ※ 01 July 2022
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MOPOST050	Third-Order Resonance Compensation at the FNAL Recycler Ring	195
SUSPMF064	use link to see paper's listing under its alternate paper code
	C.E. Gonzalez-Ortiz MSU, East Lansing, Michigan, USA R. Ainsworth Fermilab, Batavia, Illinois, USA P.N. Ostroumov FRIB, East Lansing, Michigan, USA
	The Recycler Ring (RR) at the Fermilab Accelerator Complex performs slip-stacking on 8 GeV protons, doubling the beam intensity delivered to the Main Injector (MI). At MI, the beam is accelerated to 120 GeV and delivered to the high energy neutrino experiments. Femilab’s Proton Improvement Plan II (PIP-II) will require the Recycler to store 50% more beam. Simulations have shown that the space charge tune shift at this new intensity will lead to the excitation of multiple resonance lines. Specifically, this study looks at normal sextupole lines 3 Q_x=76 and Q_x+2Q_y=74, plus skew sextupole lines 3 Q_y=73 and 2 Q_x+Q_y=75. Dedicated normal and skew sextupoles have been installed in order to compensate for these resonance lines. By measuring and calculating the Resonance Driving Terms (RDT), this study shows how each of the resonance lines can be compensated independently. Furthermore, this study shows and discusses initial investigations into compensating multiple lines simultaneously.
DOI •	reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2022-MOPOST050
About •	Received ※ 09 June 2022 — Accepted ※ 16 June 2022 — Issue date ※ 21 June 2022
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MOPOST051	Study of Transverse Resonance Island Buckets at CESR	199
	S. Wang, V. Khachatryan Cornell University (CLASSE), Cornell Laboratory for Accelerator-Based Sciences and Education, Ithaca, New York, USA
	Funding: Work supported by NSF PHYS-1416318 and DMR-1829070. A 6-GeV lattice with the horizontal tune near a 3rd-order resonance line at 3ν_x=2 is designed for studying the transverse resonance island buckets (TRIBs) at the Cornell Electron Storage Ring (CESR). The distribution of 76 sextupoles powered individually is optimized to maximize the dynamic aperture and achieve the desired amplitude-dependent tune shift α_xx and the resonant driving term h₃₀₀₀₀, which are necessary conditions to form stable island buckets. The particle tracking simulations are developed to check and confirm the formation of TRIBs at different tunes with clearing kicks in this TRIBs lattice. Finally, the lattice is loaded in CESR and the TRIBs are successfully observed when the horizontal fractional tune is adjusted to 0.665, close to the 3rd-order resonance line. Bunch-by-bunch feedback is also explored to clear the particles in the main bucket and the island buckets, respectively.
DOI •	reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2022-MOPOST051
About •	Received ※ 20 May 2022 — Revised ※ 09 June 2022 — Accepted ※ 16 June 2022 — Issue date ※ 25 June 2022
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MOPOST053	Transverse Resonance Islands Buckets at SPEAR3	203
	J. Kim, J.A. Safranek, K. Tian SLAC, Menlo Park, California, USA
	We present populating bunches into the transverse resonance islands buckets (TRIBs) on SPEAR3. As one of operation modes for the timing-mode or providing separated bunches in transverse direction, we are exploring TRIBs on SPEAR3. Experience and analysis on applying kicks multiple times using the bunch-by-bunch feedback kicker to move bunches into the TRIBs is described.
DOI •	reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2022-MOPOST053
About •	Received ※ 06 June 2022 — Revised ※ 09 June 2022 — Accepted ※ 17 June 2022 — Issue date ※ 03 July 2022
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MOPOST055	The EIC Rapid Cycling Synchrotron Dynamic Aperture Optimization	210
	H. Lovelace III, C. Montag, V.H. Ranjbar BNL, Upton, New York, USA F. Lin ORNL RAD, Oak Ridge, Tennessee, USA
	With the design of the Electron-Ion Collider (EIC), a new Rapid Cycling Synchrotron (RCS) must be designed to accelerate the electron bunches from 400 MeV up to 18 GeV. An optimized dynamic aperture with preservation of polarization through the energy ramp was found. The codes DEPOL, MAD-X, and BMAD are used in modeling the dynamics and spin preservation. The results will be discussed in this paper.
DOI •	reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2022-MOPOST055
About •	Received ※ 27 May 2022 — Revised ※ 10 June 2022 — Accepted ※ 16 June 2022 — Issue date ※ 08 July 2022
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MOPOST058	Studies on the Vertical Half-Integer Resonance in the CERN PS Booster	222
SUSPMF074	use link to see paper's listing under its alternate paper code
	T. Prebibaj, F. Antoniou, F. Asvesta, H. Bartosik CERN, Meyrin, Switzerland G. Franchetti GSI, Darmstadt, Germany
	Following the upgrades of the LHC Injectors Upgrade Project (LIU), the Proton Synchrotron Booster (PSB) at CERN successfully delivers beams with double brightness. An important contributing factor for this was the dynamic correction of the beta-beating induced by the injection chicane, which allowed stable operation closer to the half-integer resonance. Ideally, injection above the half-integer resonance could further improve the beam brightness. In this context, a series of studies were initiated in order to characterize the effects of space charge when crossing the half-integer resonance. In this contribution, the first results of these investigations are reported.
DOI •	reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2022-MOPOST058
About •	Received ※ 03 June 2022 — Revised ※ 14 June 2022 — Accepted ※ 15 June 2022 — Issue date ※ 24 June 2022
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WEIZSP1	Interpretation of Particle Motion in a Circular Accelerator as Diffraction of Light
	T. Hiraiwa RIKEN SPring-8 Center, Hyogo, Japan
	Inspired by Fermat’s principle of geometric optics 200 years ago, famous Dr. Hamilton built Hamiltonian mechanics based on the principle of minimal action. Since then, optics and mechanics have developed while stimulating each other. A new hidden link between optics and mechanics was recently found on particle motion in a circular accelerator. A forced harmonic oscillator is often used as a model to describe particle motion in a circular accelerator. Such a model sometimes assumes that, eigen frequency or frequency of the external force is changed slowly with time to simulate, for example, resonance crossing, beam dump by turning off the RF power, resonance extraction, etc. in circular accelerators. In such cases, particle motion is well described by using formulae for Fresnel or Fraunhofer diffraction, depending on simulation conditions. This presentation will comprehensively show what is essential mechanism to link resonance phenomena of mechanics and optical diffraction, relation between the real accelerator model and the harmonic oscillator, and possibility of this knowledge to apply investigation of beam dynamics in a particle accelerator.
	Slides WEIZSP1 [5.755 MB]
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WEOZSP4	Full Coupling Studies at ALBA	1667
	Z. Martí, G. Benedetti, M. Carlà, U. Iriso, L. Torino ALBA-CELLS Synchrotron, Cerdanyola del Vallès, Spain
	As other low emittance machine upgrades ALBA-II proposal considers operating in full coupling. In such configuration the horizontal emittance is further reduced while the lifetime is increased at the price of working close to equal fractional tunes. This mode of operation has not been adopted by any existing light source to date, and it presents a few disadvantages, like the optics degradation, injection efficiency reduction and beam size stability. In this paper the above mentioned difficulties are studied for the present ALBA storage ring in full coupling conditions.
	Slides WEOZSP4 [1.694 MB]
DOI •	reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2022-WEOZSP4
About •	Received ※ 07 June 2022 — Revised ※ 14 June 2022 — Accepted ※ 15 June 2022 — Issue date ※ 22 June 2022
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Paper

Title

Page

BBQ and Doughnut Beams: A Tasty Recipe for Measuring Amplitude Dependence of the Closest Tune Approach

42

E.H. Maclean, F.S. Carlier, T.H.B. Persson, R. Tomás García
CERN, Meyrin, Switzerland

Beam-based observations and theoretical studies have demonstrated the existence of a significant amplitude dependence of the closest tune approach (ADECTA) in the LHC. This effect has the potential to generate significant distortion of the tune footprint and thus is of interest in regard to Landau damping. Conventionally ADECTA has been studied through saturation of tune separation with action during amplitude-detuning type measurements. In this paper, an alternative measurement technique is proposed and results of initial tests with beam are presented. The novel technique attempts to measure ADECTA by performing a classical closest approach tune scan, using proton beams in the LHC, which have been kicked and allowed to decohere, effectively giving a large action doughnut beam. It is shown that the tune and closest approach of the doughnut beams can be measured using the existing LHC Base-Band tune (BBQ) measurement system, and an amplitude dependence can be observed.

DOI •

reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2022-MOPOST003

About •

Received ※ 08 June 2022 — Revised ※ 20 June 2022 — Accepted ※ 12 July 2022 — Issue date ※ 22 June 2022

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

MOPOST038

Excitation of the σ_l_l = 90° Resonance by the Cavity RF Accelerating Fields

152

J.-M. Lagniel
GANIL, Caen, France

In RF linacs the longitudinal focusing is done by nonlinear forces and at high accelerating fields the zero-current longitudinal phase advance per longitudinal focusing period σ₀l_l can be high. The nonlinear components of the RF field (sextupolar, octupolar and higher order components) can then excite parametric resonances, including the 4th-order resonance (σ_l_l = 90°) when σ₀l_l is higher than 90°, inducing strong longitudinal emittance growths and acceptance reductions. The longitudinal beam dynamics is therefore complex, even when the nonlinear space-charge forces are ignored. The parametric resonance excitation by the RF field is analyzed before discussing the additional effect of the nonlinear space-charge forces, in particular to explain why the zero-current longitudinal phase advance per transverse focusing period σ₀l_t is not a relevant parameter. Examples are given in the SPIRAL2 linac case.

DOI •

reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2022-MOPOST038

About •

Received ※ 16 May 2022 — Accepted ※ 17 June 2022 — Issue date ※ 22 June 2022

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

MOPOST040

On a Framework to Analyze Single-Particle Non-Linear Beam Dynamics: Normal Form on a Critical Point

160

M. Titze
HZB, Berlin, Germany

Funding: Work supported by German Bundesministerium für Bildung und Forschung, Land Berlin, and grants of Helmholtz Association.
Normal form analysis around a stable fixed point is a well-established tool in accelerator physics and has proven to be invaluable for an understanding of non-linear beam dynamics. In this work we present progress in developing a modular Python framework to analyze some of the non-linear aspects of a storage ring, by directly operating with the given Hamiltonians. Hereby we have implemented Birkhoff’s normal form and Magnus expansion. This leads to a flexible framework to perform calculations to high order and, moreover, to relax the constraint of stability to also include certain unstable fixed points in the analysis.

DOI •

reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2022-MOPOST040

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Received ※ 31 May 2022 — Revised ※ 13 June 2022 — Accepted ※ 14 June 2022 — Issue date ※ 25 June 2022

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MOPOST041

Dynamic Aperture Studies for the Transfer Line From FLUTE to cSTART

164

SUSPMF062

use link to see paper's listing under its alternate paper code

J. Schäfer, B. Härer, A.-S. Müller, A.I. Papash, R. Ruprecht, M. Schuh
KIT, Karlsruhe, Germany

Funding: J. Schäfer acknowledges the support by the DFG- funded Doctoral School "Karlsruhe School of Elementary and Astroparticle Physics: Science and Technology".
The compact STorage ring for Accelerator Research and Technology cSTART project will deliver a new KIT accelerator test facility for the application of novel acceleration techniques and diagnostics. The goal is to demonstrate storing an electron beam of a Laser Plasma Accelerator (LPA) in a compact circular accelerator for the first time. Before installing an LPA, the Far-Infrared Linac and Test Experiment (FLUTE) will serve as a full energy injector for the compact storage ring, providing stable bunches with a length down to a few femtoseconds. The transport of the bunches from FLUTE to the cSTART storage ring requires a transfer line which includes horizontal, vertical and coupled deflections which leads to coupling of the dynamics in the two transverse planes. In order to realize ultra-short bunch lengths at the end of the transport line, it relies on special optics which invokes high and negative dispersion. This contribution presents dynamic aperture studies based on six-dimensional tracking through the lattice of the transfer line.

DOI •

reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2022-MOPOST041

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Received ※ 08 June 2022 — Revised ※ 09 June 2022 — Accepted ※ 17 June 2022 — Issue date ※ 24 June 2022

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MOPOST042

Using Dynamic Indicators for Probing Single-Particle Stability in Circular Accelerators

168

C.E. Montanari, A. Bazzani, G. Turchetti
Bologna University, Bologna, Italy
M. Giovannozzi, C.E. Montanari
CERN, Meyrin, Switzerland

Computing the long-term behaviour of single-particle motion is a numerically intensive process, as it requires a large number of initial conditions to be tracked for a large number of turns to probe their stability. A possibility to reduce the computational resources required is to provide indicators that can efficiently detect chaotic motion, which are considered precursors to unbounded motion. These indicators could allow skilful selection of a set of initial conditions that could then be considered for long-term tracking. The chaotic nature of each orbit can be assessed by using fast-converging dynamic indicators, such as the Fast Lyapunov Indicator (FLI), the Reversibility Error Method (REM), and the Smallest and Global Alignment Index (SALI and GALI). These indicators are widely used in the field of Celestial Mechanics, but not so widespread in Accelerator Physics. They have been applied both to a modulated Hénon map, as a toy model, as well as to realistic lattices of the High-Luminosity LHC. In this paper, we discuss the results of detailed numerical studies, focusing on their performance in detecting chaotic motions.

DOI •

reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2022-MOPOST042

About •

Received ※ 07 June 2022 — Accepted ※ 17 June 2022 — Issue date ※ 02 July 2022

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MOPOST043

Testing the Global Diffusive Behaviour of Beam-Halo Dynamics at the CERN LHC Using Collimator Scans

172

SUSPMF063

use link to see paper's listing under its alternate paper code

C.E. Montanari, A. Bazzani
Bologna University, Bologna, Italy
M. Giovannozzi, C.E. Montanari, S. Redaelli
CERN, Meyrin, Switzerland
A.A. Gorzawski
University of Malta, Information and Communication Technology, Msida, Malta

In superconducting circular particle accelerators, controlling beam losses is of paramount importance for ensuring optimal machine performance and an efficient operation. To achieve the required level of understanding of the mechanisms underlying beam losses, models based on global diffusion processes have recently been studied and proposed to investigate the beam-halo dynamics. In these models, the building block of the analytical form of the diffusion coefficient is the stability-time estimate of the Nekhoroshev theorem. In this paper, the developed models are applied to data acquired during collimation scans at the CERN LHC. In these measurements, the collimators are moved in steps and the tail population is re-constructed from the observed losses. This allows an estimate of the diffusion coefficient. The results of the analyses performed are presented and discussed in detail.

DOI •

reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2022-MOPOST043

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Received ※ 07 June 2022 — Revised ※ 10 June 2022 — Accepted ※ 16 June 2022 — Issue date ※ 17 June 2022

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MOPOST045

A Novel Tool for Beam Dynamics Studies with Hollow Electron Lenses

176

P.D. Hermes, R. Bruce, R. De Maria, M. Giovannozzi, G. Iadarola, D. Mirarchi, S. Redaelli
CERN, Meyrin, Switzerland

Hollow Electron Lenses (HELs) are crucial components of the CERN LHC High Luminosity Upgrade (HL-LHC), serving the purpose of actively controlling the population of the transverse beam halo to reduce particle losses on the collimation system. Symplectic particle tracking simulations are required to optimize the efficiency and study potentially undesired beam dynamics effects with the HELs. With the relevant time scales in the collider in the order of several minutes, tracking simulations require considerable computing resources. A new tracking tool, Xsuite, developed at CERN since 2021, offers the possibility of performing such tracking simulations using graphics processing units (GPUs), with promising perspectives for the simulation of hadron beam dynamics with HELs. In this contribution, we present the implementation of HEL physics effects in the new tracking framework. We compare the performance with previous tools and show simulation results obtained using known and newly established simulation setups.

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reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2022-MOPOST045

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Received ※ 08 June 2022 — Revised ※ 13 June 2022 — Accepted ※ 22 June 2022 — Issue date ※ 08 July 2022

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MOPOST046

Enforcing the Convergence of Longitudinal Bunch Density Calculation in the Presence of a Harmonic Cavity Through Anderson Acceleration Method

180

I. Carvalho de Almeida
CNPEM, Campinas, SP, Brazil
M. Hoffmann Wallner, A.P.B. Lima
LNLS, Campinas, Brazil

Sirius is a 4th generation synchrotron light source at the Brazilian Center for Research in Energy and Materials in Campinas, Brazil. A passive superconducting third harmonic cavity is planned to be installed in the storage ring in order to lengthen the bunches and increase beam lifetime by reducing Touschek scattering while keeping its high brightness. This paper presents the results obtained in applying Anderson acceleration method to enforce the convergence of the self-consistent algorithm used for calculation of the equilibrium longitudinal bunch density in the presence of a harmonic cavity.

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reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2022-MOPOST046

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Received ※ 08 June 2022 — Accepted ※ 16 June 2022 — Issue date ※ 18 June 2022

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MOPOST047

Determination of the Phase-Space Stability Border with Machine Learning Techniques

183

F.F. Van der Veken, R. Akbari, M.P. Bogaert, E. Fol, M. Giovannozzi, A.L. Lowyck, C.E. Montanari, W. Van Goethem
CERN, Meyrin, Switzerland

The dynamic aperture (DA) of a hadron accelerator is represented by the volume in phase space that exhibits bounded motion, where we disregard any disconnected parts that could be due to stable islands. To estimate DA in numerical simulations, it is customary to sample a set of initial conditions using a polar grid in the transverse planes, featuring a limited number of angles and using evenly distributed radial amplitudes. This method becomes very CPU intensive when detailed scans in 4D, and even more in higher dimensions, are used to compute the dynamic aperture. In this paper, a new method is presented, in which the border of the phase-space stable region is identified using a machine learning (ML) model. This allows one to optimise the computational time by taking the complex geometry of the phase space into account, using adaptive sampling to increase the density of initial conditions along the border of stability.

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reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2022-MOPOST047

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Received ※ 06 June 2022 — Accepted ※ 17 June 2022 — Issue date ※ 20 June 2022

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MOPOST048

Efficient Representation of Realistic 3D Static Magnetic Fields for Symplectic Tracking and First Applications for Frequency Analysis and Dynamic Aperture Studies in ELENA

187

L. Bojtár
CERN, Meyrin, Switzerland

The algorithm called SIMPA has a new and unique approach to long-term 4D tracking of charged particles in arbitrary static electromagnetic fields. Field values given on the boundary of the region of interest are reproduced by an arrangement of hypothetical magnetic or electric point sources surrounding the boundary surface. The vector and scalar potentials are obtained by summing the contributions of each source. The second step of the method improves the evaluation speed of the potentials and their derivatives by orders of magnitude. This comprises covering the region of interest by overlapping spheres, then calculating the spherical harmonic expansion of the potentials on each sphere. During tracking, field values are evaluated by calculating the solid harmonics and their derivatives inside a sphere containing the particle. Frequency analysis and dynamic aperture studies in ELENA is presented. The effect of the end fields and the perturbation introduced by the magnetic system of the electron cooler on dynamic aperture is shown. The dynamic aperture calculated is the direct consequence of the geometry of the magnetic elements, no multipole errors have been added to the model.

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reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2022-MOPOST048

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Received ※ 08 June 2022 — Revised ※ 15 June 2022 — Accepted ※ 17 June 2022 — Issue date ※ 01 July 2022

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MOPOST050

Third-Order Resonance Compensation at the FNAL Recycler Ring

195

SUSPMF064

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C.E. Gonzalez-Ortiz
MSU, East Lansing, Michigan, USA
R. Ainsworth
Fermilab, Batavia, Illinois, USA
P.N. Ostroumov
FRIB, East Lansing, Michigan, USA

The Recycler Ring (RR) at the Fermilab Accelerator Complex performs slip-stacking on 8 GeV protons, doubling the beam intensity delivered to the Main Injector (MI). At MI, the beam is accelerated to 120 GeV and delivered to the high energy neutrino experiments. Femilab’s Proton Improvement Plan II (PIP-II) will require the Recycler to store 50% more beam. Simulations have shown that the space charge tune shift at this new intensity will lead to the excitation of multiple resonance lines. Specifically, this study looks at normal sextupole lines 3 Q_x=76 and Q_x+2Q_y=74, plus skew sextupole lines 3 Q_y=73 and 2 Q_x+Q_y=75. Dedicated normal and skew sextupoles have been installed in order to compensate for these resonance lines. By measuring and calculating the Resonance Driving Terms (RDT), this study shows how each of the resonance lines can be compensated independently. Furthermore, this study shows and discusses initial investigations into compensating multiple lines simultaneously.

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reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2022-MOPOST050

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Received ※ 09 June 2022 — Accepted ※ 16 June 2022 — Issue date ※ 21 June 2022

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MOPOST051

Study of Transverse Resonance Island Buckets at CESR

199

S. Wang, V. Khachatryan
Cornell University (CLASSE), Cornell Laboratory for Accelerator-Based Sciences and Education, Ithaca, New York, USA

Funding: Work supported by NSF PHYS-1416318 and DMR-1829070.
A 6-GeV lattice with the horizontal tune near a 3rd-order resonance line at 3ν_x=2 is designed for studying the transverse resonance island buckets (TRIBs) at the Cornell Electron Storage Ring (CESR). The distribution of 76 sextupoles powered individually is optimized to maximize the dynamic aperture and achieve the desired amplitude-dependent tune shift α_xx and the resonant driving term h₃₀₀₀₀, which are necessary conditions to form stable island buckets. The particle tracking simulations are developed to check and confirm the formation of TRIBs at different tunes with clearing kicks in this TRIBs lattice. Finally, the lattice is loaded in CESR and the TRIBs are successfully observed when the horizontal fractional tune is adjusted to 0.665, close to the 3rd-order resonance line. Bunch-by-bunch feedback is also explored to clear the particles in the main bucket and the island buckets, respectively.

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reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2022-MOPOST051

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Received ※ 20 May 2022 — Revised ※ 09 June 2022 — Accepted ※ 16 June 2022 — Issue date ※ 25 June 2022

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MOPOST053

Transverse Resonance Islands Buckets at SPEAR3

203

J. Kim, J.A. Safranek, K. Tian
SLAC, Menlo Park, California, USA

We present populating bunches into the transverse resonance islands buckets (TRIBs) on SPEAR3. As one of operation modes for the timing-mode or providing separated bunches in transverse direction, we are exploring TRIBs on SPEAR3. Experience and analysis on applying kicks multiple times using the bunch-by-bunch feedback kicker to move bunches into the TRIBs is described.

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reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2022-MOPOST053

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Received ※ 06 June 2022 — Revised ※ 09 June 2022 — Accepted ※ 17 June 2022 — Issue date ※ 03 July 2022

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MOPOST055

The EIC Rapid Cycling Synchrotron Dynamic Aperture Optimization

210

H. Lovelace III, C. Montag, V.H. Ranjbar
BNL, Upton, New York, USA
F. Lin
ORNL RAD, Oak Ridge, Tennessee, USA

With the design of the Electron-Ion Collider (EIC), a new Rapid Cycling Synchrotron (RCS) must be designed to accelerate the electron bunches from 400 MeV up to 18 GeV. An optimized dynamic aperture with preservation of polarization through the energy ramp was found. The codes DEPOL, MAD-X, and BMAD are used in modeling the dynamics and spin preservation. The results will be discussed in this paper.

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reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2022-MOPOST055

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Received ※ 27 May 2022 — Revised ※ 10 June 2022 — Accepted ※ 16 June 2022 — Issue date ※ 08 July 2022

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MOPOST058

Studies on the Vertical Half-Integer Resonance in the CERN PS Booster

222

SUSPMF074

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T. Prebibaj, F. Antoniou, F. Asvesta, H. Bartosik
CERN, Meyrin, Switzerland
G. Franchetti
GSI, Darmstadt, Germany

Following the upgrades of the LHC Injectors Upgrade Project (LIU), the Proton Synchrotron Booster (PSB) at CERN successfully delivers beams with double brightness. An important contributing factor for this was the dynamic correction of the beta-beating induced by the injection chicane, which allowed stable operation closer to the half-integer resonance. Ideally, injection above the half-integer resonance could further improve the beam brightness. In this context, a series of studies were initiated in order to characterize the effects of space charge when crossing the half-integer resonance. In this contribution, the first results of these investigations are reported.

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reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2022-MOPOST058

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Received ※ 03 June 2022 — Revised ※ 14 June 2022 — Accepted ※ 15 June 2022 — Issue date ※ 24 June 2022

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WEIZSP1

Interpretation of Particle Motion in a Circular Accelerator as Diffraction of Light

T. Hiraiwa
RIKEN SPring-8 Center, Hyogo, Japan

Inspired by Fermat’s principle of geometric optics 200 years ago, famous Dr. Hamilton built Hamiltonian mechanics based on the principle of minimal action. Since then, optics and mechanics have developed while stimulating each other. A new hidden link between optics and mechanics was recently found on particle motion in a circular accelerator. A forced harmonic oscillator is often used as a model to describe particle motion in a circular accelerator. Such a model sometimes assumes that, eigen frequency or frequency of the external force is changed slowly with time to simulate, for example, resonance crossing, beam dump by turning off the RF power, resonance extraction, etc. in circular accelerators. In such cases, particle motion is well described by using formulae for Fresnel or Fraunhofer diffraction, depending on simulation conditions. This presentation will comprehensively show what is essential mechanism to link resonance phenomena of mechanics and optical diffraction, relation between the real accelerator model and the harmonic oscillator, and possibility of this knowledge to apply investigation of beam dynamics in a particle accelerator.

Slides WEIZSP1 [5.755 MB]

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WEOZSP4

Full Coupling Studies at ALBA

1667

Z. Martí, G. Benedetti, M. Carlà, U. Iriso, L. Torino
ALBA-CELLS Synchrotron, Cerdanyola del Vallès, Spain

As other low emittance machine upgrades ALBA-II proposal considers operating in full coupling. In such configuration the horizontal emittance is further reduced while the lifetime is increased at the price of working close to equal fractional tunes. This mode of operation has not been adopted by any existing light source to date, and it presents a few disadvantages, like the optics degradation, injection efficiency reduction and beam size stability. In this paper the above mentioned difficulties are studied for the present ALBA storage ring in full coupling conditions.

Slides WEOZSP4 [1.694 MB]

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reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2022-WEOZSP4

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Received ※ 07 June 2022 — Revised ※ 14 June 2022 — Accepted ※ 15 June 2022 — Issue date ※ 22 June 2022

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