IPAC2015 - List of Keywords (space-charge)

Paper	Title	Other Keywords	Page
MOPWA002	Nonequilibrium Phase Transitions in Crossed-Field Devices	electron, cathode, simulation, injection	74
	S. Marini, R. Pakter, F.B. Rizzato IF-UFRGS, Porto Alegre, Brazil
	Funding: This work was partially supported by CNPq and FAPERGS, Brazil, and by the US-AFOSR under the grant FA9550-09-1-0283. This work presents a fully kinetic description to model the electron flow in the electronic crossed-field configuration observed in a smooth-bore magnetron. Through this model, it has been observed that, according to the electromagnetic field, the injection temperature and the charge density, the electron flow can be classified in two different stationary modes: magnetic insulation mode where most of the electrons returning to the cathode after a transient time and Child-Langmuir mode where most of the electrons reach the anode after a transient time. Focusing on magnetic insulated mode, it has been found that charge density and injection temperature define whether electrons are accelerated (accelerating regime) or decelerated (space-charge limited regime) on the cathode. Besides, when the injection temperature is relatively low (high), a small charge increase causes (does not cause) an abrupt transition between accelerating and space-charge limited regime. Basing on the results, it was possible to identify a critical temperature that separates abrupt and continuous behavior. The results have been verified by using self-consistent computer simulations. S. Marini, F. B. Rizzato, and R. Pakter, Phys. Plasmas 21, 083111 (2014).
DOI •	reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2015-MOPWA002
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MOPWA003	Optimal Generalized Finite Difference Solution to the Particle-in-Cell Problem	framework, simulation, plasma, factory	77
	X. Wang, X. Jiao, H. Liu, V. Samulyak, K. Yu SBU, Stony Brook, USA V. Samulyak BNL, Upton, Long Island, New York, USA
	The particle-in-cell (PIC) method is widely used in applications, such as in electromagnetics, but the accuracy of its solutions degrades when the particle distribution is highly non-uniform. In our work, we propose an adaptive PIC method with optimal point distribution and a generalized finite difference (GFD) scheme. Our method replaces the Cartesian grid in the classical PIC with adaptive computational nodes or particles, to which the charges from the sample particles are assigned by a weighted least-square approximations. The partial differential equation is then discretized using a GFD method and solved with fast linear solvers. The density of computational particles is chosen adaptively, so that the error from GFD and that from Monte Carlo integration are balanced and the total error is approximately minimized. We also present the verification results using electrostatic problems and comparison of accuracy and solution time of our method with the classical PIC.
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MOPWA006	Core-Halo Limit as an Indicator of High Intensity Beam Internal Dynamics	emittance, linac, simulation, vacuum	86
	P.A.P. Nghiem, N. Chauvin, N. Pichoff, D. Uriot, M. Valette CEA/DSM/IRFU, France
	The dynamics of high-intensity beams is mainly governed by their internal space charge forces. These forces induce emittance growth and halo generation. They contribute to shape the beam density profile. As a consequence, a careful analysis of this profile can help revealing the internal dynamics of the beam. This paper recalls the precise core-halo limit determination proposed earlier , then studies its behavior through a wide range of beam profiles and finally shows its relevance as an indicator of the limit separating the two specific space charge field regimes of the core and the halo. P. A. P. Nghiem et al., Appl. Phys. Lett. 104, 074109 (2014)
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MOPWA008	Status of TraceWin Code	simulation, linac, cavity, diagnostics	92
	D. Uriot, N. Pichoff CEA/DSM/IRFU, France
	Well known in the community of high-intensity linear accelerators, the transport code TraceWin * is able to simulate a beam from the source to the target using either simple linear model or multiparticle simulations including 2D or 3D space-charge. Continuously developed at CEA Saclay since 15 years, it is today the reference code for projects such IFMIF, ESS, MYRRHA, SPIRAL2, IPHI … The accuracy of his predictions associated with an original and powerful GUI and its numerous features have made its success, with a community of 200 users worldwide. It is now used on a larger perimeter that its initial skills. The aim of this paper is to summarize the TraceWin capabilities, including implemented last ones. * http://irfu.cea.fr/Sacm/logiciels/
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MOPWA010	Emittances of the Core and of the Halo	emittance, linac, extraction, simulation	99
	M. Valette, P.A.P. Nghiem CEA/IRFU, Gif-sur-Yvette, France
	In high intensity accelerators, the beam is often space charge dominated. The density profile then takes a shape very different from a Gaussian one, with a more or less sharp core and a more or less compact halo. Furthermore, the core and the halo can be differently focused and thus differently oriented in the phase spaces. In these conditions, classically characterizing the beam by a global set of rms values, namely Emittance and Twiss parameters, is no more meaningful. This paper extends the core-halo limit defined ealier in 1D real space * to the 2D phase space, allowing to define for the very first time Emittances and Twiss parameters for the core and the halo separately. Applications to the IFMIF accelerators are given as an example of more appropriate beam characterization for high intensity linacs. * P. A. P. Nghiem et al., Appl. Phys. Lett. 104, 074109 (2014)
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MOPWA028	Resonance Compensation for High Intensity Bunched Beams	resonance, sextupole, ion, controls	159
	G. Franchetti, S. Aumon, F. Kesting, H. Liebermann, C. Omet, D. Ondreka, R. Singh GSI, Darmstadt, Germany
	Mitigation of periodic resonance crossing induced by space charge is foreseen via classic resonance compensation. The effect of the space charge is, however, not obvious on the effectiveness on the compensation scheme. In this proceeding we report on an experimental campaign performed at SIS18 in an attempt to investigate experimentally the effect of space charge on the resonance compensation. The experimental results and their consequences are discussed through numerical simulations.
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MOPWA029	Investigations of the Space-Charge-Limited Emission in the L-Band E-Xfel Photoinjector at Desy-Pitz	simulation, gun, cathode, electron	162
	Y. Chen, H. De Gersem, E. Gjonaj, A.V. Tsakanian, T. Weiland TEMF, TU Darmstadt, Darmstadt, Germany C. Hernandez-Garcia JLab, Newport News, Virginia, USA M. Krasilnikov, F. Stephan DESY Zeuthen, Zeuthen, Germany
	Funding: work supported by DESY Hamburg and Zeuthen Sites This paper discusses the numerical modelling of electron bunch emission for an L-band normal conducting RF photogun. The main objective is clarifying the discrepancies between measurements and simulations performed for the European X-ray Free Electron Laser (E-XFEL) injector at DESY-PITZ. An iterative beam dynamics simulation procedure is proposed for the calculation of the total extracted bunch charge under the assumption that the emission source operates at the space-charge limit of the gun. This algorithm has been implemented in the three-dimensional full electromagnetic PIC Solver of the CST Particle Studio (CST-PS). Simulation results are in good agreements with measurements for a series of operation parameters. Further comparisons with a conventional Poisson-solver-based (PSB) tracking algorithm demonstrates the great significance of transient electromagnetic field effects for the beam dynamics in high brightness electron sources. Computer Simulation Technology AG, http://www.cst.com/
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MOPWA043	FEL Simulations with Ocelot	optics, FEL, simulation, electron	210
	I.V. Agapov, G. Geloni XFEL. EU, Hamburg, Germany M. Dohlus, I. Zagorodnov DESY, Hamburg, Germany S.I. Tomin NRC, Moscow, Russia
	Ocelot has been developed as a multiphysics simulation tool for FEL and synchrotron light source studies. In this work we highlight recent code developments focusing on electron tracking in linacs taking into account collective effects and on x-ray optics calculations
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MOPWA055	Study of Emittance Growth Caused by Space Charge and Lattice Induced Resonances	resonance, lattice, emittance, synchrotron	245
	K. Ohmi KEK, Ibaraki, Japan
	Resonance strength and resonance width induced by space charge and lattice nonlinearity is discussed with integrals along a ring like the radiation integrals. Emittance growth is evaluated by model with the resonance width to understand the mechanism. The results are compared with fully PIC simulations.
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MOPWA057	Space Charge Simulation and Matching at Low Energy Section of J-PARC Linac	rfq, emittance, simulation, solenoid	251
	S. Artikova, T. Morishita JAEA/J-PARC, Tokai-Mura, Naka-Gun, Ibaraki-Ken, Japan Y. Kondo JAEA, Ibaraki-ken, Japan
	An intensity upgrade of Japan Proton Accelerator Research Complex (J-PARC) included the installation of a new ion source (IS) and a radio-frequency quadrupole (RFQ) which to be used at first stage of acceleration. The linac is divided into two sections on the basis of operating frequencies and three sections on the basis of family of RF cavities to be used for the acceleration of 50 mA beam of H⁻ ions from 50 keV to 400 MeV. Low energy part of linac consists of an IS, a two-solenoid low energy beam transport (LEBT) and the RFQ. The transition from one section to another can limit the acceptance of the linac if these are not matched properly in both longitudinal and transverse plane. We performed a study to calculate the acceptance of the RFQ at zero current in which space charge effects are not considered. In addition, a particle tracking technique is employed to study the space charge effects in LEBT of the J-PARC linac after the intensity upgrade in order to match the beam to the RFQ. Also, RFQ tank level and intervene voltage calibration factor is determined by comparing the simulation results of the beam transmission with the test measurement of tank level vs. transmission.
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MOPWA061	ADS Injector I Frequency Choice at IHEP	linac, rfq, emittance, proton	265
	F. Yan, H. Geng, C. Meng, H.F. Ouyang, S. Pei, Y.L. Zhao IHEP, Beijing, People's Republic of China
	Funding: Chinese Academy of Science (CAS) strategic Priority Research Program-Future Advanced Nuclear Fission Energy (Accelerator-Driven Sub-critical System) The China ADS driver linac is composed of two major parts: the injector and the main linac. There are two frequency choices for the injector: 325 MHz and 162.5 MHz. The former choice is benefit for the same frequency with the front end of the main linac. For half frequency choice, to obtain the same longitudinal acceptance of the main linac comparing with 325MHz injector, the tune depression of the beam reaches the lower design limit of 0.5, no current upgrade opportunity is reserved; contrarily to get the same space charge effect, 16 more cavities would be the cost to get the same acceptance. However the disadvantage of the 325MHz injector choice is the bigger power density of the copper structure CW RFQ and the smaller longitudinal acceptance of the SC section. The details of the comparing for the two frequency choices are introduced and presented. *Work supported by Chinese Academy of Science (CAS) strategic Priority Research Program-Future Advanced Nuclear Fission Energy (Accelerator-Driven Sub-critical System)
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MOPWA069	Upgrades on a Scalable Software Package for Large Scale Beam Dynamic Simulations	software, simulation, DTL, solenoid	282
	X.T. Dong, K. Du, J. Xu, R. Zhao IS, Beijing, People's Republic of China Y. He, Z.J. Wang IMP/CAS, Lanzhou, People's Republic of China C. Li, Q. Qin, Y.L. Zhao IHEP, Beijing, People's Republic of China
	Large-scale particle tracking is important for precise design and optimization of the linear accelerator. In this paper a parallel software recently developed for beam dynamics simulation has been benchmarked. The software is based on Particle-In-Cell method, and calculates space charge field by an efficient three-dimension parallel fast Fourier transform method. It uses domain decomposition and MPI library for parallelization. The characteristics of this software are optimized software structure and suitable for modern supercomputers. Several standard accelerating devices have been used to compare the simulation results with other beam dynamics software. They have been run on several different platforms, such as INSPUR cluster at RDCPS, and SHENGTENG7000 at IMPCAS. At first, some simulation results for RFQ with large number of particles will be shown.
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MOPJE020	High Resolution Longitudinal Property Measurement using Emittance Exchange Beam Line	emittance, quadrupole, cavity, collective-effects	320
	G. Ha, M.-H. Cho, W. Namkung POSTECH, Pohang, Kyungbuk, Republic of Korea W. Gai, G. Ha, K.-J. Kim, J.G. Power ANL, Argonne, Illinois, USA
	Most of longitudinal measurement techniques introduce the transverse-longitudinal correlation because it is very hard to measure the longitudinal properties directly. This correlation is necessary to observe the longitudinal property through the transverse screen, but initial transverse components of the beam restrict the measurement. It is possible to overcome this intrinsic limit using emittance exchange beam line which makes transverse properties at the downstream only depend on longitudinal properties at the upstream. We present the new idea to measure the longitudinal properties using the emittance exchange beam line and preliminary simulation results.
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MOPJE030	Non-linear Dynamics model for the ESS Linac Simulator	octupole, linac, sextupole, proton	345
	E. Laface ESS, Lund, Sweden
	The ESS Proton Linac will run a beam with 62.5 mA of current. In the first meters of the accelerator, the non- linear space-charge force dominates the dynamics of the beam. The Drift Tube Linac, the Spoke resonators and the elliptical cavities, which are responsible for the 99.8% of the total energy gained by the beam along the accelerator, produce a significant longitudinal non-linear force on the proton beam. In this paper, we introduce a new theory to transport the probability density function of the beam under the effect of non-linear forces. A model based on this theory can be implemented in the ESS Linac Simulator for the fast simulations to be performed during the operations of the proton Linac.
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MOPJE031	Field Map Model for the ESS Linac Simulator	cavity, linac, proton, framework	348
	E. Laface ESS, Lund, Sweden I. List Cosylab, Ljubljana, Slovenia
	The proton beam driving the spallation process at the European Spallation Source, in Lund, will be accelerated and delivered onto a tungsten target by a linac. This linac is composed of four different families of accelerating structures: adrift tube linac, a section of spoke resonators and two sections of elliptical cavities for the particles’ medium and high relativistic β. These structures provide 99.8% of the total energy gained by the beam along the accelerator. It is necessary, then, to have an accurate model describing the physics of the cavities in the ESS Linac Simulator (ELS), which isthe online model that will simulate the accelerator during operation. Here, we present an RF-cavity model based on the field maps that we implemented in ELS, showing a maximum 10% deviation from TraceWin in the horizontal, vertical and longitudinal planes.
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MOPJE042	Longitudinal Injection Schemes For the CERN PS Booster at 160 MeV Including Space Charge Effects	injection, linac, simulation, emittance	378
	V. Forte, E. Benedetto, A.M. Lombardi, D. Quartullo CERN, Geneva, Switzerland
	In the frame of the LHC Injectors Upgrade project, the CERN PS Booster will be equipped with a H⁻ injection system at 160 MeV to tailor the initial transverse and longitudinal profiles. We are here reviewing the different multi-turn longitudinal injection schemes, from the beam dynamics point of view, taking into account the needs of the large variety of the PSB users, spanning in intensity from 5·10⁹ to about 1.6·10¹³ protons per bunch. The baseline of the longitudinal injection has always been the longitudinal stacking with central energy modulation: this scheme has the advantage of filling uniformly the RF bucket and mitigate transverse space charge, but it requires at least 40 turns of injection. A simpler injection protocol without energy modulation is here analyzed in detail to find the optimum initial conditions in terms of bucket filling and reduction of transverse and longitudinal space charge effects, with the advantage of minimizing the number of turns for the LHC beams. Simulations with space charge of the longitudinal injection process from different Linac4 trains are presented to fix possible longitudinal injection scenarios during the future commissioning and operation with Linac4.
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MOPJE045	Fixed Points in Presence of Space Charge in Circular Particle Accelerators	vacuum, simulation, extraction, resonance	389
	M. Giovannozzi, S.S. Gilardoni, A. Huschauer CERN, Geneva, Switzerland S. Machida, C.R. Prior, S.L. Sheehy STFC/RAL/ASTeC, Chilton, Didcot, Oxon, United Kingdom
	Recent measurements performed in the framework of the multi-turn extraction (MTE) studies showed a dependence of the position of beamlets obtained by crossing a stable transverse resonance on the total beam intensity. This novel observation has triggered a number of studies aiming at understanding the source of the observed effect. In this paper the results of numerical simulations performed in different conditions are discussed in detail.
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MOPJE047	Chromaticity Dependence of the Transverse Effective Impedance in the CERN Proton Synchrotron	impedance, proton, synchrotron, controls	395
	S. Persichelli, N. Biancacci, S.S. Gilardoni, A. Huschauer, E. Métral, B. Salvant, R. Wasef CERN, Geneva, Switzerland M. Migliorati University of Rome La Sapienza, Rome, Italy
	The current knowledge of the transverse impedance of the Proton Synchrotron (PS) has been established with beam-based measurements at different energies. The transverse coherent tune shift as a function of the beam intensity has been measured in order to evaluate the total effective imaginary part of the transverse impedance and its localization in the accelerator at the energies of 2, 7, 13 and 25 GeV. Measurements have been performed changing the chromaticity for every tune shift scan with intensity. The data analysis revealed an increase of impedance with chromaticity for all the energies considered. That transverse impedance can be compared with the previously evaluated theoretical impedance budget taking into account the individual contribution of several machine devices. The missing impedance is finally highlighted.
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MOPJE050	Transverse Impedance Model of the CERN-PSB	impedance, kicker, simulation, vacuum	406
	C. Zannini, G. Iadarola, K.S.B. Li, T.L. Rijoff, G. Rumolo CERN, Geneva, Switzerland B. Jones STFC/RAL/ISIS, Chilton, Didcot, Oxon, United Kingdom T.L. Rijoff TU Darmstadt, Darmstadt, Germany
	In the framework of the PS-Booster upgrade project an accurate impedance model is needed in order to determine the effect on the beam stability and assess the impact of the new devices before installation in the machine. This paper describes the PSB impedance model which includes resistive wall, indirect space charge, flanges, step transitions, ejection kicker including cables, injection kickers and cavities. Each impedance contribution has been computed for different energies in the PSB cycle. Measurements of the coherent tune shifts have been performed and compared to calculations based on the impedance model.
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MOPJE075	Tracking Through Analytic Quadrupole Fringe Fields With GPT	quadrupole, simulation, interface, multipole	489
	S.B. van der Geer, M.J. de Loos Pulsar Physics, Eindhoven, The Netherlands B.D. Muratori STFC/DL/ASTeC, Daresbury, Warrington, Cheshire, United Kingdom
	In the early design stages it is customary to work with a highly simplified analytic model to describe the beam line. Dipoles and quadrupoles are often based on hard-edged approximations. This is not only unrealistic, it also significantly slows down time-domain spacecharge tracking codes such as the General Particle Tracer (GPT) code. The underlying reason for the poor performance is that despite the fact that the simple hard-edged field equations are fast to evaluate, they force the integration process to use excessively small step sizes near the fields discontinuities in order to achieve the desired accuracy. In other worlds, the apparently simple equations turn out to be the most difficult ones to evaluate numerically. An obvious solution is to switch to field-maps, but this is not practical in the early design stages. In this contribution we show a new solution implemented in the GPT code based on analytical expressions for the fringes where the transverse size of the magnet is properly taken into account. In addition to producing more realistic results, the smooth fields increase tracking speed by over an order of magnitude for typical test cases.
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MOPMA017	Numerical simulations of transverse modes in Gaussian bunches with space charge	damping, simulation, lattice, synchrotron	575
	A. Macridin, J.F. Amundson, E.G. Stern Fermilab, Batavia, Illinois, USA
	The transverse modes and the intrinsic Landau damping in Gaussian bunched beams with space charge are numerically investigated. The evolution of the phase space density is calculated with the Synergia accelerator modeling package and analyzed with Dynamic Mode Decomposition (DMD) method. DMD is a relatively new technique used to calculate mode dynamics in both linear and nonlinear systems. The properties of the first three space charge modes, including their shape, damping rates and tune shifts are calculated over the entire range of the space charge interaction.
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MOPMA019	Simulations of the Fermilab Recycler for Losses and Collimation	simulation, collimation, proton, target	582
	E.G. Stern, R. Ainsworth, J.F. Amundson, B.C. Brown Fermilab, Batavia, Illinois, USA
	Fermilab has recently completed an upgrade to the com- plex with the goal of delivering 700 kW of beam power as 120 GeV protons to the NuMI target. A major part of boost- ing beam power is to shorten the beam cycle by accumulating up to 12 bunches of 0.5 × 10 11 protons in the Recycler ring through slip-stacking during the Main Injector ramp. This introduces much higher intensities into the Recycler than it has had before. Meeting radiation safety requirements with high intensity operations requires understanding the ef- fects of space charge induced tune spreads and resulting halo formation, and aperture restrictions in the real machine to de- velop a collimation strategy. We report on initial simulations of slip-stacking in the Recycler performed with Synergia.
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MOPMA024	A Parallel Particle-Particle, Particle-Mesh Solver for Studying Coulomb Collisions in the Code IMPACT-T	emittance, electron, simulation, plasma	593
	C.E. Mitchell, J. Qiang LBNL, Berkeley, California, USA
	Funding: This work is supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231. In intense charged-particle beams, the presence of Coulomb collisions can result in growth of the beam slice energy spread and emittance that cannot be captured correctly using traditional particle-in-cell codes. Particle-particle, particle-mesh solvers take a hybrid approach, combining features of N-body and particle-in-cell solvers, to correctly capture the effect of short-range particle interactions with less computing time than direct N-body solvers. We describe the implementation and benchmarking of such a solver in the code IMPACT-T for beam dynamics applications.
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MOPMA030	Multisymplectic Integrators for Accelerator Tracking Codes	plasma, simulation, storage-ring, DTL	614
	S.D. Webb, D.L. Bruhwiler RadiaSoft LLC, Boulder, Colorado, USA
	It has been long understood that long time single particle tracking requires symplectic integrators to keep the simulations stable. In contrast, space charge has been added to tracking codes without much regard for this. Indeed, multisymplectic integrators are a promising new field which may lead to more stable and accurate simulations of intense beams. We present here the basic concept, through a spectral electrostatic field solve which is suitable for adapting into existing tracking codes. We also discuss the limitations of current algorithms, and suggest directions for future development for the next generations of high intensity accelerators.
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MOPMA037	Electron Cloud Buildup and Dissipation Models For PIP-II	electron, simulation, plasma, proton	626
	S.A. Veitzer, P. Stoltz Tech-X, Boulder, Colorado, USA
	Funding: This work was performed under the auspices of the Department of Energy as part of the ComPASS SCiDAC-2 project (DE-FC02-07ER41499), and the SCiDAC-3 project (DE-SC0008920). Buildup of electron plasmas in accelerator cavities can cause beam degradation and limit performance in high-intensity circular particle accelerators. This is especially important in machines such as the LHC, and PIP-II, where mitigation techniques such as beam scrubbing in order to decrease the SEY are expensive and time consuming. Modeling of electron cloud buildup and dissipation can provide understanding as to the potential negative effects of electron clouds on beam properties, as well as estimates of the mitigation required to maintain accelerator performance and beam quality as accelerators move to higher intensity configurations. We report here on simulations of electron cloud buildup and dissipation for geometry, beam and magnetic field configurations describing the Recycler at Fermilab. We perform electrostatic simulations in 3D with VSim PIC, including the effects of space charge and secondary electrons. We quantify the expected survival rate of electrons in these conditions, and argue that improvements in reducing the SEY is unlikely to mitigate the electron cloud effects.
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MOPMA040	Analysis of Beam Transverse Instabilities at Fermilab	dipole, coupling, impedance, quadrupole	633
	T. Zolkin University of Chicago, Chicago, Illinois, USA
	The transverse beam dynamics in Fermilab Recycler ring has been analyzed using SCHARGEV Vlasov solver. In the first part of paper we discuss how SCHARGEV analyses collective instabilities for Gaussian bunch with strong space charge in resistive impedance environment. In the second part the bunched beam dynamics is studied depending on head-tail phase and damper gain. An example for Fermilab Recycler is presented.
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MOPMA041	Experimental Observation of Head-Tail Modes for Fermilab Booster	booster, linac, dipole, betatron	636
	T. Zolkin University of Chicago, Chicago, Illinois, USA A.V. Burov, V.A. Lebedev Fermilab, Batavia, Illinois, USA
	The Fermilab Booster is known to suffer from beam transverse instabilities. An experimental attempt of head-tail modes extraction from the stable beam motion by periodic excitement of betatron motion has been performed. The shapes of head-tail modes have been successfully obtained while eigenfrequencies separation from the betatron tune were too small to be resolved. The qualitative agreement between the theory and an experimental data has been demonstrated. This is an important step towards the understanding of general theory of collective instabilities for strong space charge case, which is a rather typical case for hadron machines.
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MOPMA043	Longitudinal Bunch Shaping at Picosecond Scales using Alpha-BBO Crystals at the Advanced Superconducting Test Accelerator	gun, electron, laser, linac	643
	B. Beaudoin UMD, College Park, Maryland, USA D.R. Edstrom, A.H. Lumpkin, J. Ruan, J.C.T. Thangaraj Fermilab, Batavia, Illinois, USA
	Funding: This works is supported by the University Research Association, Inc. Operated by the Fermi Research Alliance, LLC under Contract No. DE-AC02-07CH11359 with the United States Department of Energy The Integrable Optics Test Accelerator (IOTA) electron injector at Fermilab will enable a broad range of experiments at a national laboratory in order to study and develop solutions to the limitations that prevent the propagation of high intensity beams at picosecond lengths. One of the most significant complications towards increasing short-beam intensity is space-charge, especially in the vicinity of the gun. A few applications that require a longitudinally shaped electron beam at high intensities are for, the generation of THz waves and dielectric wakefields, each of which will encounter the effects of longitudinal space-charge. This paper investigates the effects of longitudinal space-charge on alpha-BBO UV laser shaped electron bunches in the vicinity of the 1½cell 1.3 GHz cylindrically symmetric RF photocathode gun.
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MOPMA044	Barrier Shock Compression with Longitudinal Space Charge	simulation, emittance, electron, plasma	646
	B. Beaudoin, I. Haber, R.A. Kishek UMD, College Park, Maryland, USA
	Funding: This work is supported by the US Dept. of Energy, Office of High Energy Physics. Synchrotrons and storage rings routinely employ RF barrier buckets as a means of accumulating charge to increase the peak intensity and preserve longitudinal emittance while minimizing emittance growth [1-3]. This was shown in the main injector and recycler at Fermilab as well as the SIS-18 at GSI Helmholtz center for heavy ion research. The RF cavities typically used are ferrite loaded magnetic alloys with low Q to maximize bandwidth and generate single pulses, either as delta functions, triangular or half/full period sine waves. The University of Maryland Electron Ring (UMER) group is studying a novel scheme of bunch compression in the presence of longitudinal space charge. It has been analytically shown through 1-D computations that the presence of space-charge considerably improves the efficiency of the barrier compression by taking advantage of the shock-front that launches when the barrier moves into a space-charge dominated beam. In this paper, we summarize the initial results of the study.
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MOPMA045	Conceptual Difficulties of a Thermodynamics Description of Charged-Particle Beams	emittance, simulation, focusing, beam-transport	649
	S. Bernal UMD, College Park, Maryland, USA
	Funding: This work is funded by the US Dept. of Energy We review the existing phenomenological theories of emittance growth with and without entropy terms and re-examine the condition for thermal equipartitioning in an unbunched charged-particle beam. The model incorporates linear space charge and a uniform-focusing lattice. Because of non-extensitivity of the transverse ("thermal") energy and the absence of a classical heat bath, we conclude that a rigorous classical thermodynamics treatment of charged-particle beams is not possible. In particular, the postulated relationships between the rms emittance and temperature and entropy must be qualified.
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MOPMA046	Simulations and experiments in Support of Octupole Lattice Studies at the University of Maryland Electron Ring	lattice, octupole, electron, quadrupole	653
	K.J. Ruisard, B. Beaudoin, I. Haber, T.W. Koeth UMD, College Park, Maryland, USA
	Funding: This material is based on work supported by the NSF Graduate Research Fellowship and the NSF Accelerator Science Program We present plans for a nonlinear lattice at the University of Maryland Electron Ring (UMER). Theory predicts that a strong nonlinear lattice can limit resonant behavior without reducing dynamic aperture if the nonlinear fields preserve integrability or quasi-integrability. We discuss plans for a quasi-integrable octupole lattice, based on the work of Danilov and Nagaitsev.* We use Elegant and the WARP PIC code to estimate the octupole-induced tune spread. We discuss improvements to the ring in support of octupole lattice experiments, including generation and detection of emittance-dominated, negligible space charge beams. * V. Danilov, S. Nagaitsev, Phys. Rev. STAB 13, 084002 (2010).
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MOPMA050	Smooth Fast Multipole Method for Space Charge Tracking: An Alternate to Particle-In-Cell	multipole, simulation, framework, emittance	663
	A.J. Gee, B. Erdelyi Northern Illinois University, DeKalb, Illinois, USA B. Erdelyi ANL, Argonne, USA
	The fast multipole method (FMM) algorithm was developed by Greengard and Rokhlin in 1987 . As one of the top ten algorithms of the 20th century, it has been applied in a wide range of fields. The FMM complexity is O(N), where N is the number of articles, allowing for large-scale simulations. However, it includes all the two-body collisional forces, in contrast to other methods such as the popular particle in-cell (PIC) methods. While collisionality can be very important, many applications require only the mean field effects. PIC is frequently used in this regime. Due to recent concerns of unphysical effects of grids, interpolation and other approximations in PIC codes, an alternative based on different underlying assumptions would prove enlightening. For these cases, a smoothed or softened FMM using a Plummer-like smoothing parameter holds much promise. Unfortunately, the original FMM based on analytic expansions of the 1/r-like potentials does not allow for Plummer softening. We present our new soft-FMM employing differential algebras (DA) to obtain the modified expansions. We also compare the performance of the smoothed DA-FMM with examples from PIC simulations. L. Greengard and V. Rokhlin. “A fast algorithm for particle simulations".
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MOPMA051	Generation of Modulated Bunch Using a Masked Chicane for Beam-Driven Acceleration Experiments at ASTA	simulation, bunching, dipole, emittance	666
	Y.-M. Shin, P. Piot Northern Illinois University, DeKalb, Illinois, USA D.R. Broemmelsiek, D.J. Crawford, A.H. Lumpkin Fermilab, Batavia, Illinois, USA A.T. Green Northern Illinois Univerity, Dekalb, Illinois, USA
	Funding: This work was supported by the DOE contract No. DEAC02-07CH11359 to the Fermi Research Alliance LLC. Longitudinal density modulations on electron beams can improve machine performance of beam-driven accelerators and FELs with resonance beam-wave coupling . The sub-ps beam modulation has been studied with a masked chicane * *** by the analytic model and simulations with the beam parameters of the Advanced Superconducting Test Accelerator (ASTA) in Fermilab. With the nominal 50 MeV chicane parameters and 3 ps bunch length, the analytic model showed that a slit-mask with slit period 900 um and aperture width 300 μm generates about 100-um modulation periodicity with 2.4% correlated energy spread. With the designed slit mask and a 3 ps bunch, particle-in-cell simulations (CST-PS), including nonlinear energy distributions, space charge force, and coherent synchrotron radiation (CSR) effect, also result in ~ 100 um of longitudinal modulation. The beam modulation has been extensively examined with three different beam conditions, 0.25, 1 , and 3.2 nC, by extended 3D tracking simulations (Elegant). The modulated bunch generation will be tested by a slit-mask installed at the chicane of the ASTA 50-MeV-injector beamline for beam-driven acceleration experiments. * E. Kallos, Southern California 2008 D. C. Nguyen, B. E. Carlston, NIMA 375, 597 (1996) * P. Muggli, V. Yakimenko, M. Babzien, E. Kallos, and K. P. Kusche, PRL 101, 054801 (2008)
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MOPMA057	Space Charge Neutralization of 750 keV Proton Beam in LANSCE Injector Line	emittance, simulation, proton, beam-transport	685
	Y.K. Batygin LANL, Los Alamos, New Mexico, USA
	Funding: Work supported by the United States Department of Energy, National Nuclear Security Agency, under contract DE-AC52-06NA25396 The 750-keV low-energy beam transport of the Los Alamos Neutron Science Center (LANSCE) linac consists of two independent beam lines for simultaneous injection of H⁺ and H⁻ beams into the linear accelerator. Space charge effects play an important role in the beam transport therein. A series of experiments were performed to determine the level of proton beam space charge neutralization by residual gas ionization, and time required for neutralization. Study was performed as emittance scans between pair of emittance measurement stations. The value of compensated space charge was determined through comparison of results of measurements and simulations using macroparticle method and envelope code. Obtained results provide new setup for beam tuning in transport beamline.
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MOPMA058	Effect of Spherical Aberration on Beam Emittance Growth	emittance, focusing, proton, simulation	688
	Y.K. Batygin LANL, Los Alamos, New Mexico, USA
	Funding: Work supported by the United States Department of Energy, National Nuclear Security Agency, under contract DE-AC52-06NA25396 Spherical aberration in axial-symmetric magnetic focusing lenses results in S-shape figure of beam emittance. Filamentation of beam emittance in phase space is a fundamental property of a beam affected by aberrations. Analytical expression for effective beam emittance growth due to spherical aberration as a function of lens aberraion coefficient, initial beam emittance, beam radius, and focal lens of the focusing lens is obtained. Analysis is extended for beam space charge aberrations. Analytical results are confirmed by numerical calculations.
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MOPMN004	CSR Impedance for Non-Ultrarelativistic Beams	impedance, wakefield, radiation, synchrotron	709
	R. Li JLab, Newport News, Virginia, USA C.-Y. Tsai Virginia Polytechnic Institute and State University, Blacksburg, Virginia, USA
	Funding: This work is supported by Jefferson Science Associates, LLC under U.S. DOE Contract No. DE-AC05-06OR23177. For the analysis of the coherent synchrotron radiation (CSR) induced microbunching gain in the low energy regime, such as when a high-brightness electron beam is transported through a low-energy merger in an energy-recovery linac (ERL) design, it is necessary to extend the CSR impedance expression in the ultrarelativistic limit to the non-ultrarelativistic regime. This paper presents our analysis of CSR impedance for general beam energies.
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MOPMN008	Space Charge Studies in FFAG Using the Tracking Code Zgoubi	emittance, simulation, betatron, damping	717
	M. Haj Tahar, F. Méot, N. Tsoupas BNL, Upton, Long Island, New York, USA
	Funding: Work supported by Brookhaven Science Associates, LLC under Contract No. DE-AC02-98CH10886 with the U.S. Department of Energy. A method is implemented in Zgoubi that allows the computation of space charge effects in 2D distributions and with some restrictions in 3D distributions. It relies on decomposiing field maps or analytical elements into slices and applying a space charge kick to the particles. The aim of this study is to investigate the accuracy of this technique, its limitations/advantages by comparisons with other linear/nonlinear computation methods and codes, and to apply it to high power fixed field ring design studies.
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MOPMN019	Understanding the Effect of Space Charge on Instabilities	synchrotron, impedance, hadron, operation	743
	M. Blaskiewicz BNL, Upton, Long Island, New York, USA A. Chao SLAC, Menlo Park, California, USA Y.H. Chin KEK, Ibaraki, Japan
	Funding: Work supported by Brookhaven Science Associates, LLC under Contract No. DE-AC02-98CH10886 with the U.S. Department of Energy. The combined effects of space charge and wall impedance on transverse instabilities is an important consideration in the design and operation of hadron machines as well as an intrinsic academic interest. This study explores the combined effects of space charge and wall impedance using various simplified models in an attempt to produce a better understanding of their interplay.
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MOPHA007	Modeling/Measurement Comparison of Signal Collection in Diamond Sensors in Extreme Conditions	electron, detector, simulation, scattering	787
	V. Kubytskyi, P. Bambade, S. Liu LAL, Orsay, France
	Here we present a study of charge collection dynamics in a Diamond Sensor (DS) subjected to intensities from 1 to 10⁸ Minimum Ionizing Particles (MIP). We developed a model based on the numerical solution of the 1D drift-diffusion equations, using the Scharfetter-Gummel discretization scheme. Inhomogeneity of the space-charge distribution together with the externally applied electric field are taken into account by analytically solving the Poisson equation at each time step. We identified two regimes of charge collection. The first corresponds to 1-10⁵ MIPs, in this case the externally applied electric field is negligibly perturbed by space-charge effects during the separation of the electron/hole clouds. The second corresponds to intensities larger than 10⁷ MIPs, where the space-charge effects significantly slow down the charge collection due to large concentrations of electron/hole pairs in the DS volume. The results of our modeling are in qualitative agreement with the experimental data acquired at the PHoto-Injector electron beam facility at LAL. Our model allows optimizing DS parameters to achieve desired charge collection times for different beam intensities.
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MOPTY015	Beam Compression Dynamics and Associated Measurement Methods in Superconducting THz Source	controls, simulation, gun, electron	969
	Z. Zhou, Y.-C. Du, W.-H. Huang TUB, Beijing, People's Republic of China
	To ensure the quality of high brightness electron beams needed by the terahertz FEL facility at China academy of engineering physics(CAEP), which aims to obtain 100 to 300 terahertz light, a feed-back control system is required to monitor the amplitude and phase jittering by measuring beam arrival time as well as bunch length at the site of the beam position monitor(BPM). In this paper, we make an idealized model of injector section and deduce analytic expressions of bunch arrival time and bunch length. In consideration of the space charge effect on bunch lengthening, bunch arrival time and bunch length as a function of DC gun voltage, buncher field amplitude and buncher phase is carefully calibrated by means of particle in cell (PIC) simulation. With the time and space resolution of the BPM, the control accuracy of phase is estimated to be 0.01 degree, while the amplitude is 0.04%.
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MOPWI005	Emittance and Optics Measurements on the Versatile Electron Linear Accelerator at Daresbury Laboratory	quadrupole, emittance, gun, coupling	1153
	C.P. Topping, D.J. Scott, A. Wolski Cockcroft Institute, Warrington, Cheshire, United Kingdom S.D. Barrett, C.P. Topping, A. Wolski The University of Liverpool, Liverpool, United Kingdom B.L. Militsyn, D.J. Scott STFC/DL/ASTeC, Daresbury, Warrington, Cheshire, United Kingdom
	The Versatile Electron Linear Accelerator (VELA) is a facility designed to provide a high quality electron beam for accelerator systems development, as well as industrial and scientific applications. Currently, the RF gun can deliver short (of order a few ps) bunches with charge in excess of 250 pC at up to 5.0 MeV/c beam momentum. Measurement of the beam emittance and optics in the section immediately following the gun is a key step in tuning both the gun and the downstream beamlines for optimum beam quality. We report the results of measurements (taking account of coupling and space charge) indicating normalised emittances of order 0.5 μm at low bunch charge.
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MOPWI024	Accelerator Online Simulation Platform	database, simulation, lattice, software	1204
	C.P. Chu, Y. Zhang FRIB, East Lansing, Michigan, USA
	Funding: This material is based upon work supported by the U.S. Department of Energy Office of Science under Cooperative Agreement DE-SC0000661, the State of Michigan and Michigan State University. A platform for accelerator online beam simulation has been established for Facility for Rare Isotope Beams (FRIB). This modeling platform supports multiple simulation codes for different sections of the complex machine which cannot be properly modeled with a single online simulation tool. Model data for the platform is stored in a relational database which is designed to accommodate most simulation data. The stored data is accessible with physics intuitive data API (Application Programming Interface). Presently, the platform is supporting Open XAL, MAD-X and IMPACT simulation codes. In addition to the model data storage and access, tools such as data comparison and simple graphing capability are also included in the platform.
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TUAB3	Chromaticity Effects for Space Charge Dominated Beams in the CERN PS Booster	resonance, simulation, emittance, sextupole	1335
	V. Forte Université Blaise Pascal, Clermont-Ferrand, France E. Benedetto, F. Schmidt CERN, Geneva, Switzerland
	In view of the LHC Injectors Upgrade (LIU) project, an extensive campaign is on-going in the CERN PS Booster (PSB) to study collective effects for the future operation with the 160 MeV injection from Linac4. In operation, the machine is running with uncorrected natural chromaticity. This paper focuses on the study of the effects of chromaticity on losses and beam blow-up.
	Slides TUAB3 [4.887 MB]
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TUPWA008	Mixing and Space-Charge Effects In Free-Electron Lasers	laser, electron, FEL, radiation	1410
	E.A. Peter, A. Endler, F.B. Rizzato IF-UFRGS, Porto Alegre, Brazil A.P.B. Serbeto UFF, Niterói - RJ, Brazil
	Funding: This work was supported by CNPq and FAPERGS, Brazil, and by the Air Force Office of Scientific Research (AFOSR), USA, under the Grant No. FA9550-12-1-0438 Free-electron lasers are devices which efficiently convert the kinetic energy from a relativistic electron beam into electromagnetic radiation, amplifying an initial small sign. The present work revisits the subject of mixing, saturation and space-charge effects in free-electron lasers. Use is made of the compressibility factor, which proves to be a helpful tool in the related systems of charged beams confined by static magnetic fields. The compressibility allows to build a semi-analytical model and to perform analytical estimates of the elapsed time until the onset of mixing, which in turn allows to estimate the saturated amplitude of the radiation field. In addition, the compressibility helps to pinpoint space-charge effects and the corresponding transition from Compton to Raman regimes. The semi-analytical model and the particles simulations are compared, exhibiting a good agreement.* * E. Peter, A. Endler, F. B. Rizzato, and A. Serbeto, Phys. Plasmas 20, 123104 (2013). ** E. Peter, A. Endler, and F. B. Rizzato, Phys. Plasmas 21, 113104 (2014)
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TUPWA045	Further Investigations on the MESA injector	coupling, linac, simulation, experiment	1515
	R.G. Heine, K. Aulenbacher, S. Friederich, C. Matejcek, F. Schlander IKP, Mainz, Germany
	Funding: work supported by the German Federal Ministery of Education and Research under the Cluster of Excellence "PRISMA" The MESA ERL to be build at Mainz in the next years is a multi turn recirculating linac with beam currents of up to 10 mA. The dynamic range of the beam currents demanded by the experiments is of at least two orders of magnitude. This is a special challenge for the layout design of an injector. In this paper we present the current status of the design of the injector linac called MAMBO (MilliAMpereBOoster).
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TUPWA067	Status of Higher Bunch Charge Operation in Compact ERL	operation, optics, recirculation, emittance	1583
	T. Miyajima, K. Harada, Y. Honda, T. Miura, N. Nakamura, T. Obina, F. Qiu, H. Sakai, S. Sakanaka, M. Shimada, R. Takai, K. Umemori, M. Yamamoto KEK, Ibaraki, Japan R. Hajima, R. Nagai, N. Nishimori JAEA, Ibaraki-ken, Japan D. Lee KNU, Deagu, Republic of Korea
	In the KEK compact ERL (cERL), machine studies toward higher bunch charge operation is one of the most important issues. From January 2015 to April 2015, we carried out a higher bunch charge operation with an bunch charge of 0.5 pC for the experiment of laser compton scattering. After the study of space charge effect and optics tuning, we succeeded in the recirculation operation with the emittance, which was close to the design value. Moreover, a test operation in the injector section with the bunch charge of 7.7 pC was carried out as a preparation toward the recirculation operation with the average current of 10 mA.
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TUPJE041	Progress on a Compact Accelerator Design for a Compton Light Source	gun, dipole, linac, solenoid	1706
	K.E. Deitrick, J.R. Delayen, B.R.P. Gamage, G.A. Krafft, T. Satogata ODU, Norfolk, Virginia, USA
	A compact Compton light source using an electron linear accelerator is in design at the Center for Accelerator Science at Old Dominion University and Jefferson Lab. We report on the current design, including beam properties through the entire system based on a full end-to-end simulation, compare current specifications to design goals, and target areas for improvement.
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TUPJE059	Modeling of an Electron Injector for the AWAKE Project	emittance, booster, quadrupole, linac	1762
	Ö. Mete, G.X. Xia UMAN, Manchester, United Kingdom R. Apsimon, G. Burt Cockcroft Institute, Lancaster University, Lancaster, United Kingdom S. Döbert CERN, Geneva, Switzerland R.B. Fiorito The University of Liverpool, Liverpool, United Kingdom C.P. Welsch Cockcroft Institute, Warrington, Cheshire, United Kingdom
	Funding: Cockcroft Institute Core Grant Particle in cell simulations were performed to characterise an electron injector for AWAKE project in order to provide a tuneable electron beam within a range of specifications required by the plasma wakefield experiments. Tolerances and errors were investigated. These results are presented in this paper alongside with the investigation regarding the beam dynamics implications of the 3GHz travelling wave structure developed for the injector.
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TUPMA003	Microbunching Phenomena in LCLS-II	laser, bunching, simulation, undulator	1843
	M. Venturini, C. F. Papadopoulos, J. Qiang LBNL, Berkeley, California, USA Y. Ding, P. Emma, Z. Huang, G. Marcus, A. Marinelli, Y. Nosochkov, T.O. Raubenheimer, L. Wang, M. Woodley SLAC, Menlo Park, California, USA
	Funding: Work supported by DOE, in part under Contract No. DE-AC02-05CH11231 and through the LCLS-II project. The microbunching instability has long been recognized as a potential limiting factor to the performance of X-ray FELs. It is of particular relevance in LCLS-II due, in part, to a layout that includes a long bypass beamline between the Linac and the undulators. Here we focus on two aspects of the instability that highlight the importance of 3D effects.
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TUPMA007	Numerical Investigation of a Cascaded Longitudinal Space-Charge Amplifier at the Fermilab's Advanced Superconducting Test Accelerator	radiation, bunching, simulation, impedance	1850
	A. Halavanau, P. Piot Northern Illinois University, DeKalb, Illinois, USA P. Piot Fermilab, Batavia, Illinois, USA
	In a cascaded longitudinal space-charge amplifier (LSCA), initial density noise in a relativistic e-beam is amplified via the interplay of longitudinal space charge forces and properly located dispersive sections. This type of amplification process was shown to potentially result in large final density modulations * compatible with the production of broadband electromagnetic radiation. The technique was recently demonstrated in the optical domain *. In this paper we investigate, via numerical simulations, the performances of a cascaded LSCA beamline at the Fermilab's Advanced Superconducting Test Accelerator (ASTA). We especially explore the properties of the produced broadband radiation. Our studies have been conducted with an effective three-dimensional space-charge algorithm. Dohlus, M. et al. Proc. SPIE 8779. doi:10.1117/12.2017369 ** Marinelli, A. et al. Phys. Rev. Lett. 110, 264802 (2013)
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TUPMA008	Numerical Study of Three Dimensional Effects in Longitudinal Space-Charge Impedance	impedance, simulation, detector, radiation	1853
	A. Halavanau, P. Piot Northern Illinois University, DeKalb, Illinois, USA P. Piot Fermilab, Batavia, Illinois, USA
	Longitudinal space-charge (LSC) effects are generally considered as detrimental in free-electron lasers as they can seed instabilities. Such "microbunching instabilities" were recently shown to be potentially useful to support the generation of broadband coherent radiation pulses. Therefore there has been an increasing interest in devising accelerator beamlines capable of sustaining this LSC instability as a mechanism to produce a coherent light source. To date most of these studies have been carried out with a one-dimensional impedance model for the LSC. In this paper we use a N-body "Barnes-Hut" algorithm * to simulate the 3D space charge force in the beam combined with Elegant ** and explore the limitation of the 1D model often used. * Barnes, J. & Hut, P., Nature 324, 446-449, 1986. ** Borland, M., Advanced Photon Source LS-287, 2000.
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TUPTY074	Muon Beam Emittance Evolution in the Helical Ionization Cooling Channel for Bright Muon Sources	plasma, emittance, collider, simulation	2203
	K. Yonehara, C.Y. Yoshikawa Fermilab, Batavia, Illinois, USA C.M. Ankenbrandt, R.P. Johnson, S.A. Kahn Muons, Inc, Illinois, USA M. Chung UNIST, Ulsan, Republic of Korea Y.S. Derbenev, A.V. Sy JLab, Newport News, Virginia, USA B.T. Freemire IIT, Chicago, Illinois, USA
	The six-dimensional ionization cooling is essential to design a bright muon source. A geometry constraint is a challenge issue in a compact helical cooling channel (HCC). Especially, the HCC requires a large bore helical magnet and a compact helical RF system to incorporate the RF into the magnet chamber. A new emittance evolution has been designed to mitigate the geometry constraint. The HCC was functionally separated into three parts sections. The lattice at the initial section provides a large transverse acceptance by using a strong helical focus magnet. Once the transverse beam size is small enough to get into the compact RF the HCC lattice in the middle section generates a large longitudinal beta tune to dominate the longitudinal cooling. Consequently, the longitudinal emittance becomes smaller than the transverse one at the end of middle section. In the final section, the magnetic field strength is gradually reduced to match out the helical channel to the straight solenoid. As a result, the emittance exchange takes place and the final transverse emittance becomes smaller than the longitudinal one. The new emittance evolution scenario will be discussed in this presentation.
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TUPTY078	Fixed-energy Cooling and Stacking for an Electron Ion Collider	electron, ion, ECR, collider	2214
	P.M. McIntyre, S. Assadi, J. Gerity, A. Sattarov Texas A&M University, College Station, Texas, USA
	The proposed designs for polarized-beam electron-ion colliders require cooling of the ion beam to achieve and sustain high luminosity. One attractive approach is to make a fixed-energy storage ring in which ions are con-tinuously cooled and stacked during a collider store, then transferred to the collider and accelerated for a new store when the luminosity decreases. An example design is reported for a 6 GeV/u superferric storage ring, and for a d.c. electron cooling system in which electron space charge is fully neutralized so that high-current magnetized e-cooling can be used to best advantage.
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WEYB1	Benchmarking and Application of Space Charge Codes for Rings	simulation, resonance, lattice, experiment	2402
	S. Machida STFC/RAL/ASTeC, Chilton, Didcot, Oxon, United Kingdom
	This presentation should present an overview of efforts for benchmarking and application of space charge codes for rings. After briefly recalling the historical background of the simulation efforts of space charge effects in rings, we will overview the present benchmarking efforts against experimental results.
	Slides WEYB1 [6.541 MB]
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WEYB3	Interplay of Beam-Beam, Lattice Nonlinearity, and Space Charge Effects in the SuperKEKB Collider	lattice, luminosity, quadrupole, resonance	2413
	D. Zhou, H. Koiso, A. Morita, K. Ohmi, Y. Ohnishi, K. Oide, H. Sugimoto KEK, Ibaraki, Japan Y. Zhang IHEP, Beijing, People's Republic of China
	The SuperKEKB B-factory adopts nanobeam scheme for the collision, which consists of large crossing angle and very small vertical beta function at the interaction point. Simulations have revealed that the luminosity of SuperKEKB will be very sensitive to perturbations from various sources. This paper discusses various beam dynamics issues involved in the SuperKEKB collider, including beam-beam, lattice nonlinearity, and space charge effects, as well as their interplay and planned mitigations.
	Slides WEYB3 [11.722 MB]
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WEXC2	Advances in Proton Linac Online Modeling	linac, GPU, simulation, operation	2423
	X. Pang LANL, Los Alamos, New Mexico, USA
	This talk will review current online modeling tools used for proton linacs and then focus on a new approach that marries multi-particle beam dynamics with modern GPU technology to provide pseudo real-time beam information in a control room setting. Benefits to be discussed will include fast turnaround, accurate beam quality prediction, cost efficiency, test bed for new control and operation scheme development and operator training.
	Slides WEXC2 [4.292 MB]
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WEAB1	Compensating Tune Spread Induced by Space Charge in Bunched Beams	hadron, electron, proton, collider	2450
	V. Litvinenko Stony Brook University, Stony Brook, USA G. Wang BNL, Upton, Long Island, New York, USA
	The effects of space charge play a significant role in modern-day accelerators, frequently constraining the beam parameters attainable in an accelerator or in an accelerator chain. They also can limit the luminosity of hadron colliders operating either at low energies or with sub-TeV high-brightness hadron beams. The latter is applied for strongly cooled proton and ion beams in eRHIC – the proposed future electron-ion collider at Brookhaven National Laboratory. Several schemes were proposed to compensate for space charge effects in a coasting (e.g., continuous) hadron beam, and some have been tested. Using an appropriate transverse profile of the electron beam (or plasma column) for a coasting beam would compensate both the tune shift and the tune spread in the hadron beam. But none of these methods address the issue of compensating space-charge induced tune spread in a bunched hadron beam. In this paper we propose and evaluate a novel idea of using a co-propagating electron bunch with miss-matched longitudinal velocity to compensate the space charge induced tune-shift and tune spread. We present several practical examples of such a system.
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WEPWA063	Beam-Plasma Effects in Muon Ionization Cooling Lattices	plasma, simulation, electron, ion	2649
	J.S. Ellison, P. Snopok IIT, Chicago, Illinois, USA
	Funding: Work is supported by the U.S. Department of Energy. New computational tools are essential for accurate modeling and simulation of the next generation of muon based accelerator experiments. One of the crucial physics processes specific to muon accelerators that has not yet been implemented in any current simulation code is beam induced plasma effect in liquid, solid, and gaseous absorbers. We report here on the progress of developing the required simulation tools and applying them to study the properties of plasma and its effects on the beam in muon ionization cooling channels.
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WEPWA064	Ionization Cooling Channels in COSY Infinity	emittance, simulation, multipole, solenoid	2652
	B.T. Loseth, M. Berz MSU, East Lansing, Michigan, USA P. Snopok Illinois Institute of Technology, Chicago, Illinois, USA
	Ionization cooling is a method to reduce the emittance of a beam through the use of absorbers, rf cavities, and strong solenoids for focusing, arranged into a condensed lattice. By tuning lattice parameters, it is possible to construct a staged cooling channel in which the beam emittance is always considerably greater than the minimum value. In the late stages of the cooling channel, space charge effects can become a significant obstacle to further emittance reduction once the beam becomes sufficiently condensed. A method has been implemented in COSY Infinity, a beam dynamics simulation and analysis code, which efficiently and accurately calculates the self-fields of all particles on each other based on a variant of the Fast Multipole Method (FMM). In this paper, we present simulations of a muon ionization cooling channel performed in COSY, utilizing the FMM, benchmarked against G4beamline, a standard code for muon beam analysis, in order to investigate the significance of space charge effects.
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WEPTY013	Cs2Te Photocathode Performance in the AWA High-charge High-gradient Drive Gun	laser, cathode, gun, wakefield	3283
	E.E. Wisniewski, S.P. Antipov, M.E. Conde, D.S. Doran, W. Gai, C.-J. Jing, W. Liu, J.G. Power, C. Whiteford ANL, Argonne, Illinois, USA S.P. Antipov, C.-J. Jing Euclid TechLabs, LLC, Solon, Ohio, USA
	Funding: U.S. Dept of Energy Office of Science under contract number DE-AC02-06CH11357 The unique high-charge L-band, 1.3 GHz, 1.5 cell gun for the new 75 MeV drive beam is in operation at the Argonne Wakefield Accelerator (AWA) facility (see M.E. Conde, this proceedings.) The high-field (> 80 MV/m) photoinjector has a large area, high QE Cesium telluride photocathode (diameter > 30 mm). The photocathode, a crucial component of the upgraded facility, is fabricated on-site. The photoinjector generates high-charge, short pulse, single bunches (Q > 100 nC) and long bunch-trains (Q > 600 nC) for wakefield experiments. The performance of the photocathode for the AWA drive gun is detailed. Quantum efficiency (QE) measurements indicate long, stable photocathode lifetime under demanding conditions.
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WEPWI003	Design of a Radial Klystron	cavity, klystron, electron, bunching	3489
	M. Dal Forno, A. Jensen, R.D. Ruth, S.G. Tantawi SLAC, Menlo Park, California, USA
	Funding: Work supported by the US DOE under contract DEAC03-76SF00515. The radial klystron is a multidimensional rf source where the beam is generated by a cylindrical gun and it propagates in the radial dimension. The advantage of this design is that the space charge effects are balanced in the azimuthal dimension and a lower magnetic fields is required to focus the electron beam. The bunching is made with concentric coaxial resonators, connected by drift tube. The electron beam interaction with the cavity fields has been analyzed by means of particle tracking software in order to evaluate the beam bunching and the beam dynamics. This paper shows the klystron design, optimizing the shape and the position of each cavity, in order to maximize the efficiency of the device.
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THPF002	Space Charge Effect Estimation for Synchrotrons with Third-order Resonant Extraction	extraction, resonance, proton, injection	3677
	M.T.F. Pivi, A. Garonna EBG MedAustron, Wr. Neustadt, Austria
	In proton and ion storage rings using the third-order resonance extraction mechanism, beam particles are slowly extracted from the ring when reaching the resonance stop-band. Typically at beam injection, the horizontal tune is set to a value close to the resonance value. The tune is then moved towards the resonance value to trigger beam extraction in a controlled way. The tune shift generated by space charge forces needs to be taken into account. For this, the incoherent space-charge tune shift for protons of the MedAustron accelerator main ring has been evaluated. This has been performed by multi-particle tracking using an optics model based on MADX, considering a realistic Gaussian beam distribution and exact non-linear space charge electric field forces. The MedAustron accelerator is in the beam commissioning phase and is planned to start medical commissioning at the end of 2015.
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THPF007	Optimization of Multi-turn Injection into a Heavy-Ion Synchrotron using Genetic Algorithms	injection, emittance, linac, ion	3689
	S. Appel, O. Boine-Frankenheim GSI, Darmstadt, Germany O. Boine-Frankenheim TEMF, TU Darmstadt, Darmstadt, Germany
	For heavy-ion synchrotrons an efficient multi-turn injection (MTI) from the injector linac is crucial in order to reach the specified currents using the available machine acceptance. The beam loss during the MTI must not exceed the limits determined by machine protection and vacuum requirements. Especially for low energy and intermediate charge state ions, the beam loss can cause a degradation of the vacuum and a corresponding reduction of the beam lifetime. In order to optimize the MTI a genetic algorithm based optimization is used to simultaneously minimize the loss and maximize the multiplication factor (e.g. stored currents in the synchrotron). The effect of transverse space charge force on the MTI has also been taken into account. The optimization resulted in injection parameters, which promise a significant improvement of the MTI performance for intense beams in the SIS18 synchrotron at GSI.
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THPF042	Rectlinear Cooling Scheme for Bright Muon Sources	emittance, simulation, lattice, cavity	3792
	D. Stratakis BNL, Upton, Long Island, New York, USA
	Funding: Work supported by Contract No, DE-AC02-07CH11359 with the US Department of Energy. A fast cooling technique is described that simultaneously reduces all six phase-space dimensions of a charged particle beam. In this process, cooling is accomplished by reducing the beam momentum through ionization energy loss in absorbers and replenishing the momentum loss only in the longitudinal direction rf cavities. In this work we describe its main features and describe the main results.
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THPF060	The Simulation Study of Space Charge Effects for CSNS Linac	emittance, DTL, focusing, simulation	3833
	Y. Yuan, L. Huang, J. Peng, S. Wang IHEP, Beijing, People's Republic of China
	China Spallation Neutron Source (CSNS) is a high intensity accelerator based facility. Its accelerator consists of an H⁻ injector and a proton Rapid Cycling Synchrotron. The injector includes the front end and linac. The RFQ accelerates the beam to 3MeV, and then DTL accelerates it to 80MeV. The space charge effect is the most important cause of emittance growth and beam loss due to the low beam energy and the high peak current. The paper performed simulation studies on the space charge effects at the LINAC by using three-dimensional code IMPACT-Z. The emittance evolution is studied in the point of view of the singe-particle dynamics and multi-particle dynamics with different peak beam current. The effect of mismatch is studied by simulation, and the emittance growth with different mismatch factor are given.
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THPF088	CERN PS Booster Upgrade and LHC Beams Emittance	emittance, injection, simulation, booster	3897
	E. Benedetto, J.L. Abelleira, C. Bracco, V. Forte, B. Mikulec, G. Rumolo CERN, Geneva, Switzerland V. Forte Université Blaise Pascal, Clermont-Ferrand, France
	By increasing the CERN PS Booster injection energy from 50 MeV to 160 MeV, the LHC Injector Upgrade Project aims at producing twice as brighter beams for the LHC. Previous measurements showed a linear dependence of the transverse emittance with the beam intensity and space-charge simulations confirmed the linear scaling. This paper is discussing in detail the dependence on the longitudinal emittance and on the choice of the working point, with a special attention to the H⁻ injection process and to the beam dynamics in the first 5 ms, during the fall of the injection chicane bump.
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THPF127	Scheme for a Low Energy Beam Transport with a Non-neutralized Section	ion, emittance, ion-source, rfq	4016
	A.V. Shemyakin, L.R. Prost Fermilab, Batavia, Illinois, USA
	Funding: Fermilab is operated by Fermi Research Alliance, LLC, under Contract DE-AC02-07CH11359 with the United States Department of Energy A Low Energy Beam Transport (LEBT) line is the part of a modern ion accelerator between an ion source (IS) and a Radio-Frequency Quadrupole (RFQ). Typically, it includes 1-3 solenoidal lenses for focusing and relies on transport dynamics with nearly complete beam space charge neutralization over the entire length of the LEBT. In this paper, we discuss the possibility and rationality of imposing un-neutralized transport in the portion of the LEBT adjacent to the RFQ. For estimations, we will use the parameters from PXIE, a test accelerator presently being constructed at Fermilab.
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THPF144	Analysis of FEL-based CeC Amplification at High Gain Limit	electron, FEL, free-electron-laser, laser	4063
	G. Wang, Y.C. Jing, V. Litvinenko BNL, Upton, Long Island, New York, USA V. Litvinenko Stony Brook University, Stony Brook, USA
	Funding: Work supported by Brookhaven Science Associates, LLC under Contract No. DE-AC02-98CH10886 with the U.S. Department of Energy. An analysis of CeC amplifier based on 1D FEL theory was previously performed with exact solution of the dispersion relation, assuming electrons having Lorentzian energy distribution . At high gain limit, the asymptotic behavior of the FEL amplifier can be better understood by Taylor expanding the exact solution of the dispersion relation with respect to the detuning parameter . In this work, we make quadratic expansion of the dispersion relation for Lorentzian energy distribution *** and investigate how longitudinal space charge and electrons’ energy spread affect the FEL amplification process. * G. Wang, PhD Thesis, SUNY Stony Brook, 2008. G. Stupakov, M.S. Zolotorev, Comment on “Coherent Electron Cooling”, PRL 110 (2013) 269503. * E.L. Saldin, E.A. Schneidmiller, M.V. Yurkov, The Physics of Free Electron Lasers, 1999.
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Paper

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MOPWA002

Nonequilibrium Phase Transitions in Crossed-Field Devices

electron, cathode, simulation, injection

74

S. Marini, R. Pakter, F.B. Rizzato
IF-UFRGS, Porto Alegre, Brazil

Funding: This work was partially supported by CNPq and FAPERGS, Brazil, and by the US-AFOSR under the grant FA9550-09-1-0283.
This work presents a fully kinetic description to model the electron flow in the electronic crossed-field configuration observed in a smooth-bore magnetron. Through this model, it has been observed that, according to the electromagnetic field, the injection temperature and the charge density, the electron flow can be classified in two different stationary modes: magnetic insulation mode where most of the electrons returning to the cathode after a transient time and Child-Langmuir mode where most of the electrons reach the anode after a transient time. Focusing on magnetic insulated mode, it has been found that charge density and injection temperature define whether electrons are accelerated (accelerating regime) or decelerated (space-charge limited regime) on the cathode. Besides, when the injection temperature is relatively low (high), a small charge increase causes (does not cause) an abrupt transition between accelerating and space-charge limited regime. Basing on the results, it was possible to identify a critical temperature that separates abrupt and continuous behavior. The results have been verified by using self-consistent computer simulations*.
*S. Marini, F. B. Rizzato, and R. Pakter, Phys. Plasmas 21, 083111 (2014).

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MOPWA003

Optimal Generalized Finite Difference Solution to the Particle-in-Cell Problem

framework, simulation, plasma, factory

77

X. Wang, X. Jiao, H. Liu, V. Samulyak, K. Yu
SBU, Stony Brook, USA
V. Samulyak
BNL, Upton, Long Island, New York, USA

The particle-in-cell (PIC) method is widely used in applications, such as in electromagnetics, but the accuracy of its solutions degrades when the particle distribution is highly non-uniform. In our work, we propose an adaptive PIC method with optimal point distribution and a generalized finite difference (GFD) scheme. Our method replaces the Cartesian grid in the classical PIC with adaptive computational nodes or particles, to which the charges from the sample particles are assigned by a weighted least-square approximations. The partial differential equation is then discretized using a GFD method and solved with fast linear solvers. The density of computational particles is chosen adaptively, so that the error from GFD and that from Monte Carlo integration are balanced and the total error is approximately minimized. We also present the verification results using electrostatic problems and comparison of accuracy and solution time of our method with the classical PIC.

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MOPWA006

Core-Halo Limit as an Indicator of High Intensity Beam Internal Dynamics

emittance, linac, simulation, vacuum

86

P.A.P. Nghiem, N. Chauvin, N. Pichoff, D. Uriot, M. Valette
CEA/DSM/IRFU, France

The dynamics of high-intensity beams is mainly governed by their internal space charge forces. These forces induce emittance growth and halo generation. They contribute to shape the beam density profile. As a consequence, a careful analysis of this profile can help revealing the internal dynamics of the beam. This paper recalls the precise core-halo limit determination proposed earlier *, then studies its behavior through a wide range of beam profiles and finally shows its relevance as an indicator of the limit separating the two specific space charge field regimes of the core and the halo.
* P. A. P. Nghiem et al., Appl. Phys. Lett. 104, 074109 (2014)

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MOPWA008

Status of TraceWin Code

simulation, linac, cavity, diagnostics

92

D. Uriot, N. Pichoff
CEA/DSM/IRFU, France

Well known in the community of high-intensity linear accelerators, the transport code TraceWin * is able to simulate a beam from the source to the target using either simple linear model or multiparticle simulations including 2D or 3D space-charge. Continuously developed at CEA Saclay since 15 years, it is today the reference code for projects such IFMIF, ESS, MYRRHA, SPIRAL2, IPHI … The accuracy of his predictions associated with an original and powerful GUI and its numerous features have made its success, with a community of 200 users worldwide. It is now used on a larger perimeter that its initial skills. The aim of this paper is to summarize the TraceWin capabilities, including implemented last ones.
* http://irfu.cea.fr/Sacm/logiciels/

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MOPWA010

Emittances of the Core and of the Halo

emittance, linac, extraction, simulation

99

M. Valette, P.A.P. Nghiem
CEA/IRFU, Gif-sur-Yvette, France

In high intensity accelerators, the beam is often space charge dominated. The density profile then takes a shape very different from a Gaussian one, with a more or less sharp core and a more or less compact halo. Furthermore, the core and the halo can be differently focused and thus differently oriented in the phase spaces. In these conditions, classically characterizing the beam by a global set of rms values, namely Emittance and Twiss parameters, is no more meaningful. This paper extends the core-halo limit defined ealier in 1D real space * to the 2D phase space, allowing to define for the very first time Emittances and Twiss parameters for the core and the halo separately. Applications to the IFMIF accelerators are given as an example of more appropriate beam characterization for high intensity linacs.
* P. A. P. Nghiem et al., Appl. Phys. Lett. 104, 074109 (2014)

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MOPWA028

Resonance Compensation for High Intensity Bunched Beams

resonance, sextupole, ion, controls

159

G. Franchetti, S. Aumon, F. Kesting, H. Liebermann, C. Omet, D. Ondreka, R. Singh
GSI, Darmstadt, Germany

Mitigation of periodic resonance crossing induced by space charge is foreseen via classic resonance compensation. The effect of the space charge is, however, not obvious on the effectiveness on the compensation scheme. In this proceeding we report on an experimental campaign performed at SIS18 in an attempt to investigate experimentally the effect of space charge on the resonance compensation. The experimental results and their consequences are discussed through numerical simulations.

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MOPWA029

Investigations of the Space-Charge-Limited Emission in the L-Band E-Xfel Photoinjector at Desy-Pitz

simulation, gun, cathode, electron

162

Y. Chen, H. De Gersem, E. Gjonaj, A.V. Tsakanian, T. Weiland
TEMF, TU Darmstadt, Darmstadt, Germany
C. Hernandez-Garcia
JLab, Newport News, Virginia, USA
M. Krasilnikov, F. Stephan
DESY Zeuthen, Zeuthen, Germany

Funding: work supported by DESY Hamburg and Zeuthen Sites
This paper discusses the numerical modelling of electron bunch emission for an L-band normal conducting RF photogun. The main objective is clarifying the discrepancies between measurements and simulations performed for the European X-ray Free Electron Laser (E-XFEL) injector at DESY-PITZ. An iterative beam dynamics simulation procedure is proposed for the calculation of the total extracted bunch charge under the assumption that the emission source operates at the space-charge limit of the gun. This algorithm has been implemented in the three-dimensional full electromagnetic PIC Solver of the CST Particle Studio (CST-PS)*. Simulation results are in good agreements with measurements for a series of operation parameters. Further comparisons with a conventional Poisson-solver-based (PSB) tracking algorithm demonstrates the great significance of transient electromagnetic field effects for the beam dynamics in high brightness electron sources.
* Computer Simulation Technology AG, http://www.cst.com/

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MOPWA043

FEL Simulations with Ocelot

optics, FEL, simulation, electron

210

I.V. Agapov, G. Geloni
XFEL. EU, Hamburg, Germany
M. Dohlus, I. Zagorodnov
DESY, Hamburg, Germany
S.I. Tomin
NRC, Moscow, Russia

Ocelot has been developed as a multiphysics simulation tool for FEL and synchrotron light source studies. In this work we highlight recent code developments focusing on electron tracking in linacs taking into account collective effects and on x-ray optics calculations

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MOPWA055

Study of Emittance Growth Caused by Space Charge and Lattice Induced Resonances

resonance, lattice, emittance, synchrotron

245

K. Ohmi
KEK, Ibaraki, Japan

Resonance strength and resonance width induced by space charge and lattice nonlinearity is discussed with integrals along a ring like the radiation integrals. Emittance growth is evaluated by model with the resonance width to understand the mechanism. The results are compared with fully PIC simulations.

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MOPWA057

Space Charge Simulation and Matching at Low Energy Section of J-PARC Linac

rfq, emittance, simulation, solenoid

251

S. Artikova, T. Morishita
JAEA/J-PARC, Tokai-Mura, Naka-Gun, Ibaraki-Ken, Japan
Y. Kondo
JAEA, Ibaraki-ken, Japan

An intensity upgrade of Japan Proton Accelerator Research Complex (J-PARC) included the installation of a new ion source (IS) and a radio-frequency quadrupole (RFQ) which to be used at first stage of acceleration. The linac is divided into two sections on the basis of operating frequencies and three sections on the basis of family of RF cavities to be used for the acceleration of 50 mA beam of H⁻ ions from 50 keV to 400 MeV. Low energy part of linac consists of an IS, a two-solenoid low energy beam transport (LEBT) and the RFQ. The transition from one section to another can limit the acceptance of the linac if these are not matched properly in both longitudinal and transverse plane. We performed a study to calculate the acceptance of the RFQ at zero current in which space charge effects are not considered. In addition, a particle tracking technique is employed to study the space charge effects in LEBT of the J-PARC linac after the intensity upgrade in order to match the beam to the RFQ. Also, RFQ tank level and intervene voltage calibration factor is determined by comparing the simulation results of the beam transmission with the test measurement of tank level vs. transmission.

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MOPWA061

ADS Injector I Frequency Choice at IHEP

linac, rfq, emittance, proton

265

F. Yan, H. Geng, C. Meng, H.F. Ouyang, S. Pei, Y.L. Zhao
IHEP, Beijing, People's Republic of China

Funding: Chinese Academy of Science (CAS) strategic Priority Research Program-Future Advanced Nuclear Fission Energy (Accelerator-Driven Sub-critical System)
The China ADS driver linac is composed of two major parts: the injector and the main linac. There are two frequency choices for the injector: 325 MHz and 162.5 MHz. The former choice is benefit for the same frequency with the front end of the main linac. For half frequency choice, to obtain the same longitudinal acceptance of the main linac comparing with 325MHz injector, the tune depression of the beam reaches the lower design limit of 0.5, no current upgrade opportunity is reserved; contrarily to get the same space charge effect, 16 more cavities would be the cost to get the same acceptance. However the disadvantage of the 325MHz injector choice is the bigger power density of the copper structure CW RFQ and the smaller longitudinal acceptance of the SC section. The details of the comparing for the two frequency choices are introduced and presented.
*Work supported by Chinese Academy of Science (CAS) strategic Priority Research Program-Future Advanced Nuclear Fission Energy (Accelerator-Driven Sub-critical System)

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MOPWA069

Upgrades on a Scalable Software Package for Large Scale Beam Dynamic Simulations

software, simulation, DTL, solenoid

282

X.T. Dong, K. Du, J. Xu, R. Zhao
IS, Beijing, People's Republic of China
Y. He, Z.J. Wang
IMP/CAS, Lanzhou, People's Republic of China
C. Li, Q. Qin, Y.L. Zhao
IHEP, Beijing, People's Republic of China

Large-scale particle tracking is important for precise design and optimization of the linear accelerator. In this paper a parallel software recently developed for beam dynamics simulation has been benchmarked. The software is based on Particle-In-Cell method, and calculates space charge field by an efficient three-dimension parallel fast Fourier transform method. It uses domain decomposition and MPI library for parallelization. The characteristics of this software are optimized software structure and suitable for modern supercomputers. Several standard accelerating devices have been used to compare the simulation results with other beam dynamics software. They have been run on several different platforms, such as INSPUR cluster at RDCPS, and SHENGTENG7000 at IMPCAS. At first, some simulation results for RFQ with large number of particles will be shown.

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MOPJE020

High Resolution Longitudinal Property Measurement using Emittance Exchange Beam Line

emittance, quadrupole, cavity, collective-effects

320

G. Ha, M.-H. Cho, W. Namkung
POSTECH, Pohang, Kyungbuk, Republic of Korea
W. Gai, G. Ha, K.-J. Kim, J.G. Power
ANL, Argonne, Illinois, USA

Most of longitudinal measurement techniques introduce the transverse-longitudinal correlation because it is very hard to measure the longitudinal properties directly. This correlation is necessary to observe the longitudinal property through the transverse screen, but initial transverse components of the beam restrict the measurement. It is possible to overcome this intrinsic limit using emittance exchange beam line which makes transverse properties at the downstream only depend on longitudinal properties at the upstream. We present the new idea to measure the longitudinal properties using the emittance exchange beam line and preliminary simulation results.

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MOPJE030

Non-linear Dynamics model for the ESS Linac Simulator

octupole, linac, sextupole, proton

345

E. Laface
ESS, Lund, Sweden

The ESS Proton Linac will run a beam with 62.5 mA of current. In the first meters of the accelerator, the non- linear space-charge force dominates the dynamics of the beam. The Drift Tube Linac, the Spoke resonators and the elliptical cavities, which are responsible for the 99.8% of the total energy gained by the beam along the accelerator, produce a significant longitudinal non-linear force on the proton beam. In this paper, we introduce a new theory to transport the probability density function of the beam under the effect of non-linear forces. A model based on this theory can be implemented in the ESS Linac Simulator for the fast simulations to be performed during the operations of the proton Linac.

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MOPJE031

Field Map Model for the ESS Linac Simulator

cavity, linac, proton, framework

348

E. Laface
ESS, Lund, Sweden
I. List
Cosylab, Ljubljana, Slovenia

The proton beam driving the spallation process at the European Spallation Source, in Lund, will be accelerated and delivered onto a tungsten target by a linac. This linac is composed of four different families of accelerating structures: adrift tube linac, a section of spoke resonators and two sections of elliptical cavities for the particles’ medium and high relativistic β. These structures provide 99.8% of the total energy gained by the beam along the accelerator. It is necessary, then, to have an accurate model describing the physics of the cavities in the ESS Linac Simulator (ELS), which isthe online model that will simulate the accelerator during operation. Here, we present an RF-cavity model based on the field maps that we implemented in ELS, showing a maximum 10% deviation from TraceWin in the horizontal, vertical and longitudinal planes.

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MOPJE042

Longitudinal Injection Schemes For the CERN PS Booster at 160 MeV Including Space Charge Effects

injection, linac, simulation, emittance

378

V. Forte, E. Benedetto, A.M. Lombardi, D. Quartullo
CERN, Geneva, Switzerland

In the frame of the LHC Injectors Upgrade project, the CERN PS Booster will be equipped with a H⁻ injection system at 160 MeV to tailor the initial transverse and longitudinal profiles. We are here reviewing the different multi-turn longitudinal injection schemes, from the beam dynamics point of view, taking into account the needs of the large variety of the PSB users, spanning in intensity from 5·10⁹ to about 1.6·10¹³ protons per bunch. The baseline of the longitudinal injection has always been the longitudinal stacking with central energy modulation: this scheme has the advantage of filling uniformly the RF bucket and mitigate transverse space charge, but it requires at least 40 turns of injection. A simpler injection protocol without energy modulation is here analyzed in detail to find the optimum initial conditions in terms of bucket filling and reduction of transverse and longitudinal space charge effects, with the advantage of minimizing the number of turns for the LHC beams. Simulations with space charge of the longitudinal injection process from different Linac4 trains are presented to fix possible longitudinal injection scenarios during the future commissioning and operation with Linac4.

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MOPJE045

Fixed Points in Presence of Space Charge in Circular Particle Accelerators

vacuum, simulation, extraction, resonance

389

M. Giovannozzi, S.S. Gilardoni, A. Huschauer
CERN, Geneva, Switzerland
S. Machida, C.R. Prior, S.L. Sheehy
STFC/RAL/ASTeC, Chilton, Didcot, Oxon, United Kingdom

Recent measurements performed in the framework of the multi-turn extraction (MTE) studies showed a dependence of the position of beamlets obtained by crossing a stable transverse resonance on the total beam intensity. This novel observation has triggered a number of studies aiming at understanding the source of the observed effect. In this paper the results of numerical simulations performed in different conditions are discussed in detail.

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MOPJE047

Chromaticity Dependence of the Transverse Effective Impedance in the CERN Proton Synchrotron

impedance, proton, synchrotron, controls

395

S. Persichelli, N. Biancacci, S.S. Gilardoni, A. Huschauer, E. Métral, B. Salvant, R. Wasef
CERN, Geneva, Switzerland
M. Migliorati
University of Rome La Sapienza, Rome, Italy

The current knowledge of the transverse impedance of the Proton Synchrotron (PS) has been established with beam-based measurements at different energies. The transverse coherent tune shift as a function of the beam intensity has been measured in order to evaluate the total effective imaginary part of the transverse impedance and its localization in the accelerator at the energies of 2, 7, 13 and 25 GeV. Measurements have been performed changing the chromaticity for every tune shift scan with intensity. The data analysis revealed an increase of impedance with chromaticity for all the energies considered. That transverse impedance can be compared with the previously evaluated theoretical impedance budget taking into account the individual contribution of several machine devices. The missing impedance is finally highlighted.

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MOPJE050

Transverse Impedance Model of the CERN-PSB

impedance, kicker, simulation, vacuum

406

C. Zannini, G. Iadarola, K.S.B. Li, T.L. Rijoff, G. Rumolo
CERN, Geneva, Switzerland
B. Jones
STFC/RAL/ISIS, Chilton, Didcot, Oxon, United Kingdom
T.L. Rijoff
TU Darmstadt, Darmstadt, Germany

In the framework of the PS-Booster upgrade project an accurate impedance model is needed in order to determine the effect on the beam stability and assess the impact of the new devices before installation in the machine. This paper describes the PSB impedance model which includes resistive wall, indirect space charge, flanges, step transitions, ejection kicker including cables, injection kickers and cavities. Each impedance contribution has been computed for different energies in the PSB cycle. Measurements of the coherent tune shifts have been performed and compared to calculations based on the impedance model.

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MOPJE075

Tracking Through Analytic Quadrupole Fringe Fields With GPT

quadrupole, simulation, interface, multipole

489

S.B. van der Geer, M.J. de Loos
Pulsar Physics, Eindhoven, The Netherlands
B.D. Muratori
STFC/DL/ASTeC, Daresbury, Warrington, Cheshire, United Kingdom

In the early design stages it is customary to work with a highly simplified analytic model to describe the beam line. Dipoles and quadrupoles are often based on hard-edged approximations. This is not only unrealistic, it also significantly slows down time-domain spacecharge tracking codes such as the General Particle Tracer (GPT) code. The underlying reason for the poor performance is that despite the fact that the simple hard-edged field equations are fast to evaluate, they force the integration process to use excessively small step sizes near the fields discontinuities in order to achieve the desired accuracy. In other worlds, the apparently simple equations turn out to be the most difficult ones to evaluate numerically. An obvious solution is to switch to field-maps, but this is not practical in the early design stages. In this contribution we show a new solution implemented in the GPT code based on analytical expressions for the fringes where the transverse size of the magnet is properly taken into account. In addition to producing more realistic results, the smooth fields increase tracking speed by over an order of magnitude for typical test cases.

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MOPMA017

Numerical simulations of transverse modes in Gaussian bunches with space charge

damping, simulation, lattice, synchrotron

575

A. Macridin, J.F. Amundson, E.G. Stern
Fermilab, Batavia, Illinois, USA

The transverse modes and the intrinsic Landau damping in Gaussian bunched beams with space charge are numerically investigated. The evolution of the phase space density is calculated with the Synergia accelerator modeling package and analyzed with Dynamic Mode Decomposition (DMD) method. DMD is a relatively new technique used to calculate mode dynamics in both linear and nonlinear systems. The properties of the first three space charge modes, including their shape, damping rates and tune shifts are calculated over the entire range of the space charge interaction.

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MOPMA019

Simulations of the Fermilab Recycler for Losses and Collimation

simulation, collimation, proton, target

582

E.G. Stern, R. Ainsworth, J.F. Amundson, B.C. Brown
Fermilab, Batavia, Illinois, USA

Fermilab has recently completed an upgrade to the com- plex with the goal of delivering 700 kW of beam power as 120 GeV protons to the NuMI target. A major part of boost- ing beam power is to shorten the beam cycle by accumulating up to 12 bunches of 0.5 × 10 11 protons in the Recycler ring through slip-stacking during the Main Injector ramp. This introduces much higher intensities into the Recycler than it has had before. Meeting radiation safety requirements with high intensity operations requires understanding the ef- fects of space charge induced tune spreads and resulting halo formation, and aperture restrictions in the real machine to de- velop a collimation strategy. We report on initial simulations of slip-stacking in the Recycler performed with Synergia.

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MOPMA024

A Parallel Particle-Particle, Particle-Mesh Solver for Studying Coulomb Collisions in the Code IMPACT-T

emittance, electron, simulation, plasma

593

C.E. Mitchell, J. Qiang
LBNL, Berkeley, California, USA

Funding: This work is supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231.
In intense charged-particle beams, the presence of Coulomb collisions can result in growth of the beam slice energy spread and emittance that cannot be captured correctly using traditional particle-in-cell codes. Particle-particle, particle-mesh solvers take a hybrid approach, combining features of N-body and particle-in-cell solvers, to correctly capture the effect of short-range particle interactions with less computing time than direct N-body solvers. We describe the implementation and benchmarking of such a solver in the code IMPACT-T for beam dynamics applications.

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MOPMA030

Multisymplectic Integrators for Accelerator Tracking Codes

plasma, simulation, storage-ring, DTL

614

S.D. Webb, D.L. Bruhwiler
RadiaSoft LLC, Boulder, Colorado, USA

It has been long understood that long time single particle tracking requires symplectic integrators to keep the simulations stable. In contrast, space charge has been added to tracking codes without much regard for this. Indeed, multisymplectic integrators are a promising new field which may lead to more stable and accurate simulations of intense beams. We present here the basic concept, through a spectral electrostatic field solve which is suitable for adapting into existing tracking codes. We also discuss the limitations of current algorithms, and suggest directions for future development for the next generations of high intensity accelerators.

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MOPMA037

Electron Cloud Buildup and Dissipation Models For PIP-II

electron, simulation, plasma, proton

626

S.A. Veitzer, P. Stoltz
Tech-X, Boulder, Colorado, USA

Funding: This work was performed under the auspices of the Department of Energy as part of the ComPASS SCiDAC-2 project (DE-FC02-07ER41499), and the SCiDAC-3 project (DE-SC0008920).
Buildup of electron plasmas in accelerator cavities can cause beam degradation and limit performance in high-intensity circular particle accelerators. This is especially important in machines such as the LHC, and PIP-II, where mitigation techniques such as beam scrubbing in order to decrease the SEY are expensive and time consuming. Modeling of electron cloud buildup and dissipation can provide understanding as to the potential negative effects of electron clouds on beam properties, as well as estimates of the mitigation required to maintain accelerator performance and beam quality as accelerators move to higher intensity configurations. We report here on simulations of electron cloud buildup and dissipation for geometry, beam and magnetic field configurations describing the Recycler at Fermilab. We perform electrostatic simulations in 3D with VSim PIC, including the effects of space charge and secondary electrons. We quantify the expected survival rate of electrons in these conditions, and argue that improvements in reducing the SEY is unlikely to mitigate the electron cloud effects.

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MOPMA040

Analysis of Beam Transverse Instabilities at Fermilab

dipole, coupling, impedance, quadrupole

633

T. Zolkin
University of Chicago, Chicago, Illinois, USA

The transverse beam dynamics in Fermilab Recycler ring has been analyzed using SCHARGEV Vlasov solver. In the first part of paper we discuss how SCHARGEV analyses collective instabilities for Gaussian bunch with strong space charge in resistive impedance environment. In the second part the bunched beam dynamics is studied depending on head-tail phase and damper gain. An example for Fermilab Recycler is presented.

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MOPMA041

Experimental Observation of Head-Tail Modes for Fermilab Booster

booster, linac, dipole, betatron

636

T. Zolkin
University of Chicago, Chicago, Illinois, USA
A.V. Burov, V.A. Lebedev
Fermilab, Batavia, Illinois, USA

The Fermilab Booster is known to suffer from beam transverse instabilities. An experimental attempt of head-tail modes extraction from the stable beam motion by periodic excitement of betatron motion has been performed. The shapes of head-tail modes have been successfully obtained while eigenfrequencies separation from the betatron tune were too small to be resolved. The qualitative agreement between the theory and an experimental data has been demonstrated. This is an important step towards the understanding of general theory of collective instabilities for strong space charge case, which is a rather typical case for hadron machines.

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MOPMA043

Longitudinal Bunch Shaping at Picosecond Scales using Alpha-BBO Crystals at the Advanced Superconducting Test Accelerator

gun, electron, laser, linac

643

B. Beaudoin
UMD, College Park, Maryland, USA
D.R. Edstrom, A.H. Lumpkin, J. Ruan, J.C.T. Thangaraj
Fermilab, Batavia, Illinois, USA

Funding: This works is supported by the University Research Association, Inc. Operated by the Fermi Research Alliance, LLC under Contract No. DE-AC02-07CH11359 with the United States Department of Energy
The Integrable Optics Test Accelerator (IOTA) electron injector at Fermilab will enable a broad range of experiments at a national laboratory in order to study and develop solutions to the limitations that prevent the propagation of high intensity beams at picosecond lengths. One of the most significant complications towards increasing short-beam intensity is space-charge, especially in the vicinity of the gun. A few applications that require a longitudinally shaped electron beam at high intensities are for, the generation of THz waves and dielectric wakefields, each of which will encounter the effects of longitudinal space-charge. This paper investigates the effects of longitudinal space-charge on alpha-BBO UV laser shaped electron bunches in the vicinity of the 1½cell 1.3 GHz cylindrically symmetric RF photocathode gun.

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MOPMA044

Barrier Shock Compression with Longitudinal Space Charge

simulation, emittance, electron, plasma

646

B. Beaudoin, I. Haber, R.A. Kishek
UMD, College Park, Maryland, USA

Funding: This work is supported by the US Dept. of Energy, Office of High Energy Physics.
Synchrotrons and storage rings routinely employ RF barrier buckets as a means of accumulating charge to increase the peak intensity and preserve longitudinal emittance while minimizing emittance growth [1-3]. This was shown in the main injector and recycler at Fermilab as well as the SIS-18 at GSI Helmholtz center for heavy ion research. The RF cavities typically used are ferrite loaded magnetic alloys with low Q to maximize bandwidth and generate single pulses, either as delta functions, triangular or half/full period sine waves. The University of Maryland Electron Ring (UMER) group is studying a novel scheme of bunch compression in the presence of longitudinal space charge. It has been analytically shown through 1-D computations that the presence of space-charge considerably improves the efficiency of the barrier compression by taking advantage of the shock-front that launches when the barrier moves into a space-charge dominated beam. In this paper, we summarize the initial results of the study.

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MOPMA045

Conceptual Difficulties of a Thermodynamics Description of Charged-Particle Beams

emittance, simulation, focusing, beam-transport

649

S. Bernal
UMD, College Park, Maryland, USA

Funding: This work is funded by the US Dept. of Energy
We review the existing phenomenological theories of emittance growth with and without entropy terms and re-examine the condition for thermal equipartitioning in an unbunched charged-particle beam. The model incorporates linear space charge and a uniform-focusing lattice. Because of non-extensitivity of the transverse ("thermal") energy and the absence of a classical heat bath, we conclude that a rigorous classical thermodynamics treatment of charged-particle beams is not possible. In particular, the postulated relationships between the rms emittance and temperature and entropy must be qualified.

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MOPMA046

Simulations and experiments in Support of Octupole Lattice Studies at the University of Maryland Electron Ring

lattice, octupole, electron, quadrupole

653

K.J. Ruisard, B. Beaudoin, I. Haber, T.W. Koeth
UMD, College Park, Maryland, USA

Funding: This material is based on work supported by the NSF Graduate Research Fellowship and the NSF Accelerator Science Program
We present plans for a nonlinear lattice at the University of Maryland Electron Ring (UMER). Theory predicts that a strong nonlinear lattice can limit resonant behavior without reducing dynamic aperture if the nonlinear fields preserve integrability or quasi-integrability. We discuss plans for a quasi-integrable octupole lattice, based on the work of Danilov and Nagaitsev.* We use Elegant and the WARP PIC code to estimate the octupole-induced tune spread. We discuss improvements to the ring in support of octupole lattice experiments, including generation and detection of emittance-dominated, negligible space charge beams.
* V. Danilov, S. Nagaitsev, Phys. Rev. STAB 13, 084002 (2010).

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MOPMA050

Smooth Fast Multipole Method for Space Charge Tracking: An Alternate to Particle-In-Cell

multipole, simulation, framework, emittance

663

A.J. Gee, B. Erdelyi
Northern Illinois University, DeKalb, Illinois, USA
B. Erdelyi
ANL, Argonne, USA

The fast multipole method (FMM) algorithm was developed by Greengard and Rokhlin in 1987 *. As one of the top ten algorithms of the 20th century, it has been applied in a wide range of fields. The FMM complexity is O(N), where N is the number of articles, allowing for large-scale simulations. However, it includes all the two-body collisional forces, in contrast to other methods such as the popular particle in-cell (PIC) methods. While collisionality can be very important, many applications require only the mean field effects. PIC is frequently used in this regime. Due to recent concerns of unphysical effects of grids, interpolation and other approximations in PIC codes, an alternative based on different underlying assumptions would prove enlightening. For these cases, a smoothed or softened FMM using a Plummer-like smoothing parameter holds much promise. Unfortunately, the original FMM based on analytic expansions of the 1/r-like potentials does not allow for Plummer softening. We present our new soft-FMM employing differential algebras (DA) to obtain the modified expansions. We also compare the performance of the smoothed DA-FMM with examples from PIC simulations.
* L. Greengard and V. Rokhlin. “A fast algorithm for particle simulations".

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MOPMA051

Generation of Modulated Bunch Using a Masked Chicane for Beam-Driven Acceleration Experiments at ASTA

simulation, bunching, dipole, emittance

666

Y.-M. Shin, P. Piot
Northern Illinois University, DeKalb, Illinois, USA
D.R. Broemmelsiek, D.J. Crawford, A.H. Lumpkin
Fermilab, Batavia, Illinois, USA
A.T. Green
Northern Illinois Univerity, Dekalb, Illinois, USA

Funding: This work was supported by the DOE contract No. DEAC02-07CH11359 to the Fermi Research Alliance LLC.
Longitudinal density modulations on electron beams can improve machine performance of beam-driven accelerators and FELs with resonance beam-wave coupling *. The sub-ps beam modulation has been studied with a masked chicane ** *** by the analytic model and simulations with the beam parameters of the Advanced Superconducting Test Accelerator (ASTA) in Fermilab. With the nominal 50 MeV chicane parameters and 3 ps bunch length, the analytic model showed that a slit-mask with slit period 900 um and aperture width 300 μm generates about 100-um modulation periodicity with 2.4% correlated energy spread. With the designed slit mask and a 3 ps bunch, particle-in-cell simulations (CST-PS), including nonlinear energy distributions, space charge force, and coherent synchrotron radiation (CSR) effect, also result in ~ 100 um of longitudinal modulation. The beam modulation has been extensively examined with three different beam conditions, 0.25, 1 , and 3.2 nC, by extended 3D tracking simulations (Elegant). The modulated bunch generation will be tested by a slit-mask installed at the chicane of the ASTA 50-MeV-injector beamline for beam-driven acceleration experiments.
* E. Kallos, Southern California 2008
** D. C. Nguyen, B. E. Carlston, NIMA 375, 597 (1996)
*** P. Muggli, V. Yakimenko, M. Babzien, E. Kallos, and K. P. Kusche, PRL 101, 054801 (2008)

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MOPMA057

Space Charge Neutralization of 750 keV Proton Beam in LANSCE Injector Line

emittance, simulation, proton, beam-transport

685

Y.K. Batygin
LANL, Los Alamos, New Mexico, USA

Funding: Work supported by the United States Department of Energy, National Nuclear Security Agency, under contract DE-AC52-06NA25396
The 750-keV low-energy beam transport of the Los Alamos Neutron Science Center (LANSCE) linac consists of two independent beam lines for simultaneous injection of H⁺ and H⁻ beams into the linear accelerator. Space charge effects play an important role in the beam transport therein. A series of experiments were performed to determine the level of proton beam space charge neutralization by residual gas ionization, and time required for neutralization. Study was performed as emittance scans between pair of emittance measurement stations. The value of compensated space charge was determined through comparison of results of measurements and simulations using macroparticle method and envelope code. Obtained results provide new setup for beam tuning in transport beamline.

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MOPMA058

Effect of Spherical Aberration on Beam Emittance Growth

emittance, focusing, proton, simulation

688

Y.K. Batygin
LANL, Los Alamos, New Mexico, USA

Funding: Work supported by the United States Department of Energy, National Nuclear Security Agency, under contract DE-AC52-06NA25396
Spherical aberration in axial-symmetric magnetic focusing lenses results in S-shape figure of beam emittance. Filamentation of beam emittance in phase space is a fundamental property of a beam affected by aberrations. Analytical expression for effective beam emittance growth due to spherical aberration as a function of lens aberraion coefficient, initial beam emittance, beam radius, and focal lens of the focusing lens is obtained. Analysis is extended for beam space charge aberrations. Analytical results are confirmed by numerical calculations.

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MOPMN004

CSR Impedance for Non-Ultrarelativistic Beams

impedance, wakefield, radiation, synchrotron

709

R. Li
JLab, Newport News, Virginia, USA
C.-Y. Tsai
Virginia Polytechnic Institute and State University, Blacksburg, Virginia, USA

Funding: This work is supported by Jefferson Science Associates, LLC under U.S. DOE Contract No. DE-AC05-06OR23177.
For the analysis of the coherent synchrotron radiation (CSR) induced microbunching gain in the low energy regime, such as when a high-brightness electron beam is transported through a low-energy merger in an energy-recovery linac (ERL) design, it is necessary to extend the CSR impedance expression in the ultrarelativistic limit to the non-ultrarelativistic regime. This paper presents our analysis of CSR impedance for general beam energies.

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MOPMN008

Space Charge Studies in FFAG Using the Tracking Code Zgoubi

emittance, simulation, betatron, damping

717

M. Haj Tahar, F. Méot, N. Tsoupas
BNL, Upton, Long Island, New York, USA

Funding: Work supported by Brookhaven Science Associates, LLC under Contract No. DE-AC02-98CH10886 with the U.S. Department of Energy.
A method is implemented in Zgoubi that allows the computation of space charge effects in 2D distributions and with some restrictions in 3D distributions. It relies on decomposiing field maps or analytical elements into slices and applying a space charge kick to the particles. The aim of this study is to investigate the accuracy of this technique, its limitations/advantages by comparisons with other linear/nonlinear computation methods and codes, and to apply it to high power fixed field ring design studies.

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MOPMN019

Understanding the Effect of Space Charge on Instabilities

synchrotron, impedance, hadron, operation

743

M. Blaskiewicz
BNL, Upton, Long Island, New York, USA
A. Chao
SLAC, Menlo Park, California, USA
Y.H. Chin
KEK, Ibaraki, Japan

Funding: Work supported by Brookhaven Science Associates, LLC under Contract No. DE-AC02-98CH10886 with the U.S. Department of Energy.
The combined effects of space charge and wall impedance on transverse instabilities is an important consideration in the design and operation of hadron machines as well as an intrinsic academic interest. This study explores the combined effects of space charge and wall impedance using various simplified models in an attempt to produce a better understanding of their interplay.

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MOPHA007

Modeling/Measurement Comparison of Signal Collection in Diamond Sensors in Extreme Conditions

electron, detector, simulation, scattering

787

V. Kubytskyi, P. Bambade, S. Liu
LAL, Orsay, France

Here we present a study of charge collection dynamics in a Diamond Sensor (DS) subjected to intensities from 1 to 10⁸ Minimum Ionizing Particles (MIP). We developed a model based on the numerical solution of the 1D drift-diffusion equations, using the Scharfetter-Gummel discretization scheme. Inhomogeneity of the space-charge distribution together with the externally applied electric field are taken into account by analytically solving the Poisson equation at each time step. We identified two regimes of charge collection. The first corresponds to 1-10⁵ MIPs, in this case the externally applied electric field is negligibly perturbed by space-charge effects during the separation of the electron/hole clouds. The second corresponds to intensities larger than 10⁷ MIPs, where the space-charge effects significantly slow down the charge collection due to large concentrations of electron/hole pairs in the DS volume. The results of our modeling are in qualitative agreement with the experimental data acquired at the PHoto-Injector electron beam facility at LAL. Our model allows optimizing DS parameters to achieve desired charge collection times for different beam intensities.

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MOPTY015

Beam Compression Dynamics and Associated Measurement Methods in Superconducting THz Source

controls, simulation, gun, electron

969

Z. Zhou, Y.-C. Du, W.-H. Huang
TUB, Beijing, People's Republic of China

To ensure the quality of high brightness electron beams needed by the terahertz FEL facility at China academy of engineering physics(CAEP), which aims to obtain 100 to 300 terahertz light, a feed-back control system is required to monitor the amplitude and phase jittering by measuring beam arrival time as well as bunch length at the site of the beam position monitor(BPM). In this paper, we make an idealized model of injector section and deduce analytic expressions of bunch arrival time and bunch length. In consideration of the space charge effect on bunch lengthening, bunch arrival time and bunch length as a function of DC gun voltage, buncher field amplitude and buncher phase is carefully calibrated by means of particle in cell (PIC) simulation. With the time and space resolution of the BPM, the control accuracy of phase is estimated to be 0.01 degree, while the amplitude is 0.04%.

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MOPWI005

Emittance and Optics Measurements on the Versatile Electron Linear Accelerator at Daresbury Laboratory

quadrupole, emittance, gun, coupling

1153

C.P. Topping, D.J. Scott, A. Wolski
Cockcroft Institute, Warrington, Cheshire, United Kingdom
S.D. Barrett, C.P. Topping, A. Wolski
The University of Liverpool, Liverpool, United Kingdom
B.L. Militsyn, D.J. Scott
STFC/DL/ASTeC, Daresbury, Warrington, Cheshire, United Kingdom

The Versatile Electron Linear Accelerator (VELA) is a facility designed to provide a high quality electron beam for accelerator systems development, as well as industrial and scientific applications. Currently, the RF gun can deliver short (of order a few ps) bunches with charge in excess of 250 pC at up to 5.0 MeV/c beam momentum. Measurement of the beam emittance and optics in the section immediately following the gun is a key step in tuning both the gun and the downstream beamlines for optimum beam quality. We report the results of measurements (taking account of coupling and space charge) indicating normalised emittances of order 0.5 μm at low bunch charge.

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MOPWI024

Accelerator Online Simulation Platform

database, simulation, lattice, software

1204

C.P. Chu, Y. Zhang
FRIB, East Lansing, Michigan, USA

Funding: This material is based upon work supported by the U.S. Department of Energy Office of Science under Cooperative Agreement DE-SC0000661, the State of Michigan and Michigan State University.
A platform for accelerator online beam simulation has been established for Facility for Rare Isotope Beams (FRIB). This modeling platform supports multiple simulation codes for different sections of the complex machine which cannot be properly modeled with a single online simulation tool. Model data for the platform is stored in a relational database which is designed to accommodate most simulation data. The stored data is accessible with physics intuitive data API (Application Programming Interface). Presently, the platform is supporting Open XAL, MAD-X and IMPACT simulation codes. In addition to the model data storage and access, tools such as data comparison and simple graphing capability are also included in the platform.

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TUAB3

Chromaticity Effects for Space Charge Dominated Beams in the CERN PS Booster

resonance, simulation, emittance, sextupole

1335

V. Forte
Université Blaise Pascal, Clermont-Ferrand, France
E. Benedetto, F. Schmidt
CERN, Geneva, Switzerland

In view of the LHC Injectors Upgrade (LIU) project, an extensive campaign is on-going in the CERN PS Booster (PSB) to study collective effects for the future operation with the 160 MeV injection from Linac4. In operation, the machine is running with uncorrected natural chromaticity. This paper focuses on the study of the effects of chromaticity on losses and beam blow-up.

Slides TUAB3 [4.887 MB]

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TUPWA008

Mixing and Space-Charge Effects In Free-Electron Lasers

laser, electron, FEL, radiation

1410

E.A. Peter, A. Endler, F.B. Rizzato
IF-UFRGS, Porto Alegre, Brazil
A.P.B. Serbeto
UFF, Niterói - RJ, Brazil

Funding: This work was supported by CNPq and FAPERGS, Brazil, and by the Air Force Office of Scientific Research (AFOSR), USA, under the Grant No. FA9550-12-1-0438
Free-electron lasers are devices which efficiently convert the kinetic energy from a relativistic electron beam into electromagnetic radiation, amplifying an initial small sign. The present work revisits the subject of mixing, saturation and space-charge effects in free-electron lasers. Use is made of the compressibility factor, which proves to be a helpful tool in the related systems of charged beams confined by static magnetic fields. The compressibility allows to build a semi-analytical model and to perform analytical estimates of the elapsed time until the onset of mixing, which in turn allows to estimate the saturated amplitude of the radiation field. In addition, the compressibility helps to pinpoint space-charge effects and the corresponding transition from Compton to Raman regimes. The semi-analytical model and the particles simulations are compared, exhibiting a good agreement.*
* E. Peter, A. Endler, F. B. Rizzato, and A. Serbeto, Phys. Plasmas 20,
123104 (2013).
** E. Peter, A. Endler, and F. B. Rizzato, Phys. Plasmas 21, 113104 (2014)

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TUPWA045

Further Investigations on the MESA injector

coupling, linac, simulation, experiment

1515

R.G. Heine, K. Aulenbacher, S. Friederich, C. Matejcek, F. Schlander
IKP, Mainz, Germany

Funding: work supported by the German Federal Ministery of Education and Research under the Cluster of Excellence "PRISMA"
The MESA ERL to be build at Mainz in the next years is a multi turn recirculating linac with beam currents of up to 10 mA. The dynamic range of the beam currents demanded by the experiments is of at least two orders of magnitude. This is a special challenge for the layout design of an injector. In this paper we present the current status of the design of the injector linac called MAMBO (MilliAMpereBOoster).

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TUPWA067

Status of Higher Bunch Charge Operation in Compact ERL

operation, optics, recirculation, emittance

1583

T. Miyajima, K. Harada, Y. Honda, T. Miura, N. Nakamura, T. Obina, F. Qiu, H. Sakai, S. Sakanaka, M. Shimada, R. Takai, K. Umemori, M. Yamamoto
KEK, Ibaraki, Japan
R. Hajima, R. Nagai, N. Nishimori
JAEA, Ibaraki-ken, Japan
D. Lee
KNU, Deagu, Republic of Korea

In the KEK compact ERL (cERL), machine studies toward higher bunch charge operation is one of the most important issues. From January 2015 to April 2015, we carried out a higher bunch charge operation with an bunch charge of 0.5 pC for the experiment of laser compton scattering. After the study of space charge effect and optics tuning, we succeeded in the recirculation operation with the emittance, which was close to the design value. Moreover, a test operation in the injector section with the bunch charge of 7.7 pC was carried out as a preparation toward the recirculation operation with the average current of 10 mA.

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TUPJE041

Progress on a Compact Accelerator Design for a Compton Light Source

gun, dipole, linac, solenoid

1706

K.E. Deitrick, J.R. Delayen, B.R.P. Gamage, G.A. Krafft, T. Satogata
ODU, Norfolk, Virginia, USA

A compact Compton light source using an electron linear accelerator is in design at the Center for Accelerator Science at Old Dominion University and Jefferson Lab. We report on the current design, including beam properties through the entire system based on a full end-to-end simulation, compare current specifications to design goals, and target areas for improvement.

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TUPJE059

Modeling of an Electron Injector for the AWAKE Project

emittance, booster, quadrupole, linac

1762

Ö. Mete, G.X. Xia
UMAN, Manchester, United Kingdom
R. Apsimon, G. Burt
Cockcroft Institute, Lancaster University, Lancaster, United Kingdom
S. Döbert
CERN, Geneva, Switzerland
R.B. Fiorito
The University of Liverpool, Liverpool, United Kingdom
C.P. Welsch
Cockcroft Institute, Warrington, Cheshire, United Kingdom

Funding: Cockcroft Institute Core Grant
Particle in cell simulations were performed to characterise an electron injector for AWAKE project in order to provide a tuneable electron beam within a range of specifications required by the plasma wakefield experiments. Tolerances and errors were investigated. These results are presented in this paper alongside with the investigation regarding the beam dynamics implications of the 3GHz travelling wave structure developed for the injector.

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TUPMA003

Microbunching Phenomena in LCLS-II

laser, bunching, simulation, undulator

1843

M. Venturini, C. F. Papadopoulos, J. Qiang
LBNL, Berkeley, California, USA
Y. Ding, P. Emma, Z. Huang, G. Marcus, A. Marinelli, Y. Nosochkov, T.O. Raubenheimer, L. Wang, M. Woodley
SLAC, Menlo Park, California, USA

Funding: Work supported by DOE, in part under Contract No. DE-AC02-05CH11231 and through the LCLS-II project.
The microbunching instability has long been recognized as a potential limiting factor to the performance of X-ray FELs. It is of particular relevance in LCLS-II due, in part, to a layout that includes a long bypass beamline between the Linac and the undulators. Here we focus on two aspects of the instability that highlight the importance of 3D effects.

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TUPMA007

Numerical Investigation of a Cascaded Longitudinal Space-Charge Amplifier at the Fermilab's Advanced Superconducting Test Accelerator

radiation, bunching, simulation, impedance

1850

A. Halavanau, P. Piot
Northern Illinois University, DeKalb, Illinois, USA
P. Piot
Fermilab, Batavia, Illinois, USA

In a cascaded longitudinal space-charge amplifier (LSCA), initial density noise in a relativistic e-beam is amplified via the interplay of longitudinal space charge forces and properly located dispersive sections. This type of amplification process was shown to potentially result in large final density modulations * compatible with the production of broadband electromagnetic radiation. The technique was recently demonstrated in the optical domain **. In this paper we investigate, via numerical simulations, the performances of a cascaded LSCA beamline at the Fermilab's Advanced Superconducting Test Accelerator (ASTA). We especially explore the properties of the produced broadband radiation. Our studies have been conducted with an effective three-dimensional space-charge algorithm.
* Dohlus, M. et al. Proc. SPIE 8779. doi:10.1117/12.2017369
** Marinelli, A. et al. Phys. Rev. Lett. 110, 264802 (2013)

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TUPMA008

Numerical Study of Three Dimensional Effects in Longitudinal Space-Charge Impedance

impedance, simulation, detector, radiation

1853

A. Halavanau, P. Piot
Northern Illinois University, DeKalb, Illinois, USA
P. Piot
Fermilab, Batavia, Illinois, USA

Longitudinal space-charge (LSC) effects are generally considered as detrimental in free-electron lasers as they can seed instabilities. Such "microbunching instabilities" were recently shown to be potentially useful to support the generation of broadband coherent radiation pulses. Therefore there has been an increasing interest in devising accelerator beamlines capable of sustaining this LSC instability as a mechanism to produce a coherent light source. To date most of these studies have been carried out with a one-dimensional impedance model for the LSC. In this paper we use a N-body "Barnes-Hut" algorithm * to simulate the 3D space charge force in the beam combined with Elegant ** and explore the limitation of the 1D model often used.
* Barnes, J. & Hut, P., Nature 324, 446-449, 1986.
** Borland, M., Advanced Photon Source LS-287, 2000.

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TUPTY074

Muon Beam Emittance Evolution in the Helical Ionization Cooling Channel for Bright Muon Sources

plasma, emittance, collider, simulation

2203

K. Yonehara, C.Y. Yoshikawa
Fermilab, Batavia, Illinois, USA
C.M. Ankenbrandt, R.P. Johnson, S.A. Kahn
Muons, Inc, Illinois, USA
M. Chung
UNIST, Ulsan, Republic of Korea
Y.S. Derbenev, A.V. Sy
JLab, Newport News, Virginia, USA
B.T. Freemire
IIT, Chicago, Illinois, USA

The six-dimensional ionization cooling is essential to design a bright muon source. A geometry constraint is a challenge issue in a compact helical cooling channel (HCC). Especially, the HCC requires a large bore helical magnet and a compact helical RF system to incorporate the RF into the magnet chamber. A new emittance evolution has been designed to mitigate the geometry constraint. The HCC was functionally separated into three parts sections. The lattice at the initial section provides a large transverse acceptance by using a strong helical focus magnet. Once the transverse beam size is small enough to get into the compact RF the HCC lattice in the middle section generates a large longitudinal beta tune to dominate the longitudinal cooling. Consequently, the longitudinal emittance becomes smaller than the transverse one at the end of middle section. In the final section, the magnetic field strength is gradually reduced to match out the helical channel to the straight solenoid. As a result, the emittance exchange takes place and the final transverse emittance becomes smaller than the longitudinal one. The new emittance evolution scenario will be discussed in this presentation.

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TUPTY078

Fixed-energy Cooling and Stacking for an Electron Ion Collider

electron, ion, ECR, collider

2214

P.M. McIntyre, S. Assadi, J. Gerity, A. Sattarov
Texas A&M University, College Station, Texas, USA

The proposed designs for polarized-beam electron-ion colliders require cooling of the ion beam to achieve and sustain high luminosity. One attractive approach is to make a fixed-energy storage ring in which ions are con-tinuously cooled and stacked during a collider store, then transferred to the collider and accelerated for a new store when the luminosity decreases. An example design is reported for a 6 GeV/u superferric storage ring, and for a d.c. electron cooling system in which electron space charge is fully neutralized so that high-current magnetized e-cooling can be used to best advantage.

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WEYB1

Benchmarking and Application of Space Charge Codes for Rings

simulation, resonance, lattice, experiment

2402

S. Machida
STFC/RAL/ASTeC, Chilton, Didcot, Oxon, United Kingdom

This presentation should present an overview of efforts for benchmarking and application of space charge codes for rings. After briefly recalling the historical background of the simulation efforts of space charge effects in rings, we will overview the present benchmarking efforts against experimental results.

Slides WEYB1 [6.541 MB]

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WEYB3

Interplay of Beam-Beam, Lattice Nonlinearity, and Space Charge Effects in the SuperKEKB Collider

lattice, luminosity, quadrupole, resonance

2413

D. Zhou, H. Koiso, A. Morita, K. Ohmi, Y. Ohnishi, K. Oide, H. Sugimoto
KEK, Ibaraki, Japan
Y. Zhang
IHEP, Beijing, People's Republic of China

The SuperKEKB B-factory adopts nanobeam scheme for the collision, which consists of large crossing angle and very small vertical beta function at the interaction point. Simulations have revealed that the luminosity of SuperKEKB will be very sensitive to perturbations from various sources. This paper discusses various beam dynamics issues involved in the SuperKEKB collider, including beam-beam, lattice nonlinearity, and space charge effects, as well as their interplay and planned mitigations.

Slides WEYB3 [11.722 MB]

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WEXC2

Advances in Proton Linac Online Modeling

linac, GPU, simulation, operation

2423

X. Pang
LANL, Los Alamos, New Mexico, USA

This talk will review current online modeling tools used for proton linacs and then focus on a new approach that marries multi-particle beam dynamics with modern GPU technology to provide pseudo real-time beam information in a control room setting. Benefits to be discussed will include fast turnaround, accurate beam quality prediction, cost efficiency, test bed for new control and operation scheme development and operator training.

Slides WEXC2 [4.292 MB]

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WEAB1

Compensating Tune Spread Induced by Space Charge in Bunched Beams

hadron, electron, proton, collider

2450

V. Litvinenko
Stony Brook University, Stony Brook, USA
G. Wang
BNL, Upton, Long Island, New York, USA

The effects of space charge play a significant role in modern-day accelerators, frequently constraining the beam parameters attainable in an accelerator or in an accelerator chain. They also can limit the luminosity of hadron colliders operating either at low energies or with sub-TeV high-brightness hadron beams. The latter is applied for strongly cooled proton and ion beams in eRHIC – the proposed future electron-ion collider at Brookhaven National Laboratory. Several schemes were proposed to compensate for space charge effects in a coasting (e.g., continuous) hadron beam, and some have been tested. Using an appropriate transverse profile of the electron beam (or plasma column) for a coasting beam would compensate both the tune shift and the tune spread in the hadron beam. But none of these methods address the issue of compensating space-charge induced tune spread in a bunched hadron beam. In this paper we propose and evaluate a novel idea of using a co-propagating electron bunch with miss-matched longitudinal velocity to compensate the space charge induced tune-shift and tune spread. We present several practical examples of such a system.

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WEPWA063

Beam-Plasma Effects in Muon Ionization Cooling Lattices

plasma, simulation, electron, ion

2649

J.S. Ellison, P. Snopok
IIT, Chicago, Illinois, USA

Funding: Work is supported by the U.S. Department of Energy.
New computational tools are essential for accurate modeling and simulation of the next generation of muon based accelerator experiments. One of the crucial physics processes specific to muon accelerators that has not yet been implemented in any current simulation code is beam induced plasma effect in liquid, solid, and gaseous absorbers. We report here on the progress of developing the required simulation tools and applying them to study the properties of plasma and its effects on the beam in muon ionization cooling channels.

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reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2015-WEPWA063

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WEPWA064

Ionization Cooling Channels in COSY Infinity

emittance, simulation, multipole, solenoid

2652

B.T. Loseth, M. Berz
MSU, East Lansing, Michigan, USA
P. Snopok
Illinois Institute of Technology, Chicago, Illinois, USA

Ionization cooling is a method to reduce the emittance of a beam through the use of absorbers, rf cavities, and strong solenoids for focusing, arranged into a condensed lattice. By tuning lattice parameters, it is possible to construct a staged cooling channel in which the beam emittance is always considerably greater than the minimum value. In the late stages of the cooling channel, space charge effects can become a significant obstacle to further emittance reduction once the beam becomes sufficiently condensed. A method has been implemented in COSY Infinity, a beam dynamics simulation and analysis code, which efficiently and accurately calculates the self-fields of all particles on each other based on a variant of the Fast Multipole Method (FMM). In this paper, we present simulations of a muon ionization cooling channel performed in COSY, utilizing the FMM, benchmarked against G4beamline, a standard code for muon beam analysis, in order to investigate the significance of space charge effects.

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WEPTY013

Cs2Te Photocathode Performance in the AWA High-charge High-gradient Drive Gun

laser, cathode, gun, wakefield

3283

E.E. Wisniewski, S.P. Antipov, M.E. Conde, D.S. Doran, W. Gai, C.-J. Jing, W. Liu, J.G. Power, C. Whiteford
ANL, Argonne, Illinois, USA
S.P. Antipov, C.-J. Jing
Euclid TechLabs, LLC, Solon, Ohio, USA

Funding: U.S. Dept of Energy Office of Science under contract number DE-AC02-06CH11357
The unique high-charge L-band, 1.3 GHz, 1.5 cell gun for the new 75 MeV drive beam is in operation at the Argonne Wakefield Accelerator (AWA) facility (see M.E. Conde, this proceedings.) The high-field (> 80 MV/m) photoinjector has a large area, high QE Cesium telluride photocathode (diameter > 30 mm). The photocathode, a crucial component of the upgraded facility, is fabricated on-site. The photoinjector generates high-charge, short pulse, single bunches (Q > 100 nC) and long bunch-trains (Q > 600 nC) for wakefield experiments. The performance of the photocathode for the AWA drive gun is detailed. Quantum efficiency (QE) measurements indicate long, stable photocathode lifetime under demanding conditions.

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WEPWI003

Design of a Radial Klystron

cavity, klystron, electron, bunching

3489

M. Dal Forno, A. Jensen, R.D. Ruth, S.G. Tantawi
SLAC, Menlo Park, California, USA

Funding: Work supported by the US DOE under contract DEAC03-76SF00515.
The radial klystron is a multidimensional rf source where the beam is generated by a cylindrical gun and it propagates in the radial dimension. The advantage of this design is that the space charge effects are balanced in the azimuthal dimension and a lower magnetic fields is required to focus the electron beam. The bunching is made with concentric coaxial resonators, connected by drift tube. The electron beam interaction with the cavity fields has been analyzed by means of particle tracking software in order to evaluate the beam bunching and the beam dynamics. This paper shows the klystron design, optimizing the shape and the position of each cavity, in order to maximize the efficiency of the device.

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THPF002

Space Charge Effect Estimation for Synchrotrons with Third-order Resonant Extraction

extraction, resonance, proton, injection

3677

M.T.F. Pivi, A. Garonna
EBG MedAustron, Wr. Neustadt, Austria

In proton and ion storage rings using the third-order resonance extraction mechanism, beam particles are slowly extracted from the ring when reaching the resonance stop-band. Typically at beam injection, the horizontal tune is set to a value close to the resonance value. The tune is then moved towards the resonance value to trigger beam extraction in a controlled way. The tune shift generated by space charge forces needs to be taken into account. For this, the incoherent space-charge tune shift for protons of the MedAustron accelerator main ring has been evaluated. This has been performed by multi-particle tracking using an optics model based on MADX, considering a realistic Gaussian beam distribution and exact non-linear space charge electric field forces. The MedAustron accelerator is in the beam commissioning phase and is planned to start medical commissioning at the end of 2015.

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THPF007

Optimization of Multi-turn Injection into a Heavy-Ion Synchrotron using Genetic Algorithms

injection, emittance, linac, ion

3689

S. Appel, O. Boine-Frankenheim
GSI, Darmstadt, Germany
O. Boine-Frankenheim
TEMF, TU Darmstadt, Darmstadt, Germany

For heavy-ion synchrotrons an efficient multi-turn injection (MTI) from the injector linac is crucial in order to reach the specified currents using the available machine acceptance. The beam loss during the MTI must not exceed the limits determined by machine protection and vacuum requirements. Especially for low energy and intermediate charge state ions, the beam loss can cause a degradation of the vacuum and a corresponding reduction of the beam lifetime. In order to optimize the MTI a genetic algorithm based optimization is used to simultaneously minimize the loss and maximize the multiplication factor (e.g. stored currents in the synchrotron). The effect of transverse space charge force on the MTI has also been taken into account. The optimization resulted in injection parameters, which promise a significant improvement of the MTI performance for intense beams in the SIS18 synchrotron at GSI.

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THPF042

Rectlinear Cooling Scheme for Bright Muon Sources

emittance, simulation, lattice, cavity

3792

D. Stratakis
BNL, Upton, Long Island, New York, USA

Funding: Work supported by Contract No, DE-AC02-07CH11359 with the US Department of Energy.
A fast cooling technique is described that simultaneously reduces all six phase-space dimensions of a charged particle beam. In this process, cooling is accomplished by reducing the beam momentum through ionization energy loss in absorbers and replenishing the momentum loss only in the longitudinal direction rf cavities. In this work we describe its main features and describe the main results.

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THPF060

The Simulation Study of Space Charge Effects for CSNS Linac

emittance, DTL, focusing, simulation

3833

Y. Yuan, L. Huang, J. Peng, S. Wang
IHEP, Beijing, People's Republic of China

China Spallation Neutron Source (CSNS) is a high intensity accelerator based facility. Its accelerator consists of an H⁻ injector and a proton Rapid Cycling Synchrotron. The injector includes the front end and linac. The RFQ accelerates the beam to 3MeV, and then DTL accelerates it to 80MeV. The space charge effect is the most important cause of emittance growth and beam loss due to the low beam energy and the high peak current. The paper performed simulation studies on the space charge effects at the LINAC by using three-dimensional code IMPACT-Z. The emittance evolution is studied in the point of view of the singe-particle dynamics and multi-particle dynamics with different peak beam current. The effect of mismatch is studied by simulation, and the emittance growth with different mismatch factor are given.

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THPF088

CERN PS Booster Upgrade and LHC Beams Emittance

emittance, injection, simulation, booster

3897

E. Benedetto, J.L. Abelleira, C. Bracco, V. Forte, B. Mikulec, G. Rumolo
CERN, Geneva, Switzerland
V. Forte
Université Blaise Pascal, Clermont-Ferrand, France

By increasing the CERN PS Booster injection energy from 50 MeV to 160 MeV, the LHC Injector Upgrade Project aims at producing twice as brighter beams for the LHC. Previous measurements showed a linear dependence of the transverse emittance with the beam intensity and space-charge simulations confirmed the linear scaling. This paper is discussing in detail the dependence on the longitudinal emittance and on the choice of the working point, with a special attention to the H⁻ injection process and to the beam dynamics in the first 5 ms, during the fall of the injection chicane bump.

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THPF127

Scheme for a Low Energy Beam Transport with a Non-neutralized Section

ion, emittance, ion-source, rfq

4016

A.V. Shemyakin, L.R. Prost
Fermilab, Batavia, Illinois, USA

Funding: Fermilab is operated by Fermi Research Alliance, LLC, under Contract DE-AC02-07CH11359 with the United States Department of Energy
A Low Energy Beam Transport (LEBT) line is the part of a modern ion accelerator between an ion source (IS) and a Radio-Frequency Quadrupole (RFQ). Typically, it includes 1-3 solenoidal lenses for focusing and relies on transport dynamics with nearly complete beam space charge neutralization over the entire length of the LEBT. In this paper, we discuss the possibility and rationality of imposing un-neutralized transport in the portion of the LEBT adjacent to the RFQ. For estimations, we will use the parameters from PXIE, a test accelerator presently being constructed at Fermilab.

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THPF144

Analysis of FEL-based CeC Amplification at High Gain Limit

electron, FEL, free-electron-laser, laser

4063

G. Wang, Y.C. Jing, V. Litvinenko
BNL, Upton, Long Island, New York, USA
V. Litvinenko
Stony Brook University, Stony Brook, USA

Funding: Work supported by Brookhaven Science Associates, LLC under Contract No. DE-AC02-98CH10886 with the U.S. Department of Energy.
An analysis of CeC amplifier based on 1D FEL theory was previously performed with exact solution of the dispersion relation, assuming electrons having Lorentzian energy distribution *. At high gain limit, the asymptotic behavior of the FEL amplifier can be better understood by Taylor expanding the exact solution of the dispersion relation with respect to the detuning parameter **. In this work, we make quadratic expansion of the dispersion relation for Lorentzian energy distribution * *** and investigate how longitudinal space charge and electrons’ energy spread affect the FEL amplification process.
* G. Wang, PhD Thesis, SUNY Stony Brook, 2008.
** G. Stupakov, M.S. Zolotorev, Comment on “Coherent Electron Cooling”, PRL 110 (2013) 269503.
*** E.L. Saldin, E.A. Schneidmiller, M.V. Yurkov, The Physics of Free Electron Lasers, 1999.

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