IPAC2021 - Classification: MC5: Beam Dynamics and EM Fields / D02 Non-linear Single Particle Dynamics

Paper	Title	Page
MOPAB037	On Possibility of Alpha-buckets Detecting at the KIT Storage Ring KARA (Karlsruhe Research Accelerator)	167
	A.I. Papash, T. Boltz, M. Brosi, A.-S. Müller, R. Ruprecht, P. Schreiber, M. Schuh, N.J. Smale KIT, Karlsruhe, Germany
	Computer studies of longitudinal motion have been performed with the objective to estimate the possibility of detection of alpha-buckets at the KIT storage ring KARA (Karlsruhe Research Accelerator). The longitudinal equations of motion and the Hamiltonian were expanded to high order terms of the energy deviation of particles in a beam. Roots of third order equation for three leading terms of momentum compaction factor and free energy independent term were derived in a form suitable for analytical estimations. Averaged quadratic terms of closed orbit distortions caused by misalignment of magnetic elements in a ring lead to orbit lengthening independent of particle energy deviation. Particle transverse excursions were estimated and are taken into account. Simulations have been bench-marked on existing experiments at Metrology Light Source (MLS) in Berlin (Germany) and SOLEIL (France). Parameters of three simultaneous beams and alpha buckets at MLS and SOLEIL have been reproduced with high accuracy. A computer model of KARA was used to predict behavior and the dynamics of possible simultaneous beams in the ring.
	Poster MOPAB037 [1.269 MB]
DOI •	reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2021-MOPAB037
About •	paper received ※ 11 May 2021 paper accepted ※ 28 May 2021 issue date ※ 29 August 2021
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MOPAB041	Convergence Map with Action-Angle Variables Based on Square Matrix for Nonlinear Lattice Optimization	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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MOPAB235	Transverse 2d Phase-Space Tomography Using Beam Position Monitor Data of Kicked Beams	763
	K. Hwang, C.E. Mitchell, R.D. Ryne LBNL, Berkeley, California, USA
	Funding: U.S. Department of Energy under Contract No. DE-AC02-05CH11231 The time-series Beam Position Monitor (BPM) data of kicked beam is a function of lattice parameters and beam parameters including phase-space density. The decoherence model using the first-order detuning parameter has an exact solution when the beam is Gaussian. We parameterize the beam phase-space density by multiple Gaussian kernels of different weights, means, and sizes to formulate the inverse problem for 2D phase-space tomography. Numerical optimization and Bayesian inference are used to infer the beam density.
	Poster MOPAB235 [1.253 MB]
DOI •	reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2021-MOPAB235
About •	paper received ※ 20 May 2021 paper accepted ※ 02 June 2021 issue date ※ 01 September 2021
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MOPAB273	Nonlinear Coupling Resonances in X-Y Coupled Betatron Oscillations Near the Main Coupling Resonance in VEPP-2000 Collider	863
	S.A. Kladov, E. Perevedentsev BINP SB RAS, Novosibirsk, Russia S.A. Kladov, E. Perevedentsev NSU, Novosibirsk, Russia
	In the vicinity of the linear coupling resonance where the working point of the collider is positioned, we study the effect of nonlinear coupling resonances on the single-particle phase space, beam sizes and the waveform of coherent beam motion. The latter is interesting for diagnostics of the nonlinear dynamics.
	Poster MOPAB273 [1.142 MB]
DOI •	reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2021-MOPAB273
About •	paper received ※ 19 May 2021 paper accepted ※ 28 May 2021 issue date ※ 21 August 2021
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TUXA04	Coherent Excitations and Circular Attractors in Cooled Ion Bunches	1279
	S. Seletskiy, A.V. Fedotov, D. Kayran BNL, Upton, New York, USA
	Funding: Work supported by Brookhaven Science Associates, LLC under Contract No. DE-SC0012704 with the U.S. Department of Energy In electron coolers, under certain conditions, a mismatch in either gamma-factors or trajectory angles between an electron and an ion beam can cause the formation of a circular attractor in the ion beam phase space. This leads to coherent excitations of the ions with a small synchrotron or betatron amplitude and results in unusual beam dynamics, including bifurcations. In this paper, we consider the effect of coherent excitations and discuss its implications both for Low Energy RHIC Electron Cooler (LEReC) and for high energy electron coolers proposed for the Electron-Ion Collider (EIC).
DOI •	reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2021-TUXA04
About •	paper received ※ 19 May 2021 paper accepted ※ 20 July 2021 issue date ※ 11 August 2021
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TUPAB062	Expediting APS-U Long-Term Particle Tracking with Arbitrary Order Taylor Map	1505
	Y.P. Sun ANL, Lemont, Illinois, USA
	Funding: The work is supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under Contract No. DE-AC02-06CH11357. Truncated power series algebra was integrated within explicit symplectic integration to formulate an arbitrary order multivariate Taylor map for any given particle accelerator lattice. Tracking simulation performed with these Taylor maps shows good long term stability and physics accuracy. There is good agreement in long term particle tracking simulations between Taylor map and element by element tracking of APS-U lattice, when the particle is within 1 to 10 σ of stored beam. It is demonstrated that most of the lower order resonance driving terms, plus chromatic and geometric aberrations are reasonably preserved by the Taylor map approach. Last but maybe most important, the computation time is reduced by a factor of 20 to 50, when compared to symplectic integration based element by element tracking.
DOI •	reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2021-TUPAB062
About •	paper received ※ 19 May 2021 paper accepted ※ 17 June 2021 issue date ※ 29 August 2021
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TUPAB213	Important Drift Space Contributions to Non-Linear Beam Dynamics	1914
	J. Frank, M. Arlandoo, P. Goslawski, J. Li, T. Mertens, M. Ries HZB, Berlin, Germany
	This paper presents an in-depth analysis of the non-linear contributions of drift spaces in beam dynamics for the creation of Transverse Resonance Island Buckets (TRIBs). TRIBs have been successfully generated in BESSY II and MLS at the Helmholtz-Zentrum Berlin für Materialien und Energie GmbH (HZB). They offer the possibility of generating a second stable orbit and, by populating the orbit with a different electron bunch pattern, allow to effectively have two distinct radiation sources in the same machine individually tailored to different user needs. We demonstrate the generation of TRIBs by order of non-linearity on simple lattice configurations by only treating the drift space as the non-linear element. Moreover, we also insert other non-linear magnets to show how they modify the already generated TRIBs from the drift spaces. We conclude by giving a qualitative analysis of the occurring effects, which provides a guideline as to when the linear approximation is insufficient and the non-linear contribution has to be taken into account.
DOI •	reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2021-TUPAB213
About •	paper received ※ 12 May 2021 paper accepted ※ 31 August 2021 issue date ※ 29 August 2021
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TUPAB214	Alpha Buckets in Longitudinal Phase Space: A Bifurcation Analysis	1917
	J. Frank, M. Arlandoo, P. Goslawski, T. Mertens, M. Ries HZB, Berlin, Germany
	At HZB’s BESSY II and MLS facilities we have the ability to tune the momentum compaction factor α up to second non-linear order. The non-linear dependence α(δ) brings qualitative changes to the longitudinal phase space and introduces new fix points α(δ)=0 which produce the so-called α-buckets. We present with this paper an analysis of this phenomena from the standpoint of bifurcation theory. With this approach we were able to characterize the nature of the fix points and their position in direct dependence on the tunable parameters. Furthermore, we are able to place stringent conditions onto the tunable parameters to either create or destroy α-buckets.
DOI •	reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2021-TUPAB214
About •	paper received ※ 12 May 2021 paper accepted ※ 17 June 2021 issue date ※ 26 August 2021
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TUPAB216	Modeling Particle Stability Plots for Accelerator Optimization Using Adaptive Sampling	1923
	M. Schenk, L. Coyle, T. Pieloni EPFL, Lausanne, Switzerland M. Giovannozzi, A. Mereghetti CERN, Meyrin, Switzerland E. Krymova, G. Obozinski SDSC, Lausanne, Switzerland
	Funding: This work is partially funded by the Swiss Data Science Center (SDSC), project C18-07. One key aspect of accelerator optimization is to maximize the dynamic aperture (DA) of a ring. Given the number of adjustable parameters and the compute-intensity of DA simulations, this task can benefit significantly from efficient search algorithms of the available parameter space. We propose to gradually train and improve a surrogate model of the DA from SixTrack simulations while exploring the parameter space with adaptive sampling methods. Here we report on a first model of the particle stability plots using convolutional generative adversarial networks (GAN) trained on a subset of SixTrack numerical simulations for different ring configurations of the Large Hadron Collider at CERN.
DOI •	reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2021-TUPAB216
About •	paper received ※ 19 May 2021 paper accepted ※ 17 June 2021 issue date ※ 22 August 2021
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TUPAB217	Effect of Undulators on Transverse Resonant Island Orbits	1927
	E.C.M. Rial, J. Bahrdt, P. Goslawski, A. Meseck, M. Ries, M. Scheer HZB, Berlin, Germany
	For one week in October 2020, BESSY II offered a Two Orbit mode to users for the first time. In this Two Orbit mode, the existence of transverse resonant island buckets* are exploited to store a second beam in the storage ring as an ’island orbit’, away from the primary beam axis. This mode was offered with free range of motion of the 12 out of vacuum undulators installed at the BESSY II ring. Diagnostics of the island orbit were limited to a single camera monitoring bending magnet radiation from a single dipole. A significant motion of the island orbit was observed on this diagnostic and correlated with undulator motion. This observation is reported, and simulations presented to demonstrate how this motion could arise. Correction schemes are suggested and discussed. Two Orbit - a report on the first scheduled week of TRIBs user operation at BESSY II, M. Ries et al, these proceedings *Proc. IPAC 2016, Busan, S Korea, paper THPMR017, p. 3427
DOI •	reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2021-TUPAB217
About •	paper received ※ 19 May 2021 paper accepted ※ 21 June 2021 issue date ※ 22 August 2021
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TUPAB218	Fully Covariant Two-Particle Space-Charge Dynamics Using the Liénard-Wiechert Potentials	1931
	B.T. Folsom, E. Laface ESS, Lund, Sweden
	Space charge models typically assume instantaneous propagation of the electromagnetic fields between particles in a bunch, describing forces in the frame of the reference particle. In this paper, we construct a space-charge tracking code from the retarded Liénard-Wiechert potentials, which are covariant by design, in a Lagrangian formulation. Such potentials are manipulated with covariant derivatives to produce the necessary equations of motion that will be solved in a test system of two particles at various relative energies. Magnetic dipole moment dynamics are also evaluated where applicable.
DOI •	reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2021-TUPAB218
About •	paper received ※ 19 May 2021 paper accepted ※ 19 July 2021 issue date ※ 11 August 2021
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TUPAB219	Equilibrium and Nonlinear Beam Dynamics Parameters From Sirius Turn-by-Turn BPM Data	1935
	X.R. Resende, M.B. Alves, L. Liu, F.H. de Sá LNLS, Campinas, Brazil
	A considerable amount of beam information is conveyed by Turn-by-Turn (TbT) data of Beam Position Monitors (BPM). In this work such data sets are analyzed for Sirius, the Brazilian 4th Generation 3GeV synchrotron light source. In particular, equilibrium and non-linear beam dynamics parameters determining decoherence patterns in TbT position data are estimated and compared with corresponding values of the nominal storage ring model.
DOI •	reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2021-TUPAB219
About •	paper received ※ 20 May 2021 paper accepted ※ 23 June 2021 issue date ※ 15 August 2021
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TUPAB220	Longitudinal Dynamics with Harmonic Cavities under the Over-stretching Conditions	1939
	J.Y. Xu, H.S. Xu IHEP, Beijing, People’s Republic of China
	Higher harmonic cavities (HHCs) are often used to lengthen the bunches, mainly for increasing the Touschek lifetime or for suppressing the coupled-bunch instabilities in electron storage rings. There have been quite many studies on the beam dynamics with the consideration of HHCs. We revisited the basic longitudinal dynamics with HHCs. The derivation of the longitudinal equations of motion with HHCs will be presented in this paper. The difference in the number of fixed points at different HHC settings (mainly under the over-stretching conditions) is also discussed.
	Poster TUPAB220 [1.082 MB]
DOI •	reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2021-TUPAB220
About •	paper received ※ 19 May 2021 paper accepted ※ 02 August 2021 issue date ※ 29 August 2021
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TUPAB223	Design of Double- and Multi-Bend Achromat Lattices with Large Dynamic Aperture and Approximate Invariants	1945
	Y. Li, R.S. Rainer, V.V. Smaluk BNL, Upton, New York, USA K. Hwang, C.E. Mitchell, R.D. Ryne LBNL, Berkeley, California, USA
	Funding: Funded by U.S. Department of Energy (DOE) under Contract No. DE-SC0012704 (BNL) and DE-AC02-05CH11231 (LBNL), U.S. DOE Early Career Research Program under the Office of High Energy Physics. A numerical method to design nonlinear double- and multi-bend achromat (DBA and MBA) lattices with approximate invariants of motion is described. The search for such nonlinear lattices is motivated by Fermilab’s Integrable Optics Test Accelerator (IOTA), whose design is based on an integrable Hamiltonian system with two invariants of motion. While it may not be possible to design an achromatic lattice for a dedicated synchrotron light source storage ring with one or more exact invariants of motion, it is possible to tune the sextupoles and octupoles in existing DBA and MBA lattices to produce approximate invariants. In our procedure, the lattice is tuned while minimizing the turn-by-turn fluctuations of the Courant-Snyder actions Jx and Jy at several distinct amplitudes, while simultaneously minimizing diffusion of the on-energy betatron tunes. The resulting lattices share some important features with integrable ones, such as a large dynamic aperture, trajectories confined to invariant tori, robustness to resonances and errors, and a large amplitude-dependent tune-spread.
	Poster TUPAB223 [2.392 MB]
DOI •	reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2021-TUPAB223
About •	paper received ※ 10 May 2021 paper accepted ※ 15 June 2021 issue date ※ 20 August 2021
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TUPAB224	Non-Linear Variation of the Beta-Beating Measured From Amplitude	1949
	T. Pugnat, B. Dalena CEA-IRFU, Gif-sur-Yvette, France A. Franchi ESRF, Grenoble, France R. Tomás García CERN, Geneva, Switzerland
	Accelerator physics needs advanced modeling and simulation techniques, for beam stability studies but also for the measurement of beam parameters like the Twiss parameters. A deeper understanding of magnetic field non-linearities effects will greatly help in the improvement of future circular collider design, performance, and diagnostics. This paper studies the variation of the \beta-beating with the action of the particle generated by non-linear Resonance Driving Terms, both from a theoretical and an experimental point of view.
DOI •	reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2021-TUPAB224
About •	paper received ※ 18 May 2021 paper accepted ※ 06 July 2021 issue date ※ 21 August 2021
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TUPAB226	Study of the Third-Order Parametric Resonance Induced by RF Modulation	1956
	P.F. Liang, H.S. Xu IHEP, Beijing, People’s Republic of China
	There were both analytic and experimental studies on the effects of RF modulation on bunch lengthening in electron storage rings. Nevertheless, the increase of bunch energy spread will happen in the meantime. Therefore, the degradation of bunch quality may limit the potential applications of the RF modulation technique. As a consequence, we believe that the comprehensive studies of the parametric resonance induced by RF modulation are necessary for understanding the physics picture better and seeking new possibilities of applications of this technique. The studies on the beam dynamics closed to the 3v_s RF phase modulation would be presented here. Based on the basic longitudinal synchrotron equations of motion, we obtained analytically the longitudinal modulated Hamiltonian and various parameters in longitudinal phase space, such as the fixed points, island tune, island width. The validity of the analytic results was checked by simulations. Furthermore, the dependence of the bunch parameters, such as energy spread and bunch length, on the modulation settings is also discussed in this paper.
DOI •	reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2021-TUPAB226
About •	paper received ※ 19 May 2021 paper accepted ※ 21 June 2021 issue date ※ 13 August 2021
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TUPAB227	Simultaneous Compensation of Phase and Amplitude Dependent Geometrical Resonances Using Octupoles	1960
	F. Plassard, Y. Hidaka, Y. Li, T.V. Shaftan, V.V. Smaluk, G.M. Wang BNL, Upton, New York, USA
	As the new generation of light sources are pushing toward diffraction limited storage rings with ultra-low emittance beams, nonlinear beam dynamics become increasingly difficult to control. It is a common practice for modern designs to use a sextupole scheme that allows simultaneous correction of natural chromaticity and energy independent, or geometrical, sextupolar resonances. However, the remaining higher order terms arising from the cross talks of the sextupole families set a strong limitation on the achievable dynamic aperture. This paper presents a simulation-based recipe to use octupoles together with this sextupole scheme to provide simultaneous self-compensation of linear amplitude dependent tune shift together with phase-dependent octupolar and higher order geometrical resonant driving terms. The correction method was built based on observations made on a simple FODO model, then applied to a realistic low emittance lattice, designed in the framework of the upgrade of the National Synchrotron Light Source II (NSLS-II).
DOI •	reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2021-TUPAB227
About •	paper received ※ 19 May 2021 paper accepted ※ 23 June 2021 issue date ※ 14 August 2021
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TUPAB228	IOTA Run 2 Beam Dynamics Studies in Nonlinear Integrable Systems	1964
	N. Kuklev, Y.K. Kim University of Chicago, Chicago, Illinois, USA S. Nagaitsev, A.L. Romanov, A. Valishev Fermilab, Batavia, Illinois, USA
	Funding: Work supported by the U.S. NSF under award PHY-1549132, the Center for Bright Beams. Fermi Research Alliance, LLC operates Fermilab under Contract DE-AC02-07CH11359 with the US Department of Energy. Nonlinear integrable optics is a promising design approach for suppressing fast collective instabilities. To study it experimentally, a new storage ring, the Integrable Optics Test Accelerator (IOTA), was built at Fermilab. IOTA has recently completed its second scientific run, incorporating many hardware and instrumentation improvements. This report presents the results of the two integrable optics experiments - the quasi-integrable Henon-Heiles octupole system and the fully integrable Danilov-Nagaitsev system. We demonstrate tune spread and dynamic aperture in agreement with tracking simulations, and a stable crossing of the integer resonance. Based on recovered single-particle phase space dynamics, we show improved invariant jitter consistent with intended effective Hamiltonian. We conclude by outlining future plans and efforts towards proton studies and larger designs.
DOI •	reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2021-TUPAB228
About •	paper received ※ 31 May 2021 paper accepted ※ 23 June 2021 issue date ※ 10 August 2021
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TUPAB231	Cooling of an Annular Beam by Using Nonlinear Effects	1968
	F. Capoani, M. Giovannozzi, R. Tomás García CERN, Geneva, Switzerland A. Bazzani, F. Capoani Bologna University, Bologna, Italy
	In recent years, nonlinear effects have been used to modify the transverse beam distribution by crossing nonlinear resonances adiabatically. This allows generating transversally split beams, in which the initial single Gaussian is divided into several ones depending on the order and stability type of the resonance used. Nonlinear effects could be used to try and cool a beam by acting on its transverse beam distribution. In this paper, we present and discuss the special case of a beam with an annular distribution, showing how the resulting emittance could be reduced by means of nonlinear effects.
DOI •	reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2021-TUPAB231
About •	paper received ※ 10 May 2021 paper accepted ※ 16 June 2021 issue date ※ 21 August 2021
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TUPAB232	Linear Coupling and Adiabaticity of Emittance Exchange	1972
	F. Capoani, M. Giovannozzi CERN, Geneva, Switzerland A. Bazzani, F. Capoani Bologna University, Bologna, Italy A.I. Neishtadt IKI, Moscow, Russia A.I. Neishtadt Loughborough University, Leicestershre, United Kingdom
	In circular accelerators, crossing the coupling resonance induces the exchange of the transverse emittances, provided the process is adiabatic. In this paper, we introduce a theoretical framework to analyze the resonance-crossing process, based on Hamiltonian mechanics, which is capable of explaining all the features of the emittance exchange process.
DOI •	reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2021-TUPAB232
About •	paper received ※ 11 May 2021 paper accepted ※ 16 June 2021 issue date ※ 27 August 2021
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TUPAB233	Diffusive Models for Nonlinear Beam Dynamics	1976
	C.E. Montanari, A. Bazzani Bologna University, Bologna, Italy M. Giovannozzi, C.E. Montanari CERN, Geneva, Switzerland
	Diffusive models for representing the nonlinear beam dynamics in a circular accelerator ring have been developed in recent years. The novelty of the work presented here with respect to older approaches is that the functional form of the diffusion coefficient is derived from the time stability estimate of the Nekhoroshev theorem. In this paper, we discuss the latest results obtained for simple models of nonlinear betratron motion.
	Poster TUPAB233 [0.574 MB]
DOI •	reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2021-TUPAB233
About •	paper received ※ 11 May 2021 paper accepted ※ 23 June 2021 issue date ※ 23 August 2021
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TUPAB235	Dynamic Aperture Optimization in the EIC Electron Storage Ring with Two Interaction Points	1984
	D. Marx, Y. Li, C. Montag, S. Tepikian, F.J. Willeke BNL, Upton, New York, USA Y. Cai, Y.M. Nosochkov SLAC, Menlo Park, California, USA G.H. Hoffstaetter, J.E. Unger Cornell University (CLASSE), Cornell Laboratory for Accelerator-Based Sciences and Education, Ithaca, New York, USA
	Funding: Work supported by Brookhaven Science Associates, LLC under Contract No. DE-SC0012704 and by SLAC under Contract No. DE-AC02-76SF00515 with the U.S. Department of Energy. In the Electron-Ion Collider (EIC), which is currently being designed for construction at Brookhaven National Laboratory, electrons from the electron storage ring will collide with hadrons, producing luminosities up to 10³⁴ cm^-2 s^-1. The baseline design includes only one interaction point (IP), and optics have been found with a suitable dynamic aperture in each dimension. However, the EIC project asks for the option of a second IP. The strong focusing required at the IPs creates a very large natural chromaticity (about -125 in the vertical plane for the ring). Compensating this linear chromaticity while simultaneously controlling the nonlinear chromaticity to high order to achieve a sufficient momentum acceptance of 1% (10 σ) at 18 GeV is a considerable challenge. A scheme to compensate higher-order chromatic effects from 2 IPs by setting the phase advance between them does not, by itself, provide the required momentum acceptance for the EIC Electron Storage Ring. A thorough design of the nonlinear optics is underway to increase the momentum acceptance using multiple sextupole families, and the latest results are presented here.
	Poster TUPAB235 [3.426 MB]
DOI •	reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2021-TUPAB235
About •	paper received ※ 19 May 2021 paper accepted ※ 19 July 2021 issue date ※ 20 August 2021
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TUPAB236	Progress on the Electron Gun Design for a McMillan Electron Lens in the Fermilab Integrable Optics Test Accelerator (IOTA)	1988
	B.L. Cathey, G. Stancari Fermilab, Batavia, Illinois, USA
	Funding: This manuscript has been authored by Fermi Research Alliance, LLC under Contract No. DE-AC02-07CH11359 with the U.S. Department of Energy, Office of Science, Office of High Energy Physics. This paper covers the progress made so far in designing the first McMillan electron lens for the Fermilab IOTA ring. The novel design allows for an increase in tune spread without limiting the dynamic aperture due to its integrability. Shown are simulations for an electron gun design to generate the specific required current density distribution for the nonlinear integrable system in IOTA.
	Poster TUPAB236 [5.391 MB]
DOI •	reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2021-TUPAB236
About •	paper received ※ 19 May 2021 paper accepted ※ 19 July 2021 issue date ※ 10 August 2021
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TUPAB237	Symplectic Tracking Through Field Maps	1992
	S.D. Webb RadiaSoft LLC, Boulder, Colorado, USA B.T. Folsom, E. Laface, R. Miyamoto ESS, Lund, Sweden
	For many applications, it is necessary to track particles using field maps, instead of an analytic representation of the fields which is typically not available. These field maps come about while designing elements such as realistic magnets or radiofrequency cavities, and represent the field geometry on a mesh in space. However, simple interpolation of the fields from the field maps does not guarantee that the resulting tracking scheme satisfies the symplectic condition. Here we present a general method to decompose the field-map potential in the sum of interpolating functions that produces, by construction, a symplectic integrator.
	Poster TUPAB237 [0.307 MB]
DOI •	reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2021-TUPAB237
About •	paper received ※ 19 May 2021 paper accepted ※ 22 July 2021 issue date ※ 22 August 2021
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TUPAB258	Impact of Coherent Beam-Beam Interaction on the Landau Damping of the Transverse Coupled-Bunch Instability	2062
	R. Li JLab, Newport News, Virginia, USA M. Blaskiewicz BNL, Upton, New York, USA
	Funding: This work is supported by the U.S. Department of Energy, Office of Science, Office of Nuclear Physics under contract DE-AC05-06OR23177. In the EIC design, at high average-current operation, the transverse coupled-bunch instability (TCBI) induced by the long-range transverse resistive-wall wakefield in the electron storage ring (eSR) has a fast growth rate and requires efficient mitigation. A natural mitigation mechanism is provided by the beam-beam interaction at the interaction point (IP), which gives a strong Landau damping for the TCBI in the eSR. In this study, using a simplified simulation model, we investigate how this Landau damping from the beam-beam interaction behaves when the coherent beam-beam interaction at IP is considered. Our method and results will be presented in this paper.
DOI •	reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2021-TUPAB258
About •	paper received ※ 21 June 2021 paper accepted ※ 01 July 2021 issue date ※ 25 August 2021
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THPAB016	Revisit of Nonlinear Dynamics in Hénon Map Using Square Matrix Method	3788
	Y. Hao, K.J. Anderson FRIB, East Lansing, Michigan, USA L.H. Yu BNL, Upton, New York, USA
	Funding: Work supported by the Accelerator Stewardship program, award number DE-SC0019403 with the U.S. Department of Energy Hénon map (2D or 4D) represents a thin lens sextupole in an otherwise linear lattice and had been well studied for many decades. We revisit the nonlinear properties of the Hénon map with the aid of the square matrix method and Arnold theorem, including acquiring the resonance structure and amplitude-dependent frequency.
DOI •	reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2021-THPAB016
About •	paper received ※ 17 May 2021 paper accepted ※ 12 July 2021 issue date ※ 17 August 2021
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THPAB169	A Mechanism for Emittance Growth Based on Non-Linear Islands in LHC	4082
	E.H. Maclean, M. Giovannozzi, T.H.B. Persson, R. Tomás García CERN, Geneva, Switzerland
	Landau octupoles are used in the LHC to prevent coherent instabilities of the circulating beam. The reduction of their strength occurring during the energy ramp can transport particles in nonlinear islands to larger amplitude. This has the potential to lead to emittance growth and to beam-losses. Beam-based studies and simulations of emittance growth during Landau octupole ramps performed in the LHC are presented to explore this mechanism in more detail.
DOI •	reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2021-THPAB169
About •	paper received ※ 18 May 2021 paper accepted ※ 14 July 2021 issue date ※ 14 August 2021
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THPAB232	Study of Nonlinear Properties of ESR via Tune Scans	4250
	G. Franchetti GSI, Darmstadt, Germany
	The ESR storage ring at GSI is a key accelerator for the FAIR phase zero. This phase requires several highly specialized beam manipulations, which range from beam storage to deceleration of several ion species with the ultimate goal to provide intense highly charge ions to CRYRING. This plan will bring the ESR storage ring into a unique unexplored regime of accelerator operations where nonlinear dynamics, IBS, cooling, and high intensity will all become strongly interdependent. It is, therefore, necessary to acquire the best knowledge of the machine starting from its nonlinear dynamics properties. In this work, we present the development of a strategy to be used in the ESR, in which tune scans are used to explore the nonlinear properties of the accelerator. This approach is discussed with the help of simulations.
DOI •	reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2021-THPAB232
About •	paper received ※ 13 May 2021 paper accepted ※ 13 July 2021 issue date ※ 25 August 2021
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THPAB233	Could "Flakes" of Neutral Paramagnetic or Dipolar Molecules Explain Beam Losses in the LHC?	4254
	G. Franchetti GSI, Darmstadt, Germany F. Zimmermann CERN, Meyrin, Switzerland
	"Flakes" of neutral water or oxygen molecules carrying an electric or magnetic dipole moment can be attracted and trapped by the electromagnetic field of the circulating LHC proton beam. The possible presence of such flakes in the vacuum system could explain beam losses and beam instabilities encountered during the 2017 and 2018 LHC runs, and the observed effect of an external magnetic field.
DOI •	reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2021-THPAB233
About •	paper received ※ 09 May 2021 paper accepted ※ 12 July 2021 issue date ※ 02 September 2021
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FRXB07	Injector Optimization for the IR-FEL Operation at the Compact ERL at KEK	4531
	O.A. Tanaka, N. Higashi, T. Miyajima KEK, Ibaraki, Japan
	Funding: Work supported by NEDO project "Development of advanced laser processing with intelligence based high-brightness and high-efficiency laser technologies (TACMI project)". The Compact Energy Recovery Linac (cERL) at KEK is a test accelerator to develop ERL technologies and to operate with a high average beam current and a high beam quality. cERL consists of a photoinjector, a main linac for energy recovery, a recirculation loop and a beam dump. A recent upgrade of the cERL to the middle Infrared Free Electron Laser (IR-FEL) imposed new conditions to maintain beam parameters. Therefore, the injector should be optimized to meet the following requirements at the exit of the main linac. The rms bunch length should be 2 ps, the rms longitudinal emittance should be kept the least, and simultaneously the rms transverse emittance should be kept less than 3 c mm mrad. In this work we describe the strategy and results of the injector optimization to achieve the better performance of the cERL-FEL.
	Slides FRXB07 [3.450 MB]
DOI •	reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2021-FRXB07
About •	paper received ※ 19 May 2021 paper accepted ※ 22 July 2021 issue date ※ 14 August 2021
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Paper

Title

Page

On Possibility of Alpha-buckets Detecting at the KIT Storage Ring KARA (Karlsruhe Research Accelerator)

167

A.I. Papash, T. Boltz, M. Brosi, A.-S. Müller, R. Ruprecht, P. Schreiber, M. Schuh, N.J. Smale
KIT, Karlsruhe, Germany

Computer studies of longitudinal motion have been performed with the objective to estimate the possibility of detection of alpha-buckets at the KIT storage ring KARA (Karlsruhe Research Accelerator). The longitudinal equations of motion and the Hamiltonian were expanded to high order terms of the energy deviation of particles in a beam. Roots of third order equation for three leading terms of momentum compaction factor and free energy independent term were derived in a form suitable for analytical estimations. Averaged quadratic terms of closed orbit distortions caused by misalignment of magnetic elements in a ring lead to orbit lengthening independent of particle energy deviation. Particle transverse excursions were estimated and are taken into account. Simulations have been bench-marked on existing experiments at Metrology Light Source (MLS) in Berlin (Germany) and SOLEIL (France). Parameters of three simultaneous beams and alpha buckets at MLS and SOLEIL have been reproduced with high accuracy. A computer model of KARA was used to predict behavior and the dynamics of possible simultaneous beams in the ring.

Poster MOPAB037 [1.269 MB]

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reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2021-MOPAB037

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paper received ※ 11 May 2021 paper accepted ※ 28 May 2021 issue date ※ 29 August 2021

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MOPAB041

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

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.

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

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

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MOPAB235

Transverse 2d Phase-Space Tomography Using Beam Position Monitor Data of Kicked Beams

763

K. Hwang, C.E. Mitchell, R.D. Ryne
LBNL, Berkeley, California, USA

Funding: U.S. Department of Energy under Contract No. DE-AC02-05CH11231
The time-series Beam Position Monitor (BPM) data of kicked beam is a function of lattice parameters and beam parameters including phase-space density. The decoherence model using the first-order detuning parameter has an exact solution when the beam is Gaussian. We parameterize the beam phase-space density by multiple Gaussian kernels of different weights, means, and sizes to formulate the inverse problem for 2D phase-space tomography. Numerical optimization and Bayesian inference are used to infer the beam density.

Poster MOPAB235 [1.253 MB]

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reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2021-MOPAB235

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paper received ※ 20 May 2021 paper accepted ※ 02 June 2021 issue date ※ 01 September 2021

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MOPAB273

Nonlinear Coupling Resonances in X-Y Coupled Betatron Oscillations Near the Main Coupling Resonance in VEPP-2000 Collider

863

S.A. Kladov, E. Perevedentsev
BINP SB RAS, Novosibirsk, Russia
S.A. Kladov, E. Perevedentsev
NSU, Novosibirsk, Russia

In the vicinity of the linear coupling resonance where the working point of the collider is positioned, we study the effect of nonlinear coupling resonances on the single-particle phase space, beam sizes and the waveform of coherent beam motion. The latter is interesting for diagnostics of the nonlinear dynamics.

Poster MOPAB273 [1.142 MB]

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reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2021-MOPAB273

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paper received ※ 19 May 2021 paper accepted ※ 28 May 2021 issue date ※ 21 August 2021

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TUXA04

Coherent Excitations and Circular Attractors in Cooled Ion Bunches

1279

S. Seletskiy, A.V. Fedotov, D. Kayran
BNL, Upton, New York, USA

Funding: Work supported by Brookhaven Science Associates, LLC under Contract No. DE-SC0012704 with the U.S. Department of Energy
In electron coolers, under certain conditions, a mismatch in either gamma-factors or trajectory angles between an electron and an ion beam can cause the formation of a circular attractor in the ion beam phase space. This leads to coherent excitations of the ions with a small synchrotron or betatron amplitude and results in unusual beam dynamics, including bifurcations. In this paper, we consider the effect of coherent excitations and discuss its implications both for Low Energy RHIC Electron Cooler (LEReC) and for high energy electron coolers proposed for the Electron-Ion Collider (EIC).

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reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2021-TUXA04

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paper received ※ 19 May 2021 paper accepted ※ 20 July 2021 issue date ※ 11 August 2021

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TUPAB062

Expediting APS-U Long-Term Particle Tracking with Arbitrary Order Taylor Map

1505

Y.P. Sun
ANL, Lemont, Illinois, USA

Funding: The work is supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under Contract No. DE-AC02-06CH11357.
Truncated power series algebra was integrated within explicit symplectic integration to formulate an arbitrary order multivariate Taylor map for any given particle accelerator lattice. Tracking simulation performed with these Taylor maps shows good long term stability and physics accuracy. There is good agreement in long term particle tracking simulations between Taylor map and element by element tracking of APS-U lattice, when the particle is within 1 to 10 σ of stored beam. It is demonstrated that most of the lower order resonance driving terms, plus chromatic and geometric aberrations are reasonably preserved by the Taylor map approach. Last but maybe most important, the computation time is reduced by a factor of 20 to 50, when compared to symplectic integration based element by element tracking.

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reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2021-TUPAB062

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paper received ※ 19 May 2021 paper accepted ※ 17 June 2021 issue date ※ 29 August 2021

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TUPAB213

Important Drift Space Contributions to Non-Linear Beam Dynamics

1914

J. Frank, M. Arlandoo, P. Goslawski, J. Li, T. Mertens, M. Ries
HZB, Berlin, Germany

This paper presents an in-depth analysis of the non-linear contributions of drift spaces in beam dynamics for the creation of Transverse Resonance Island Buckets (TRIBs). TRIBs have been successfully generated in BESSY II and MLS at the Helmholtz-Zentrum Berlin für Materialien und Energie GmbH (HZB). They offer the possibility of generating a second stable orbit and, by populating the orbit with a different electron bunch pattern, allow to effectively have two distinct radiation sources in the same machine individually tailored to different user needs. We demonstrate the generation of TRIBs by order of non-linearity on simple lattice configurations by only treating the drift space as the non-linear element. Moreover, we also insert other non-linear magnets to show how they modify the already generated TRIBs from the drift spaces. We conclude by giving a qualitative analysis of the occurring effects, which provides a guideline as to when the linear approximation is insufficient and the non-linear contribution has to be taken into account.

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reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2021-TUPAB213

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paper received ※ 12 May 2021 paper accepted ※ 31 August 2021 issue date ※ 29 August 2021

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TUPAB214

Alpha Buckets in Longitudinal Phase Space: A Bifurcation Analysis

1917

J. Frank, M. Arlandoo, P. Goslawski, T. Mertens, M. Ries
HZB, Berlin, Germany

At HZB’s BESSY II and MLS facilities we have the ability to tune the momentum compaction factor α up to second non-linear order. The non-linear dependence α(δ) brings qualitative changes to the longitudinal phase space and introduces new fix points α(δ)=0 which produce the so-called α-buckets. We present with this paper an analysis of this phenomena from the standpoint of bifurcation theory. With this approach we were able to characterize the nature of the fix points and their position in direct dependence on the tunable parameters. Furthermore, we are able to place stringent conditions onto the tunable parameters to either create or destroy α-buckets.

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reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2021-TUPAB214

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paper received ※ 12 May 2021 paper accepted ※ 17 June 2021 issue date ※ 26 August 2021

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TUPAB216

Modeling Particle Stability Plots for Accelerator Optimization Using Adaptive Sampling

1923

M. Schenk, L. Coyle, T. Pieloni
EPFL, Lausanne, Switzerland
M. Giovannozzi, A. Mereghetti
CERN, Meyrin, Switzerland
E. Krymova, G. Obozinski
SDSC, Lausanne, Switzerland

Funding: This work is partially funded by the Swiss Data Science Center (SDSC), project C18-07.
One key aspect of accelerator optimization is to maximize the dynamic aperture (DA) of a ring. Given the number of adjustable parameters and the compute-intensity of DA simulations, this task can benefit significantly from efficient search algorithms of the available parameter space. We propose to gradually train and improve a surrogate model of the DA from SixTrack simulations while exploring the parameter space with adaptive sampling methods. Here we report on a first model of the particle stability plots using convolutional generative adversarial networks (GAN) trained on a subset of SixTrack numerical simulations for different ring configurations of the Large Hadron Collider at CERN.

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reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2021-TUPAB216

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paper received ※ 19 May 2021 paper accepted ※ 17 June 2021 issue date ※ 22 August 2021

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TUPAB217

Effect of Undulators on Transverse Resonant Island Orbits

1927

E.C.M. Rial, J. Bahrdt, P. Goslawski, A. Meseck, M. Ries, M. Scheer
HZB, Berlin, Germany

For one week in October 2020, BESSY II offered a Two Orbit mode to users for the first time*. In this Two Orbit mode, the existence of transverse resonant island buckets** are exploited to store a second beam in the storage ring as an ’island orbit’, away from the primary beam axis. This mode was offered with free range of motion of the 12 out of vacuum undulators installed at the BESSY II ring. Diagnostics of the island orbit were limited to a single camera monitoring bending magnet radiation from a single dipole. A significant motion of the island orbit was observed on this diagnostic and correlated with undulator motion. This observation is reported, and simulations presented to demonstrate how this motion could arise. Correction schemes are suggested and discussed.
*Two Orbit - a report on the first scheduled week of TRIBs user operation at BESSY II, M. Ries et al, these proceedings
**Proc. IPAC 2016, Busan, S Korea, paper THPMR017, p. 3427

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reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2021-TUPAB217

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paper received ※ 19 May 2021 paper accepted ※ 21 June 2021 issue date ※ 22 August 2021

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TUPAB218

Fully Covariant Two-Particle Space-Charge Dynamics Using the Liénard-Wiechert Potentials

1931

B.T. Folsom, E. Laface
ESS, Lund, Sweden

Space charge models typically assume instantaneous propagation of the electromagnetic fields between particles in a bunch, describing forces in the frame of the reference particle. In this paper, we construct a space-charge tracking code from the retarded Liénard-Wiechert potentials, which are covariant by design, in a Lagrangian formulation. Such potentials are manipulated with covariant derivatives to produce the necessary equations of motion that will be solved in a test system of two particles at various relative energies. Magnetic dipole moment dynamics are also evaluated where applicable.

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reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2021-TUPAB218

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paper received ※ 19 May 2021 paper accepted ※ 19 July 2021 issue date ※ 11 August 2021

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TUPAB219

Equilibrium and Nonlinear Beam Dynamics Parameters From Sirius Turn-by-Turn BPM Data

1935

X.R. Resende, M.B. Alves, L. Liu, F.H. de Sá
LNLS, Campinas, Brazil

A considerable amount of beam information is conveyed by Turn-by-Turn (TbT) data of Beam Position Monitors (BPM). In this work such data sets are analyzed for Sirius, the Brazilian 4th Generation 3GeV synchrotron light source. In particular, equilibrium and non-linear beam dynamics parameters determining decoherence patterns in TbT position data are estimated and compared with corresponding values of the nominal storage ring model.

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reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2021-TUPAB219

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paper received ※ 20 May 2021 paper accepted ※ 23 June 2021 issue date ※ 15 August 2021

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TUPAB220

Longitudinal Dynamics with Harmonic Cavities under the Over-stretching Conditions

1939

J.Y. Xu, H.S. Xu
IHEP, Beijing, People’s Republic of China

Higher harmonic cavities (HHCs) are often used to lengthen the bunches, mainly for increasing the Touschek lifetime or for suppressing the coupled-bunch instabilities in electron storage rings. There have been quite many studies on the beam dynamics with the consideration of HHCs. We revisited the basic longitudinal dynamics with HHCs. The derivation of the longitudinal equations of motion with HHCs will be presented in this paper. The difference in the number of fixed points at different HHC settings (mainly under the over-stretching conditions) is also discussed.

Poster TUPAB220 [1.082 MB]

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reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2021-TUPAB220

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paper received ※ 19 May 2021 paper accepted ※ 02 August 2021 issue date ※ 29 August 2021

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TUPAB223

Design of Double- and Multi-Bend Achromat Lattices with Large Dynamic Aperture and Approximate Invariants

1945

Y. Li, R.S. Rainer, V.V. Smaluk
BNL, Upton, New York, USA
K. Hwang, C.E. Mitchell, R.D. Ryne
LBNL, Berkeley, California, USA

Funding: Funded by U.S. Department of Energy (DOE) under Contract No. DE-SC0012704 (BNL) and DE-AC02-05CH11231 (LBNL), U.S. DOE Early Career Research Program under the Office of High Energy Physics.
A numerical method to design nonlinear double- and multi-bend achromat (DBA and MBA) lattices with approximate invariants of motion is described. The search for such nonlinear lattices is motivated by Fermilab’s Integrable Optics Test Accelerator (IOTA), whose design is based on an integrable Hamiltonian system with two invariants of motion. While it may not be possible to design an achromatic lattice for a dedicated synchrotron light source storage ring with one or more exact invariants of motion, it is possible to tune the sextupoles and octupoles in existing DBA and MBA lattices to produce approximate invariants. In our procedure, the lattice is tuned while minimizing the turn-by-turn fluctuations of the Courant-Snyder actions Jx and Jy at several distinct amplitudes, while simultaneously minimizing diffusion of the on-energy betatron tunes. The resulting lattices share some important features with integrable ones, such as a large dynamic aperture, trajectories confined to invariant tori, robustness to resonances and errors, and a large amplitude-dependent tune-spread.

Poster TUPAB223 [2.392 MB]

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reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2021-TUPAB223

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paper received ※ 10 May 2021 paper accepted ※ 15 June 2021 issue date ※ 20 August 2021

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TUPAB224

Non-Linear Variation of the Beta-Beating Measured From Amplitude

1949

T. Pugnat, B. Dalena
CEA-IRFU, Gif-sur-Yvette, France
A. Franchi
ESRF, Grenoble, France
R. Tomás García
CERN, Geneva, Switzerland

Accelerator physics needs advanced modeling and simulation techniques, for beam stability studies but also for the measurement of beam parameters like the Twiss parameters. A deeper understanding of magnetic field non-linearities effects will greatly help in the improvement of future circular collider design, performance, and diagnostics. This paper studies the variation of the \beta-beating with the action of the particle generated by non-linear Resonance Driving Terms, both from a theoretical and an experimental point of view.

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reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2021-TUPAB224

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paper received ※ 18 May 2021 paper accepted ※ 06 July 2021 issue date ※ 21 August 2021

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TUPAB226

Study of the Third-Order Parametric Resonance Induced by RF Modulation

1956

P.F. Liang, H.S. Xu
IHEP, Beijing, People’s Republic of China

There were both analytic and experimental studies on the effects of RF modulation on bunch lengthening in electron storage rings. Nevertheless, the increase of bunch energy spread will happen in the meantime. Therefore, the degradation of bunch quality may limit the potential applications of the RF modulation technique. As a consequence, we believe that the comprehensive studies of the parametric resonance induced by RF modulation are necessary for understanding the physics picture better and seeking new possibilities of applications of this technique. The studies on the beam dynamics closed to the 3v_s RF phase modulation would be presented here. Based on the basic longitudinal synchrotron equations of motion, we obtained analytically the longitudinal modulated Hamiltonian and various parameters in longitudinal phase space, such as the fixed points, island tune, island width. The validity of the analytic results was checked by simulations. Furthermore, the dependence of the bunch parameters, such as energy spread and bunch length, on the modulation settings is also discussed in this paper.

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reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2021-TUPAB226

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paper received ※ 19 May 2021 paper accepted ※ 21 June 2021 issue date ※ 13 August 2021

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TUPAB227

Simultaneous Compensation of Phase and Amplitude Dependent Geometrical Resonances Using Octupoles

1960

F. Plassard, Y. Hidaka, Y. Li, T.V. Shaftan, V.V. Smaluk, G.M. Wang
BNL, Upton, New York, USA

As the new generation of light sources are pushing toward diffraction limited storage rings with ultra-low emittance beams, nonlinear beam dynamics become increasingly difficult to control. It is a common practice for modern designs to use a sextupole scheme that allows simultaneous correction of natural chromaticity and energy independent, or geometrical, sextupolar resonances. However, the remaining higher order terms arising from the cross talks of the sextupole families set a strong limitation on the achievable dynamic aperture. This paper presents a simulation-based recipe to use octupoles together with this sextupole scheme to provide simultaneous self-compensation of linear amplitude dependent tune shift together with phase-dependent octupolar and higher order geometrical resonant driving terms. The correction method was built based on observations made on a simple FODO model, then applied to a realistic low emittance lattice, designed in the framework of the upgrade of the National Synchrotron Light Source II (NSLS-II).

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reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2021-TUPAB227

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paper received ※ 19 May 2021 paper accepted ※ 23 June 2021 issue date ※ 14 August 2021

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TUPAB228

IOTA Run 2 Beam Dynamics Studies in Nonlinear Integrable Systems

1964

N. Kuklev, Y.K. Kim
University of Chicago, Chicago, Illinois, USA
S. Nagaitsev, A.L. Romanov, A. Valishev
Fermilab, Batavia, Illinois, USA

Funding: Work supported by the U.S. NSF under award PHY-1549132, the Center for Bright Beams. Fermi Research Alliance, LLC operates Fermilab under Contract DE-AC02-07CH11359 with the US Department of Energy.
Nonlinear integrable optics is a promising design approach for suppressing fast collective instabilities. To study it experimentally, a new storage ring, the Integrable Optics Test Accelerator (IOTA), was built at Fermilab. IOTA has recently completed its second scientific run, incorporating many hardware and instrumentation improvements. This report presents the results of the two integrable optics experiments - the quasi-integrable Henon-Heiles octupole system and the fully integrable Danilov-Nagaitsev system. We demonstrate tune spread and dynamic aperture in agreement with tracking simulations, and a stable crossing of the integer resonance. Based on recovered single-particle phase space dynamics, we show improved invariant jitter consistent with intended effective Hamiltonian. We conclude by outlining future plans and efforts towards proton studies and larger designs.

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reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2021-TUPAB228

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paper received ※ 31 May 2021 paper accepted ※ 23 June 2021 issue date ※ 10 August 2021

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TUPAB231

Cooling of an Annular Beam by Using Nonlinear Effects

1968

F. Capoani, M. Giovannozzi, R. Tomás García
CERN, Geneva, Switzerland
A. Bazzani, F. Capoani
Bologna University, Bologna, Italy

In recent years, nonlinear effects have been used to modify the transverse beam distribution by crossing nonlinear resonances adiabatically. This allows generating transversally split beams, in which the initial single Gaussian is divided into several ones depending on the order and stability type of the resonance used. Nonlinear effects could be used to try and cool a beam by acting on its transverse beam distribution. In this paper, we present and discuss the special case of a beam with an annular distribution, showing how the resulting emittance could be reduced by means of nonlinear effects.

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reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2021-TUPAB231

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paper received ※ 10 May 2021 paper accepted ※ 16 June 2021 issue date ※ 21 August 2021

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TUPAB232

Linear Coupling and Adiabaticity of Emittance Exchange

1972

F. Capoani, M. Giovannozzi
CERN, Geneva, Switzerland
A. Bazzani, F. Capoani
Bologna University, Bologna, Italy
A.I. Neishtadt
IKI, Moscow, Russia
A.I. Neishtadt
Loughborough University, Leicestershre, United Kingdom

In circular accelerators, crossing the coupling resonance induces the exchange of the transverse emittances, provided the process is adiabatic. In this paper, we introduce a theoretical framework to analyze the resonance-crossing process, based on Hamiltonian mechanics, which is capable of explaining all the features of the emittance exchange process.

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reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2021-TUPAB232

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paper received ※ 11 May 2021 paper accepted ※ 16 June 2021 issue date ※ 27 August 2021

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TUPAB233

Diffusive Models for Nonlinear Beam Dynamics

1976

C.E. Montanari, A. Bazzani
Bologna University, Bologna, Italy
M. Giovannozzi, C.E. Montanari
CERN, Geneva, Switzerland

Diffusive models for representing the nonlinear beam dynamics in a circular accelerator ring have been developed in recent years. The novelty of the work presented here with respect to older approaches is that the functional form of the diffusion coefficient is derived from the time stability estimate of the Nekhoroshev theorem. In this paper, we discuss the latest results obtained for simple models of nonlinear betratron motion.

Poster TUPAB233 [0.574 MB]

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reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2021-TUPAB233

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paper received ※ 11 May 2021 paper accepted ※ 23 June 2021 issue date ※ 23 August 2021

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TUPAB235

Dynamic Aperture Optimization in the EIC Electron Storage Ring with Two Interaction Points

1984

D. Marx, Y. Li, C. Montag, S. Tepikian, F.J. Willeke
BNL, Upton, New York, USA
Y. Cai, Y.M. Nosochkov
SLAC, Menlo Park, California, USA
G.H. Hoffstaetter, J.E. Unger
Cornell University (CLASSE), Cornell Laboratory for Accelerator-Based Sciences and Education, Ithaca, New York, USA

Funding: Work supported by Brookhaven Science Associates, LLC under Contract No. DE-SC0012704 and by SLAC under Contract No. DE-AC02-76SF00515 with the U.S. Department of Energy.
In the Electron-Ion Collider (EIC), which is currently being designed for construction at Brookhaven National Laboratory, electrons from the electron storage ring will collide with hadrons, producing luminosities up to 10³⁴ cm^-2 s^-1. The baseline design includes only one interaction point (IP), and optics have been found with a suitable dynamic aperture in each dimension. However, the EIC project asks for the option of a second IP. The strong focusing required at the IPs creates a very large natural chromaticity (about -125 in the vertical plane for the ring). Compensating this linear chromaticity while simultaneously controlling the nonlinear chromaticity to high order to achieve a sufficient momentum acceptance of 1% (10 σ) at 18 GeV is a considerable challenge. A scheme to compensate higher-order chromatic effects from 2 IPs by setting the phase advance between them does not, by itself, provide the required momentum acceptance for the EIC Electron Storage Ring. A thorough design of the nonlinear optics is underway to increase the momentum acceptance using multiple sextupole families, and the latest results are presented here.

Poster TUPAB235 [3.426 MB]

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reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2021-TUPAB235

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paper received ※ 19 May 2021 paper accepted ※ 19 July 2021 issue date ※ 20 August 2021

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TUPAB236

Progress on the Electron Gun Design for a McMillan Electron Lens in the Fermilab Integrable Optics Test Accelerator (IOTA)

1988

B.L. Cathey, G. Stancari
Fermilab, Batavia, Illinois, USA

Funding: This manuscript has been authored by Fermi Research Alliance, LLC under Contract No. DE-AC02-07CH11359 with the U.S. Department of Energy, Office of Science, Office of High Energy Physics.
This paper covers the progress made so far in designing the first McMillan electron lens for the Fermilab IOTA ring. The novel design allows for an increase in tune spread without limiting the dynamic aperture due to its integrability. Shown are simulations for an electron gun design to generate the specific required current density distribution for the nonlinear integrable system in IOTA.

Poster TUPAB236 [5.391 MB]

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reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2021-TUPAB236

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paper received ※ 19 May 2021 paper accepted ※ 19 July 2021 issue date ※ 10 August 2021

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TUPAB237

Symplectic Tracking Through Field Maps

1992

S.D. Webb
RadiaSoft LLC, Boulder, Colorado, USA
B.T. Folsom, E. Laface, R. Miyamoto
ESS, Lund, Sweden

For many applications, it is necessary to track particles using field maps, instead of an analytic representation of the fields which is typically not available. These field maps come about while designing elements such as realistic magnets or radiofrequency cavities, and represent the field geometry on a mesh in space. However, simple interpolation of the fields from the field maps does not guarantee that the resulting tracking scheme satisfies the symplectic condition. Here we present a general method to decompose the field-map potential in the sum of interpolating functions that produces, by construction, a symplectic integrator.

Poster TUPAB237 [0.307 MB]

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reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2021-TUPAB237

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paper received ※ 19 May 2021 paper accepted ※ 22 July 2021 issue date ※ 22 August 2021

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TUPAB258

Impact of Coherent Beam-Beam Interaction on the Landau Damping of the Transverse Coupled-Bunch Instability

2062

R. Li
JLab, Newport News, Virginia, USA
M. Blaskiewicz
BNL, Upton, New York, USA

Funding: This work is supported by the U.S. Department of Energy, Office of Science, Office of Nuclear Physics under contract DE-AC05-06OR23177.
In the EIC design, at high average-current operation, the transverse coupled-bunch instability (TCBI) induced by the long-range transverse resistive-wall wakefield in the electron storage ring (eSR) has a fast growth rate and requires efficient mitigation. A natural mitigation mechanism is provided by the beam-beam interaction at the interaction point (IP), which gives a strong Landau damping for the TCBI in the eSR. In this study, using a simplified simulation model, we investigate how this Landau damping from the beam-beam interaction behaves when the coherent beam-beam interaction at IP is considered. Our method and results will be presented in this paper.

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reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2021-TUPAB258

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paper received ※ 21 June 2021 paper accepted ※ 01 July 2021 issue date ※ 25 August 2021

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THPAB016

Revisit of Nonlinear Dynamics in Hénon Map Using Square Matrix Method

3788

Y. Hao, K.J. Anderson
FRIB, East Lansing, Michigan, USA
L.H. Yu
BNL, Upton, New York, USA

Funding: Work supported by the Accelerator Stewardship program, award number DE-SC0019403 with the U.S. Department of Energy
Hénon map (2D or 4D) represents a thin lens sextupole in an otherwise linear lattice and had been well studied for many decades. We revisit the nonlinear properties of the Hénon map with the aid of the square matrix method and Arnold theorem, including acquiring the resonance structure and amplitude-dependent frequency.

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reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2021-THPAB016

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paper received ※ 17 May 2021 paper accepted ※ 12 July 2021 issue date ※ 17 August 2021

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THPAB169

A Mechanism for Emittance Growth Based on Non-Linear Islands in LHC

4082

E.H. Maclean, M. Giovannozzi, T.H.B. Persson, R. Tomás García
CERN, Geneva, Switzerland

Landau octupoles are used in the LHC to prevent coherent instabilities of the circulating beam. The reduction of their strength occurring during the energy ramp can transport particles in nonlinear islands to larger amplitude. This has the potential to lead to emittance growth and to beam-losses. Beam-based studies and simulations of emittance growth during Landau octupole ramps performed in the LHC are presented to explore this mechanism in more detail.

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reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2021-THPAB169

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paper received ※ 18 May 2021 paper accepted ※ 14 July 2021 issue date ※ 14 August 2021

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THPAB232

Study of Nonlinear Properties of ESR via Tune Scans

4250

G. Franchetti
GSI, Darmstadt, Germany

The ESR storage ring at GSI is a key accelerator for the FAIR phase zero. This phase requires several highly specialized beam manipulations, which range from beam storage to deceleration of several ion species with the ultimate goal to provide intense highly charge ions to CRYRING. This plan will bring the ESR storage ring into a unique unexplored regime of accelerator operations where nonlinear dynamics, IBS, cooling, and high intensity will all become strongly interdependent. It is, therefore, necessary to acquire the best knowledge of the machine starting from its nonlinear dynamics properties. In this work, we present the development of a strategy to be used in the ESR, in which tune scans are used to explore the nonlinear properties of the accelerator. This approach is discussed with the help of simulations.

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reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2021-THPAB232

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paper received ※ 13 May 2021 paper accepted ※ 13 July 2021 issue date ※ 25 August 2021

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THPAB233

Could "Flakes" of Neutral Paramagnetic or Dipolar Molecules Explain Beam Losses in the LHC?

4254

G. Franchetti
GSI, Darmstadt, Germany
F. Zimmermann
CERN, Meyrin, Switzerland

"Flakes" of neutral water or oxygen molecules carrying an electric or magnetic dipole moment can be attracted and trapped by the electromagnetic field of the circulating LHC proton beam. The possible presence of such flakes in the vacuum system could explain beam losses and beam instabilities encountered during the 2017 and 2018 LHC runs, and the observed effect of an external magnetic field.

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reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2021-THPAB233

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paper received ※ 09 May 2021 paper accepted ※ 12 July 2021 issue date ※ 02 September 2021

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FRXB07

Injector Optimization for the IR-FEL Operation at the Compact ERL at KEK

4531

O.A. Tanaka, N. Higashi, T. Miyajima
KEK, Ibaraki, Japan

Funding: Work supported by NEDO project "Development of advanced laser processing with intelligence based high-brightness and high-efficiency laser technologies (TACMI project)".
The Compact Energy Recovery Linac (cERL) at KEK is a test accelerator to develop ERL technologies and to operate with a high average beam current and a high beam quality. cERL consists of a photoinjector, a main linac for energy recovery, a recirculation loop and a beam dump. A recent upgrade of the cERL to the middle Infrared Free Electron Laser (IR-FEL) imposed new conditions to maintain beam parameters. Therefore, the injector should be optimized to meet the following requirements at the exit of the main linac. The rms bunch length should be 2 ps, the rms longitudinal emittance should be kept the least, and simultaneously the rms transverse emittance should be kept less than 3 c mm mrad. In this work we describe the strategy and results of the injector optimization to achieve the better performance of the cERL-FEL.

Slides FRXB07 [3.450 MB]

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reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2021-FRXB07

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paper received ※ 19 May 2021 paper accepted ※ 22 July 2021 issue date ※ 14 August 2021

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