• D.J. Kelliher, S. Machida
  STFC/RAL/ASTeC, Chilton, Didcot, Oxon
• S.L. Sheehy
  JAI, Oxford

A novel nonlinear, nonscaling FFAG ring has been designed for proton and ion acceleration [1]. It can be used for proton and carbon therapy as well as a proton driver for various facilities such as a high intensity neutrino factory. The machine has novel features including variable energy extraction and a high repetition rate of about 1 kHz. Taking as an example the PAMELA proton ring, under study at the John Adams Institute in Oxford, we present results of an error study. A calculation of alignment tolerance is made, in which the effects of translational misalignments of the triplet magnets are included. The effect of misalignments on the dynamic aperture of the machine is investigated.

[1] S. L. Sheehy, K. J. Peach, H. Witte, D. J. Kelliher and S. Machida, Phys. Rev. ST Accel. Beams, 13 (2010) 040101

• 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.

• J.-H. Jang, Y.-S. Cho, H.S. Kim, H.-J. Kwon
  KAERI, Daejon
• Y.Y. Lee
  BNL, Upton, Long Island, New York

As a feasible extension plan of the proton engineering frontier project (PEFP) 100-MeV proton linac, the conceptual design of an rapid cycling synchrotron (RCS) is under progress. The main purpose of the synchrotron is a spallation neutron source and it also includes the slow extraction option for basic and applied science research. In the initial stage, the beam power is 60 kW by using a scheme of 100-MeV injection and 1-GeV extraction. There is a scheme to increase power to 500 kW through a 3-stage upgrade. The injection and extraction energies will be 200-MeV and 2-GeV respectively after the final upgrade. This article summarizes the present status of the RCS design. It includes the physics design including injection and acceleration, and conceptual design of some magnets and RF cavity.

• M. Meng, Y.B. Chen, J.H. Wang, Y.L. Yang, Z.R. Zhou
  USTC/NSRL, Hefei, Anhui

In HLS we employ the TED FPGA based processor for digital feedback system. To make feedback system work better and more easily, we developed the control and analysis system based on matlab chiefly. The system do jobs as following: sampling data online and finishing its analysis; calculating fir filter parameters and generating .csv(format for FPGA) file to get the best gain and phase flexibly according to different beam working point; simulating the beam changes in different feedback gain and other stations to check whether the system work properly.

• K. Ohmi, H. Koiso
  KEK, Ibaraki

Progress of Graphic Processor Unit (GPU) is marveled. The performance is 1TFlops per unit. Simulation of electron gun can be performed by particle-particle interactions, in which the calculation cost is NxN. Since the calculation of each interaction is very simple, GPU can demonstrate its ability. We show simulation results and discuss the possibilities to extend other simulations.

• Y. Alexahin, E. Gianfelice-Wendt, A.V. Netepenko
  Fermilab, Batavia

Muon collider is a promising candidate for the next energy frontier machine. However, in order to obtain peak luminosity in the 10³⁵/cm²/s range the collider lattice design must satisfy a number of stringent requirements, such as low beta at IP (beta*<1 cm), large momentum acceptance and dynamic aperture and small value of the momentum compaction factor. Here we present a particular solution for the interaction region optics whose distinctive feature is a three-sextupole local chromatic correction scheme. Together with a new flexible momentum compaction arc cell design this scheme allows to satisfy all the above-mentioned requirements and is relatively insensitive to the beam-beam effect.

• A.I. Papash
  MPI-K, Heidelberg
• O.E. Gorda
  GSI, Darmstadt
• A.I. Papash
  JINR, Dubna, Moscow Region
• C.P. Welsch
  Cockcroft Institute, Warrington, Cheshire

Electrostatic storage rings have proven to be invaluable tools for atomic and molecular physics. Due to the mass independence of the electrostatic rigidity, these machines are able to store a wide range of different particles, from light ions to heavy singly charged bio-molecules. However, earlier measurements showed strong space charge limitations; probably linked to non-linear fields that cannot be completely avoided in such machines. The nature of these effects is not fully understood. In this contribution, we present the results from simulating an electrostatic storage ring under consideration of non-linear fields as well as space charge effects using the computer code SCALA.

• H.J. Kim, T. Sen
  Fermilab, Batavia
• W. Fischer
  BNL, Upton, Long Island, New York

In order to avoid the effects of long-range beam-beam interactions which produce beam blow-up and deteriorate beam life time, a compensation scheme with current carrying wires has been proposed. Two long-range beam-beam compensators were installed in RHIC rings in 2006. The effects of the compensators have been experimentally investigated. An indication was observed that the compensators are beneficial to beam life time in measurements performed in RHIC during 2009. In this paper, we report the effects of wire compensator on beam loss and emittance for proton-proton beams at collision energy.

• L. Liu, X.R. Resende, A.R.D. Rodrigues
  LNLS, Campinas

We report on the status of SIRIUS (BR), the new 3 GeV synchrotron light source currently being designed at the Brazilian Synchrotron Light Laboratory (LNLS) in Campinas, Brazil. The new light source will consist of a low emittance storage ring based on the use of permanent magnet technology for the dipoles. An innovative approach is adopted to enhance the performance of the storage ring dipoles by combining low field (0.5 T) magnets for the main beam deflection and a short slice of high field magnet. This short slice will create a high bending field (2.0 T) only over a short longitudinal extent, generating high critical photon energy with modest energy loss from the complete dipole. There are several attractive features in this proposal, including necessity for lower RF power, less heating of the vacuum chambers and possibility to reduce the beam emittance by placing the longitudinal field gradient at a favorable place.

• A. Kling, K. Balewski
  DESY, Hamburg

PETRA III is a 3rd generation synchrotron radiation light source which started commissioning in April 2009. Recently, first frequency map measurements have been made using the turn-by-turn capabilities of the beam position monitors and horizontal as well as vertical kicker magnets. The results are in good agreement with expectations from tracking studies performed with SixTrack.

• K. Soutome, H. Ohkuma, J. Schimizu, Y. Shimosaki, M. Takao
  JASRI/SPring-8, Hyogo-ken

The SPring-8 storage ring has been operated for more than ten years and provided brilliant hard X-ray radiation to users. In recent years there are some discussions on upgrade plans of existing synchrotron radiation facilities and proposals of new facilities. In these the target brilliance of photons is set to be comparable or even higher, in some energy range, than that of the present value of SPring-8. At SPring-8 a design study of a new storage ring is now in progress for the future upgrade plan. The lattice structure will be changed from the present double-bend type to the multi-bend one, keeping the source position of all insertion devices unchanged. The emittance will be lowered from the present value of 3.4nmrad at 8GeV to 0.4nmrad at 6GeV (or 0.8nmrad at 8GeV) in the case of triple-bend lattice and 0.2nmrad at 6GeV (or 0.3nmrad at 8GeV) in the case of quadruple-bend lattice. We will report the present state of our preliminary work on lattice design. Nonlinear resonance correction to enlarge the dynamic aperture for on- and off-momentum electrons will also be discussed.

• Y. Nosochkov, Y. Cai, M.-H. Wang
  SLAC, Menlo Park, California

Design of PEP-X high brightness light source machine is under development at SLAC. The PEP-X is a proposed replacement of the PEP-II in the existing 2.2 km tunnel. Two of the PEP-X six arcs contain DBA type lattice providing 30 dispersion free straights suitable for 3.5 m long undulators. The lattice contains TME cells in the other four arcs and a 90 m wiggler in a long straight section yielding an ultra low horizontal emittance of ~0.1 nm-rad at 4.5 GeV for a high brightness. The recent lattice modifications further increase the predicted brightness and improve beam dynamic properties. The standard DBA cells are modified into supercells for providing low beta undulator straights. The DBA and TME lattice parameters are better optimized. Harmonic sextupoles are added into the DBA arcs to minimize the sextupole driven resonance effects and amplitude dependent tune shift. Finally, the injection scheme is changed from vertical to horizontal plane in order to avoid large vertical amplitudes of injected beam within small vertical aperture of undulators.

• W. Guo, S.L. Kramer, S. Krinsky, B. Nash, J. Skarita, F.J. Willeke
  BNL, Upton, Long Island, New York

NSLS-II is a third-generation light source that is being built at the Brookhaven National Laboratory. The storage ring has 30 double-bend-achromatic cells. Six 3.5-m-long damping wigglers (DW) will be installed in three straight section to lower the emittance. The civil construction of the facility started in June 2009 and major accelerator components, such as magnets and vacuum chambers, have entered production phase. This paper will summarize the physics considerations for the NSLS-II magnet specifications. In particular, we discuss the tuning range required by the lattice flexibility, and the issues which lead to the specification for the higher-order multipoles.

• M.-H. Wang, Y. Cai, Y. Nosochkov
  SLAC, Menlo Park, California

SLAC is developing a long-range plan to transfer the evolving scientific programs at SSRL from the SPEAR3 light source to a much higher performing photon source that would be housed in the 2.2-km PEP-II tunnel*,**. The proposed PEP-X storage ring is one of the possibilities. The goal of the PEP-X design is to develop an optimal light source design with horizontal emittance less than 100 pm at 4.5 GeV and vertical emittance of 8 pm corresponding to the diffraction limit of 1-Å X-ray. The low emittance design requires a lattice with strong focusing leading to high natural chromaticity and therefore to strong sextupoles. The latter cause reduction of dynamic aperture. The horizontal dynamic aperture required at PEP-X injection point is about 10 mm. In order to achieve the desired dynamic aperture, transverse non-linearities of PEP-X are studied. The program LEGO*** is used for particle tracking simulations. The technique of frequency map is used to analyze the nonlinear behavior. The effects of the non-linearities are tried to minimize. The details and results of dynamic aperture optimization are discussed in this paper.

*,** R. Hettel et al., 'IDEAS FOR A FUTURE PEP-X LIGHT SOURCE', EPAC08, 'CONCEPTS FOR THE PEP-X LIGHT SOURCE', PAC09.
*** Y. Cai et al., 'LEGO: A Modular accelerator design code', PAC97, 1997.

• S. Guiducci, M.E. Biagini
  INFN/LNF, Frascati (Roma)

A new baseline parameter set has been proposed for the ILC with a reduction by a factor 2 in the number of bunches. This option will allow for a corresponding factor 2 decrease in the Damping Ring circumference, with significant cost savings. A low emittance lattice for a 3.2 km long damping ring has been designed, with the same racetrack layout of the present reference 6.4 km long lattice and similar straight sections. The technical work done for the longer ring can be easily applied to the shorter one. The lattice is based on an arc cell design adopted for the SuperB collider and allows some flexibility in tuning emittance and momentum compaction.

• 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.

• K. Soutome, K. Fukami, M. Oishi, Y. Okayasu, J. Schimizu, Y. Shimosaki, M. Shoji, M. Takao, H. Yonehara
  JASRI/SPring-8, Hyogo-ken

A set of three in-vacuum undulators is going to be installed in one of four long straight sections of the SPring-8 storage ring. In order to make the undulator gap as narrow as possible, we plan to divide this long straight section into three sub-sections and install quadrupole magnets between these sub-sections to lower the vertical betatron function. In the modified lattice, however, the symmetry of the ring is lowered and in general it becomes difficult to keep a sufficient dynamic aperture for on- and off-momentum electrons. The long straight sections were originally introduced in the year 2000 and at that time we developed a method of "quasi-transparent matching of sextupole fields" where two key concepts of betatron phase matching and local chromaticity correction were combined to obtain a sufficient dynamic aperture and momentum acceptance. Then, in the year 2007 "counter-sextupole magnets" were further installed to cancel the effect due to non-linear kick by sextupole magnets used for local chromaticity correction. In designing the new lattice with a modified long straight section, we followed the same line and could recover the dynamic aperture and momentum acceptance.

• J.G. Hwang, S.W. Jang, E.-S. Kim
  Kyungpook National University, Daegu

Pohang Light Source-Ⅱ (PLS-Ⅱ) is an upgrade project of the existing 2.5 GeV PLS. The circumference, beam current and energy of PLS-Ⅱ storage ring are 281.82 m, 400 mA and 3 GeV, respectively. The upgrade project has many issues on beam dynamics. We investigated lattice optimization such as lattice corrections, dynamic aperture, selection of optimized tune & emittance and effects of insertion devices. MAD, SAD and Elegant have been used to the lattice optimization. We investigated the effects of machine errors and 20 IDs to the dynamic aperture. PLS-Ⅱ lattice include twenty insertion devices and their effects on the beam dynamics are investigated. We also investigate possibility to reduce the emittance by increasing horizontal betatron tune and adjusting the dispersion by using of MAD, SAD and Elegant and also examined the required strengths of sextupoles for the various emittances.

• 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.

• H. Bartosik, M. Benedikt, Y. Papaphilippou
  CERN, Geneva

This paper describes a detailed analysis of various non-linear effects of the nominal Negative Momentum Compaction lattice for PS2. Chromaticity and orbit correction schemes together with dynamic aperture studies are presented. The impact of magnet errors is being assessed and tolerances are evaluated. Frequency and diffusion maps are produced and, combined with non-linear driving terms analysis, are used for working point optimization.

• M.-S. Chiu, H.-P. Chang, H.C. Chao, C.-C. Kuo, H.-J. Tsai, C.H. Yang
  NSRRC, Hsinchu

To evaluate the feasibility for installing two insertion devices in the long straight sections (12 m long) of the TPS storage ring, two different kinds of the double mini-betay optics (symmetric and asymmetric configurations) were proposed to fulfill this purpose. In the symmetric case a quadrupole triplet is located at the center of the long straight, while in the asymmetric case a quadrupole doublet is used. The effects on the beam dynamics, such as the dynamic aperture, injection efficiency, and lifetime, etc., are presented.

• D.M. Welsch, A. Lehrach, B. Lorentz, R. Maier, D. Prasuhn, R. Tölle
  FZJ, Jülich

The High-Energy Storage Ring (HESR) is part of the upcoming Facility for Antiproton and Ion Research (FAIR). The HESR will provide antiprotons in the momentum range from 1.5 to 15 GeV/c for the internal target experiment PANDA. The demanding requirements of PANDA in terms of beam quality and luminosity together with a limited production rate of antiprotons call for a long beam life time and a minimum of beam loss. Thus, a sufficiently large dynamic aperture of the HESR is crucial. To provide this, a chromaticity correction scheme for the HESR has been developed to reduce tune spread and thus to minimize the emittance growth caused by betatron resonances. The chromaticity correction scheme has been optimized through dynamic aperture calculations. The estimated field errors of the HESR dipole and quadrupole magnets have been included in the non-linear beam dynamics studies. The ion optical settings of the HESR have been improved using dynamic aperture calculations and frequency map analysis technique. In this presentation comprehensive beam simulations are presented and predictions of long-term stability based on short-term particle tracking and orbit diffusion discussed.

• M. Takao, J. Schimizu, Y. Shimosaki, K. Soutome
  JASRI/SPring-8, Hyogo-ken

The dynamic aperture is of importance for high injection efficiency and long lifetime of a storage ring. At the SPring-8 storage ring, a third generation light source facility, various improvements of the dynamic aperture were developed, e.g. the introduction of supplemental sextupole magnets at long straight sections, and the symmetry restoration of linear lattice. To understand the nonlinear dynamics limiting the aperture, the measurements were performed for the various operation conditions with the improvements. Using injection bump magnets and turn-by-turn beam position monitor system, we measured the horizontal dynamic aperture. The Fourier analysis of the oscillation of the kicked beam shows the resonance excitation influential on the dynamic aperture. The knowledge through the experiments is essential to the further improvements of the dynamic aperture of the present ring and the new storage ring design of the future SPring-8 upgrades.

• Z. Martí, G. Benedetti, D. Einfeld, M. Muñoz
  CELLS-ALBA Synchrotron, Cerdanyola del Vallès

The synchrotron light source ALBA incorporates 6 insertion devices (2 Apple-II type undulators, 2 plannar in-vacuum undulators, 1 normal conducting multipole wiggler and 1 superconduction multipole wiggler) at the start of operation. The effect of the different IDs in the performance of the facility is evaluated, using several methods (kick maps, hard edge models, dynamic multipoles, …), including a comparison of the agreement of the different models and simulation codes. According to the results, and due mainly to the influence of the superconducting wiggler, a new working point has been selected.

• M. Muñoz, G. Benedetti, D. Einfeld, Z. Martí
  CELLS-ALBA Synchrotron, Cerdanyola del Vallès

The high order magnetic multipole components of all the magnets in the ALBA storage ring have been measured. Previous studies have simulated the effects of the HOMs using statistic methods. The magnets have been installed now in the tunnel, allowing for a better simulation of the future impact of the HOMs in the performance of the light source. In this paper, the effect of the high order multipoles of the dipole, quadrupole and sextupole magnets in the dynamic aperture and the Touschek lifetime are reviewed.

• M. Giovannozzi
  CERN, Geneva

A scaling law for the time-dependence of the dynamic aperture, i.e., the region of phase space where stable motion occurs, was proposed in previous papers, about ten years ago. The use of fundamental theorems of the theory of dynamical systems allowed showing that the dynamic aperture has a logarithmic dependence on time. In this paper this result, proven by mean of numerical simulations, is used as a basis for deriving a scaling law for the intensity evolution in a storage ring. The proposed scaling law is also tested against experimental data showing a remarkable agreement.

• 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.

• Y. Luo, W. Fischer
  BNL, Upton, Long Island, New York

An electron lens was proposed to compensate the head-on beam-beam effect for polarized proton operations in the Relativistic Heady Ion Collider (RHIC). With head-on beam-beam compensation, we plan to reduce the beam-beam tune footprint and increase the beam-beam parameter to increase the luminosity. Here we carry out 6-D weak-strong beam-beam simulations to study the stability of proton particles and the proton beam lifetime in the presence of head-on beam-beam compensation. The effects and tolerances of the errors and noises in the compensation are also calculated.