IPAC2012 - List of Keywords (dynamic-aperture)

Paper	Title	Other Keywords	Page
MOEPPB004	A Compact Ring Design with Tunable Momentum Compaction	damping, dipole, quadrupole, emittance	82
	Y. Sun SLAC, Menlo Park, California, USA
	A storage ring with tunable momentum compaction has the advantage in achieving diﬀerent RMS bunch length with similar RF capacity, which is potentially useful for many applications, such as linear collider damping ring and pre- damping ring where injected beam has a large energy spread and a large transverse emittance. A tunable bunch length also makes the commissioning and ﬁne tuning easier in manipulating the single bunch instabilities. In this paper, a compact ring design based on a supercell is presented, which achieves a tunable momentum compaction while maintaining a large dynamic aperture.

MOPPC011	Optics and Layout Solutions for the HL-LHC with Large Aperture Nb3Sn and Nb-Ti Inner Triplets	optics, quadrupole, insertion, injection	145
	S.D. Fartoukh, R. De Maria CERN, Geneva, Switzerland
	Funding: The research leading to these results has received funding from the European Commission under the FP7 project HiLumi LHC, GA no. 284404, co-funded by the DoE, USA and KEK, Japan. The LHC Upgrade studies, formalized into the High-Luminosity LHC (HL-LHC) project, relies on the feasibility of very low β^, and in particular on a novel achromatic squeezing mechanism, the ATS scheme which is presently under test in the LHC. We present two optics and layout scenario for the HL-LHC using the ATS scheme, one based on Nb3Sn triplet quadrupoles with a coil aperture compatible with an operational gradient of 150T/m and a backup scenario based on NbTi compatible with an operational gradient of 100T/m. The solution obtained are analyzed in terms of β^* reach (flat or round), mechanical acceptance, optics flexibility, chromatic properties, and impact on the dynamic aperture due to the large beta-beating waves induced in the arcs by the ATS scheme. * S. Fartoukh et al., "The Achromatic Telescopic Squeezing (ATS) scheme: from initial motivations to basic principles, and first demonstration at the LHC," these proceedings.

MOPPC020	Field Tolerances for the Triplet Quadrupoles of the LHC High Luminosity Lattice	quadrupole, multipole, target, lattice	169
	Y. Jiao, Y. Cai, Y. Nosochkov, M.-H. Wang SLAC, Menlo Park, California, USA R. De Maria, S.D. Fartoukh, M. Giovannozzi, E. McIntosh CERN, Geneva, Switzerland
	Funding: This work is supported by the U.S. Department of Energy under contract # DE-AC02-76SF00515 and the US LHC Accelerator Research Program (LARP). It has been proposed to implement an Achromatic Telescopic Squeezing (ATS) scheme* in the high luminosity LHC lattice to reduce the beta functions at the Interaction Points (IP) up to a factor of 8. As a consequence, the nominal 4.5-km peak beta functions reached in the inner triplets at collision will be increased by the same factor. This therefore justifies the installation of new, larger aperture superconducting triplet quadrupoles. These higher beta functions will enhance the effects of the triplet quadrupole field errors leading to smaller beam dynamic aperture. To maintain the acceptable dynamic aperture, the effects of the triplet multipole field errors must be re-evaluated, thus specifying new tolerances. Such a study has been performed for the so-called “4444” collision optics of the ATS scheme, where the IP beta functions are reduced by a factor of 4 in both planes with respect to a pre-squeezed value of 60 cm at two collision points. The dynamic aperture calculations were performed using SixTrack. The impact on the triplets’ field quality is studied and presented in details. * S. Fartoukh, “An Achromatic Telescopic Squeezing (ATS) Scheme for LHC Upgrade”, Proc. of IPAC11, p. 2088 (2011).

MOPPC076	New Features of the Parallel TRACY for Nonlinear Beam Dynamics	lattice, sextupole, closed-orbit, betatron	310
	M.-S. Chiu, H.-P. Chang NSRRC, Hsinchu, Taiwan
	The TRACY code is used to analyze and simulate the nonlinear beam dynamics of the designed lattice. To speed up the lattice design flow, we parallelized the TRACY by MPI and developed a GUI by GTK+ to integrate the functions of TRACY and added a function of nonlinear optimization adapted from OPA, which is used to optimize the nonlinear driving terms by powell algorithm. The GUI is used for parameter input and data visualization. The procedures of nonlinear optimization and beam dynamics analysis are integrated and streamlined. Users do not need to write and compile the code any more. The results will be demonstrated in this report.

MOPPD019	Vertical Orbit Excursion FFAG Accelerators with Edge Focussing	proton, injection, lattice, neutron	406
	S.J. Brooks STFC/RAL/ASTeC, Chilton, Didcot, Oxon, United Kingdom
	FFAGs with vertical orbit excursion (VFFAGs) provide a promising alternative design for the magnets in fixed-field machines. They have a vertical magnetic field component that increases with height in the vertical aperture, yielding a skew quadrupole focussing structure. The end fields of such magnets with edge angles provide an alternating gradient without the need for reverse bends, thus reducing the machine circumference. Similarly to spiral scaling horizontal FFAGs (but unlike non-scaling versions), the machine has fixed tunes and no intrinsic limitation on momentum range. Rings capable of boosting the 150mm.mrad geometric emittance beam from the ISIS proton synchrotron to 3, 5 and 12GeV using superconducting magnets are presented, the latter corresponding to 2.5MW beam power.

MOPPD020	A Model for a High-Power Scaling FFAG Ring	injection, lattice, extraction, proton	409
	G.H. Rees, D.J. Kelliher, S. Machida, C.R. Prior, S.L. Sheehy STFC/RAL/ASTeC, Chilton, Didcot, Oxon, United Kingdom
	High-power FFAG rings are under study to serve as drivers for neutron spallation, muon production, and accelerator-driven reactor systems. In this paper, which follows on from earlier work, a 20 - 70 MeV model for a high-power FFAG driver is described. This model would serve as a test bed to study topics such as space charge and injection in such rings. The design incorporates a long straight to facilitate H^- charge exchange injection. The dynamic aperture is calculated in order to optimize the working point in tune space. The injection scheme is also described. A separate design for an ISIS injector, featuring a novel modification to the scaling law, was also studied. G.H. Rees and D.J. Kelliher, “New, high power, scaling, FFAG driver ring designs” HB2010, Morschach, September 2010, MOPD07, p. 54, http://www. JACoW.org

MOPPP054	Study of a New Injection Scheme for the SSRF Storage Ring	injection, kicker, storage-ring, emittance	685
	M.Z. Zhang, B.C. Jiang, L. Ouyang, Q.L. Sun, S.Q. Tian SINAP, Shanghai, People's Republic of China
	A low emittance configuration of the SSRF storage ring had been designed and commissioned. Along with reducing the emittance, the dynamic aperture decreases quickly. It doesn’t meet aperture require of the normal injection scheme anymore and the injection efficiency is lower. The pulsed multi-pole magnets give the opportunity to overcome the smaller dynamic aperture. Pulsed quadrupole and sextupole both are study for the injection scheme. With and without the orbit bump kickers are also considered in this study. The injection scheme suggestions are presented in this paper.

TUPPC005	Optimization of the SIS100 Nonlinear Magnet Scheme for Slow Extraction	extraction, sextupole, octupole, lattice	1158
	A. Saa Hernandez, M.M. Kirk, D. Ondreka, N. Pyka, S. Sorge, P.J. Spiller GSI, Darmstadt, Germany
	The SIS100 superconducting synchrotron was initially planned mainly for fast extraction of protons and heavy ions. Due to the delay of the construction of the SIS300 synchrotron, SIS100 has to be able to provide slowly extracted heavy ion beams to the experiments. To improve the robustness of the slow extraction from SIS100, a lattice review was performed, resulting in an optimization of the nonlinear magnet scheme. In the original scheme the Hardt condition cannot be established due to a collapse of the dynamic aperture caused by the chromatic sextupoles. In the optimized scheme the positions of the chromatic sextupoles are modified and octupoles are employed to compensate the second order effects of these sextupoles. In addition, the number of resonance sextupole magnets is reduced. With the new scheme, the Hardt condition can be established, leading to higher extraction efficiency. The separatrix can be freely adjusted, and closed orbit control is improved.

TUPPC015	Local Modification of Lattice of a Long Straight Section for Installing Small Gap In-vacuum Undulators at SPring-8	lattice, betatron, sextupole, electron	1188
	K. Soutome, T. Fujita, K. Fukami, K.K. Kaneki, C. Mitsuda, H. Ohkuma, M. Oishi, Y. Okayasu, S. Sasaki, J. Schimizu, Y. Shimosaki, M. Shoji, M. Takao, Y. Taniuchi, C. Zhang JASRI/SPring-8, Hyogo-ken, Japan M. Hasegawa, K. Kajimoto, T. Nakanishi SES, Hyogo-pref., Japan
	In the SPring-8 storage ring there are four magnet-free long straight sections (LSS) of about 30m. Recently we locally modified one of these sections by installing two quadrupole-triplets and divided it into three sub-sections. The vertical beta at the middle of each sub-section was lowered to 2.5m so that small gap in-vacuum undulators with a short period (min. gap: 5.2mm, period: 19mm) can be installed to build a high performance beamline for inelastic X-ray scattering. After modifying the lattice, however, the symmetry of the ring is lowered and, in general, it becomes difficult to keep sufficient dynamic aperture (DA) and momentum acceptance (MA). We solved this problem by combining the betatron phase matching, local chromaticity correction in LSS and cancellation of non-linear kicks due to sextupoles used for this correction. We could then recover DA and MA to almost the same level for the original one. The beam commissioning of the new lattice has successfully been finished, and from September 2011 it is used in user-operation. We will report our method of realizing a storage ring lattice having a very low symmetry and review the operation performance of the modified lattice.

TUPPC042	Effect of Field Errors in Muon Collider IR Magnets on Beam Dynamics	multipole, dipole, sextupole, quadrupole	1257
	Y. Alexahin, E. Gianfelice-Wendt, V.V. Kapin Fermilab, Batavia, USA
	Funding: Work supported by Fermi Research Alliance, LLC, under contract No. DE-AC02-07CH11359 with the U.S. Department of Energy In order to achieve peak luminosity of a Muon Collider (MC) in the 10³⁵/cm²/s range very small values of beta-function at the interaction point (IP) are necessary (β^* ~ 5 mm) while the distance from IP to the first quadrupole can not be made shorter than ~6m as dictated by the necessity of detector protection from backgrounds. In the result the beta-function at the final focus quadrupoles can reach 100 km making beam dynamics very sensitive to all kind of errors. In the present report we consider the effects on momentum acceptance and dynamic aperture of multipole field errors in the body of IR dipoles as well as of fringe-fields in both dipoles and quadrupoles in the case of 1.5 TeV (c.o.m.) MC. Analysis shows these effects to be strong but correctable with dedicated multipole correctors.

TUPPC059	Extraction of the Lie Map from Realistic 3D Magnetic Field Map	dipole, quadrupole, extraction, lattice	1308
	Y. Li BNL, Upton, Long Island, New York, USA X. Huang SLAC, Menlo Park, California, USA
	Funding: Supported by Department of Energy Contract No. DE-AC02-98CH10886. We present a method to extract the Lie map of any arbitrary accelerator magnet from its actual 3D field map. After fitting a Taylor map from multi-particle tracking trajectories through the actual field, we factorize the map into a Lie map using Dragt-Finn's method. This method is validated by comparing with COSY-infinity for a soft-edge quadrupole model. Applications of extracting symplectic maps for the SPEAR and NSLS-II dipoles are shown as examples. A comparison of the map-tracking results against the direct field-integration-based method also is given.

TUPPC073	Frequency Map Analysis for SuperB	resonance, lattice, emittance, sextupole	1341
	S.M. Liuzzo, M.E. Biagini, P. Raimondi INFN/LNF, Frascati (Roma), Italy T. Demma LAL, Orsay, France Y. Papaphilippou CERN, Geneva, Switzerland
	The frequency map analysis is applied to the SuperB HER and LER lattices including the Final Focus, in order to understand the dynamic aperture limitation and provide insight for a working point optimization. In this respect, frequency and diffusion maps are evaluated applying random magnet misalignments and tilts, before and after correction of orbit, dispersion and coupling using Low Emittance Tuning techniques. The same analysis is performed for on and off momentum particles. The lattice properties are further investigated using working point scans and the correction of non linear resonance driving terms and amplitude detuning.

TUPPC078	Proposal of an Inverse Logarithm Scaling Law for the Luminosity Evolution	luminosity, collider, emittance, hadron	1353
	M. Giovannozzi CERN, Geneva, Switzerland C.H. Yu IHEP, Beijing, People's Republic of China
	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. It was showed that dynamic aperture has a logarithmic dependence on time, which would be suggested by some fundamental theorems of the theory of dynamical systems. Such a scaling law was recently extended also to the intensity evolution in a storage ring. In this paper, inspired by these results, and inverse logarithm scaling law for the luminosity in a circular collider is proposed. The law is then tested against the data from the LHC physics runs and also with some examples from other machines. The results are presented and discussed in details.

TUPPC080	Investigations of Scaling Laws of Dynamic Aperture with Time for Numerical Simulations including Weak-Strong Beam-Beam Effects	simulation, injection, beam-beam-effects, lattice	1359
	M. Giovannozzi CERN, Geneva, Switzerland E. Laface ESS, Lund, Sweden
	A scaling law describing 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. It was shown that dynamic aperture has a logarithmic dependence on time, which would be suggested by some fundamental theorems of the theory of dynamical systems. So far, such a law was applied to single-particle effects only, i.e., the only source of non-linear effects was the magnetic imperfections. In this paper an attempt is made to extend the scaling law to the case of weak-strong beam-beam effects. The results of numerical simulations performed, including both non-linear magnetic imperfections and weak-strong beam-beam effects, are presented and discussed in detail.

TUPPC081	First Experimental Observations from the LHC Dynamic Aperture Experiment	kicker, beam-losses, synchrotron, injection	1362
	M. Giovannozzi, M. Albert, G.E. Crockford, S.D. Fartoukh, W. Höfle, E.H. Maclean, A. Macpherson, L. Ponce, S. Redaelli, H. Renshall, F. Roncarolo, R.J. Steinhagen, E. Todesco, R. Tomás, W. Venturini Delsolaro CERN, Geneva, Switzerland R. Miyamoto BNL, Upton, Long Island, New York, USA
	Following intensive numerical simulations to compute the dynamic aperture for the LHC in the design phase, the successful beam commissioning and the ensuing beam operations opened the possibility of performing beam measurements of the dynamics aperture. In this paper the experimental set-up and the first observations based on the few experimental sessions performed will be presented and discussed in detail.

TUPPC096	Optimization of the Dynamic Aperture for SPEAR3 Low-emittance Upgrade	sextupole, emittance, resonance, optics	1380
	L. Wang, X. Huang, Y. Nosochkov, J.A. Safranek SLAC, Menlo Park, California, USA M. Borland ANL, Argonne, USA
	A low emittance upgrade is planned for SPEAR3. As the first phase, the emittance is reduced from 10nm to 7nm without addition magnets. A further upgrade with even lower emittance will require a damping wiggler. There is a smaller dynamic aperture for the lower emittance optics due to the stronger nonlinearity. A Multi-Objective Genetic Optimization (MOGA) code is used to maximize the dynamic aperture. Both the dynamic aperture and beam lifetime are optimized simultaneously. Various configurations of the sextupole magnets have been studied in order to find the best configuration. The betatron tune also can be optimized to minimize resonance effects. The optimized dynamic aperture increases 15% from the normal case and the life time increases from 15 hours to 17 hours. It is important that the increase of the dynamic aperture is mainly in the beam injection direction. Therefore the injection efficiency will benefit from this improvement.

TUPPC099	Optimization of Chromaticity Compensation and Dynamic Aperture in MEIC Collider Rings	sextupole, ion, octupole, collider	1389
	F. Lin, Y.S. Derbenev, V.S. Morozov, Y. Zhang JLAB, Newport News, Virginia, USA K.B. Beard Muons, Inc, Batavia, USA
	Funding: Authored by Jefferson Science Associates, LLC under U.S. DOE Contract No. DE-AC05-06OR23177. Supported in part by US DOE STTR grant DE-SC0006272. The conceptual design of the Medium-energy Electron-Ion Collider (MEIC) at Jefferson Lab relies on an ultra-small beta-star to achieve high luminosities of up to 10³⁴ cm^-2s⁻¹. A low-beta insertion for interaction regions unavoidably induces large chromatic effects that demand a proper compensation. The present approach of chromatic compensation in the MEIC collider rings is based on a local correction scheme using two symmetric chromatic compensation blocks that includes families of sextupoles, and are placed in a beam extension area on both sides of a collision point. It can simultaneously compensate the first order chromaticity and chromatic beam smear at the IP without inducing significant second order aberrations. In this paper, we investigate both the momentum acceptance and dynamic aperture in the MEIC ion collider ring by considering the aberration effects up to the third order, such as amplitude dependent tune shift. We also explore the compensation of the third order effects by introducing families of octupoles in the extended beam area. Authored by Jefferson Science Associates, LLC under U.S. DOE Contract No. DE-AC05-06OR23177. Supported in part by US DOE STTR grant DE-SC0006272.

TUPPP001	Beam Based Measurements with Superconducting Wigglers at the Canadian Light Source with Applications to Nonlinear Beam Dynamics	wiggler, injection, optics, multipole	1599
	W.A. Wurtz, L.O. Dallin, M.J. Sigrist CLS, Saskatoon, Saskatchewan, Canada
	The Canadian Light Source (CLS) employs two superconducting wigglers for the production of hard x-rays. These wigglers cause a large decrease in injection efficiency. While such a decrease is not unexpected due to the large distortion to the linear optics, a correction to the linear optics does not restore injection efficiency. This inability to restore injection is not predicted by a kickmap model of the wiggler. We performed beam based measurements to construct a phenomenological, nonlinear model of the wiggler. Particle tracking with this wiggler model shows that the reduction in dynamic aperture is due to the amplitude dependent tune shift crossing a resonance, even with the linear optics corrected. Moving the tunes allows us to avoid this resonance and measurements at these tunes show that injection efficiency is not greatly affected by the wigglers.

TUPPP002	GLASS Study of the Canadian Light Source Storage Ring Lattice	emittance, lattice, quadrupole, sextupole	1602
	W.A. Wurtz, L.O. Dallin CLS, Saskatoon, Saskatchewan, Canada
	GLASS is a technique for finding all potential operating points of a storage ring lattice by examining all possible configurations of the linear lattice. The Canadian Light Source (CLS) storage ring uses three quadrupole families, making it computationally efficient to use GLASS to study the lattice with unbroken symmetry. CLS does not employ harmonic sextupoles and has only two families of chromatic sextupoles. We can exhaust the sextupole degrees of freedom by requiring the horizontal and vertical chromaticities to be both zero. With no remaining free parameters in our lattice, it is possible to calculate dynamic aperture and momentum acceptance for select regions of interest uncovered by the GLASS scan. We find two regions with reasonable dynamic aperture and momentum acceptance: the region where we presently operate and a region that can be accessed by reversing the polarity of one quadrupole family.

TUPPP013	Effects of Multipoles in Dynamic Aperture of the ILSF Storage Ring	multipole, sextupole, quadrupole, lattice	1632
	S. Fatehi, E. Ahmadi, F. Saeidi ILSF, Tehran, Iran D. Einfeld CELLS-ALBA Synchrotron, Cerdanyola del Vallès, Spain H. Ghasem IPM, Tehran, Iran
	Dynamic aperture of a synchrotron light source shrinks to small value due to the multipole errors caused by magnet design. In the ILSF storage ring, the tolerance of magnets has been taken into account in the simulation and sextupole magnets reoptimized to improve the dynamic aperture. This paper yields the evaluated dynamic aperture include of multipole errors.

TUPPR085	Recycler Chromaticities and End Shims for NOvA at Fermilab	lattice, sextupole, quadrupole, dipole	2023
	M. Xiao Fermilab, Batavia, USA
	In era of NOvA operation, it is planned to slip-stack six on six Booster proton batches in the Recycler ring for a total intensity of 5×10¹³ protons/cycle. During the slip-stacking, the chromaticities are required to be jumped from (-2,-2) to (-20,-20). However, they can only be adjusted to (-12,-12) from (-2,-2) using existing 2 families of powered sextupoles. On the other hand, the presently designed Recycler lattice for Nova replaces the 30 straight section with 8 “D-D half FODO cells”. We use 3 quads in a half-cell to obtain the working point under the limit of the feasible quad strength, and the maximum beta-function in this section cannot be less than 80 m. In this paper, we re-designed the end shims of the permanent magnets in the ring lattice with appropriate quadrupole and sextupole components to meet both chromaticity and tune requirements. We are able to use 2 quads in a half cell in RR30 straight section within feasible quad strength. The maximum beta-functions are also lowered to around 55 m. The dynamic aperture tracking has been done using MAD to simulate the scenario of beam injection into the Recycler ring for Nova.

WEPPR052	Octupole Magnets for the Instability Damping at the J-PARC Main Ring	octupole, damping, resonance, sextupole	3045
	S. Igarashi, T. Koseki, K. Ohmi, M.J. Shirakata, H. Someya, T. Toyama KEK, Ibaraki, Japan A. Ando J-PARC, KEK & JAEA, Ibaraki-ken, Japan
	Octupole magnets have been installed for the instability damping at the J-PARC main ring. The transverse instability was observed during the injection and acceleration periods and caused the beam losses. The chromaticity tuning and bunch-by-bunch feedback system have been applied to suppress the instability. Octupole magnets were considered to create a larger amplitude dependent betatron tune shift and to supply additional option for the instability damping. The side effects of the dynamic aperture reduction and the resonances have been studied.

Paper

Title

Other Keywords

Page

MOEPPB004

A Compact Ring Design with Tunable Momentum Compaction

damping, dipole, quadrupole, emittance

82

Y. Sun
SLAC, Menlo Park, California, USA

A storage ring with tunable momentum compaction has the advantage in achieving diﬀerent RMS bunch length with similar RF capacity, which is potentially useful for many applications, such as linear collider damping ring and pre- damping ring where injected beam has a large energy spread and a large transverse emittance. A tunable bunch length also makes the commissioning and ﬁne tuning easier in manipulating the single bunch instabilities. In this paper, a compact ring design based on a supercell is presented, which achieves a tunable momentum compaction while maintaining a large dynamic aperture.

MOPPC011

Optics and Layout Solutions for the HL-LHC with Large Aperture Nb3Sn and Nb-Ti Inner Triplets

optics, quadrupole, insertion, injection

145

S.D. Fartoukh, R. De Maria
CERN, Geneva, Switzerland

Funding: The research leading to these results has received funding from the European Commission under the FP7 project HiLumi LHC, GA no. 284404, co-funded by the DoE, USA and KEK, Japan.
The LHC Upgrade studies, formalized into the High-Luminosity LHC (HL-LHC) project, relies on the feasibility of very low β^*, and in particular on a novel achromatic squeezing mechanism, the ATS scheme which is presently under test in the LHC*. We present two optics and layout scenario for the HL-LHC using the ATS scheme, one based on Nb3Sn triplet quadrupoles with a coil aperture compatible with an operational gradient of 150T/m and a backup scenario based on NbTi compatible with an operational gradient of 100T/m. The solution obtained are analyzed in terms of β^* reach (flat or round), mechanical acceptance, optics flexibility, chromatic properties, and impact on the dynamic aperture due to the large beta-beating waves induced in the arcs by the ATS scheme.
* S. Fartoukh et al., "The Achromatic Telescopic Squeezing (ATS) scheme: from initial motivations to basic principles, and first demonstration at the LHC," these proceedings.

MOPPC020

Field Tolerances for the Triplet Quadrupoles of the LHC High Luminosity Lattice

quadrupole, multipole, target, lattice

169

Y. Jiao, Y. Cai, Y. Nosochkov, M.-H. Wang
SLAC, Menlo Park, California, USA
R. De Maria, S.D. Fartoukh, M. Giovannozzi, E. McIntosh
CERN, Geneva, Switzerland

Funding: This work is supported by the U.S. Department of Energy under contract # DE-AC02-76SF00515 and the US LHC Accelerator Research Program (LARP).
It has been proposed to implement an Achromatic Telescopic Squeezing (ATS) scheme* in the high luminosity LHC lattice to reduce the beta functions at the Interaction Points (IP) up to a factor of 8. As a consequence, the nominal 4.5-km peak beta functions reached in the inner triplets at collision will be increased by the same factor. This therefore justifies the installation of new, larger aperture superconducting triplet quadrupoles. These higher beta functions will enhance the effects of the triplet quadrupole field errors leading to smaller beam dynamic aperture. To maintain the acceptable dynamic aperture, the effects of the triplet multipole field errors must be re-evaluated, thus specifying new tolerances. Such a study has been performed for the so-called “4444” collision optics of the ATS scheme, where the IP beta functions are reduced by a factor of 4 in both planes with respect to a pre-squeezed value of 60 cm at two collision points. The dynamic aperture calculations were performed using SixTrack. The impact on the triplets’ field quality is studied and presented in details.
* S. Fartoukh, “An Achromatic Telescopic Squeezing (ATS) Scheme for LHC Upgrade”, Proc. of IPAC11, p. 2088 (2011).

MOPPC076

New Features of the Parallel TRACY for Nonlinear Beam Dynamics

lattice, sextupole, closed-orbit, betatron

310

M.-S. Chiu, H.-P. Chang
NSRRC, Hsinchu, Taiwan

The TRACY code is used to analyze and simulate the nonlinear beam dynamics of the designed lattice. To speed up the lattice design flow, we parallelized the TRACY by MPI and developed a GUI by GTK+ to integrate the functions of TRACY and added a function of nonlinear optimization adapted from OPA, which is used to optimize the nonlinear driving terms by powell algorithm. The GUI is used for parameter input and data visualization. The procedures of nonlinear optimization and beam dynamics analysis are integrated and streamlined. Users do not need to write and compile the code any more. The results will be demonstrated in this report.

MOPPD019

Vertical Orbit Excursion FFAG Accelerators with Edge Focussing

proton, injection, lattice, neutron

406

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

FFAGs with vertical orbit excursion (VFFAGs) provide a promising alternative design for the magnets in fixed-field machines. They have a vertical magnetic field component that increases with height in the vertical aperture, yielding a skew quadrupole focussing structure. The end fields of such magnets with edge angles provide an alternating gradient without the need for reverse bends, thus reducing the machine circumference. Similarly to spiral scaling horizontal FFAGs (but unlike non-scaling versions), the machine has fixed tunes and no intrinsic limitation on momentum range. Rings capable of boosting the 150mm.mrad geometric emittance beam from the ISIS proton synchrotron to 3, 5 and 12GeV using superconducting magnets are presented, the latter corresponding to 2.5MW beam power.

MOPPD020

A Model for a High-Power Scaling FFAG Ring

injection, lattice, extraction, proton

409

G.H. Rees, D.J. Kelliher, S. Machida, C.R. Prior, S.L. Sheehy
STFC/RAL/ASTeC, Chilton, Didcot, Oxon, United Kingdom

High-power FFAG rings are under study to serve as drivers for neutron spallation, muon production, and accelerator-driven reactor systems. In this paper, which follows on from earlier work*, a 20 - 70 MeV model for a high-power FFAG driver is described. This model would serve as a test bed to study topics such as space charge and injection in such rings. The design incorporates a long straight to facilitate H^- charge exchange injection. The dynamic aperture is calculated in order to optimize the working point in tune space. The injection scheme is also described. A separate design for an ISIS injector, featuring a novel modification to the scaling law, was also studied.
*G.H. Rees and D.J. Kelliher, “New, high power, scaling, FFAG driver ring designs” HB2010, Morschach, September 2010, MOPD07, p. 54, http://www. JACoW.org

MOPPP054

Study of a New Injection Scheme for the SSRF Storage Ring

injection, kicker, storage-ring, emittance

685

M.Z. Zhang, B.C. Jiang, L. Ouyang, Q.L. Sun, S.Q. Tian
SINAP, Shanghai, People's Republic of China

A low emittance configuration of the SSRF storage ring had been designed and commissioned. Along with reducing the emittance, the dynamic aperture decreases quickly. It doesn’t meet aperture require of the normal injection scheme anymore and the injection efficiency is lower. The pulsed multi-pole magnets give the opportunity to overcome the smaller dynamic aperture. Pulsed quadrupole and sextupole both are study for the injection scheme. With and without the orbit bump kickers are also considered in this study. The injection scheme suggestions are presented in this paper.

TUPPC005

Optimization of the SIS100 Nonlinear Magnet Scheme for Slow Extraction

extraction, sextupole, octupole, lattice

1158

A. Saa Hernandez, M.M. Kirk, D. Ondreka, N. Pyka, S. Sorge, P.J. Spiller
GSI, Darmstadt, Germany

The SIS100 superconducting synchrotron was initially planned mainly for fast extraction of protons and heavy ions. Due to the delay of the construction of the SIS300 synchrotron, SIS100 has to be able to provide slowly extracted heavy ion beams to the experiments. To improve the robustness of the slow extraction from SIS100, a lattice review was performed, resulting in an optimization of the nonlinear magnet scheme. In the original scheme the Hardt condition cannot be established due to a collapse of the dynamic aperture caused by the chromatic sextupoles. In the optimized scheme the positions of the chromatic sextupoles are modified and octupoles are employed to compensate the second order effects of these sextupoles. In addition, the number of resonance sextupole magnets is reduced. With the new scheme, the Hardt condition can be established, leading to higher extraction efficiency. The separatrix can be freely adjusted, and closed orbit control is improved.

TUPPC015

Local Modification of Lattice of a Long Straight Section for Installing Small Gap In-vacuum Undulators at SPring-8

lattice, betatron, sextupole, electron

1188

K. Soutome, T. Fujita, K. Fukami, K.K. Kaneki, C. Mitsuda, H. Ohkuma, M. Oishi, Y. Okayasu, S. Sasaki, J. Schimizu, Y. Shimosaki, M. Shoji, M. Takao, Y. Taniuchi, C. Zhang
JASRI/SPring-8, Hyogo-ken, Japan
M. Hasegawa, K. Kajimoto, T. Nakanishi
SES, Hyogo-pref., Japan

In the SPring-8 storage ring there are four magnet-free long straight sections (LSS) of about 30m. Recently we locally modified one of these sections by installing two quadrupole-triplets and divided it into three sub-sections. The vertical beta at the middle of each sub-section was lowered to 2.5m so that small gap in-vacuum undulators with a short period (min. gap: 5.2mm, period: 19mm) can be installed to build a high performance beamline for inelastic X-ray scattering. After modifying the lattice, however, the symmetry of the ring is lowered and, in general, it becomes difficult to keep sufficient dynamic aperture (DA) and momentum acceptance (MA). We solved this problem by combining the betatron phase matching, local chromaticity correction in LSS and cancellation of non-linear kicks due to sextupoles used for this correction. We could then recover DA and MA to almost the same level for the original one. The beam commissioning of the new lattice has successfully been finished, and from September 2011 it is used in user-operation. We will report our method of realizing a storage ring lattice having a very low symmetry and review the operation performance of the modified lattice.

TUPPC042

Effect of Field Errors in Muon Collider IR Magnets on Beam Dynamics

multipole, dipole, sextupole, quadrupole

1257

Y. Alexahin, E. Gianfelice-Wendt, V.V. Kapin
Fermilab, Batavia, USA

Funding: Work supported by Fermi Research Alliance, LLC, under contract No. DE-AC02-07CH11359 with the U.S. Department of Energy
In order to achieve peak luminosity of a Muon Collider (MC) in the 10³⁵/cm²/s range very small values of beta-function at the interaction point (IP) are necessary (β^* ~ 5 mm) while the distance from IP to the first quadrupole can not be made shorter than ~6m as dictated by the necessity of detector protection from backgrounds. In the result the beta-function at the final focus quadrupoles can reach 100 km making beam dynamics very sensitive to all kind of errors. In the present report we consider the effects on momentum acceptance and dynamic aperture of multipole field errors in the body of IR dipoles as well as of fringe-fields in both dipoles and quadrupoles in the case of 1.5 TeV (c.o.m.) MC. Analysis shows these effects to be strong but correctable with dedicated multipole correctors.

TUPPC059

Extraction of the Lie Map from Realistic 3D Magnetic Field Map

dipole, quadrupole, extraction, lattice

1308

Y. Li
BNL, Upton, Long Island, New York, USA
X. Huang
SLAC, Menlo Park, California, USA

Funding: Supported by Department of Energy Contract No. DE-AC02-98CH10886.
We present a method to extract the Lie map of any arbitrary accelerator magnet from its actual 3D field map. After fitting a Taylor map from multi-particle tracking trajectories through the actual field, we factorize the map into a Lie map using Dragt-Finn's method. This method is validated by comparing with COSY-infinity for a soft-edge quadrupole model. Applications of extracting symplectic maps for the SPEAR and NSLS-II dipoles are shown as examples. A comparison of the map-tracking results against the direct field-integration-based method also is given.

TUPPC073

Frequency Map Analysis for SuperB

resonance, lattice, emittance, sextupole

1341

S.M. Liuzzo, M.E. Biagini, P. Raimondi
INFN/LNF, Frascati (Roma), Italy
T. Demma
LAL, Orsay, France
Y. Papaphilippou
CERN, Geneva, Switzerland

The frequency map analysis is applied to the SuperB HER and LER lattices including the Final Focus, in order to understand the dynamic aperture limitation and provide insight for a working point optimization. In this respect, frequency and diffusion maps are evaluated applying random magnet misalignments and tilts, before and after correction of orbit, dispersion and coupling using Low Emittance Tuning techniques. The same analysis is performed for on and off momentum particles. The lattice properties are further investigated using working point scans and the correction of non linear resonance driving terms and amplitude detuning.

TUPPC078

Proposal of an Inverse Logarithm Scaling Law for the Luminosity Evolution

luminosity, collider, emittance, hadron

1353

M. Giovannozzi
CERN, Geneva, Switzerland
C.H. Yu
IHEP, Beijing, People's Republic of China

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. It was showed that dynamic aperture has a logarithmic dependence on time, which would be suggested by some fundamental theorems of the theory of dynamical systems. Such a scaling law was recently extended also to the intensity evolution in a storage ring. In this paper, inspired by these results, and inverse logarithm scaling law for the luminosity in a circular collider is proposed. The law is then tested against the data from the LHC physics runs and also with some examples from other machines. The results are presented and discussed in details.

TUPPC080

Investigations of Scaling Laws of Dynamic Aperture with Time for Numerical Simulations including Weak-Strong Beam-Beam Effects

simulation, injection, beam-beam-effects, lattice

1359

M. Giovannozzi
CERN, Geneva, Switzerland
E. Laface
ESS, Lund, Sweden

A scaling law describing 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. It was shown that dynamic aperture has a logarithmic dependence on time, which would be suggested by some fundamental theorems of the theory of dynamical systems. So far, such a law was applied to single-particle effects only, i.e., the only source of non-linear effects was the magnetic imperfections. In this paper an attempt is made to extend the scaling law to the case of weak-strong beam-beam effects. The results of numerical simulations performed, including both non-linear magnetic imperfections and weak-strong beam-beam effects, are presented and discussed in detail.

TUPPC081

First Experimental Observations from the LHC Dynamic Aperture Experiment

kicker, beam-losses, synchrotron, injection

1362

M. Giovannozzi, M. Albert, G.E. Crockford, S.D. Fartoukh, W. Höfle, E.H. Maclean, A. Macpherson, L. Ponce, S. Redaelli, H. Renshall, F. Roncarolo, R.J. Steinhagen, E. Todesco, R. Tomás, W. Venturini Delsolaro
CERN, Geneva, Switzerland
R. Miyamoto
BNL, Upton, Long Island, New York, USA

Following intensive numerical simulations to compute the dynamic aperture for the LHC in the design phase, the successful beam commissioning and the ensuing beam operations opened the possibility of performing beam measurements of the dynamics aperture. In this paper the experimental set-up and the first observations based on the few experimental sessions performed will be presented and discussed in detail.

TUPPC096

Optimization of the Dynamic Aperture for SPEAR3 Low-emittance Upgrade

sextupole, emittance, resonance, optics

1380

L. Wang, X. Huang, Y. Nosochkov, J.A. Safranek
SLAC, Menlo Park, California, USA
M. Borland
ANL, Argonne, USA

A low emittance upgrade is planned for SPEAR3. As the first phase, the emittance is reduced from 10nm to 7nm without addition magnets. A further upgrade with even lower emittance will require a damping wiggler. There is a smaller dynamic aperture for the lower emittance optics due to the stronger nonlinearity. A Multi-Objective Genetic Optimization (MOGA) code is used to maximize the dynamic aperture. Both the dynamic aperture and beam lifetime are optimized simultaneously. Various configurations of the sextupole magnets have been studied in order to find the best configuration. The betatron tune also can be optimized to minimize resonance effects. The optimized dynamic aperture increases 15% from the normal case and the life time increases from 15 hours to 17 hours. It is important that the increase of the dynamic aperture is mainly in the beam injection direction. Therefore the injection efficiency will benefit from this improvement.

TUPPC099

Optimization of Chromaticity Compensation and Dynamic Aperture in MEIC Collider Rings

sextupole, ion, octupole, collider

1389

F. Lin, Y.S. Derbenev, V.S. Morozov, Y. Zhang
JLAB, Newport News, Virginia, USA
K.B. Beard
Muons, Inc, Batavia, USA

Funding: Authored by Jefferson Science Associates, LLC under U.S. DOE Contract No. DE-AC05-06OR23177. Supported in part by US DOE STTR grant DE-SC0006272.
The conceptual design of the Medium-energy Electron-Ion Collider (MEIC) at Jefferson Lab relies on an ultra-small beta-star to achieve high luminosities of up to 10³⁴ cm^-2s⁻¹. A low-beta insertion for interaction regions unavoidably induces large chromatic effects that demand a proper compensation. The present approach of chromatic compensation in the MEIC collider rings is based on a local correction scheme using two symmetric chromatic compensation blocks that includes families of sextupoles, and are placed in a beam extension area on both sides of a collision point. It can simultaneously compensate the first order chromaticity and chromatic beam smear at the IP without inducing significant second order aberrations. In this paper, we investigate both the momentum acceptance and dynamic aperture in the MEIC ion collider ring by considering the aberration effects up to the third order, such as amplitude dependent tune shift. We also explore the compensation of the third order effects by introducing families of octupoles in the extended beam area.
Authored by Jefferson Science Associates, LLC under U.S. DOE Contract No. DE-AC05-06OR23177. Supported in part by US DOE STTR grant DE-SC0006272.

TUPPP001

Beam Based Measurements with Superconducting Wigglers at the Canadian Light Source with Applications to Nonlinear Beam Dynamics

wiggler, injection, optics, multipole

1599

W.A. Wurtz, L.O. Dallin, M.J. Sigrist
CLS, Saskatoon, Saskatchewan, Canada

The Canadian Light Source (CLS) employs two superconducting wigglers for the production of hard x-rays. These wigglers cause a large decrease in injection efficiency. While such a decrease is not unexpected due to the large distortion to the linear optics, a correction to the linear optics does not restore injection efficiency. This inability to restore injection is not predicted by a kickmap model of the wiggler. We performed beam based measurements to construct a phenomenological, nonlinear model of the wiggler. Particle tracking with this wiggler model shows that the reduction in dynamic aperture is due to the amplitude dependent tune shift crossing a resonance, even with the linear optics corrected. Moving the tunes allows us to avoid this resonance and measurements at these tunes show that injection efficiency is not greatly affected by the wigglers.

TUPPP002

GLASS Study of the Canadian Light Source Storage Ring Lattice

emittance, lattice, quadrupole, sextupole

1602

W.A. Wurtz, L.O. Dallin
CLS, Saskatoon, Saskatchewan, Canada

GLASS is a technique for finding all potential operating points of a storage ring lattice by examining all possible configurations of the linear lattice. The Canadian Light Source (CLS) storage ring uses three quadrupole families, making it computationally efficient to use GLASS to study the lattice with unbroken symmetry. CLS does not employ harmonic sextupoles and has only two families of chromatic sextupoles. We can exhaust the sextupole degrees of freedom by requiring the horizontal and vertical chromaticities to be both zero. With no remaining free parameters in our lattice, it is possible to calculate dynamic aperture and momentum acceptance for select regions of interest uncovered by the GLASS scan. We find two regions with reasonable dynamic aperture and momentum acceptance: the region where we presently operate and a region that can be accessed by reversing the polarity of one quadrupole family.

TUPPP013

Effects of Multipoles in Dynamic Aperture of the ILSF Storage Ring

multipole, sextupole, quadrupole, lattice

1632

S. Fatehi, E. Ahmadi, F. Saeidi
ILSF, Tehran, Iran
D. Einfeld
CELLS-ALBA Synchrotron, Cerdanyola del Vallès, Spain
H. Ghasem
IPM, Tehran, Iran

Dynamic aperture of a synchrotron light source shrinks to small value due to the multipole errors caused by magnet design. In the ILSF storage ring, the tolerance of magnets has been taken into account in the simulation and sextupole magnets reoptimized to improve the dynamic aperture. This paper yields the evaluated dynamic aperture include of multipole errors.

TUPPR085

Recycler Chromaticities and End Shims for NOvA at Fermilab

lattice, sextupole, quadrupole, dipole

2023

M. Xiao
Fermilab, Batavia, USA

In era of NOvA operation, it is planned to slip-stack six on six Booster proton batches in the Recycler ring for a total intensity of 5×10¹³ protons/cycle. During the slip-stacking, the chromaticities are required to be jumped from (-2,-2) to (-20,-20). However, they can only be adjusted to (-12,-12) from (-2,-2) using existing 2 families of powered sextupoles. On the other hand, the presently designed Recycler lattice for Nova replaces the 30 straight section with 8 “D-D half FODO cells”. We use 3 quads in a half-cell to obtain the working point under the limit of the feasible quad strength, and the maximum beta-function in this section cannot be less than 80 m. In this paper, we re-designed the end shims of the permanent magnets in the ring lattice with appropriate quadrupole and sextupole components to meet both chromaticity and tune requirements. We are able to use 2 quads in a half cell in RR30 straight section within feasible quad strength. The maximum beta-functions are also lowered to around 55 m. The dynamic aperture tracking has been done using MAD to simulate the scenario of beam injection into the Recycler ring for Nova.

WEPPR052

Octupole Magnets for the Instability Damping at the J-PARC Main Ring

octupole, damping, resonance, sextupole

3045

S. Igarashi, T. Koseki, K. Ohmi, M.J. Shirakata, H. Someya, T. Toyama
KEK, Ibaraki, Japan
A. Ando
J-PARC, KEK & JAEA, Ibaraki-ken, Japan

Octupole magnets have been installed for the instability damping at the J-PARC main ring. The transverse instability was observed during the injection and acceleration periods and caused the beam losses. The chromaticity tuning and bunch-by-bunch feedback system have been applied to suppress the instability. Octupole magnets were considered to create a larger amplitude dependent betatron tune shift and to supply additional option for the instability damping. The side effects of the dynamic aperture reduction and the resonances have been studied.