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optics

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MOOCRA01 The Magnetic Model of the LHC in the Early Phase of Beam Commissioning quadrupole, injection, dipole, sextupole 55
 
  • E. Todesco, N. Aquilina, B. Auchmann, L. Bottura, M.C.L. Buzio, R. Chritin, G. Deferne, L. Deniau, L. Fiscarelli, J. Garcia Perez, M. Giovannozzi, P. Hagen, M. Lamont, G. Montenero, G.J. Müller, S. Redaelli, RV. Remondino, F. Schmidt, R.J. Steinhagen, M. Strzelczyk, M. Terra Pinheiro Fernandes Pereira, R. Tomás, W. Venturini Delsolaro, J. Wenninger, R. Wolf
    CERN, Geneva
  • N.J. Sammut
    University of Malta, Faculty of Engineering, Msida
 
 

The relation between field and current in each family of the Large Hadron Collider magnets is modeled with a set of empirical equations (FiDeL) whose free parameters are fitted on magnetic measurements. They take into account of residual magnetization, persistent currents, hysteresis, saturation, decay and snapback during initial part of the ramp. Here we give a first summary of the reconstruction of the magnetic field properties based on the beam observables (orbit, tune, coupling, chromaticity) and a comparison with the expectations based on the large set of magnetic measurements carried out during the 5-years-long production. The most critical issues for the machine performance in terms of knowledge of the relation magnetic field vs current are pinned out.

 

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MOPEA042 Epicyclic Twin-helix Magnetic Structure for Parametric-resonance Ionization Cooling dipole, resonance, quadrupole, betatron 166
 
  • A. Afanasev, R.P. Johnson
    Muons, Inc, Batavia
  • Y.S. Derbenev
    JLAB, Newport News, Virginia
  • V.S. Morozov
    ODU, Norfolk, Virginia
 
 

Parametric-resonance Ionization Cooling (PIC) is envisioned as the final 6D cooling stage of a high-luminosity muon collider. Implementing PIC imposes stringent constraints on the cooling channel's magnetic optics design. This paper presents a linear optics solution compatible with PIC. Our solution consists of a superposition of two opposite-helicity equal-period and equal-strength helical dipole harmonics and a straight normal quadrupole. We demonstrate that such a system can be adjusted to meet all of the PIC linear optics requirements while retaining large acceptance.

 
MOPEC001 Numerical Analysis of Machine Background in the LHCb Experiment for the Early and Nominal Operation of LHC proton, background, simulation, betatron 450
 
  • M.H. Lieng
    UNIDO, Dortmund
  • R. Appleby, G. Corti
    CERN, Geneva
  • V. Talanov
    IHEP Protvino, Protvino, Moscow Region
 
 

We consider the formation of machine background induced by proton losses in the long straight section of the LHCb experiment at LHC. Both sources showering from the tertiary collimators located in the LHCb insertion region as well as local beam-gas interaction are taken into account. We present the procedure for, and results of, numerical studies of such background for various conditions. The expected impact on the experiment and signal characteristics are also discussed.

 
MOPEC002 Dynamic Aperture Studies and Field Quality Considerations for the LHC Upgrade Optics multipole, quadrupole, simulation, ion 453
 
  • B.J. Holzer, S.D. Fartoukh, F. Schmidt
    CERN, Geneva
 
 

The layout of the interaction region for the LHC upgrade project is based on a number of new magnets that will provide the required strengths to focus the colliding beams as well as to separate them after the collision. As in the nominal LHC, a triplet of quadrupole magnets is foreseen for the upgrade optics and in addition a separator dipole to limit the parasitic bunch crossings of the two counter rotating bunch trains. Due to the smaller beta function at the IP however, the requirements for the free aperture of these IR magnets are more demanding and the effect of the higher order multipoles is more severe than under the nominal LHC conditions. Using the tracking simulations to study these effects, target values for the multipole coefficients of the new magnets have been defined as well as a multipole correction scheme that will be used to compensate those field errors which cannot be avoided due to design and construction tolerances. Based on these considerations the required field quality of the new LHC low beta magnets is discussed and the resulting dynamic aperture for different multipole correction scheme is presented.

 
MOPEC003 Operational Experience during Initial Beam Commissioning of the LHC injection, instrumentation, collimation, feedback 456
 
  • K. Fuchsberger, R. Alemany-Fernandez, G. Arduini, R.W. Assmann, R. Bailey, O.S. Brüning, B. Goddard, V. Kain, M. Lamont, A. Macpherson, M. Meddahi, G. Papotti, M. Pojer, L. Ponce, S. Redaelli, M. Solfaroli Camillocci, W. Venturini Delsolaro, J. Wenninger
    CERN, Geneva
 
 

After the incident on the 19th September 2008 and more than one year without beam the commissioning of the LHC started again on November 20, 2009. Progress was rapid and collisions under stable beam conditions were established at 1.2 TeV within 3 weeks. In 2010 after qualification of the new quench protection system the way to 3.5 TeV was open and collisions were delivered at this energy after a month of additional commissioning. This paper describes the experiences and issues encountered during these first periods of commissioning with beam.

 
MOPEC005 Kick Response Measurements during LHC Injection Tests and Early LHC Beam Commissioning injection, quadrupole, simulation, dipole 462
 
  • K. Fuchsberger, S.D. Fartoukh, B. Goddard, V. Kain, M. Meddahi, F. Schmidt, J. Wenninger
    CERN, Geneva
 
 

The transfer lines from the SPS to the LHC, TI2 and TI8, with a total length of almost 6km are the longest ones in the world. For that reason even small systematic optics errors are not negligible because they add up and result in an injection mismatch in the LHC. Next to other lattice measurement methods Kick-response measurements were the most important sources of information during the early phases of beam commissioning of these transfer lines and the LHC ring. This measurement technique was used to verify orbit-corrector and BPM gains as well as to sort out optics errors. Furthermore fits to off-momentum kick response turned out to be an appropriate method to establish a model for systematic errors of the transfer line magnets. This paper shortly describes the tools and methods developed for the analysis of the taken data and presents the most important results of the analysis.

 
MOPEC006 JMAD - Integration of MADX into the JAVA World lattice, controls, quadrupole, status 465
 
  • K. Fuchsberger, V. Baggiolini, R. Gorbonosov, W. Herr, V. Kain, G.J. Müller, S. Redaelli, F. Schmidt, J. Wenninger
    CERN, Geneva
 
 

MADX (Methodical Accelerator Design) is the de-facto standard software for modeling accelerator lattices at CERN. This feature-rich software package is implemented and maintained in the programming languages C and FORTRAN. Nevertheless the controls environment of modern accelerators at CERN, e.g. of the LHC, is dominated by JAVA applications. A lot of these applications, for example for lattice measurement and fitting, require a close interaction with the numerical models, which are all defined by the use of the proprietary MADX scripting language. To close this gap an API to MADX for the JAVA programming language (JMAD) was developed. Already the current implementation provides access to a large subset of the MADX capabilities (e.g. twiss-calculations, matching or querying and setting arbitrary model parameters) without any necessity to define the models in yet another environment. This paper describes shortly the design of this project as well as the current status and some usage examples.

 
MOPEC007 Operational Experience during the LHC Injection Tests injection, kicker, ion, quadrupole 468
 
  • K. Fuchsberger, R. Alemany-Fernandez, G. Arduini, R.W. Assmann, R. Bailey, O.S. Brüning, B. Goddard, V. Kain, M. Lamont, A. Macpherson, M. Meddahi, G. Papotti, M. Pojer, L. Ponce, S. Redaelli, M. Solfaroli Camillocci, W. Venturini Delsolaro, J. Wenninger
    CERN, Geneva
 
 

Following the LHC injection tests of 2008, two injection tests took place in October and November 2009 as preparation for the LHC restart on November 20, 2009. During these injection tests beam was injected through the TI2 transfer line into sector 23 of ring 1 and through TI8 into the sectors 78, 67 and 56 of ring 2. The beam time was dedicated to injection steering, optics measurements and debugging of all the systems involved. Because many potential problems were sorted out in advance, these tests contributed to the rapid progress after the restart. This paper describes the experiences and issues encountered during these tests as well as related measurement results.

 
MOPEC010 LHC Aperture Measurements beam-losses, betatron, closed-orbit, emittance 477
 
  • S. Redaelli, M.C. Alabau Pons, M. Giovannozzi, G.J. Müller, F. Schmidt, R. Tomás, J. Wenninger
    CERN, Geneva
 
 

The mechanical aperture of the Large Hadron Collider (LHC) is a critical parameter for the operation of the machine due to the high stored beam intensities in the superconducting environment. Betatron and momentum apertures must be therefore precisely measured and optimized. In this paper, we present the results of beam-based measurements of the LHC aperture. The experimental results are compared with the expectations from the as-built model of the LHC aperture, taking into account the optics imperfections of the superconducting magnets. The impact of these measurements on various aspects of the LHC operation are also discussed.

 
MOPEC011 The Online Model for the Large Hadron Collider controls, simulation, betatron, extraction 480
 
  • S. Redaelli, M.C. Alabau Pons, K. Fuchsberger, M. Giovannozzi, M. Lamont, G.J. Müller, F. Schmidt
    CERN, Geneva
  • X. Buffat
    EPFL, Lausanne
 
 

The control of the high intensity beams of the CERN Large Hadron Collider (LHC) is particular challenging and requires a precise knowledge of the critical beam and machine parameters. In recent years efforts were devoted to the design of a software infrastructure aimed at mimicking the behavior of the LHC. An online model of the machine, based on the accelerator design tool MADX, has been developed to support the commissioning and the operation of the LHC. This model is integrated into the JAVA-based LHC software framework and provides the full computing power of MADX, including the best knowledge of the machine aperture and magnetic models. The MADX implementation is server-based and provides various facilities for optics computation to other application clients. In this paper, we present the status of the MADX online application and illustrate how it has been used during the LHC commissioning. Possible future implementations are also discussed.

 
MOPEC015 Single-pass Beam Measurements for the Verification of the LHC Magnetic Model sextupole, quadrupole, octupole, kicker 489
 
  • F. Zimmermann, M. Giovannozzi, S. Redaelli, Y. Sun, R. Tomás, W. Venturini Delsolaro
    CERN, Geneva
  • R. Calaga
    BNL, Upton, Long Island, New York
 
 

During the 2009 LHC injection tests, the polarities and effects of specific quadrupole and higher-order magnetic circuits were investigated. A set of magnet circuits had been selected for detailed investigation based on a number of criteria. On or off-momentum difference trajectories launched via appropriate orbit correctors for varying strength settings of the magnet circuits under study - e.g. main, trim and skew quadrupoles; sextupole families and spool piece correctors; skew sextupoles, octupoles - were compared with predictions from various optics models. These comparisons allowed confirming or updating the relative polarity conventions used in the optics model and the accelerator control system, as well as verifying the correct powering and assignment of magnet families. Results from measurements in several LHC sectors are presented.

 
MOPEC029 Global Orbit Feedback at Rhic feedback, controls, target, injection 519
 
  • M.G. Minty, R.L. Hulsart, A. Marusic, R.J. Michnoff, V. Ptitsyn, G. Robert-Demolaize, T. Satogata
    BNL, Upton, Long Island, New York
 
 

For improved reproducibility of good operating conditions and ramp commissioning efficiency, new dual-plane slow orbit feedback during the energy ramp was implemented during run-10 in the Relativistic Heavy Ion Collider (RHIC). The orbit feedback is based on steering the measured orbit, after subtraction of the dispersive component, to either a design orbit or to a previously saved reference orbit. Using multiple correctors and beam position monitors, an SVD-based algorithm is used for determination of the applied corrections. The online model is used as a basis for matrix computations. In this report we describe the feedback design, review the changes made to realize its implementation, and assess system performance.

 
MOPEC034 Experience with Split Transition Lattices at RHIC lattice, acceleration, storage-ring, ion 534
 
  • C. Montag, M. Blaskiewicz, J.M. Brennan, S. Tepikian
    BNL, Upton, Long Island, New York
 
 

During the acceleration process, heavy ion beams in RHIC cross the transition energy. When RHIC was colliding deuterons and gold ions during Run-8, lattices with different integer tunes were used for the two rings. This resulted in the two rings crossing transition at different times, which proved beneficial for the "Yellow" ring, the RF system of which is slaved to the "Blue" ring. For the symmetric gold-gold run in FY2010, lattices with different transition energies but equal tunes were implemented. We report the optics design concept as well as operational experience with this configuration.

 
MOPEC037 High Beta Operation Scenarios for Crab Cavities in the Insertion Region 4 of the CERN Large Hadron Collider cavity, luminosity, quadrupole, insertion 540
 
  • R. De Maria, R. Calaga
    BNL, Upton, Long Island, New York
  • M. Giovannozzi, Y. Sun, R. Tomás, F. Zimmermann
    CERN, Geneva
 
 

IR4 is a potential candidate for the installation of crab cavities in the CERN Large Hadron Collider. In this paper we present several operational scenarios in which the effect of the kick imparted by the cavity is enhanced by performing a dynamic unsqueeze of the beta function at collision energy. Linear optics, power supply requirements, beam aperture and finally potential luminosity increase studies will be discussed in order to rank and assess the feasibility of the various options.

 
MOPEC044 A Fixed Field Alternating Gradient Accelerator With Long Straight Sections lattice, synchrotron, focusing, dynamic-aperture 558
 
  • S. Machida
    STFC/RAL/ASTeC, Chilton, Didcot, Oxon
 
 

The lattice of a Fixed Field Alternating Gradient (FFAG) accelerator normally has high symmetry. The whole ring consists of many identical cells which have a simple FODO, double or triplet focusing unit. There is, however, no real reason for an FFAG lattice to have high symmetry, except for a linear nonscaling design which relies on high symmetry to avoid betatron resonances. We propose an FFAG lattice design with a superperiod that makes it possible to have long straight sections for injection, extraction and rf cavities. We discuss how to introduce a superperiod structure. The impact on dynamic aperture, dispersion function, longitudinal dynamics as well as the advantage of having long straight sections will be presented.

 
MOPEC082 Lattice Design for Project -X CW Superconducting Linac linac, focusing, cavity, cryomodule 657
 
  • N. Solyak, I.G. Gonin, J.-F. Ostiguy, V.P. Yakovlev
    Fermilab, Batavia
  • N. Perunov
    MIPT, Dolgoprudniy, Moscow Region
 
 

In this paper, we discuss beam dynamics optimization for a proposed continuous wave (CW) Project-X superconducting (SC) linac. This 2.6 GeV linac has an average current (over few microseconds) of 1 mA, with a pulsed current of up to 5-10 mA. The beam power is 2.6 MW. The CW linac consists of a low-energy 325 MHz section (2.5 MeV - 470 MeV) containing three families of SC single-spoke resonators and one family of triple-spoke resonators followed by a high-energy 1.3 GHz SC section (470 MeV - 2.6 GeV) containing squeezed elliptical (β=0.81) and ILC-type (β=1) cavities. Transverse and longitudinal dynamics in the CW linac are modeled assuming a peak current 10 mA. Different options for focusing structures are considered: solenoidal, doublet, and triplet focusing in the low-energy section; FODO and doublet focusing in the high energy section.

 
MOPD010 Lattice of the NICA Collider Rings collider, lattice, sextupole, proton 690
 
  • A.O. Sidorin, O.S. Kozlov, I.N. Meshkov, V.A. Mikhaylov, G.V. Trubnikov
    JINR, Dubna, Moscow Region
  • V.A. Lebedev, S. Nagaitsev
    Fermilab, Batavia
  • Y. Senichev
    FZJ, Jülich
 
 

Main element of the NICA facility is the collider equipped with stochastic and electron cooling systems to provide experiment with heavy ions like Au, Pb or U at energy from 1 to 4.5 GeV/u with average luminosity of the level of 1027 cm-2 s-1. The possible lattices providing the required parameters are discussed.

 
MOPD084 Highly sensitive beam size monitor for pA currents at the MLS electron storage ring electron, storage-ring, radiation, monitoring 894
 
  • C. Koschitzki, A. Hoehl, R. Klein, R. Thornagel
    PTB, Berlin
  • J. Feikes, M.V. Hartrott, G. Wüstefeld
    Helmholtz-Zentrum Berlin für Materialien und Energie GmbH, Elektronen-Speicherring BESSY II, Berlin
 
 

For the operation of the Metrology Light Source (MLS)*, the electron storage ring of the Physikalisch-Technische Bundesanstalt (PTB), as a primary radiation source standard all storage ring parameters have to be known absolutely. For the measurement of the electron beam size and the monitoring of the stability of the orbit location a new imaging system has been set up, that operates at very different intensity levels covering more than 11 decades, given by the variation of the electron beam current. The system uses a commercial zoom lens for the achromatic optical imaging of the electron beam source point onto two different camera systems. One camera system is for life-imaging of the electron beam at electron beam currents from 200 mA down to some μA. The second system is a cooled CCD-camera that allows imaging of the electron beam size and location at very low currents, down to only one stored electron.


* R. Klein et al., Phys. Rev. ST-AB 11, 110701 (2008).

 
MOPD089 PETRA III Diagnostics Beamline for Emittance Measurements emittance, diagnostics, vacuum, photon 909
 
  • G. Kube, J. Gonschior, U. Hahn, G. Priebe, H. Schulte-Schrepping, Ch. Wiebers
    DESY, Hamburg
  • P. Ilinski
    BNL, Upton, Long Island, New York
  • C.G. Schroer
    TUD, Dresden
  • S. Weisse
    DESY Zeuthen, Zeuthen
 
 

PETRA III is the new 3rd generation hard X-ray synchrotron light source at DESY, operating at a beam energy of 6 GeV. Machine commissioning began in April 2009 and user operation starts in 2010. In order to achieve a high brilliance, damping wigglers with a total length of 80 m are installed to reduce the horizontal emittance down to an extremely low value of 1 nm rad. For a precise emittance online control, a dedicated diagnostics beamline was built up to image the beam profile with synchrotron radiation from a bending magnet in the X-ray region. The beamline is equipped with two interchangeable X-ray optical systems, a pinhole optic for standard operation and a high resolution compound refractive lens optic. In addition, the synchrotron radiation angular distribution can be exploited at high photon energies. In this presentation, first experience with the system will be reported.

 
MOPD090 Upgrade and Evaluation of the Bunch Compression Monitor at the Free-electron Laser in Hamburg (FLASH) radiation, simulation, electron, FEL 912
 
  • C. Behrens, B. Schmidt, S. Wesch
    DESY, Hamburg
  • D. Nicoletti
    Università di Roma I La Sapienza, Roma
 
 

The control and stabilization of RF systems for accelerators has a considerable importance. In case of high-gain free-electron lasers (FEL) with magnetic bunch compressors, the RF phases determine the attainable bunch peak current, which is a relevant parameter for driving the FEL process. In order to measure the bunch peak current in a simple and fast but indirect way, both bunch compressors at FLASH are equipped with compression monitors (BCM) based on pyroelectrical detectors and diffraction radiators (CDR). They provide substantial information to tune the bunch compression and are used for beam-based feedback to stabilize RF phases. This monitor system becomes more important and more challenging after the installation of a third-harmonic RF system for longitudinal phase space linearization in front of the first bunch compressor. In this paper, we describe the hardware upgrade of the bunch compression monitor and show the expected performance by simulations of the CDR source and the radiation transport optics. Particle tracking simulations are used for generation of the simulated BCM-signal for various compression schemes. Comparison with experimental data will be presented.

 
MOPE007 Measurement of Low-Emittance Beam with Coded Aperture X Ray Optics at CesrTA emittance, simulation, single-bunch, electron 966
 
  • J.W. Flanagan, H. Fukuma, H. Ikeda, T.M. Mitsuhashi
    KEK, Ibaraki
  • J.P. Alexander, N. Eggert, W.H. Hopkins, M.A. Palmer, D.P. Peterson
    CLASSE, Ithaca, New York
  • B. Kreis
    Cornell University, Ithaca, New York
  • G.S. Varner
    UH, Honolulu, HI
 
 

An x-ray beam size monitor based on coded aperture imaging* has been developed at CesrTA, for the purpose of making bunch-by-bunch, turn-by-turn measurements of low emittance beams. Using low-emittance beam (~44 pm, or 16 microns at the x-ray source point) we have been able to make detailed comparisons between the measured mask response and that predicted by theory, validating our simulations of the mask response. In turn, we demonstrate the ability to measure both integrated and single-bunch turn-by-turn beam sizes and positions for monitoring the progress of the low-emittance tuning of the machine, and for electron-cloud instability-related beam dynamics studies.


* J.W. Flanagan et al., EPAC08, 1029 (2008).

 
MOPE008 Improved Measurement of Crabbing Angle by a Streak Camera at KEKB cavity, luminosity, synchrotron, collider 969
 
  • H. Ikeda, J.W. Flanagan, H. Fukuma, T.M. Mitsuhashi
    KEK, Ibaraki
 
 

Crab cavities were installed in the KEKB rings in order to increase the luminosity. We measured the tilt of the bunches in the x-z plane using streak cameras. In a previous report*, the measured tilt in the HER was 2 times smaller than the expected crabbing angle, while the LER measurement was consistent with that expected. After the streak camera's vertical sweep speed was calibrated, the results were consistent with the expected crabbing angle in both rings.


* H. Ikeda et al., PAC07, 4018.

 
MOPE009 Improvement of the Resolution of SR Interferometer at KEK-ATF Damping Ring emittance, damping, synchrotron, synchrotron-radiation 972
 
  • T. Naito, T.M. Mitsuhashi
    KEK, Ibaraki
 
 

Some of the improvement were done for an SR interferometer with the Herschelian reflective optics*. Previously, the measured vertical beam size was limited to around 5μm with a double slit separation of 40mm and wavelength of 400nm at the ATF damping ring. Double slit separation was mainly limited to the effective aperture of the optical path between the source point and interferometer. This time, we re-aligned the optical path, and as a result, the effective aperture was increased. Using this re-alignment we can have a double slit separation of up to 60mm. To reduce air turbulence, the optical path was covered with a tight air duct. After these improvements were made, we succeeded in measuring a vertical beam size of 3.4μm with double slit separation of 60mm and wavelength of 550nm, which corresponds to 5pm of the vertical emittance assuming 3m of the beta function.


* T. Naito et. al. "Very Small Beam Size Measurement by Reflective SR Interferometer at KEK-ATF", Proc. of EPAC06, pp2772-2274.

 
MOPE020 Beam Based Alignment of the Beam Position Monitor at J-PARC RCS synchrotron, focusing, alignment, dipole 1005
 
  • N. Hayashi, H. Harada, H. Hotchi
    JAEA/J-PARC, Tokai-Mura, Naka-Gun, Ibaraki-Ken
  • M. Tejima
    KEK, Ibaraki
  • T. Toyama
    J-PARC, KEK & JAEA, Ibaraki-ken
 
 

The J-PARC RCS is an M-Watt class rapid cycling synchrotron and it has delivered an intensive beam to the neutron target and the MR. In order to overcome large space charge effect, its physical aperture is designed to be more than 250mm in diameter. Even though its chamber size is very large, the BPM system gives precise data to determine beam optics parameters of the ring. For this purpose, only relative positions and resolutions are important. However, for much higher intensity, the absolute beam position and accurate COD correction are indispensable. We have carefully installed the BPM and measured the position with respect to the quadrupole magnet (QM) nearby. But it is also necessary to estimate its absolute position by using beam. If each QM could be controlled independently, the simple beam based alignment technique can be utilized, but it is not the case for RCS. There are seven families of QM, and only each family can be controlled at one time. We developed a new technique by expanding the simple method for the case of multiple QM focusing changed simultaneously, and applied to the J-PARC RCS. The paper describes this method and discussed about experimental results.

 
MOPE022 Development of Shintake Beam Size Monitor for ATF2 laser, target, background, alignment 1011
 
  • Y. Kamiya
    ICEPP, Tokyo
  • S. Araki, T. Okugi, T. Tauchi, N. Terunuma, J. Urakawa
    KEK, Ibaraki
  • S. Komamiya, M. Oroku, T.S. Suehara, Y. Yamaguchi, T. Yamanaka
    University of Tokyo, Tokyo
 
 

In this paper, we describe a system design and current status of Shintake beam size monitor. Shintake monitor is a laser-based beam diagnostics tool, which provides a non-invasive measurement of transverse beam sizes. The interaction target probing the electron beam is interference fringes build up by the two coherent lasers that have narrow bandwidth and long coherent length. A scale of the target structure corresponds to approximately one fourth of the laser wave length, and the smallest measurable size reaches down to several tens of nanometers. The monitor we described here is installed at the virtual interaction point of the ATF2 beam line, which is built to confirm the proposed final focus system for Future Linear Colliders. We adopt second harmonics of Nd:YAG laser of 532 nm wavelength, and phase stabilization feedback system to allow to measure the designed beam size of about 37 nm. To widen a measurable range up to about 5 microns (wire scanner's range), we also prepare three crossing modes that change an effective wavelength for the fringes. The monitor is used to measure a focus size during the tuning process. The system is based on the Shintake monitor for FFTB.

 
MOPE024 Development of Radiation Registant Optics System for High Intensity Proton Beamline at the J-PARC radiation, proton, background, target 1017
 
  • A. Toyoda, A. Agari, E. Hirose, M. Ieiri, Y. Katoh, A. Kiyomichi, M. Minakawa, T.M. Mitsuhashi, R. Muto, M. Naruki, Y. Sato, S. Sawada, Y. Suzuki, H. Takahashi, M. Takasaki, K.H. Tanaka, H. Watanabe, Y. Yamanoi
    KEK, Tsukuba
  • H. Noumi
    RCNP, Osaka
 
 

Optical beam measurement such as OTR(Optical Transition Radiation), ODR(Optical Diffraction Radiation), gas Cerenkov, and so on is a powerful tool to observe a two-dimensional information of high intensity beam profile, so that this method is widely used at various electron and hadron accelerators. However, high radiation field to damage an optical system gradually becomes a major issue with increasing the beam intensity to explore new physics. Our present effort is devoted to develop a high efficient optical system to resist such high radiation field. We newly designed an optical system composed of two spherical mirrors which do not have any lenses vulnerable to radiation. Detailed optics design and a result of optical performance test will be presented. Also we will report a result of a beam test experiment of this optics system combined with an OTR screen performed at high intensity proton extraction beamline of the J-PARC.

 
MOPE037 Measurement of Beam Size at Pohang Light Source background, radiation, synchrotron, ion 1056
 
  • J.Y. Ryu, E.-S. Kim, H.D. Kim, H.K. Park
    KNU, Deagu
  • J.G. Hwang
    Kyungpook National University, Daegu
  • C. Kim
    PAL, Pohang, Kyungbuk
 
 

The synchrotron-radiation interferometer was employed for the beam size measurement of electron beam circulating in the storage ring at 2.5 GeV Pohang Light Source. We measured the beam sizes in both vertical and horizontal directions as function of stored beam current. In this presentation, we will discuss the interferometer system, analysis method for the measurement and the measured results. We also compared the measured beam sizes with predicted values from the lattice parameters in the ring.

 
MOPE043 Reversed Cherenkov-transition Radiation and Prospect of its Application to Beam Diagnostics vacuum, radiation, plasma, diagnostics 1068
 
  • A.V. Tyukhtin, S.N. Galyamin
    Saint-Petersburg State University, Saint-Petersburg
  • E.S. Belonogaya
    LETI, Saint-Petersburg
 
 

We describe both analytically and numerically beams radiation in presence of media which can be realized as modern metamaterials. In particular, effects of reversed Cherenkov radiation (RCR)* and reversed Cherenkov-transition radiation (RCTR)** are considered. These phenomena can be used for detection of charged particles and diagnostics of beams. Earlier we noted some useful properties of radiation in the case of the boundary between an ordinary medium and an isotropic left-handed metamaterial (LHM)*. Now we continue to analyze prospects of use of LHM for beam diagnostics. Moreover, we investigate RCR and RCTR in the case of certain anisotropic materials with properties being similar to properties of LHM. The useful features are reversed character of radiation and, particularly, existence of two thresholds for RCTR (lower threshold and upper one). This fact allows selection of particles (or beams) with energy in some predetermined range. The specific radiation patterns (having two or three lobes in anisotropic metamaterial) can be useful for particle energy measurement as well.


* Z.Y. Duan, B.-I. Wu, S. Xi, H.S. Chen., M. Chen, Progress in Electromagn. Research, v.90, p.75 (2009).
** S.N. Galyamin, A.V. Tyukhtin, A. Kanareykin, P. Schoessow, PRL, v.103, p.194802 (2009).

 
MOPE058 Measuring the Bunch Frequency Multiplication at CTF3 linac, diagnostics, radiation, electron 1107
 
  • A.E. Dabrowski, S. Bettoni, E. Bravin, R. Corsini, S. Döbert, T. Lefèvre, A. Rabiller, P.K. Skowronski, L. Søby, F. Tecker
    CERN, Geneva
  • D. Egger
    EPFL, Lausanne
  • A. Ferrari
    Uppsala University, Uppsala
  • C.P. Welsch
    The University of Liverpool, Liverpool
 
 

The CTF3 facility is being built and commissioned by an international collaboration in order to test the feasibility of the proposed CLIC drive beam generation scheme. Central to this scheme is the use of RF deflectors to inject bunches into a Delay Loop and a Combiner Ring, in order to transform the initial bunch spacing of 1.5 GHz from the linac to a final bunch spacing of 12 GHz. The optimization procedure relies on several steps. The active length of each ring is carefully adjusted to within a few millimeters accuracy using a two‐period undulator. The transverse optics of the machine must be set-up in a way so as to ensure the beam isochronicity. Diagnostics based on optical streak cameras and RF power measurements have been designed to measure the longitudinal behaviour of the beam during the combination. This paper presents their performance and highlights recent measurements.

 
MOPE059 Commissioning and First Performance of the LHC Beam Current Measurement Systems injection, instrumentation, proton, feedback 1110
 
  • M. Ludwig, D. B. Belohrad, JJ.G. Gras, L.K. Jensen, O.R. Jones, OP. Odier, J.-J. Savioz, S. Thoulet
    CERN, Geneva
 
 

CERN's Large Hadron Collider (LHC) is equipped with three distinct types of intensity measurement systems: total intensity measurement using DC transformers (DCCTs) with a bandwidth up to a few kHz; total intensity measurements on a turn-by-turn basis for lifetime measurements using AC-coupled fast transformers (fast BCTs); bunch-by-bunch intensity measurements with a bandwidth up to a few hundred MHz also using the fast BCTs. In addition to providing intensity information these devices are part of the machine protection system, indicating whether or not there is beam circulating, transmitting intensity for evaluation of safe beam conditions and capable of triggering a beam dump if fast losses are detected. This paper reports on the commissioning of all these systems and their initial performance.

 
MOPE060 Spectrometry in the Test Beam Line at CTF3 simulation, diagnostics, electron, linac 1113
 
  • M. Olvegård, E. Bravin, F. Carra, N.C. Chritin, A.E. Dabrowski, A. Dallocchio, S. Döbert, T. Lefèvre
    CERN, Geneva
  • E. Adli
    University of Oslo, Oslo
 
 

The CLIC study is based on the so‐called two‐beam acceleration concept and one of the main goals of the CLIC Test Facility 3 is to demonstrate the efficiency of the CLIC RF power production scheme. As part of this facility a Test Beam Line (TBL), presently under commissioning, is a small scale version of a CLIC decelerator. To perform as expected the beam line must show efficient and stable RF power production over 16 consecutive decelerating structures. As the high intensity electron beam is decelerated its energy spread grows by up to 60%. A novel segmented beam dump for time resolved energy measurements has been designed to match the requirements of the TBL. As a complement, a diffusive OTR screen is also installed in the same spectrometer line. The combination of these two devices will provide both a high spatial resolution measurement of both the energy and energy spread and a measurement with a few nanoseconds time response. This paper describes the design of the new segmented dump and presents the results from the first commissioning of the TBL spectrometer line.

 
MOPE081 Performance of a Streak Camera using Reflective Input Optics synchrotron, photon, synchrotron-radiation, radiation 1170
 
  • C.A. Thomas, G. Rehm
    Diamond, Oxfordshire
  • I.P.S. Martin
    JAI, Oxford
 
 

Electron bunch profile and length measurement from large bandwidth synchrotron radiation with a streak camera can be strongly limited by the chirp introduced by the length of material present in the input refractive optics of streak cameras. Elimination of the chirp can be done either by filtering the bandwidth of the synchrotron radiation pulses, by measuring time resolved spectra with the streak camera, or by replacing the front optics lenses by focussing mirrors. The first solution reduces the power available, thus limiting measurements to minimum bunch current that can be too high to assess the 'zero' current bunch length. The second elegant solution allows measurement of the bunch length with the whole bandwidth and available power but with loss of the second sweep axis in the camera, so that no beam dynamics can be observed. In order to prevent any pulse chirp, keep all the available power and capability of beam dynamics observation, we designed a new input optics exclusively with mirrors. We present here our design and the results of the system with our streak camera, measuring 2ps bunch in the new Diamond low-alpha lattice.

 
MOPE085 Rapid-cycling Synchrotron with Variable Momentum Compaction proton, dipole, lattice, collider 1182
 
  • Y. Alexahin
    Fermilab, Batavia
  • D.J. Summers
    UMiss, University, Mississippi
 
 

There are conflicting requirements on the value of the momentum compaction factor during energy ramp in a synchrotron: at low energies it should be positive and sufficiently large to make the slippage factor small so that it is possible to work closer to the RF voltage crest and ensure sufficient RF bucket area, whereas at higher energies it should be small or negative to avoid transition crossing. In the present report we propose a lattice with variable momentum compaction factor and consider the possibility of using it in a high repetition rate proton driver for muon collider and neutrino factory.

 
MOPE089 CESR Beam Position Monitor System Upgrade for CesrTA and CHESS Operations electron, emittance, positron, controls 1191
 
  • M.A. Palmer, M.G. Billing, R.E. Meller, M.C. Rendina, N.T. Rider, D. L. Rubin, J.P. Shanks, C.R. Strohman
    CLASSE, Ithaca, New York
  • R. Holtzapple
    CalPoly, San Luis Obispo, CA
 
 

The beam position monitor (BPM) system at the Cornell Electron Storage Ring (CESR) has been upgraded for use in both CESR Test Accelerator (CesrTA) and Cornell High Energy Synchrotron Source (CHESS) operations. CesrTA operates with electron and positron bunch trains with as little as 4ns bunch spacing. CHESS operates with simultaneous counter-rotating electron and positron trains with 14ns bunch spacing. The upgraded BPM system provides high resolution measurement capability as is needed for the CesrTA ultra low emittance operations, turn-by-turn digitization of multiple bunches for beam dynamics studies, and the capability for real-time dual beam monitoring in CHESS conditions. In addition to standard position measurement capability, the system is also required to measure betatron phase by synchronous detection of a driven beam for optics diagnosis and correction. This paper describes the characteristics of the BPM hardware upgrade, performance figures of the electronics designed for this purpose and the overall status of the upgrade effort. Examples of key measurement types and the analysis of data acquired from the new instruments will also be presented.

 
MOPE096 Progress Report on the Development of the Real Time Interferometer for Bunch Length Determination laser, radiation, diagnostics, synchrotron 1212
 
  • G. Andonian, A.Y. Murokh, A.G. Ovodenko, M. Ruelas, R. Tikhoplav
    RadiaBeam, Marina del Rey
  • D. Dooley
    Spectrum Detector, Lake Oswego, Oregon
  • U. Happek
    UGA, Athens, Georgia
  • S. Reiche
    PSI, Villigen
 
 

This paper reports on the progress of the development of a bunch length diagnostic for high brightness beams. The diagnostic, termed the real time interferometer, is a single shot, autocorrelator that outputs the interferogram of coherent radiation emitted from compressed, high-brightness beams. The device uses all-reflective terahertz optics as well as a highly sensitive pyroelectric-based detector array. For initial testing, coherent transition radiation is used, however, the diagnostic can be used in a non-destructive manner if coherent edge or synchrotron radiation is employed. Current research includes diagnostic design and preliminary tests conducted at the BNL Accelerator Test Facility.

 
TUXMH02 LHC Optics Model Measurements and Corrections dipole, quadrupole, coupling, injection 1232
 
  • R. Tomás, O.S. Brüning, M. Giovannozzi, M. Lamont, F. Schmidt, G. Vanbavinckhove
    CERN, Geneva
  • M. Aiba
    PSI, Villigen
  • R. Calaga, R. Miyamoto
    BNL, Upton, Long Island, New York
 
 

Optics stability during all phases of operation is crucial for the LHC. The optical properties of the machine have been optimized based on a detailed magnetic model of the SC magnets and on their sorting. Tools and procedures have been developed for rapid checks of beta beating, dispersion, and linear coupling, as well as for prompt optics correction. Initial optics errors, correction performance and optics stability from the first LHC run will be reported, and compared with expectations. Possible implications for the collimation cleaning efficiency and LHC machine protection will be discussed.

 

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TUOARA02 The FERMI@Elettra Commissioning linac, gun, laser, emittance 1293
 
  • G. Penco, E. Allaria, L. Badano, S. Bassanese, M. Bossi, D. Castronovo, G. Ciani, S. Cleva, P. Craievich, M.B. Danailov, R. De Monte, G. De Ninno, A.A. Demidovich, S. Di Mitri, M. Ferianis, O. Ferrando, S. Ferry, L. Froehlich, G. Gaio, R. Ivanov, M. Lonza, A.A. Lutman, S.V. Milton, M. Petronio, M. Predonzani, F. Rossi, L. Rumiz, C. Scafuri, G. Scalamera, P. Sigalotti, S. Spampinati, C. Spezzani, M. Trovò, M. Veronese
    ELETTRA, Basovizza
  • L. Pavlovič
    Uni LJ, Ljubljana
 
 

The FERMI@Elettra injector, comprised of a high-gradient, s-band, photo-cathode rf gun, the PC gun driven laser, the first two accelerating sections, controls, and suite of diagnostics has been commissioned in 2009. The electron beam has been characterized in terms of charge, energy, energy spread and transverse emittance, and results are provided in this paper. In early 2010 linac commissioning up to 250MeV continued, and by using the RF deflecting cavity, the slice parameters of the beam have been measured. Moreover, studies on the laser pulse shaping and the relative optimization of the longitudinal ramp profile required by the nominal bunch configuration are presented in this paper.

 

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TUPEA033 Stable Transmission of RF Signals on Optical Fiber Links laser, controls, FEL, radio-frequency 1399
 
  • J.M. Byrd, L.R. Doolittle, G. Huang, J.W. Staples, R.B. Wilcox
    LBNL, Berkeley, California
 
 

Stabilized optical fiber links have been under development for several years for high precision transmission of timing signals for remote synchronization of accelerator and laser systems. In our approach, a master clock signal is modulated on an optical carrier over a fiber link. The optical carrier is also used as the reference in a heterodyne interferometer which is used to precisely measure variations, mainly thermal, in the fiber length. The measured variations are used to correct the phase of the transmitted clock signal. We present experimental results showing sub-10 fsec relative stability of a 200 m link a sub-20 fsec stability of a 2.2 km link.

 
TUPEA034 Laser Recycler Using An Asymmetrical Con-focal Cavity laser, cavity, ion, beam-losses 1402
 
  • I. Yamane
    KEK, Ibaraki
  • M. Nakamura, H. Okuno
    RIKEN Nishina Center, Wako
 
 

An asymmetrical con-focal cavity is composed of tow concave mirrors with different focal length, placed face to face, and their axes and focal points coincide. When a laser beam is injected in parallel with the mirror axis, from backward of and just outside of the mirror with the smaller focal length, the laser beam is trapped in the cavity and repeats reflection by mirrors. Then, the beam reflected by the mirror with the larger focal length passes every time the focal point and the period by which pulses return to the focal point is constant. Therefore, if the repetition period of the injected laser pulse is equal to the repetition period in the cavity, all laser pulses comes to the focal point at the same time and the beam intensity is stacked up. Calculation on the performance of an asymmetrical con-focal cavity shows that a laser pulse can be recycled more than a few tens turns and the beam intensity can be stacked to more than a few tens times of the original beam intensity when the laser beam is a Gaussian beam and the reflectance of the mirrors is 100%. Results of calculation is examined using a He-Ne laser and a pair of high reflection mirrors.

 
TUPEB005 High Luminosity Interaction Region Design for Collisions with Detector Solenoid coupling, quadrupole, luminosity, collider 1524
 
  • C. Milardi, M.A. Preger, P. Raimondi, G. Sensolini, F. Sgamma
    INFN/LNF, Frascati (Roma)
 
 

An innovatory interaction region has been recently conceived and realized on the Frascati DAΦNE lepton collider. The concept of tight focusing and small crossing angle adopted until now to achieve high luminosity in multibunch collisions has evolved towards enhanced beam focusing at the interaction point with large horizontal crossing angle, thanks to a new compensation mechanism for the beam-beam resonances. The novel configuration has been tested with a small detector without solenoidal field yielding a remarkable improvement in term of peak as well as integrated luminosity. The high luminosity interaction region has now been modified to host a large detector with a strong solenoidal field integral which significantly perturbs the beam optics introducing new design challenges in terms of interaction region optics design, beam transverse coupling control and beam stay clear requirements.

 
TUPEB012 Optics Measurement at the Interaction Point using Nearby Position Monitors in KEKB coupling, luminosity, simulation, positron 1539
 
  • K. Ohmi, T. Ieiri, Y. Ohnishi, Y. Seimiya, M. Tejima, M. Tobiyama, D.M. Zhou
    KEK, Ibaraki
 
 

Optics parameters at the interaction point, beta, x-y coupling, dispersion and their chromatic aberrations, seriously affect the beam-beam performance as is shown in experiments and simulations. The control of the optics parameters is essential to maintain the high luminosity in KEKB. They drift day by day, or before and after the beam abort. They were often monitored at intervals of the operation with taking the study time. They are recently measured during the physics run using a pilot bunch without collision. We show the measured the optics parameters and their variations and discuss the relation to the luminosity.

 
TUPEB019 Evaluation of the Detector BG for SuperKEKB background, vacuum, scattering, simulation 1557
 
  • M. Iwasaki, Y. Funakoshi, J. Haba, N. Iida, K. Kanazawa, H. Koiso, Y. Ohnishi, K. Shibata, S. Tanaka, T. Tsuboyama, S. Uno, Y. Ushiroda
    KEK, Ibaraki
  • H. Aihara, C. Ng, S. Sugihara
    University of Tokyo, Tokyo
  • H. Nakano, H. Yamamoto
    Tohoku University, Graduate School of Science, Sendai
 
 

SuperKEKB is the upgrade plan of the current B-factory experiment with the KEKB accelerator at KEK. Its luminosity is designed to be 8x1035 /cm2/s (40 times higher than KEKB) and the integrated luminosity is expected to be 50 ab-1. In SuperKEKB, it is important to evaluate the beam induced BG and design the interaction region (IR) to assure the stable detector operation. To estimate the beam induced BG, we construct the beam-line simulation based on the GEANT4 simulation. In this paper, we report the BG evaluation and the IR design for SuperKEKB.

 
TUPEB037 Interaction-Region Design Options for a Linac-Ring LHeC proton, electron, dipole, quadrupole 1605
 
  • F. Zimmermann, S. Bettoni, O.S. Brüning, B.J. Holzer, S. Russenschuck, D. Schulte, R. Tomás
    CERN, Geneva
  • H. Aksakal
    N.U, Nigde
  • R. Appleby
    UMAN, Manchester
  • S. Chattopadhyay, M. Korostelev
    Cockcroft Institute, Warrington, Cheshire
  • A.K. Çiftçi, R. Çiftçi, K. Zengin
    Ankara University, Faculty of Sciences, Tandogan/Ankara
  • J.B. Dainton, M. Klein
    The University of Liverpool, Liverpool
  • E. Eroglu, I. Tapan
    UU, Bursa
  • P. Kostka
    DESY Zeuthen, Zeuthen
  • V. Litvinenko
    BNL, Upton, Long Island, New York
  • E. Paoloni
    University of Pisa and INFN, Pisa
  • A. Polini
    INFN-Bologna, Bologna
  • U. Schneekloth
    DESY, Hamburg
  • M.K. Sullivan
    SLAC, Menlo Park, California
 
 

In a linac-ring electron-proton collider based on the LHC ("LR-LHeC"), the final focusing quadrupoles for the electron beam can be installed far from the collision point, as far away as the proton final triplet (e.g. 23 m) if not further, thanks to the small electron-beam emittance. The inner free space could either be fully donated to the particle-physics detector, or accommodate "slim" dipole magnets providing head-on collisions of electron and proton bunches. We present example layouts for either scenario considering electron beam energies of 60 and 140 GeV, and we discuss the optics for both proton and electron beams, the implied minimum beam-pipe dimensions, possible design parameters of the innermost proton and electron magnets, the corresponding detector acceptance, the synchrotron radiation power and its possible shielding or deflection, constraints from long-range beam-beam interactions as well as from the LHC proton-proton collision points and from the rest of the LHC ring, the passage of the second proton beam, and the minimum beta* for the colliding protons.

 
TUPEB042 The Transverse Linac Optics Design in Multi-pass ERL linac, quadrupole, electron, focusing 1620
 
  • Y. Hao, J. Kewisch, V. Litvinenko, E. Pozdeyev, V. Ptitsyn, D. Trbojevic, N. Tsoupas
    BNL, Upton, Long Island, New York
 
 

In this paper, we analyzed the linac optics design requirement for a multi-pass energy recovery linac (ERL) with one or more linacs. A set of general formula of constrains for the 2-D transverse matrix is derived to ensure design optics acceptance matching throughout the entire accelerating and decelerating process. Meanwhile, the rest free parameters can be adjusted for fulfilling other requirements or optimization purpose. As an example, we design the linac optics for the future MeRHIC (Medium Energy eRHIC) project and the optimization for enlarging the BBU threshold.

 
TUPEB055 Optics correction at BEPCII Storage Ring quadrupole, sextupole, dipole, luminosity 1644
 
  • D. Ji, Y. Jiao, Q. Qin, Y. Wei
    IHEP Beijing, Beijing
 
 

Optics correction is an important issue at BEPCII. Due to the errors in all kinds of components of a storage ring, the real optics of a storage ring is different from the design one. This paper introduces some developments of optics calibration at BEPCII storage ring. We use the method that fit the measured response matrix to the model response matrix to get the fudge factor of the quadrupole field and the sextupole field. On the other hand, in considering fringing fields of quadrupole magnet and interaction of quadrupole magnet iron core and sextupole magnet iron core, the model is calibrated.

 
TUPEB058 Online Analyzer System for the Development of the Long-lived Charge-Stripping Foil at the J-PARC dipole, proton, quadrupole, emittance 1653
 
  • H. Fujimori, Z. Igarashi, Y. Irie, Y. Sato, M.J. Shirakata, I. Sugai, A. Takagi, Y. Takeda
    KEK, Ibaraki
 
 

The carbon stripping foil is the key element for the high-intensity proton accelerator. At KEK, the foil test system using the 650keV H- Cockcroft-Walton accelerator is in operation, which can simulate the energy depositions to the foil with the same amount in the J-PARC. In order to quantatively observe the foil degradations (such as foil thinning, pin-hole production) during irradiation, online energy and particle analyzing system is under construction. This report outlines the design detail of the analyzing system including the detectors.

 
TUPEB069 Results of 2009 Optics Studies of the SPS to LHC Transfer Lines injection, quadrupole, dipole, alignment 1680
 
  • M. Meddahi, S.D. Fartoukh, K. Fuchsberger, B. Goddard, W. Herr, V. Kain, V. Mertens, J. Wenninger
    CERN, Geneva
  • D. Kaltchev
    TRIUMF, Vancouver
 
 

In 2008, the SPS-to-LHC transfer line operation allowed for the first time to perform beam measurements in the last part of the lines and into the LHC. Beam parameters were measured and compared with expectation. Discrepancies were observed in the dispersion matching into the LHC, and also in the vertical phase advance along the line. In 2009, extensive theoretical and simulation work was performed in order to understand the possible sources of these discrepancies. This allowed establishing an updated model of the beam line, taking into account the importance of the full magnetic model, the limited dipole corrector strengths and the precise alignment of beam elements. During 2009, beam time was allocated in order to perform further measurements, checking and refining the optical model of the transfer line and LHC injection region and validating the different assumptions. Results of the 2009 optics measurements and comparison with the beam specification and model are presented.

 
TUPEB072 Beam-gas Loss Rates in the LHC proton, simulation, background, hadron 1686
 
  • Y.I. Levinsen, R. Appleby, H. Burkhardt
    CERN, Geneva
 
 

We report on first observations and detailed simulations of beam gas rates in the LHC. For the simulations, a comprehensive tool has been set up to simulate in a few hours the expected beam gas losses when pressure maps, collimator settings, and/or beam optics changes. The simulation includes both elastic and inelastic scattering, with subsequent multiturn tracking of proton residues. This provides amongst others a more realistic collimator loss distributions from elastic interactions than what was previously available.

 
TUPD090 The Development of New Terahertz Generator using Beam Optics and RF Deflector electron, cathode, simulation, quadrupole 2114
 
  • F. Furugohri, H. Hioka, S. Someya
    SUT, Noda-shi, Chiba
  • M. Yoshida
    KEK, Ibaraki
 
 

New terahertz(THz) generator using the non-relativistic electron beam was developed based on the beam optics and the RF deflector. The conventional THz generators using the electron beam are almost based on the relativistic beam to utilize the lorentz factor as FELs or the strong magnet to make high electron density like gyrotrons or BWOs. Thus it causes that the total equipment becomes large. New THz generator uses the non-relativistic electron beam. And it consists of the beam optics which makes the sliced beam by using a anode slit to focus at second slit as the THz radiation plane. In this configuration, the RF deflector works to move for the transverse direction matched with the phase velocity of the radiated electromagnetic field. The moving sliced beam separates into a number of bunches through the second slit and the bunches makes the THz coherent radiation in zero time interval. In this new THz generator, no strong magnet is required and the large diameter beam can be utilized to generate the high power THz electromagnetic wave. In this paper, the design of new THz generator and its experimental results are reported.

 
TUPD102 Magnet Optics and Beam Dynamics of BERLinPro linac, lattice, multipole, cavity 2135
 
  • M. Abo-Bakr, B.C. Kuske, A.N. Matveenko
    Helmholtz-Zentrum Berlin für Materialien und Energie GmbH, Elektronen-Speicherring BESSY II, Berlin
 
 

The Helmholtz Zentrum Berlin (HZB) is proposing to build an Energy Recovery Linac Prototype, called BERLinPro, at its site in Berlin Adlershof. A gun test stand for a superconducting RF gun is already under construction at HoBiCaT. In this paper we concentrate on the recirculator part of the ERL and discuss the ERL requirements to the magnet optics. The current design of the magnet lattice will be described and main parameters and simulation results introduced. Since BERLinPro aims to demonstrate high current operation at short pulses according optics aspects will be also discussed. The focus here will be on longitudinal phase space manipulations and lattice layout options, suppressing the BBU instability and increasing its threshold currents.

 
TUPE019 Integration of Elegant Tracking Code into the Tango Server-based High Level Software of FERMI@elettra for Optics Measurements and Modeling quadrupole, controls, linac, laser 2179
 
  • C. Scafuri, S. Di Mitri, G. Penco
    ELETTRA, Basovizza
 
 

The electron beam transverse emittance and Twiss parameters have been measured during the commissioning of FERMI@elettra. Matching of the beam optics to the lattice transverse acceptance and beam transport was performed by means of the elegant particle tracking code; this was integrated with the Tango-server based high level software of FERMI@elettra. Matlab scripts were used as an intermediate layer between the code and the server to automate the matching procedure. The software environment, the experimental results and the comparison with the model are described in this paper.

 
TUPE098 Cornell Energy Recovery Linac Lattice and Layout undulator, lattice, simulation, linac 2356
 
  • C.E. Mayes, G.H. Hoffstaetter
    CLASSE, Ithaca, New York
 
 

The current status of the lattice and layout for the proposed Cornell Energy Recovery Linac lightsource is presented. This design is centered about a new hard X-ray user facility to be located on Cornell's campus, and is adapted to the local topography in order to incorporate the existing CESR tunnel and Wilson Laboratory. Nonlinear charged-particle optics for this new machine have been designed and analyzed. The lattice is populated with various components for the appropriate accelerator physics requirements for orbit, bunch length, and emittance growth control, including a vacuum system compatible with rest-gas-scattering limits, a collimation system for halo from effects like Touschek scattering, and correction coils and BPMs for sub-micron beam stabilization. We also show calculations for an additional bunch compression mode, which compresses 19~pC bunches at a 1.3~GHz repetition rate to 25~fs.

 
WEOBMH01 Operational Experiences Tuning the ATF2 Final Focus Optics Towards Obtaining a 37nm Electron Beam IP Spot Size emittance, quadrupole, coupling, background 2383
 
  • G.R. White, A. Seryi, M. Woodley
    SLAC, Menlo Park, California
  • S. Bai
    IHEP Beijing, Beijing
  • P. Bambade, Y. Renier
    LAL, Orsay
  • B. Bolzon
    IN2P3-LAPP, Annecy-le-Vieux
  • Y. Kamiya
    ICEPP, Tokyo
  • S. Komamiya, M. Oroku, Y. Yamaguchi, T. Yamanaka
    University of Tokyo, Tokyo
  • K. Kubo, S. Kuroda, T. Okugi, T. Tauchi
    KEK, Ibaraki
  • E. Marin
    CERN, Geneva
 
 

The primary aim of the ATF2 research accelerator is to test a scaled version of the final focus optics planned for use in next-generation linear lepton colliders. ATF2 consists of a 1.3 GeV linac, damping ring providing low-emittance electron beams (<12pm in the vertical plane), extraction line and final focus optics. The design details of the final focus optics and implementation at ATF2 are presented elsewhere* . The ATF2 accelerator is currently being commissioned, with a staged approach to achieving the design IP spot size. It is expected that as we implement more demanding optics and reduce the vertical beta function at the IP, the tuning becomes more difficult and takes longer. We present here a description of the implementation of the overall tuning algorithm and describe operational experiences and performances


* Beam-Based Alignment, Tuning and Beam Dynamics Studies for the ATF2 Extraction Line and Final Focus System. Glen R. White , S. Molloy, M. Woodley, (SLAC). EPAC08-MOPP039, SLAC-PUB-13303.

 

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WEOCMH03 Bunch Length Measurements with Laser/SR Cross-Correlation laser, photon, synchrotron, storage-ring 2408
 
  • A. Miller, D.R. Daranciang, A. Lindenberg
    Stanford University, Stanford, California
  • W.J. Corbett, A.S. Fisher, J.J. Goodfellow, X. Huang, W.Y. Mok, J.A. Safranek, H. Wen
    SLAC, Menlo Park, California
 
 

By operating SPEAR3 in the quasi-isochronous (low-alpha) mode, one can produce synchrotron radiation with pulse durations of order 1ps. Applications include pump-probe x-ray science and the production of THz radiation. Measurements of short pulse lengths are difficult, however, because the light intensity is low and streak camera resolution is of order 2ps. Bunch arrival time and timing jitter are also important factors. In order to further quantify the pulse length and timing system performance, a 5MHz, 50fs mode-locked laser was used to cross-correlate with the visible SR beam in a BBO crystal. The 800nm laser pulse was delayed with a precision mechanical stage and the product SHG radiation detected with a photodiode / lock-in amplifier using the ring frequency as reference. In this paper we report on the experimental setup, preliminary pulse length measurements and prospects for further improvement.

 

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WEOBRA03 Beam Break-up Estimates for the ERL at BNL cavity, HOM, linac, damping 2441
 
  • I. Ben-Zvi, R. Calaga, H. Hahn, L.R. Hammons, E.C. Johnson, A. Kayran, J. Kewisch, V. Litvinenko, W. Xu
    BNL, Upton, Long Island, New York
 
 

A prototype ampere-class superconducting energy recovery linac (ERL) is under advanced construction at BNL. The ERL facility is comprised of a five-cell SC Linac plus a half-cell SC photo-injector RF electron gun, both operating at 703.75 MHz. The facility is designed for either a high-current mode of operation up to 0.5 A at 703.75 MHz or a high-bunch-charge mode of 5 nC at 10 MHz bunch frequency. The R&D facility serves a test bed for an envisioned electron-hadron collider, eRHIC. The high-current, high-charge operating parameters make effective higher-order-mode (HOM) damping mandatory, and requires to determination of HOM tolerances for a cavity upgrade. The niobium cavity has been tested at superconducting temperatures and has provided measured dipole shunt impedances for the estimate of a beam breakup instability. The facility will be assembled with a highly flexible lattice covering a vast operational parameter space for verification of the estimates and to serve as a test bed for the concepts directed at future projects.

 

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Slides

 
WEPEA011 Double Low Beta Straight Section for Dual Canted Undulators at SOLEIL lattice, quadrupole, resonance, sextupole 2496
 
  • A. Loulergue, C. Benabderrahmane, F. Bouvet, P. Brunelle, M.-E. Couprie, J.-C. Denard, J.-M. Filhol, C. Herbeaux, P. Lebasque, V. Leroux, A. Lestrade, O. Marcouillé, J.L. Marlats, F. Marteau, T. Moreno, A. Nadji, L.S. Nadolski, F. Polack, A. Somogyi, M.-A. Tordeux
    SOLEIL, Gif-sur-Yvette
 
 

SOLEIL is the French 2.75 GeV high brilliance third generation synchrotron light source delivering photons to 20 beamlines with a current of 400 mA in multibunch or hybrid modes, and 60 mA in 8 bunch mode. There are already 17 insertion devices installed and 9 others are planned in the next 2 coming years. Among them, two canted in vacuum insertion devices are planned, for the Nanoscopium and Tomography beamlines, and will be accommodated in a 12 m long straight section, with a 6.5 mrad separation angle. These ~150 m long beamlines will exploit the high brilliance and coherence characteristics of the X-ray (5-20 keV) beam both for diffraction limited focusing and for contrast formation. To provide low vertical beta functions at each undulator, an extra triplet of quadrupoles was added in the middle of the section. We present here the lattice implementation footprint, the different working point under investigations as well as the first results of the measurements on the machine performances.

 
WEPEA014 Optics calibration at the MLS and at BESSY II synchrotron, quadrupole, lattice, radiation 2505
 
  • P.O. Schmid, P. Kuske
    Helmholtz-Zentrum Berlin für Materialien und Energie GmbH, Berlin
  • D.B. Engel, J. Feikes, R. Müller, G. Wüstefeld
    Helmholtz-Zentrum Berlin für Materialien und Energie GmbH, Elektronen-Speicherring BESSY II, Berlin
 
 

In this paper we present the results of our studies employing LOCO and MML for optics calibration at the MLS and at the BESSY II storage rings. Both the standard user modes and dedicated low alpha modes were analysed.

 
WEPEA015 Coherent THz Measurements at the Metrology Light Source radiation, single-bunch, ion, vacuum 2508
 
  • G. Wüstefeld, J. Feikes, M.V. Hartrott, M. Ries
    Helmholtz-Zentrum Berlin für Materialien und Energie GmbH, Elektronen-Speicherring BESSY II, Berlin
  • A. Hoehl, R. Klein, R. Müller, A. Serdyukov, G. Ulm
    PTB, Berlin
 
 

The Metrology Light Source* is the first storage ring optimized for THz generation**. It applies a bunch shortening mode, based on a flexible momentum compaction factor 'alpha'. The emitted THz radiation is very sensitive to the machine tuning, its power could vary by many orders of magnitude. We report on coherent THz signal intensities as a function of different machine parameters, such as beam energy, beam current, rf voltage and alpha tuning.


* R. Klein et al., Phys. Rev. ST. Accel. Beams vol. 11, 110701 (2008). ** J. Feikes et al., The Metrology Light Source: The First Electron Storage Ring Optimized for Generating Coherent THz Radiation, submitted to Phys. Rev. ST. Accel. Beams (2009).

 
WEPEA017 Turn-by-turn Data Analysis for PETRA III kicker, resonance, betatron, sextupole 2514
 
  • A. Kling, K. Balewski
    DESY, Hamburg
  • R. Bartolini
    JAI, Oxford
 
 

PETRA III is a 3rd generation synchrotron radiation light source which started commissioning in April 2009. Turn-by-turn capabilities are available for all 227 BPMs installed in the storage ring thus providing a powerful diagnostic tool for the characterization of the linear and nonlinear motion of the stored beam. We report on first results of beam dynamics studies using multiturn data acquired at PETRA III and first steps towards a calibration of the linear and nonlinear lattice model of the storage ring.

 
WEPEA020 Observation of Bunch Deformation at the ANKA Storage Ring synchrotron, radiation, storage-ring, impedance 2523
 
  • N. Hiller, S. Hillenbrand, A. Hofmann, E. Huttel, V. Judin, B. Kehrer, M. Klein, S. Marsching, A.-S. Müller, A. Plech, N.J. Smale, K.G. Sonnad, P.F. Tavares
    KIT, Karlsruhe
 
 

A dedicated optics with a low momentum compaction factor is used at the ANKA storage ring to reduce the bunch length to generate coherent synchrotron radiation (CSR). A double sweep streak camera is employed to determine the bunch length and shape for different optics and as a function of the beam current. Measurements of the longitudinal bunch profile have been performed for many different momentum compaction factors and various bunch currents. This paper describes the set up of the streak camera experiments and compares the measured bunch lengths to theoretical expectations.

 
WEPEA048 A Design Approach of the Beam Optics in the Complex Storage Ring lattice, storage-ring, emittance, quadrupole 2597
 
  • S.Q. Tian, H.H. Li, X.Y. Sun, M.Z. Zhang, W.Z. Zhang
    SINAP, Shanghai
 
 

Beam optics design is a crucial issue in modern synchrotron radiation facility. A design approach of the beam optics is presented here. It provides much convenience for effectively exploring achievable linear optics and globally investigating flexibility of a complex lattice with super-periodicity. Low-ε optics and low-αC optics are emphasized, and the SSRF storage ring is taken as a test lattice.

 
WEPEA059 Energy Acceptance and Touschek Lifetime Calculations for the TPS Storage Ring coupling, emittance, lattice, multipole 2621
 
  • H.-J. Tsai, H.-P. Chang, M.-S. Chiu, P.J. Chou, C.-C. Kuo, W.T. Liu, G.-H. Luo, F.H. Tseng, C.H. Yang
    NSRRC, Hsinchu
 
 

Touschek scattering is an important beam lifetime limiting effect for the TPS storage ring due to several challenges such as low emittance, small physical aperture and large second-order momentum compaction factor (nonlinear longitudinal motion). The Touschek relevant energy acceptance is determined by these challenges, therefore a reliable estimate of the Touschek lifetime is essential. We obtained Touschek induced betatron oscillation amplitudes in three sections (LS, SS and ARC) and RF bucket acceptance analytically and with simulations. In this paper, we present the energy acceptance and Touschek lifetime calculations for the TPS storage ring in the cases for different chromaticity settings, ID chamber limitations, magnet multipole field errors and optics correction effects.

 
WEPEA083 Application of Model Independent Analysis with EPICS-DDS EPICS, booster, controls, lattice 2675
 
  • N. Malitsky, I. Pinayev
    BNL, Upton, Long Island, New York
  • R.M. Talman
    CLASSE, Ithaca, New York
  • C. Xiaomeng
    Stony Brook University, Stony Brook
 
 

Model Independent Analysis (MIA) is an essential approach for measuring optical properties of accelerators. In the paper, we evaluate its application in the context of the NSLS-II Light Source storage ring. It is the first application of the new high-level application environment based on the EPICS-DDS middle layer. Using a full-scale virtual accelerator, the paper explores the tolerance of the MIA approach against the different conditions such as measurement noise in the beam position monitors, magnet errors, misalignments, etc.

 
WEPEA084 Study of Beam Emittance and Energy Spread Measurements Using SVD and Multiple Flags in the NSLS-II Booster Extraction Beamline booster, emittance, extraction, kicker 2677
 
  • G.M. Wang, R.P. Fliller, W. Guo, R. Heese, T.V. Shaftan, L.-H. Yu
    BNL, Upton, Long Island, New York
  • Y.-C. Chao
    TRIUMF, Vancouver
 
 

The low beam emittance requirement in the NSLS-II storage ring imposes a very tight constraint on its acceptance. This requires the injected beam emittance to be very small, for which a reliable scheme of measurement to determine the phase space and momentum characteristics of the beam coming out the booster is necessary. The original scheme based on the booster-to-dump transport line was hampered by the difficulty in decoupling betatron oscillation from dispersion, due to high concentration of dipoles and limited number of quads after the booster. This paper will describe the alternative method being planned to use the booster extraction line to measure the beam emittance and energy spread, as well as the associated errors.

 
WEPEB042 Optimization of the Position of the Radial Loop Pickups in the CERN PS pick-up, beam-losses, controls, quadrupole 2782
 
  • S. Aumon
    EPFL, Lausanne
  • S. Aumon, H. Damerau, S.S. Gilardoni
    CERN, Geneva
 
 

A part of the beam losses at transition crossing of high intensity beams in the CERN PS have been attributed to an excursion of the closed orbit. The orbit jump occurs simultaneously with the jump of the transition energy triggered by pulsed quadrupoles. Investigations showed that the position of the pickups used for the radial loop system was not optimized with respect to the dispersion change caused by the fast change of the transition energy. Thanks to new electronics of the orbit measurement system, turn-by-turn orbit data could be recorded around transition crossing. Their analysis, together with calculations of the transverse optics, allowed determining a new choice of pickup positions for the radial loop. In comparison to the previous pickup configuration, the new configuration improves the mean radial position not only during transition crossing, but all along the acceleration cycle.

 
WEPEB046 Optimization of the CLIC Baseline Collimation System collimation, wakefield, betatron, luminosity 2794
 
  • J. Resta-López
    JAI, Oxford
  • D. Angal-Kalinin, J.-L. Fernandez-Hernando, F. Jackson
    STFC/DL/ASTeC, Daresbury, Warrington, Cheshire
  • B. Dalena, D. Schulte, R. Tomás
    CERN, Geneva
  • A. Seryi
    SLAC, Menlo Park, California
 
 

Important efforts have recently been dedicated to the improvement of the design of the baseline collimation system of the Compact Linear Collider (CLIC). Different aspects of the design have been optimized: the transverse collimation depths have been recalculated in order to reduce the collimator wakefield effects while maintaining a good efficiency in cleaning the undesired beam halo; the geometric design of the spoilers have also been reviewed to minimize wakefields; in addition, the optics design have been polished to improve the collimation efficiency. This paper describes the current status of the CLIC collimation system after this optimization.

 
WEPD004 Modelling of Elliptically Polarizing Undulators sextupole, multipole, quadrupole, undulator 3087
 
  • L.O. Dallin, D.G. Bilbrough
    CLS, Saskatoon, Saskatchewan
 
 

To investigate the effect of an elliptically polarized undulator (EPU) on the dynamic aperture of storage ring a model is required for use in an optics code. An EPU can be modelled as an array of skew dipole magnets. The skew angle ranges from zero to ninety degrees depending on the degree of polarization. Crudely the EPU can be modelled using alternating skew dipole blocks. A model that better reproduces the sinusoidally varying fields can be achieved by slicing blocks into smaller subsets. Field roll-off produced by the limited transverse dimensions of the magnet blocks can be included as skew multipoles. For example the roll-off of the horizontal field in the vertical undulator mode is very nearly a skew sextupole. The model has the advantage of correctly calculating the path length through the EPU which is important for tracking in six dimensions.

 
WEPD057 Linac Energy Management for LCLS klystron, lattice, linac, controls 3224
 
  • P. Chu, R.H. Iverson, P. Krejcik, D. Rogind, G.R. White, M. Woodley
    SLAC, Menlo Park, California
 
 

Linac Energy Management (LEM) is a control system program which calculates, and optionally implements, magnet setpoint settings (BDESs) following a change in Energy (such as a change in the number, phase, and amplitude of active klystrons). The change is made relative to those magnets' existing BDES setpoints by a factor encoding the change in energy. LEM is necessary because changes in the number, phase, and amplitude of the active klystrons (the so-called "Klystron complement") change the beam's rigidity, and therefore, to maintain constant optics, one has to change focusing gradients and bend fields. This paper describes the basic process and some of the implementation lessons learned for LEM at the LCLS.

 
WEPE007 Simulation Study of Scale Error Effect of BPM in ILC Main Linac Corrections emittance, linac, simulation, quadrupole 3353
 
  • K. Kubo
    KEK, Ibaraki
  • D. Wang
    IHEP Beijing, Beijing
 
 

For preserving low emittance beam in the ILC (International Linear Collider) main linacs, Dispersion Matching Steering (DMS) is planed to be used as a main correction method. The linacs are following the earth's curvature and the designed vertical dispersion in the linacs should not be zero. For this reason, the orbit difference due to beam energy difference will have to be measured accurately and tolerance of scale error of beam position monitors (BPM) can be tight. Here, the tolerance of the scale error are estimated by tracking simulations. Choice of optics design for relaxing the tolerance is also discussed.

 
WEPE027 Progress towards the CLIC Feasibility Demonstration in CTF3 linac, ion, klystron, controls 3410
 
  • P.K. Skowronski, S. Bettoni, R. Corsini, A.E. Dabrowski, S. Döbert, A. Dubrovskiy, F. Tecker
    CERN, Geneva
  • C. Biscari
    INFN/LNF, Frascati (Roma)
  • W. Farabolini
    CEA, Gif-sur-Yvette
  • R.J.M.Y. Ruber
    Uppsala University, Uppsala
 
 

The objective of the CLIC Test Facility CTF3 is to demonstrate the key feasibility issues of the CLIC two-beam technology: the efficient generation of a very high current drive beam and its stable deceleration in 12 GHz resonant structures, to produce high-power RF pulses and accelerate the main beam with an accelerating gradient of 100 MV/m. The construction and commissioning of CTF3 has taken place in stages from 2003. Many milestones had already been reached, including the first demonstration at the end of 2009 of a factor 2 x 4 re-combination of the initial drive beam pulse, thus reaching a beam current of 25 A. In this paper we summarise the commissioning highlights and the issues already validated at the earlier stages. We then show and discuss the latest results obtained, in view of the completion of the CLIC feasibility demonstration due for the end of 2010.

 
WEPE052 Optimization of the MICE Muon Beam Line emittance, target, quadrupole, solenoid 3461
 
  • M. Apollonio
    Imperial College of Science and Technology, Department of Physics, London
  • M.A. Rayner
    OXFORDphysics, Oxford, Oxon
 
 

In the Muon Ionization Cooling Experiment (MICE) at RAL muons are produced and transported in a dedicated beamline connecting the production point (target) to the diffuser, a mechanism inside the first spectrometer solenoid designed to inflate the initial normalized emittance up to 10 mm rad in a controlled fashion. In order to match the incoming muons to the downstream experiment, covering all the possible values of the emittance-momentum matrix, an optimisation procedure has been devised which is based upon a genetic algorithm coupled to the tracking code G4Beamline. Details of beamline tuning and initial measurements are discussed.

 
WEPE061 Measurements of Muon Beam Properties in MICE emittance, lattice, factory, solenoid 3482
 
  • M.A. Rayner, J.H. Cobb
    OXFORDphysics, Oxford, Oxon
 
 

The Muon Ionization Cooling Experiment is one lattice section of a cooling channel suitable for conditioning the muon beam at the front end of a Neutrino Factory or Muon Collider. Scintillating fibre spectrometers and 50 ps resolution timing detectors provide the unprecedented opportunity to measure the initial and final six-dimensional phase space vectors of individual muons. The capability of MICE to study the evolution of muon beams through a solenoidal lattice will be described.

 
WEPE084 Muon Acceleration with RLA and Non-scaling FFAG Arcs linac, sextupole, quadrupole, lattice 3539
 
  • V.S. Morozov
    ODU, Norfolk, Virginia
  • S.A. Bogacz
    JLAB, Newport News, Virginia
  • D. Trbojevic
    BNL, Upton, Long Island, New York
 
 

Recirculating linear accelerators (RLA) are the most likely means to achieve the rapid acceleration of short-lived muons to multi-GeV energies required for Neutrino Factories and TeV energies required for Muon Colliders. In the work described here, a novel arc optics based on a Non Scaling Fixed Field Alternating Gradient (NS-FFAG) lattice is developed, which would provide sufficient momentum acceptance to allow multiple passes (two or more consecutive energies) to be transported in one string of magnets. We present a combination of the non-scaling NS-FFAG RLA placed in a straight section. Orbit offsets of different energy muons are kept small in the NS-FFAG arcs during multiple passes. The NS-FFAG, made of densely packed FODO cells, allows momentum acceptance of dp/p=±60%. This solution would reduce overall cost and simplify the operation. Difference in a muon path length for corresponding energies is corrected with a chicane. We will also discuss technical requirements to allow the maximum number of passes by using an adjustable path length to accurately control the returned beam phase to synchronize with the RF.

 
THOAMH01 Recirculating Linear Accelerators for Future Muon Facilities linac, focusing, acceleration, lattice 3602
 
  • S.A. Bogacz
    JLAB, Newport News, Virginia
  • K.B. Beard, R.P. Johnson
    Muons, Inc, Batavia
 
 

Neutrino Factories and Muon Colliders require rapid acceleration of short-lived muons to multi-GeV and TeV energies. A Recirculating Linear Accelerator (RLA) that uses superconducting RF structures can provide exceptionally fast and economical acceleration to the extent that the focusing range of the RLA quadrupoles allows each muon to pass several times through each high-gradient cavity. A new concept of rapidly changing the strength of the RLA focusing quadrupoles as the muons gain energy is being developed to increase the number of passes that each muon will make in the RF cavities, leading to greater cost effectiveness. We discuss the optics and technical requirements for RLA designs, using RF cavities capable of simultaneous acceleration of both μ+ and μ- species, with pulsed Linac quadrupoles and arc magnets to allow the maximum number of passes. The design will include the optics for the multi-pass linac and droplet-shaped return arcs.

 

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Slides

 
THOBRA03 Observation of Transverse-Longitudinal Coupling Effect at UVSOR-II electron, laser, betatron, coupling 3650
 
  • M. Shimada
    KEK, Ibaraki
  • M. Adachi, M. Katoh, S.I. Kimura
    UVSOR, Okazaki
  • M. Hosaka, Y. Takashima, N. Yamamoto
    Nagoya University, Nagoya
  • T. Takahashi
    KURRI, Osaka
  • T. Tanikawa
    Sokendai - Okazaki, Okazaki, Aichi
 
 

It was theoretically predicted that, when the electron pulse length comes into the femto-second range, transverse motion of the electrons is strongly coupled with the longitudinal one and makes significant effect on the pulse shape. In the experiments, a fine dip structure was created on the electron bunches circulating in a storage ring by a so-called laser bunch slicing technique and then the evolution of the structure was measured through the spectrum of the coherent synchrotron radiation. When the ring was operated in a low-alpha mode, the shape of the dip structure was oscillating with the transverse betatron frequency, which clearly indicates the existence of the longitudinal-transverse coupling effect. This understanding will be crucially important for generation and transportation of ultra-short electron bunches in light sources or colliders for high energy physics. In this presentation, the dependency of the CSR signal intensity on the wavelength of the THz CSR and the electron beam current are also reported.

 

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Slides

 
THPEB006 Optics Measurements and Transfer Line Matching for the SPS Injection of the CERN Multi-turn Extraction Beam extraction, injection, emittance, proton 3888
 
  • E. Benedetto
    National Technical University of Athens, Zografou
  • G. Arduini, S. Cettour Cave, F. Follin, S.S. Gilardoni, M. Giovannozzi, F. Roncarolo
    CERN, Geneva
 
 

Dispersion and beam optics measurements were carried out in the transfer line between the CERN PS and SPS for the new Multi-Turn Extraction beam. Since the extraction conditions of the four islands and the core are different and strongly dependent on the non-linear effects used to split the beam in the transverse plane, a special care was taken during the measurement campaigns. Furthermore, an appropriate strategy was devised to minimize the overall optical mismatch at SPS injection. All this led to a new optical configuration that will be presented in detail in the paper.

 
THPEB027 Transfer Lines to and from PS2 injection, extraction, emittance, proton 3942
 
  • C. Heßler, W. Bartmann, M. Benedikt, B. Goddard, M. Meddahi, J.A. Uythoven
    CERN, Geneva
 
 

Within the scope of the LHC injector upgrade, it is proposed to replace the present injector chain by new accelerators, Linac4, SPL and PS2, for which new beam transfer lines are required. The beam properties and requirements for each of the lines are summarized. The original design of the beam lines has been fully reconsidered due to the very demanding constraints on the beam line layouts at the PS2 injection / extraction regions and a new straight section of the PS2 which led to a much improved beam line geometry. The relevant modifications and optics designs are described and a preliminary specification of the beam line equipment is also given.

 
THPEB028 A Doublet-based Injection-extraction Straight Section for PS2 injection, extraction, quadrupole, laser 3945
 
  • W. Bartmann, B. Goddard, C. Heßler
    CERN, Geneva
 
 

A new design of the injection-extraction straight section for PS2 has been made, motivated by problematic intersections of the PS2 transfer lines, potential gain in drift length for the beam transfer systems and reduction of the total straight section length. The new straight contains two injection systems with separate beam lines and three extraction systems to the SPS sharing a single beam line, together with an extracted "waste" beam from the H- injection with its line to a beam dump. A symmetric doublet structure was chosen, with a reduced number of cells and quadrupoles. The optics solutions are described and the matching and tuning flexibility investigated. The implications for the different injection and extraction systems and transfer lines will be discussed, together with the specific issues of integration into the overall lattice.

 
THPEB029 The Final Beam Line Design for the HiRadMat Test Facility target, vacuum, instrumentation, quadrupole 3948
 
  • C. Heßler, B. Goddard, M. Meddahi
    CERN, Geneva
 
 

The High Radiation to Materials facility - thereafter HiRadMat - is designed to allow testing of accelerator components, in particular those of the LHC and its injectors, with the impact of high-intensity pulsed beams. The facility is currently under construction, as an approved CERN project. The installation of the dedicated primary beam line and experimental area is planned during the 2010-2011 CERN accelerator technical shutdown. It will be ready for users after commissioning and some initial running in October 2011. A detailed proton beam line design has been performed in order to fulfill the beam parameter specification, in particular the demanding optics flexibility at the test stand location. The studies presented include trajectory correction and aperture studies as well as specifications of magnetic systems, power converters, beam instrumentation and vacuum systems.

 
THPEC085 Beam-beam Effect for the LHC Phase I Luminosity Upgrade luminosity, injection, dynamic-aperture, simulation 4255
 
  • E. Laface, S.D. Fartoukh, F. Schmidt
    CERN, Geneva
 
 

The Phase I Luminosity Upgrade of LHC (SLHC) will be based on a new Nb-Ti inner triplet for the high luminosity region ATLAS and CMS. The new proposed layout aims at pushing beta* down to 30 cm replacing the current LHC inner triplet, with longer ones operating at lower gradient (123 T/m) and therefore offering enough aperture for the beam to reduce beta* to its prescribed value. As a consequence of this new longer interaction region, the number of parasitic encounters will increase from 15 to 21 before the separation dipole D1, with an impact on the dynamic aperture of the machine. In this paper the effect of the beam-beam interaction is evaluated for the SLHC layout and optics, at injection and in collision, evaluating the possible impact of a few additional parasitic collisions inside and beyond the D1 separation dipole till the two beams do no longer occupy the same vacuum chamber. Whenever needed, a comparison with the nominal LHC will be given. Then a possible backup collision optics will be discussed for the SLHC, offering a much wider crossing angle at an intermediate beta* of 40 cm in order to reach a target dynamic aperture of 7.5 σ.

 
THPD004 Design of the Positron Transport System for SuperKEKB linac, positron, emittance, injection 4284
 
  • N. Iida, T. Kamitani, M. Kikuchi, Y. Ogawa, K. Oide
    KEK, Ibaraki
 
 

SuperKEKB, the upgrade plan of KEKB, aims to boost the luminosity up to 8·1035 /cm2/s. The beam energy of the Low Energy Ring (LER) is 4 GeV for positrons, and that of the High Energy Ring is 7 GeV for electrons. SuperKEKB is designed to produce low emittance beams. The horizontal and vertical emittances of the injection beams are 4nm and 1nm, respectively, which are one or two orders smaller than those of KEKB. The positron injector system consists of the source, capture system, L-band and S-band linacs, collimators, an energy compression system (ECS), a 1-GeV damping ring, a bunch compression system (BCS), S-band and C-band linacs, and a beam transport line into the LER. This paper reports a design of the positron beam transport system from L-band linacs to SuperKEKB.

 
THPD077 Linear Collider Test Facility: Twiss Parameter Analysis at the IP/Post-IP location of the ATF2 beam line emittance, laser, controls, simulation 4458
 
  • B. Bolzon, A. Jeremie
    IN2P3-LAPP, Annecy-le-Vieux
  • S. Bai
    IHEP Beijing, Beijing
  • P. Bambade
    KEK, Ibaraki
  • G.R. White
    SLAC, Menlo Park, California
 
 

At the first stage of the ATF2 beam tuning, vertical beam size is usually bigger than 3um at the IP. Beam waist measurements using wire scanners and a laser wire are usually performed to check the initial matching of the beam through to the IP. These measurements are described in this paper for the optics currently used (βx=4cm and βy=1mm). Software implemented in the control room to automate these measurements with integrated analysis is also described. Measurements showed that beta functions and emittances were within errors of measurements when no rematching and coupling corrections were done. However, it was observed that the waist in the horizontal (X) and vertical (Y) plane was abnormally shifted and simulations were performed to try to understand these shifts. They also showed that multiknobs are needed in the current optics to correct simultaneously αx, αy and the horizontal dispersion (Dx). Such multiknobs were found and their linearity and orthogonality were successfully checked using MAD optics code. The software for these multiknobs was implemented in the control room and waist scan measurements using the αy knob were successfully performed.

 
THPD085 Correction of the Linear Optics at PETRA III quadrupole, undulator, emittance, wiggler 4482
 
  • J. Keil, K. Balewski
    DESY, Hamburg
 
 

PETRA III is a 6 GeV third generation light source located at DESY/Hamburg. The former pre-accelerator of HERA has been converted in 2007/2008 into a high brilliance synchrotron light source with an emittance of 1 nm*rad. The commissioning of PETRA III started in 2009. PETRA III is like other third generation light sources very sensitive to errors of the linear optics. Gradient errors reduce the dynamic aperture, increase the emittance and change the beam size. The correction of the optics is based on orbit response matrix data which were analyzed both with the program LOCO and with a fit of the beta-functions and phase-functions at BPMs and correctors. Initial results of the modelling of the machine and the correction of the linear optics functions will be presented.

 
THPD087 Potential Forms for Electrostatic and Magnetic Cylindrical Lens and Tracking of Charged Particle solenoid, induction, proton, focusing 4488
 
  • M.H. Rashid, R.K. Bhandari, C. Mallik
    DAE/VECC, Calcutta
 
 

A cylindrical lens is mainly used for focusing and transporting low energy beam. Some analytical forms of scalar potential have been formulated to evaluate electric and magnetic field and its derivatives on the central axis, which help in evaluation of potential and field in the region about the central axis. They are, subsequently, used to analytically find out the optical properties of a lens as well as in tracking of charged particles. It turns into a tool to design an electrostatic or a magnetic cylindrical lens. A section-technique has been developed to evaluate the optical cardinal points of a thick lens very accurately. Smooth profiles of the field and potential along the axis are divided into large number of small stepped profile. Each step represents a weak thin lens as change in radial movement is very small. The effect of the individual weak lenses is evaluated and combined by matrix multiplication method to get optical property of the thick lens. The obtained values are verified by exactly tracking the particles by solving the Lorentz equation of motion of charged particle in electric or magnetic field.

 
THPD091 Explicit Maps for the Fringe Field of a Quadrupole quadrupole, focusing, storage-ring, simulation 4500
 
  • D.M. Zhou
    KEK, Ibaraki
  • Y. Chen, J. Tang, N. Wang
    IHEP Beijing, Beijing
 
 

A perturbation method based on Lie technique, originated by J. Irwin and C.-x. Wang, was extended to calculate the linear maps for the fringe field of a quadrupole. In our method, the fringe field shape is not necessarily anti-symmetric with respect to the hard-edge position. The linear maps were explicitly expressed as functions of fringe field integrals. Thus they can be used to assess the influence of the quadrupole fringe fields in beam dynamics.

 
THPD096 Simulation of Multiknobs Correction at ATF2 coupling, simulation, quadrupole, emittance 4512
 
  • S. Bai, J. Gao
    IHEP Beijing, Beijing
  • P. Bambade
    KEK, Ibaraki
  • B. Bolzon
    IN2P3-LAPP, Annecy-le-Vieux
 
 

The ATF2 project is the final focus system prototype for ILC and CLIC linear collider projects, with a purpose to reach a 37nm vertical beam size at the interaction point. During initial commissioning, we started with larger than nominal β-functions at the IP, to reduce the effects from higher-order optical aberrations and thereby simplify the optical corrections needed. We report on simulation studies at two different IP locations developed based on waist scan, dispersion, coupling and β function multiknobs correction in the large β optics of ATF2, in the presence of two kinds of magnet inaccuracies (quadrupole gradient and roll errors) to generate all possible linear optics distortions at the IP. A vertical beam size which is very close to the nominal beam size is obtained based on the simulation study.

 
THPE001 Low Emittance Lattice Optimization Using Multiobjective Genetic Algorithm lattice, emittance, storage-ring, quadrupole 4515
 
  • W.W. Gao, W. Li, L. Wang
    USTC/NSRL, Hefei, Anhui
 
 

Low emittance is a desirable performance for high brightness synchrotron light source and damping ring. The work presented in this paper demonstrates that the lattice of a given electron storage ring, which has fixed circumference and magnet layout, can be optimized to obtain low emittance by using MOGA (Multi-objective Genetic Algorithm). Both dispersion-free and non-dispersion-free lattices of HLS (Hefei Light Source) upgrade project are computed as an illustration. Simulation result shows that this method is fast and straightforward.

 
THPE018 Layout and Optics Solution for the LHC Insertion Upgrade Phase I insertion, quadrupole, injection, sextupole 4548
 
  • S.D. Fartoukh
    CERN, Geneva
 
 

The main guidelines of the LHC insertion (IR) upgrade Phase I are 1) the development of wider aperture (120 mm) and lower gradient (~120 T/m) quadrupoles using the well-characterized Nb-Ti technology in order to replace the existing inner triplets (IT) equipping the ATLAS and CMS high-luminosity IRs of the LHC, 2) while maximizing the use of the current LHC infrastructure, in particular leaving unchanged the so-called "matching sections" (MS) and "dispersion suppressors" (DS) of these two insertions. One of the initial goals was to be able to squeeze the optics up to a beta* of 25 cm. However, optics solutions with a beta* of 30 cm seems already to be at edge of achievability, both in terms of the IT and MS mechanical acceptance, gradients of the MS and DS quadrupole magnets, and correctability by the LHC arc sextupoles of the huge chromatic aberrations induced by the new inner triplet at ultimate beta*. The layout of the new inner triplet and the corresponding injection and collision optics will be presented and analyzed both in terms of aperture, squeeze-ability and chromatic correction.

 
THPE021 Comparison of PS2 Lattices with Different Geometries lattice, quadrupole, resonance, dynamic-aperture 4557
 
  • Y. Papaphilippou, W. Bartmann, H. Bartosik, M. Benedikt, B. Goddard, A. Lachaize
    CERN, Geneva
  • Y. Senichev
    FZJ, Jülich
 
 

The PS2 ring is designed with negative momentum compaction arc cells and doublet straights. In this paper, different lattice geometries are considered. In particular, a two-fold symmetric lattice with dispersion suppressors and a 3-fold symmetric one with resonant arc cells are compared with respect to their optics properties, and ability to satisfy space and magnet constraints. The tuning flexibility of rings based on these two options is presented. Finally, the impact of different geometries on resonance excitation and dynamic aperture is evaluated.

 
THPE022 Linear Optimization and Tunability of the PS2 Lattice quadrupole, lattice, injection, vacuum 4560
 
  • H. Bartosik, W. Bartmann, M. Benedikt, B. Goddard, Y. Papaphilippou
    CERN, Geneva
 
 

The PS2 lattice, based on Negative Momentum Compaction (NMC) arc cells is being optimized in order to accommodate a new all-doublet long-straight section (LSS) design. Apart from smoothing the optics and enabling different tuning solutions for H- injection, the optimization focuses on increasing the available magnet-to-magnet drift space and reducing the quadrupole types and strengths. The variation of lattice parameters for a wide range of working points is presented.

 
THPE026 Software Package for Optics Measurement and Correction in the LHC dipole, coupling, synchrotron, resonance 4572
 
  • G. Vanbavinckhove, M. Aiba, R. Tomás
    CERN, Geneva
  • R. Calaga
    BNL, Upton, Long Island, New York
 
 

A software package has been developed for the LHC on-line optics measurement and correction. This package includes several different algorithms to measure phase advance, beta functions, dispersion, coupling parameters and even some non-linear terms. A Graphical User Interface provides visualization tools to compare measurements to model predictions, fit analytical formula, localize error sources and compute and send corrections to the hardware.

 
THPE027 Construction and Performance of IP Optics Tuning Knobs in the LHC injection, luminosity, quadrupole, insertion 4575
 
  • S.M. White, R. Tomás, G. Vanbavinckhove, W. Venturini Delsolaro
    CERN, Geneva
 
 

During the first years of operation of the LHC unknown field errors or misalignments could lead to unmatched optics and discrepancies with respect to the model. This could affect some critical parameters such as the luminosity or the lifetime. It is therefore desirable to implement tools which allow for fine tuning of the IP optics and could be used during the commissioning phase of the LHC. In this paper we report on the implementation the performances and the limitations of these commissioning tools.

 
THPE032 Calculation of Coupled Lattice Functions from Turn-by-turn Trajectory Data in Storage Rings lattice, betatron, quadrupole, coupling 4587
 
  • A. Wolski, M. Korostelev, K.G. Panagiotidis
    The University of Liverpool, Liverpool
 
 

BPMs capable of high resolution turn-by-turn bunch position measurements are becoming increasingly widely used in electron storage rings. Analysis of the data from a set of such BPMs following the excitation of a coherent betatron oscillation can yield useful information for tuning the optics and improving machine performance. This approach to optics measurement has the benefits that the data collection is very fast, and analysis can be local, so that application is as easy for a large ring as for a small one. Here, we describe a technique for using turn-by-turn BPM data to determine lattice functions that describe the local coupling in a storage ring; this may be helpful, for example, for achieving low vertical emittance. We discuss the principles of the technique, give some examples, and discuss possible limitations arising from BPM gain and coupling errors.

 
THPE047 Lattice Calibration with Turn-by-turn BPM Data quadrupole, lattice, simulation, target 4623
 
  • X. Huang, J.J. Sebek
    SLAC, Menlo Park, California
 
 

Turn-by-turn beam position monitor (BPM) data from multiple BPMs are fitted with a tracking code to calibrate magnet strengths in similar manner as the well known LOCO code. Simulation shows that this method can be a quick and efficient way for optics calibration. The method is applicable to both linacs and ring accelerators. We also show experimental measurement of the transfer matrix with turn by turn BPM data.

 
THPE050 Real Beam Line Optics from a Synthetic Beam beam-losses, quadrupole, emittance, diagnostics 4629
 
  • R.M. Bodenstein, Y. Roblin, M.G. Tiefenback
    JLAB, Newport News, Virginia
 
 

The Continuous Electron Beam Accelerator Facility (CEBAF) at Jefferson Lab can be described as a series of concatenated beamlines. Methods used to measure the Twiss parameters in closed orbit machines are not applicable in such open ended systems. We are using properly selected sets of real orbits in the accelerator, as one would for numerical analysis. The evolution of these trajectories along the beamline models the behavior of a synthetic beam which deterministically supplements beam profile-based Twiss parameter measurements and optimizes the efficiency of beamline tuning. Examples will be presented alongside a description of the process.

 
THPE051 Magnet Optical and Beam Matching Issues in a Medium Energy Beam Transport line of SNS Linac lattice, simulation, focusing, quadrupole 4632
 
  • J. G. Wang, Y. Zhang
    ORNL, Oak Ridge, Tennessee
 
 

A Medium Energy Beam Transport line (MEBT) is employed in the SNS linac to match the beam from an RFQ to a DTL and to perform other functions. The MEBT lattice consists of fourteen electromagnetic quadrupoles. The quads have very small aspect ratios (steel length over aperture diameter), and they are densely packed in the lattice. Significant fringe fields and magnetic interference cause difficulties in beam matching. We have performed 3D simulations of the magnets, computed their optical properties, and compared their performance with what predicted by simple hard edge models. This paper reports our findings and possible solutions to the problem.

 
THPE053 Linear and Chromatic Optics Measurements at RHIC injection, quadrupole, coupling, lattice 4638
 
  • R. Calaga
    BNL, Upton, Long Island, New York
  • M. Aiba
    PSI-LRF, Villigen, PSI
  • R. Tomás, G. Vanbavinckhove
    CERN, Geneva
 
 

Measurements of chromatic beta-beating were carried out for the first time in the RHIC accelerator during Run 2009. The analysis package developed for the LHC was used to extract the off-momentum optics for injection and top energy. Results from the beam experiments and comparison to the optics model are presented.

 
THPE055 Linear Optics Measurements and Corrections Using AC Dipole In RHIC dipole, quadrupole, beam-losses, injection 4644
 
  • G. Wang, M. Bai, L. Yang
    BNL, Upton, Long Island, New York
 
 

We report recent experimental results on linear optics measurements and corrections using ac dipole. In RHIC 2009 run, the concept of the SVD correction algorithm is tested at injection energy for both identifying the artificial gradient errors and correcting it using the trim quadrupoles. The measured phase beatings were reduced by 30% and 40% respectively for two dedicated experiments. In RHIC 2010 run, ac dipole is used to measure beta* and chromatic beta function. For the 0.65m beta* lattice, we observed a factor of 3 discrepancy between model and measured chromatic function in the yellow ring.

 
THPE070 Synchro-beta Resonance Simulation using Measured Chromatic Aberrations simulation, resonance, coupling, emittance 4680
 
  • Y. Seimiya, K. Ohmi
    KEK, Ibaraki
 
 

Synchro-beta resonances enhance beam sizes dynamically. For accelerators aimed for high luminosity, the effect can be more serious since a difference between vertical emittance and longitudinal emittance tends to be larger. Therefore, it is necessary to estimate a tune spread of the synchro-beta resonances properly. Synchro-beta effect is caused by chromatic aberrations, which characterize how optics parameters, including tune, Twiss parameter, X-Y coupling parameter, and other parameters, depend on the momentum deviation. The chromatic aberrations are actually defined by coefficients of an optics parameter in is expansion in terms of momentum deviation. The synchro-beta resonances caused by chromatic aberrations are discussed in this conference. We use 6-dimensional symplectic map which is obtained from measured optics parameters in order to simulate beam motion precisely*.


* Y. Seimiya and K. Ohmi, TH6PFP020, Particle Accelerator Conference PAC09, 4-8 May 2009, Vancouver, Canada.

 
THPE080 Dynamic Aperture Computation for the as-built CERN Large Hadron Collider injection, dynamic-aperture, simulation, target 4707
 
  • M. Giovannozzi
    CERN, Geneva
 
 

During the design phase of the CERN Large Hadron Collider the dynamic aperture, i.e., the domain in phase space where stable motion occurs, was used as figure-of-merit to specify the field quality of the various classes of superconducting magnets. The programme of magnetic measurements performed within the framework of the magnets' acceptance process has produced a large amount of information available, which can be used to estimate the value of the dynamic aperture for the actual machine. In this paper the results of massive numerical simulations based on the measured field quality, both for injection and top energy configurations, are presented and discussed in detail.

 
THPE083 Signal Quality of the LHC AC Dipoles and its Impact on Beam Dynamics dipole, emittance, simulation, synchrotron 4716
 
  • R. Miyamoto
    BNL, Upton, Long Island, New York
  • M. Cattin, J. Serrano, R. Tomás
    CERN, Geneva
 
 

The adiabaticity of the AC dipole might be compromised by noise or unwanted frequency components in its signal. An effort has been put to characterize and optimize the signal quality of the LHC AC dipoles. The measured signal is used in realistic simulations in order to evaluate its impact on beam dynamics and to ultimately establish safe margins for the operation of the LHC AC dipoles.

 
THPE088 Beam Dynamics Effect of Insertion Devices at Diamond Storage Ring wiggler, injection, resonance, vacuum 4731
 
  • B. Singh, R.T. Fielder, J. Rowland
    Diamond, Oxfordshire
  • R. Bartolini, I.P.S. Martin
    JAI, Oxford
 
 

Diamond operates with 10 in-vacuum insertion devices at 5 mm gap, two Apple-II, two superconducting and two normal conducting wigglers. We report here the correction of the linear optics of wigglers and measurements of nonlinear effects such as dynamic aperture and frequency maps and their impacts on injection efficiency, lifetime and loss distribution in operation of the storage ring.

 
THPE091 Simultaneous Measurement of all Sextupole Offsets using the Response Matrix Fit sextupole, quadrupole, storage-ring, coupling 4737
 
  • V. Sajaev, A. Xiao
    ANL, Argonne
 
 

APS linear model is defined by the quadrupole and skew quadrupole errors that are determined using the response matrix fit. What was missing until now were the sextupole offsets relative to the beam orbit. At APS the orbit is routinely steered according to user requests, and at some locations the steering has accumulated to rather large values. That is why the usual sextupole changes that are performed during operation mode switches lead to optics and coupling changes. Knowledge of the sextupole offsets would allow us to predict and control those changes. There are a number of ways to measure sextupole offsets but most of them utilize element by element approach. This would take very long time for the 280 sextupoles at APS. Here we describe a method that determines the beam offsets of all sextupoles based on fitted values of local optics and coupling changes at each sextupole. We perform response matrix measurement, fit several lattices with different sextupoles, and derive the sextupole offsets. The results are included in the linear model of the APS storage ring.

 
THPE094 A Search for Integrable Four-dimensional Nonlinear Accelerator Lattices betatron, lattice, octupole, focusing 4743
 
  • S. Nagaitsev
    Fermilab, Batavia
  • V.V. Danilov
    ORNL, Oak Ridge, Tennessee
 
 

Integrable nonlinear motion in accelerators has the potential to introduce a large betatron tune spread to suppress instabilities and to mitigate the effects of space charge and magnetic field errors. To create such an accelerator lattice one has to find magnetic and/or electrtic field combinations leading to a stable integrable motion. This paper presents families of lattices with one invariant where bounded motion can be easily created in large volumes of the phase space. In addition, it presents two examples of integrable nonlinear accelerator lattices, realizable with longitudinal-coordinate-dependent magnetic or electric fields with the stable nonlinear motion, which can be solved in terms of separable variables.