05 Beam Dynamics and Electromagnetic Fields
D02 Non-linear Dynamics - Resonances, Tracking, Higher Order

Paper	Title	Page
TUOAB02	Simultaneous Long and Short Bunch Operation in an Electron Storage Ring - a Hybrid Mode based on Nonlinear Momentum Compaction	945
	M. Ries, J. Feikes, A. Jankowiak, P.O. Schmid, G. Wüstefeld HZB, Berlin, Germany
	The generation of short pulses in electron storage rings is driven by different user groups like time resolved x-ray spectroscopy users or users of coherent synchrotron radiation. The required optics and operation conditions to generate this short bunches are worsening the experimental conditions, e.g. strongly reducing the average photon flux, for the regular user. Therefore short bunch operation is usually limited to dedicated user shifts. By controlling higher orders of the momentum compaction factor by higher multipoles it is possible to introduce a hybrid mode and simultaneously supplying long and short bunches*. The Metrology Light Source (MLS) has the means to control these higher orders**, therefore it is an ideal machine to investiate the feasibility of such a hybrid mode. Tracking results and first measurements will be shown. * D. Robin et al., Proc. of EPAC08, p. 2100-2102, Genoa, Italy (2008). ** J. Feikes et al., Phys. Rev. ST Accel. Beams 14, 030705 (2011).
	Slides TUOAB02 [7.817 MB]
WEPC032	First Measurements of Higher Order Optics Parameters in the LHC	2073
	G. Vanbavinckhove NIKHEF, Amsterdam, The Netherlands M. Aiba PSI, Villigen, Switzerland R. Bartolini Diamond, Oxfordshire, United Kingdom R. Calaga, R. Miyamoto BNL, Upton, Long Island, New York, USA M. Giovannozzi, F. Schmidt, R. Tomás CERN, Geneva, Switzerland E.H. Maclean JAI, Oxford, United Kingdom
	Higher order effects can play an important role in the performance of the LHC. Lack of knowledge of these parameters can increase the tune footprint and compromise the beam lifetime. First measurements of these parameters at injection and flattop have been conducted. Detailed simulations are compared to the measurements together with discussions on the measurement limitations.
WEPC049	Operation and Storage Ring Calibration with the Transverse Bunch-by-Bunch Feedback System at the Australian Synchrotron	2121
	M.J. Boland, Y.E. Tan ASCo, Clayton, Victoria, Australia D.J. Peake, R.P. Rassool, K.P. Wootton The University of Melbourne, Melbourne, Australia
	The first operational experience with the transverse bunch-by-bunch feedback system for the storage ring shows a doubling of the lifetime and the ability to damp instabilities caused by IVU gap changes. The system was also used to calibrate the ring by doing simultaneous measurements on several single bunches with different bunch currents. Using the bunch-by-bunch system's capability to excite the beam to large amplitudes, the non-linear beam dynamics were also measured and compared with the model.
WEPC050	New Optics for the SOLEIL Storage Ring	2124
	P. Brunelle, F. Briquez, A. Loulergue, O. Marcouillé, A. Nadji, L.S. Nadolski, M.-A. Tordeux, J.F. Zhang SOLEIL, Gif-sur-Yvette, France
	SOLEIL, the French 2.75GeV synchrotron light source is delivering photons to 24 beam lines and is presently equipped with 22 insertion devices (ID) including a high field and small gap in-vacuum wiggler*. This paper presents the continuous work performed to reduce the strong non linear effects of several IDs. On one side, the ID defaults have been precisely identified using on-beam measurements, and magnetic correction developments are going on, especially for the in-vacuum wiggler and for the 10m long HU640 undulator. On the other side, a new optics has been optimised in terms of beta-functions (at the ID location) and non linear dynamics in order to improve the injection efficiency and the beam lifetime in the presence of IDs. The modified optics has been used daily in operation since November 2010 and ensures a beam lifetime greater than 10h for a 400mA stored beam with the users ID configuration. In parallel, an extensive experimental optimization has been performed to prepare the operation with an additional quadrupole triplet that provides double low vertical beta functions in one long straight section that will accommodate two canted in-vacuum insertion devices**. * O. Marcouillé et al., IPAC10, p. 3102 (2010). ** A. Loulergue et al., IPAC10, p. 2496 (2010).
WEPC051	Effect of Compton Scattering on the Electron Beam Dynamics at the ATF Damping Ring	2127
	I. Chaikovska, C. Bruni, N. Delerue, A. Variola, Z.F. Zomer LAL, Orsay, France K. Kubo, T. Naito, T. Omori, N. Terunuma, J. Urakawa KEK, Ibaraki, Japan
	Compton scattering provides one of the most promising scheme to obtain polarized positrons for the next generation of e+e− colliders. Moreover it is an attractive method to produce monochromatic high energy polarized gammas for nuclear applications and X-rays for compact light sources. In this framework a four-mirror Fabry-Perot cavity has been installed at the Accelerator Test Facility (ATF - KEK, Tsukuba, Japan) and will be used to produce an intense flux of polarized gamma rays by Compton scattering. For electrons at the energy of the ATF (1.28GeV) Compton scattering may result in a shorter lifetime due to the limited bucket acceptance. We have implemented the effect of Compton scattering on a 2D tracking code with a Monte-Carlo method. This code has been used to study the longitudinal dynamics of the electron beam at the ATF damping ring, in particular the evolution of the energy spread and the bunch length under Compton scattering. The results obtained are presented and discussed. Possible methods to observe the effect of Compton scattering on the ATF beam are proposed.
WEPC052	Spinor Based Calculation of Depolarizing Effects in Circular Lepton Accelerators	2130
	O. Boldt, A. Dieckmann, F. Frommberger, W. Hillert ELSA, Bonn, Germany
	Funding: BMBF The emission of synchrotron radiation strongly influences the beam dynamics in case of ultra relativistic leptons. When storing or accelerating leptons in circular accelerators, the acting magnetic field shows an oscillating behavior in the rest frame of the leptons. Its properties can be determined by a spectral analysis. The stochastic emission of synchrotron light leads to a line broadening within the magnetic field spectrum. This spectrum can be used to simulate depolarizing effects in circular accelerators. Our contribution will present a tracking based calculation of the mentioned spectrum and a spinor-based determination of the resulting population of the spin-up state. These calculations base on the lattice of the electron stretcher accelerator (ELSA, Bonn) and are confirmed by measurements of the polarization.
WEPC053	Crossing of Depolarizing Resonances in Circular Electron Accelerators	2133
	W. Hillert, A. Balling, O. Boldt, A. Dieckmann, F. Frommberger ELSA, Bonn, Germany
	Funding: Supported by the German Research Foundation (DFG) through SFB/TR 16 In flat electron storage rings, only the vertical component of the beam polarization is preserved. During acceleration, the crossing of several depolarizing resonances may cause severe beam depolarization. Even in case of fast ramping speeds of up to 6 GeV/sec, first order effects like imperfection and intrinsic resonances have to be compensated by dedicated measures. At the accelerator facility ELSA, schemes like fast tune jumping and harmonic orbit correction are successfully applied on the fast energy ramp up to 3.2 GeV. Characteristics of the setup as well as the optimization efforts to improve the resonance compensation will be reported in detail.
WEPC054	Amplitude Dependent Tune Spread in the CR Operated as an Antiproton Collector	2136
	A. Dolinskii, C. Dimopoulou, O.E. Gorda, S.A. Litvinov, F. Nolden, M. Steck GSI, Darmstadt, Germany
	The Collector Ring is planned to be built for efficient cooling of antiprotons and rare isotopes beams. In order to accept hot antiproton beams coming from a separator large aperture magnets are required. This paper examines the effects which, may influence on the beam dynamic because of both large both betatron amplitude oscillations (240 mm mrad) and momentum spread (6%). Using analytic expressions the amplitude-dependent tune shifts driven by sextupole magnets, fringe field of quadrupole magnets and kinematics effects have been calculated. The results are compared with numerical simulations. Tracking studies for the CR operated as an antiproton collector have been performed considering the real shape of the magnetic field of the wide aperture quadrupole. We report on quantitative studies of the effects on the tune spread and its influence on the beam losses.
WEPC056	Beam Test of Slow Extraction from the ESR	2142
	A. Dolinskii, C. Dimopoulou, O.E. Gorda, S.A. Litvinov, F. Nolden, M. Steck GSI, Darmstadt, Germany
	In the frame of a dedicated ESR machine development the conventional third order resonant slow extraction was theoretically investigated and experimentally tested. The possibility to extract a beam from the ESR by preparing a resonant closed orbit, which has strong nonlinear characteristics, was demonstrated. A third-integer resonance slow extraction has been adopted for the 100 MeV/u Ar beam.
WEPC057	Estimation of the Dynamic Aperture by Transverse Beam Excitation with Noise Close to a Resonance	2145
	S. Sorge, G. Franchetti GSI, Darmstadt, Germany
	The present heavy ion synchrotron SIS-18 will be upgraded to be used as a booster for further synchrotrons being part of the FAIR project underway at GSI. Recently, a method was developed to measure the physical aperture of SIS-18 using transverse RF noise. This method is based on the transverse expansion of the beam with noise beyond the limiting aperture generating beam loss. The aperture was determined from the comparison of the resulting time evolution of the beam current in the machine with that obtained from a numerical simulation. In this study we attempt to apply this method to determine the dynamic aperture of SIS-18.
WEPC058	Field Properties of the ESR Magnets and their Influence on Beam Optics	2148
	O.E. Gorda, C. Dimopoulou, A. Dolinskii, S.A. Litvinov, F. Nolden, M. Steck GSI, Darmstadt, Germany
	Machine experiments at the experimental storage ring (ESR) demonstrated that the ring acceptance is strongly restricted by field errors. Higher-order field harmonics of the dipole and quadrupole magnets have been calculated and then used in particle tracking simulations in order to find out the dynamic aperture of the ESR. To benchmark the results of numerical calculations, betatron tune measurements have been performed with a uranium beam at the energy of 400 MeV/u. The results of the magnetic field simulations for the ESR magnets and a comparison between the measured and calculated tune behavioгr are presented.
WEPC059	Optimization of the Sextupole Scheme and Compensation of the Time-Dependent Field Errors during Slow Extraction from the Superconducting Synchrotron SIS300	2151
	A. Saa Hernandez, P.J. Spiller GSI, Darmstadt, Germany U. Ratzinger IAP, Frankfurt am Main, Germany
	The SIS300 synchrotron, planned for the new Facility for Antiproton and Ion Research (FAIR) at GSI-Darmstadt, will become the first superconducting synchrotron worldwide using cos(θ) magnets for resonant slow extraction. A multi-objective optimization algorithm has been developed for the design of the non-linear magnet scheme. The optimization algorithm makes use of the analytical model for the slow extraction from Kobayashi, the analytical description of the resonance excitation and amplitude-dependent tune-shift from Bengtsson, and corrects the chromaticity in order to fulfill the Hardt condition. As a result, the placement of the chromatic and harmonic sextupole magnets in SIS300, the number of sextupole families and the gradients of these families have been optimized for a high efficiency slow extraction. The algorithm accounts also for the sextupole errors on the dipole magnets, compensating its effects. Furthermore, optimized time-dependent settings for the sextupole magnets are generated to compensate the persistent current decay occurring at slow extraction. Tolerances for the magnets are set for the limits where the compensation is no longer valid.
WEPC060	Magnetic Field Description in Curved Accelerator Magnets using Local Toroidal Multipoles	2154
	P. Schnizer, E.S. Fischer GSI, Darmstadt, Germany B. Schnizer TUG/ITP, Graz, Austria
	Any introduction on beam dynamics describes the field homogeneity of the accelerator magnets using local derivatives. These are then typically described as plane circular multipoles or 2D harmonics; solutions to the potential equation. The high current operation, foreseen for SIS100 accelerator of FAIR, requires an in detail understanding of the different beam effects, driven by the resonance of the magnets. Therefore different multipole sets were developed and are now finalised in the Local Elliptic Toroidal Multipoles. These are a first order approximation while the plane circular ones are a zero order one in the inverse aspect ratio.
WEPC062	Second Order Achromats with Arbitrary Linear Transfer Matrices	2160
	V. Balandin, R. Brinkmann, W. Decking, N. Golubeva DESY, Hamburg, Germany
	The most obvious method to construct a second order achromat with an arbitrary (predefined) linear transfer matrix is to take a bend magnet system arranged in an achromat like fashion with the total transfer matrix equal to the identity matrix, attach a drift-quadrupole block with the desired linear transfer matrix and then adjust the sextupoles installed in the first part in such a way that the total system becomes a second order achromat. Unfortunately this is not always possible and, in general, the parts of such a system can not be designed independently. In this paper we give the necessary and sufficient conditions which must be satisfied for both parts of the system in order to become a second order achromat. In addition we provide some practical recommendations showing how these conditions can be fulfilled. We formulate these necessary and sufficient conditions using the group-theoretical point of view for the design of magnetic optical achromats as introduced in *. * V. Balandin, R. Brinkmann, W. Decking, N. Golubeva, "Two Cell Repetitive Achromats and Four Cell Mirror Symmetric Achromats", Proc. IPAC'10, Kyoto, Japan (2010).
WEPC063	Apochromatic Twiss Parameters of Drift-quadrupole Systems with Symmetries	2163
	V. Balandin, R. Brinkmann, W. Decking, N. Golubeva DESY, Hamburg, Germany
	It was shown in *, that for every drift-quadrupole system there exists an unique set of Twiss parameters (apochromatic Twiss parameters), which will be transported through that system without first order chromatic distortions. In this paper we investigate apochromatic Twiss parameters of periodic, mirror symmetric and other drift-quadrupole systems with symmetries. * V. Balandin, R. Brinkmann, W. Decking, N. Golubeva, "Apochromatic Beam Transport in Drift-Quadrupole Systems", Proc. IPAC'10, Kyoto, Japan (2010).
WEPC064	Long Term Beam Dynamics in Ultra-Low Energy Storage Rings	2166
	A.V. Smirnov MPI-K, Heidelberg, Germany A.I. Papash, A.V. Smirnov JINR, Dubna, Moscow Region, Russia M.R.F. Siggel-King, C.P. Welsch Cockcroft Institute, Warrington, Cheshire, United Kingdom
	Funding: "Work supported by STFC, the Helmholtz Association and GSI under contract VH-NG-328." Electrostatic storage rings operate at very low energies in the tens of keV range and have proven to be invaluable tools for atomic and molecular physics experiments. However, earlier measurements showed strong limitations in beam intensity, a fast reduction in the stored ion current, as well as significantly reduced beam life time at higher beam intensities and as a function of the ion optical elements used in the respective storage ring. In this contribution, the results from studies with the computer code BETACOOL into the long term beam dynamics in such storage rings, based on the examples of ELISA, the AD Recycler and the USR are presented.
WEPC066	High Order Non-linear Motion in Electrostatic Rings	2172
	D. Zyuzin, R. Maier, Y. Senichev FZJ, Jülich, Germany
	The advantages of an electrostatic storage ring as compared to a magnetic ring are obvious from the point of view to search for the proton electric dipole moment (pEDM). However the magnetic and electrostatic fields have the different nature and, consequently, different features. In particular, particles moving in electrostatic field, can change their own kinetic energy as electrical field coincides with the direction of motion, which is not so for the magnetic field, where the force is always perpendicular to the direction of motion. The electrostatic rings found many applications in the atomic physics and partly the beam dynamics has been already investigated. However in EDM ring some additional specific features are added, which are considered in this paper.
WEPC067	The Spin Aberration of Polarized Beam in Electrostatic Rings	2175
	Y. Senichev, A. Lehrach, R. Maier, D. Zyuzin FZJ, Jülich, Germany
	For a beam with nonzero transverse emittance and momentum spread passing through an electric field, for example an electric focusing lens or deflector, the orientation of a spin vector becomes a function of 6D initial phase coordinates that leads to spin aberrations. We investigate this process analytically and numerically.
WEPC068	Amplitude Dependent Betatron Oscillation Center Shift by Non-linearity and Beam Instability Interlock	2178
	T. Nakamura, K. Kobayashi, J. Schimizu, T. Seike, K. Soutome, M. Takao JASRI/SPring-8, Hyogo-ken, Japan T. Hara RIKEN SPring-8 Center, Sayo-cho, Sayo-gun, Hyogo, Japan
	The center of the betatron oscillation in storage rings shifts as the amplitude of the oscillation increases. This effect is produced by non-linear components like sextupole magnets with its first-order perturbation. This shift can be observed as the shift of the closed orbit with usual slow beam position monitor (BPM) for closed orbit measurement. At the SPring-8 storage ring, the insertion devices (IDs) have their dedicated BPMs for monitoring the beam axis in the IDs. If some amount of the shift of beam axis is observed, the beam is aborted to avoid the damage by the irradiation of the ring components by ID radiation. When a betatron oscillation is excited by a beam transverse instability, the beam axis also oscillates and might produce the damage. Though it is not easy to detect the oscillation amplitude in various bunch current and filling patterns like in SPring-8, the oscillation produces the shift of the center of the betatron oscillation and can be observed by the BPM of IDs, and the beam is aborted. Calculation, tracking simulation and observation will be reported.
WEPC069	Impact of Nonlinear Resonances on Beam Dynamics at the SPring-8 Storage Ring	2181
	M. Takao, J. Schimizu, Y. Shimosaki, K. Soutome JASRI/SPring-8, Hyogo-ken, Japan
	For a low emittance storage ring like high brilliant light sources, the improvement of nonlinear beam dynamics is necessary for the stable operation, or for providing large dynamic aperture and momentum acceptance for efficient injection and long Touschek lifetime. At the SPring-8 storage ring it is observed that injection efficiency is affected by the gap heights of the magnet arrays of the in-vacuum insertion devices. The fact that the injected beam of fundamentally oscillating in horizontal direction is limited by the vertical aperture means that coupling resonances influence the beam dynamics. To clarify the phenomena, we studied the nonlinear beam dynamics of transverse betatron motion by means of turn-by-turn method. Then, we found some nonlinear coupling resonances, such as the one by skew sextupole field, are excited to enhance vertical oscillation and to deteriorate the injection efficiency. By analyzing these results, we developed measures to suppress the effect of the nonlinear coupling resonances and to improve the injection efficiency.
WEPC071	The Motion of an Electron in the Periodic Cusped Magnetic Fields	2184
	G. Du, B.L. Qian, H. Wang National University of Defense Technology, Changsha, Kaifu District, People's Republic of China
	Funding: National High Technology Research and Development Program of P. R. China The motion and its stability of an electron in the periodic cusped magnetic fields have been analyzed theoretically and calculated numerically, as the stability could not be well predicted by the Mathieu’s equation to guide the design of the magnetic focusing system for the propagation of the sheet electron beams in the waveguides. The precise solution to the motion equations of the electron has been obtained by iteration. To validate the analytical solution and to evaluate the stability of the motion, numerical calculations have been carried out. And the results show that the analytical solution is reliable, and there is only one stable region in the (p0, B0) space, where the parameter p0 is the period of the magnetic fields, and B0 is the magnitude of the magnetic fields. Besides, the stability of the electron motion would become weaker while the initial distance between the electron and the axis becomes larger. These results are interesting to the area of the sheet-electron-beam microwave sources focused by the periodical cusped magnetic fields.
WEPC072	Insertion Devices and Beam Dynamics in the PLS-II Storage Ring	2187
	S. Chunjarean, S. Shin PAL, Pohang, Kyungbuk, Republic of Korea
	Effects of insertion devices like a superconducting multipole wiggler or an in-vacuum undulator on the beam dynamics of tghe upgraded Pohang Light Source (PLS-II) storage ring have been investigated. The narrow gap related to a short period length of the in-vacuum undulator or a transverse magnetic field roll off can impact the dynamic aperture or Touschek lifetime or injection efficiency. A three dimensional magnetic field model has been developed based on numerical data consisting of several coefficients in the Taylor expansion to accurately represent the actual field. In this paper, the magnetic field model has been produced with the differential algebraic code COSY INFINITY to formulate the Taylor transfer map for the wiggler and undulator. Frequency map analysis (FMA) and full 6D tracking has been performed to investigate resonances which may affect the particle stability and causing a reduction in injection efficiency.
WEPC074	Investigation of the Nonlinear Transformation of an Ion Beam in the Plasma Lens*	2190
	N.N. Alexeev, A.A. Drozdovsky, S.A. Drozdovsky, A. Golubev, Yu.B. Novozhilov, P.V. Sasorov, S.M. Savin, V.V. Yanenko ITEP, Moscow, Russia
	The plasma lens can carry out not only sharp focusing of ions beam. At those stages at which the magnetic field is nonlinear, formation of other interesting configurations of beams is possible. Plasma lens provides formation of hollow beams of ions in a wide range of parameters*. Application of the several plasma lenses allow to create some nontrivial spatial configurations of ions beams**: to get a conic and a cylindrical beams. The plasma lens can be used for transformation of beams with Gaussian distribution of particles density in a beams with homogeneous spatial distribution. The calculations showed that it is possible for a case of equilibrium Bennett's distribution of a discharge current. This requires a long duration of a discharge current pulse of > 10 μs. The first beam tests have essentially confirmed expected result. Calculations and measurements were performed for a C+6 and Fe+26 beams of 200-300 MeV/a.u.m. energy. The obtained results and analysis are reported. * A. Drozdovskiy et al., IPAC'10, Kioto, Japan, http://cern.ch/AccelConf/IPAC10 /MOPE040. ** A.Drozdovskiy et al., RUPAC’10, Protvino, Russia, http://cern.ch/AccelConf/RUPAC10 /THCHA01.
WEPC077	Beam Based Measurements with the Modified Wigglers in DAΦNE	2196
	S. Bettoni CERN, Geneva, Switzerland A. Drago, S. Guiducci, C. Milardi, M.A. Preger, P. Raimondi INFN/LNF, Frascati (Roma), Italy
	A novel idea to minimize the odd high order non-linearities in periodic magnets has been presented in other articles in the past. The optimization of this method on the wigglers of the main rings in DAΦNE has been performed by means of multipolar and tracking analysis. After the magnetic measurements on a spare wiggler confirmed the magnetic model used to optimize the DAΦNE wigglers, all the insertion devices in the main rings have been modified accordingly. In fall last year tune variation measurements as a function of closed orbit bumps around the wigglers confirmed the validity of the method. In this paper the beam based measurement results with the new configuration are discussed and compared with those obtained in the previous configurations.
WEPC078	Non-linear Chromaticity Studies of the LHC at Injection	2199
	E.H. Maclean, M. Giovannozzi, F. Schmidt, R.J. Steinhagen, E. Todesco, R. Tomás, G. Vanbavinckhove CERN, Geneva, Switzerland R. Bartolini JAI, Oxford, United Kingdom
	The non-linear chromaticity of the LHC has been studied. Measurements of variation in tune with dp/p on both beams at injection optics are being compared with Q'' and Q''' as calculated with the LHC effective model. This model uses the best currently available measurements of magnetic field harmonics. An attempt is being made to optimize the b4 and b5 pool-pieces corrections in view of the corresponding chromaticity terms.
WEPC080	Non-linear Dynamics Optimization of the CLIC Damping Rings	2205
	Y. Renier, F. Antoniou, H. Bartosik, Y. Papaphilippou CERN, Geneva, Switzerland K.P. Wootton The University of Melbourne, Melbourne, Australia
	Non-linear dynamics studies are undertaken in order to optimize the dynamic aperture of the CLIC damping rings. In this respect, advanced methods such as frequency map and resonance driving term analysis are used in order to explore the working point space with respect to single particle stability. The impact of magnet errors and misalignments, and in particular, the effect of the super-conducting damping wigglers is evaluated. Additional considerations for the working point choice are presented.
WEPC081	Beam-Beam Induced Orbit Effects at LHC	2208
	M. Schaumann, R. Alemany-Fernandez CERN, Geneva, Switzerland
	For high bunch intensities the beam-beam force is strong enough to expect orbit effects if the two beams do not collide head-on but with a crossing angle or with a given offset. As a consequence the closed orbit changes. The closed orbit of an unperturbed machine with respect to a machine where the beam-beam force becomes more and more important has been studied and the results are presented in this paper.
WEPC085	Multipole Fringe Fields	2211
	B.D. Muratori, J.K. Jones STFC/DL/ASTeC, Daresbury, Warrington, Cheshire, United Kingdom M.J. de Loos, S.B. van der Geer Pulsar Physics, Eindhoven, The Netherlands
	When creating an initial model of an accelerator, one usually has to resort to a hard edge model for the quadrupoles and higher order multipoles at the start of the project. Ordinarily, it is not until much later on that one has a field map for the given multipoles. This can be rather inconvenient when one is dealing with particularly thin elements or elements which are rather close together in a beamline as the hard edge model may be inadequate for the level of precision desired. For example, in the EMMA project, the two types of quadrupoles used are so close together that they are usually described by a single field map or via hard edge models. The first method has the desired accuracy but was not available at the start of the project and the second is known to be a rough approximation. In this paper, an analytic expression is derived and presented for fringe fields for a multipole of any order with a view to applying it to cases like EMMA.
WEPC087	Dark Current Simulations for the Cornell ERL	2214
	C.E. Mayes, C.S. Chiu, G.H. Hoffstaetter, V.O. Kostroun, D. Sagan CLASSE, Ithaca, New York, USA L.M. Nash North Carolina University, Chapel Hill, North Carolina, USA
	Funding: Supported by NSF award DMR-0807731 Charged particles unintentionally transported through an accelerator, collectively called the dark current, can be lost in the beam chamber and create a radiation hazard for both equipment and personnel. Here we simulate the creation of particles by field emission in the superconducting accelerating cavities of the Cornell Energy Recovery Linac, and track them to their loss points. These lost particles can then be used to simulate background radiation. The presented calculations are therefore an essential step in the design of appropriate radiation-shielding of components around the linac.
WEPC162	Investigations into Non-linear Beam Dynamics in Electrostatic Storage Rings	2361
	D. Newton, C.P. Welsch Cockcroft Institute, Warrington, Cheshire, United Kingdom O.E. Gorda MPI-K, Heidelberg, Germany D. Newton The University of Liverpool, Liverpool, United Kingdom A.I. Papash JINR, Dubna, Moscow Region, Russia
	Funding: Work supported by STFC, the Helmholtz Association and GSI under contract VH-NG-328. Electrostatic (ES) storage rings provide a cost-effective solution to the problem of confining low energy (beta << 1) charged particles and ions, whilst controlling the beam properties, for use in multi-pass experiments. However, compared to magnetic storage rings, the beam dynamics calculations for an ES ring show subtle differences, especially in the coupling of the longitudinal and transverse velocities and in the focusing properties of bending element fringe fields. Using the nominal design for a prototype ES ring, realistic trajectories (including fringe fields and non-linear field components) have been calculated and a comparison is made with linear lattice simulations. The effect of the non-linear field components on the beam parameters is discussed.
THOBA03	Dual AC Dipole Excitation for the Measurement of Magnetic Multipole Strength from Beam Position Monitor Data*	2865
	M. Spata, G.A. Krafft JLAB, Newport News, Virginia, USA
	Funding: Notice: Authored by Jefferson Science Associates, LLC under U.S. DOE Contract No. DE-AC05-06OR23177. An experiment was conducted at Jefferson Lab's Continuous Electron Beam Accelerator Facility to develop a technique for characterizing the nonlinear fields of the beam transport system. Two air-core dipole magnets were simultaneously driven at two different frequencies to provide a time-dependent transverse modulation of the electron beam. Fourier decomposition of beam position monitor data was then used to measure the amplitude of these frequencies at different positions along the beamline. For a purely linear transport system one expects to find solely the frequencies that were applied to the dipoles with amplitudes that depend on the phase advance of the lattice. In the presence of nonlinear fields one expects to also find harmonics of the driving frequencies that depend on the order of the nonlinearity. The technique was calibrated using one of the sextupole magnets in a CEBAF beamline and then applied to a dipole to measure the sextupole and octupole strength of the magnet. A comparison is made between the beam-based measurements, results from TOSCA and data from our Magnet Measurement Facility.
	Slides THOBA03 [6.193 MB]