EPAC08 - Classification:05 Beam Dynamics and Electromagnetic Fields/D02 Non-linear Dynamics

05 Beam Dynamics and Electromagnetic Fields

D02 Non-linear Dynamics - Resonances, Tracking, Higher Order

Paper	Title	Page
TUOBG01	Observations of Beam-beam Tune Spectrum and Measurement of Coherent Tune Shift at KEKB	962
	T. Ieiri, Y. Ohnishi, M. Tobiyama, S. Uehara KEK, Ibaraki
	KEKB is a double-ring electron/positron collider with a horizontal crossing angle. The crab cavities installed in 2007 achieved an effective head-on collision and gained a higher specific luminosity. Under the new crabbing collision as well as the horizontal crossing collision, tune spectra of a colliding bunch were observed on a spectrum analyzer to study beam-beam effects. The beam-beam spectrum showed strong nonlinear resonant phenomena. Considering the nonlinearity, the coherent beam-beam tune shift was measured as a function of the bunch current. It was confirmed that the vertical beam-beam parameter estimated from the coherent beam-beam tune shift agreed with a value obtained from a bunch-by-bunch luminosity monitor. The estimated vertical beam-beam parameter was saturated on a level of about 0.04, which is called a beam-beam limit. We found that the bunch current corresponding to the beam-beam limit was far below the bunch current used in the usual operation.
	Slides
TUOBG02	Study of Beam Dynamics During the Crossing of Resonances in the VEPP-4M Storage Ring	965
	P. A. Piminov, V. A. Kiselev, E. B. Levichev, O. I. Meshkov, S. A. Nikitin BINP SB RAS, Novosibirsk
	The influence of resonances on the beam dynamics in the storage rings is of a substantial interest for the accelerator physics. For example, a fast crossing of resonances occurs in the damping rings of future linear colliders during the beam damping due to the coherent shift that can result in a loss of particles. We have studied experimentally the crossing of resonances of different power nearby the working point of the VEPP-4M storage ring. The observation of the beam sizes and particle losses has been done with a single-turn time resolution. The comparison with the numerical simulation has been made.
	Slides
THYM01	Simulation of Beam-beam Effects and Tevatron Experience	2937
	A. Valishev Fermilab, Batavia, Illinois
	Simulations of beam-beam effects in the Tevatron correctly describe reality, have predictive power and have been used to support a change in the Tevatron working point to near the half integer. The simulation models and tools are discussed, and comparisons made with observations and measurements.
	Slides
THPC002	Synthesis of Optimal Nanoprobe (Nonlinear Approximation)	2972
	S. N. Andrianov, N. S. Edamenko, Yu. V. Tereshonkov St. Petersburg State University, Applied Mathematics & Control Processes Faculty, St. Petersburg
	This paper is a continuation of the paper devoted to synthesis of optimal nanoprobe in linear approximation. Here the main goal is the optimization of nanoprobe including nonlinear aberrations of different nature up to third order. The matrix formalism for Lie algebraic methods is used to account for nonlinear aberrations. This method gives a possibility to consider nonlinear effects separately. Here we mean that a researcher can start or remove different kind of nonlinearities. This problem is separated into several parts. On the first step, we consider possibilities of additional optimization for some structures, selected on the step of linear approximation. The most of aberrations have harmful character, and their effect must be maximally decreased. Therefore, on the next steps, some we use analytical and numerical methods for generation of nonlinear corrected elements. The matrix formalism allows reducing the correction procedure to linear algebraic equations for aberration coefficients. Some examples of corresponding results are given.
THPC050	Experimental Evidence of Beam Trapping with One-third and One-fifth Resonance Crossing	3092
	S. S. Gilardoni, F. Franchi, M. Giovannozzi CERN, Geneva
	Beam trapping in stable islands of the horizontal phase space generated by non-linear magnetic fields is realized by means of a given tune variation so to cross a resonance of order n. Whenever the resonance is stable, n+1 beamlets are created whereas if the resonance is unstable, the beam is split in n parts. Experiments at the CERN Proton Synchrotron showed protons trapped in stable islands while crossing the one-third and one-fifth resonance with the creation of 3 and 6 stable beamlets, respectively. The results are presented and discussed in details.
THPC051	Adiabaticity and Reversibility Studies for Beam Splitting Using Stable Resonances	3095
	S. S. Gilardoni, F. Franchi, M. Giovannozzi CERN, Geneva
	At the CERN Proton Synchrotron, a series of beam experiments proved beam splitting by crossing the one-fourth resonance. Depending on the speed at which the horizontal resonance is crossed, the splitting process is more or less adiabatic, and a different fraction of the initial beam is trapped in the islands. Experiments prove that when the trapping process is reversed and the islands merged together, the final distribution features thick tails. The beam population in such tails is correlated to the speed of the resonance crossing and to the fraction of the beam trapped in the stable islands. Experiments, simulations, and possible theoretical explanations are discussed.
THPC052	Beam Losses and Collimation Considerations for PS2	3098
	J. Barranco, W. Bartmann, M. Benedikt, Y. Papaphilippou CERN, Geneva
	The high intensity beams with different emittances foreseen to be delivered by the PS2, an upgraded version of the actual CERN Proton Synchrotron, require strict control of beam losses in order to protect the machine components and enable their hands-on maintenance. Beam loss simulations based on dedicated numerical tools are undertaken for a variety of PS2 beams and for different loss mechanisms, along the whole accelerating cycle. In this respect, the design of a collimation system is presented and its performance is compared within different lattice options.
THPC053	Turn-by-turn Data Analysis at the Diamond Storage Ring	3101
	R. Bartolini, I. P.S. Martin, G. Rehm, J. Rowland Diamond, Oxfordshire
	The Diamond Storage Ring has been recently equipped with a set of two pinger magnets that can excite betatron oscillations to large amplitudes in both planes of motion. In conjunction with the turn-by-turn capabilities available at all BPMs, the system provides a powerful diagnostic tools for the characterisation of the linear and non-linear beam dynamics of the electron beam in the storage ring. We report the first results on the application of the Frequency Map Analysis and the measurement of the resonant driving terms at the Diamond Storage Ring.
THPC054	Transportation of Decay Products in the Beta-beam Decay Ring	3104
	A. Chancé, J. Payet CEA, Gif-sur-Yvette
	The principle of the neutrino production in the beta-beams relies on the beta-decay of the radioactive ions Neon 18 and Helium 6 in a storage ring. After decaying, the daughter particles have their magnetic rigidity significantly changed (-33% for Helium and +11% for Neon). Therefore, the decay products will be quickly lost on the walls of the decay ring after entering a dipole. Absorbers have been inserted in the decay ring in order to collect most decay products. Their optimization implies to calculate the trajectories of the decay products in the dipoles for very large momentum differences with a good accuracy. For pure dipoles without fringe field as in the decay ring, an analytic treatment can be used to simulate the transportation. It is then possible to obtain the equivalent dipole which gives the beam sizes of the daughter particles. In a first part, we will describe the analytic treatment of the central trajectory and the motion of the ions around. In a second part, we will compare this treatment with the one with matrices for different orders in the case of the beta-beam decay ring.
THPC055	Dynamic Aperture Studies for PETRA III Including Magnet Imperfections	3107
	A. Kling, K. Balewski, W. Decking DESY, Hamburg Y. J. Li BNL, Upton, New York
	PETRA III is a 3rd generation synchrotron radiation light source. Efficient injection in the top up mode requires a dynamic aperture of 30 mmmrad or larger, while a 2 hour Touschek lifetime needs an average momentum aperture of around 1.5 %. We present studies on the impact of recently measured magnet imperfections on the available dynamic aperture. To this end, tracking simulations have been performed including the effects of measured multipole errors of lattice magnets and of 20 four-meters-long damping wigglers.
THPC056	Stability Change of Fourth-order Resonance with Application to Multi-turn Extraction Schemes	3110
	M. Giovannozzi, D. Quatraro CERN, Geneva G. Turchetti Bologna University, Bologna
	Recently, a novel multi-turn extraction scheme was proposed, based on particle trapping inside stable resonances. Numerical simulations and experimental tests confirmed the feasibility of such a scheme for low order resonances. While the 3rd order resonance is generically unstable and those higher than 4th order are generically stable, the 4th order resonance can be either stable or unstable depending on the details of the system under consideration. By means of the normal form approach a general formula to control the stability of the 4th order resonance is derived. Numerical simulations confirm the analytical results and show that by crossing the unstable 4th order resonance the region around the centre of phase space is depleted and particles are trapped only in the four stable islands. This indicates that a four-turn extraction could be envisaged based on this technique.
THPC057	Field Interference of Magnets in the Large Acceptance Storage Ring CR of the Fair Project	3113
	O. E. Gorda, C. Dimopoulou, A. Dolinskii, F. Nolden, M. Steck GSI, Darmstadt
	The large acceptance storage ring CR is planned to be used for accumulation and cooling of rare isotope and antiproton beams at the future FAIR accelerator facility. The huge apertures as well as the close arrangement of the dipoles and quadrupoles make overlapping between the end fields of the magnets unavoidable. In addition, corrector magnets are planned to be installed in the drift sections between the dipoles and quadrupoles for closed orbit corrections. The presence of additional iron can have a significant influence on the magnetic field distribution. This interference can lead to a reduction of the integral field quality decline that is undesirable since it can affect the beam dynamics. In this contribution we present the results of 3D magnetic field simulations performed using the OPERA computer code. The field maps were derived and further analyzed. The corresponding sets of multipole components were calculated and were then implemented into one of the codes for the beam dynamics calculations. The MAD code was used to calculate the dynamic aperture and to estimate the effect of the field interference on the beam dynamics of the ring.
THPC058	High Order Super-periodic Structural Resonances	3116
	Y. Jiao, S. X. Fang, J. Q. Wang IHEP Beijing, Beijing
	High order super-periodic structural resonances, which arise from the study of SSRF lattice optimization, are found to have large effects on beam dynamics. The mechanism and feature of this kind of resonances are described in the text. The limit to beam dynamics of other light sources are also found from these resonances.
THPC059	Studies of Wire Compensation and Beam-beam Interaction in RHIC	3119
	H. J. Kim, T. Sen Fermilab, Batavia, Illinois N. P. Abreu, W. Fischer BNL, Upton, Long Island, New York
	Beam-beam interaction is one of the dominant source of emittance growth and luminosity lifetime deterioration. A current carrying wire has been proposed to compensate long-range beam-beam effects in the LHC and the principle is now being experimentally investigated at RHIC. In this paper, we use simulations to study the effectiveness of wire compensation based on tune footprints, diffusive apertures, and beam loss rates using a parallel weak-strong beam simulation code (BBSIM). In addition we extensively study the diffusion properties of RHIC beams for different beam and wire parameters. Beam-beam effects on emittance growth are investigated through the solution of the diffusion equation for the transverse action variables.
THPC060	Spin Flip of Deuterons in COSY - Spink Tracking	3122
	A. U. Luccio BNL, Upton, Long Island, New York A. Lehrach FZJ, Jülich
	The spin tracking code Spink, as recently overhauled, has been used to study the deuteron spin resonances and spin flipping induced by a RF dipole and a RF solenoid. The modifications of the code followed extended discussions on the formalism used to model spin evolution in a synchrotron. The simulation shows a good agreement with published results of the measurements. A. U. Luccio et al. See another contribution to this Conference. **A. D. Krisch et al. PR-STAB 10, 07100-1, 2007.
THPC062	Multi-Particle Weak-Strong Simulations of RHIC Head-on Beam-Beam Compensation	3125
	Y. Luo, N. P. Abreu, W. Fischer, G. Robert-Demolaize BNL, Upton, Long Island, New York
	An electron beam has been proposed in the Relativistic Heavy Ion Collider (RHIC) to compensate beam-beam effects in polarized proton collisions. This electron beam will collide head-on with the proton beam. Using the weak-strong beam-beam interaction model, we have carried out six-dimensional multiparticle simulations to investigate the effects of head-on beam-beam compensation. Beam lifetime, transverse emittances, and luminosity are calculated for cases with and without beam-beam compensation for up to 10 million turns. The migrations of particles between different actions and the beam spectrum are also calculated.
THPC063	First Frequency Maps for Probing the Non-linear Dynamics of SOLEIL	3128
	L. S. Nadolski, P. Brunelle, J.-P. Lavieville, P. Lebasque, A. Nadji, M.-A. Tordeux SOLEIL, Gif-sur-Yvette
	SOLEIL is a 2.75 GeV third generation synchrotron light source delivering photons to beam-lines since January 2007. With a 3.7 nm.rad horizontal emittance, its optics is based on a strong focusing lattice. Large on- and off-momentum apertures are required in order to provide good injection efficiency and as large as possible beam lifetime. It is then fundamental to be able to understand the limitations of these key figures. In order to probe the transverse non linear dynamics two pinger magnets have been installed into the injection straight section during last summer shutdown period. In this paper, their calibration will be described. Then first comparisons between modeled and real machine will be given for betatron tune shifts with amplitudes, and frequency maps. To end the non linear impact of insertion devices on beam dynamics will be discussed.
THPC066	Measuring Ring Nonlinear Components via Induced Linear "Feed-down"	3137
	A. S. Parfenova, G. Franchetti, I. Hofmann GSI, Darmstadt
	The knowledge of the distribution in a ring of the non-linear components is important for the resonance compensation. We present a method to measure the lattice nonlinear components based on the non-linear tune response to a locally controlled closed orbit deformation. A test of this concept in the SIS18 synchrotron is presented and discussed.
THPC067	ALBA Dynamic Aperture Optimization	3140
	P. A. Piminov, E. B. Levichev BINP SB RAS, Novosibirsk D. Einfeld ALBA, Bellaterra
	The lattice of ALBA, the 3 GeV synchrotron light source in Spain, provides extremely low emittance of the beam. It is known that such lattices require strong sextupole magnets to compensate natural chromaticities. The paper describes strategy and results of the ALBA dynamic aperture optimization including both tune point selecting and sextupoles arrangement to increase the DA size.
THPC068	Effect of Magnetic Multipoles on the ALBA Dynamic	3143
	P. A. Piminov, E. B. Levichev BINP SB RAS, Novosibirsk D. Einfeld ALBA, Bellaterra
	For modern synchrotron light sources the main limitation of dynamic aperture is due to the strong chromatic sextupoles. However, small multipole errors in magnetic elements can reduce the original dynamic aperture by generating high order resonances at the aperture boundary. For the ALBA synchrotron light source a dynamic aperture in the presence of magnetic multipoles in the main magnets was simulated by tracking code. Both systematic and random magnetic errors were taken into account. In this paper we report on the results of our considerations.
THPC069	Impact of Magnet Misalignment in an ERL for Electron Cooling in RHIC	3146
	V. H. Ranjbar, D. T. Abell, K. Paul Tech-X, Boulder, Colorado I. Ben-Zvi, J. Kewisch BNL, Upton, Long Island, New York R. D. Ryne LBNL, Berkeley, California
	The MaryLie/IMPACT code was recently upgraded to include magnet errors. We have used the code to assess the sensitivity of final emittance of an ERL injector for the proposed RHIC electron cooler to up-stream magnetic element misalignments. This calculation will help determine the error tolerance for the construction of the ERL.
THPC070	Symmetry Restoration of the SPring-8 Storage Ring by Counter-sextupole Magnets	3149
	K. Soutome, S. Daté, T. Fujita, K. Fukami, C. Mitsuda, A. Mochihashi, H. Ohkuma, M. Oishi, S. Sasaki, J. Schimizu, Y. Shimosaki, M. Shoji, M. Takao, K. Tsumaki, H. Yonehara, C. Zhang JASRI/SPring-8, Hyogo-ken S. Matsui, H. Takebe, H. Tanaka RIKEN/SPring-8, Hyogo
	In the SPring-8 storage ring there are four magnet-free long straight sections of about 30m. These were realized in 2000 by locally rearranging quadrupole and sextupole magnets. In modifying the optics we took care of the periodicity of cell structure, especially of sextupole field distribution along the ring. To keep the periodicity high and hence the dynamic aperture large, we adopted a scheme in which "betatron phase matching" and "local chromaticity correction" are combined. In this scheme the dynamic aperture for on-momentum electrons is kept by the phase matching and that for off-momentum electrons is enlarged by the local chromaticity correction with weak sextupoles (SL). After modifying the lattice, we tried to recover the symmetry of the ring further and found that a harmful effect of nonlinear kick due to SL can be minimized by additional "counter-sextupole magnets" placed 180 degrees apart in horizontal betatron phase from SL. We installed such counter-sextupoles in every long straight sections and confirmed that the aperture was improved. In the paper we discuss these topics showing experimental data of injection efficiency, momentum acceptance, etc.
THPC072	Impact of Betatron Motion on Path Lengthening and Momentum Aperture in a Storage Ring	3152
	M. Takao JASRI/SPring-8, Hyogo-ken
	The amplitude of the betatron motion in an electron storage ring becomes large in some cases, e.g. Touschek scattered electrons or injected beam. Then we cannot ignore the effect of a finite amplitude of betatron motion on the beam dynamics. The path lengthening of the central trajectory of betatron motion is one of the most serious manifestations of such an influence. Due to the synchrotron motion, the variation of the path length is converted into the energy deviation, so that the betatron motion gives the impact on the momentum aperture in the storage ring. In this paper the path lengthening by a finite amplitude betatron motion is calculated by means of the canonical perturbation method. The derived formula for the path lengthening is simply represented by the product of the chromaticity and the invariant amplitude. Using the formula, we discuss the impact of the betatron motion on momentum aperture in a Touschek effect.
THPC073	Measurement of Resonance Driving Terms in the ATF Damping Ring	3155
	R. Tomas, F. Zimmermann CERN, Geneva K. Kubo, S. Kuroda, T. Naito, T. Okugi, J. Urakawa KEK, Ibaraki
	The measurement of resonance driving terms in the Damping Ring of the Accelerator Test Facility in KEK could help finding possible machine imperfections and even to optimize single particle stability through the minimization of non-linearities. The first experimental attempts of this enterprise are reported in this note.
THPC074	Observation of Coherent Oscillations of Colliding Bunches at the Tevatron	3158
	A. Valishev, V. Kamerdzhiev, V. A. Lebedev Fermilab, Batavia, Illinois F. A. Emanov BINP SB RAS, Novosibirsk
	Commissioning of the new digital tune monitor (DTM) at the Tevatron made it possible to observe vertical dipole oscillations of individual bunches at any time during an HEP store. Since all the bunches have significantly different collision conditions, this device provides vast possibilities for investigation of coherent beam-beam effects. We present theoretical model and experimental observations of coherent beam-beam modes. Analysis of the DTM data and its agreement with theory are discussed.
THPC076	Closed Orbit Correction and Sextupole Compensation Schemes for Normal-conducting HESR	3161
	D. M. Welsch, A. Lehrach, B. Lorentz, R. Maier, D. Prasuhn, R. Tölle FZJ, Jülich
	The High Energy Storage Ring (HESR) will be part of the future Facility for Antiproton and Ion Research (FAIR) located at GSI in Darmstadt, Germany. The HESR will be operated with antiprotons in the momentum range from 1.5 to 15 GeV/c, which makes a long beam life time and a minimum of particle losses crucial. This and the demanding requirements of the PANDA experiment lead to the necessity of a good orbit correction and an effective multipole compensation. We developed a closed orbit correction scheme and tested it with Monte Carlo simulations. We assigned different sets of angular and spatial errors to all elements (magnets, bpms, etc.) within the lattice of the HESR. For correction we applied the orbit response matrix method. We carried out investigations concerning higher-order multipoles and created a scheme for chromaticity correction and compensation of arising resonances utilising analytic formulae and dynamic aperture calculations. In this presentation we give an overview of the correction and compensation schemes and of the corresponding results.
THPC078	Injection Scheme of X-rays Source NESTOR	3167
	A. Y. Zelinsky, I. M. Karnaukhov, A. Mytsykov, V. L. Skirda NSC/KIPT, Kharkov
	In the paper the injection scheme of the X-ray source NESTOR based on the compact storage ring and Compton scattering is described. It is supposed to inject electron beam through fringe fields of a bending magnet. For final beam deflection electrical inflector on the running wave will be used. The layout of the injection scheme and elements characteristics are presented. The results of simulations of electron beam motion through 3-d fields of electro-magnetic devices of the injection channel are presented.
THPC080	The VEPP-4M Dynamic Aperture Determination with Beam-beam Effects	3170
	A. N. Zhuravlev, V. A. Kiselev, E. B. Levichev, O. I. Meshkov, P. A. Piminov, D. N. Shatilov, V. V. Smaluk BINP SB RAS, Novosibirsk
	To determine experimentally the particle stable area under the influence of beam-beam effects in the electron-positron collider VEPP-4M we measure the beam lifetime with high accuracy as a function of moving aperture. The measurement is performed by a photodiode installed in the collider diagnostic beam line. The experimental setup and the measurement results are described. Comparison with the tracking simulation is presented.
THPC081	RF Wire Compensator of Long-range Beam-beam Effects	3173
	U. Dorda, F. Caspers, T. Kroyer, F. Zimmermann CERN, Geneva
	The dynamic aperture of the proton beam circulating in the Large Hadron Collider (LHC) is expected to be limited by up to 120 long-range beam-beam encounters. In order to perfectly compensate the LHC long-range beam-beam effect for nominal as well as for so-called 'PACMAN' bunches, i.e. bunches at the start or end of a bunch train, the wire compensator strength should be adjusted for each bunch individually. Here an RF-based compensator is proposed as a practical solution for the PACMAN compensation. We show that this approach also allows relaxing the power and precision requirements compared with those of a pulsed DC device, to a level within the state-of-the-art of RF technology. Furthermore it allows the use of a passive circulator in the tunnel close to the beam and thus a significantly reduction of the transmission line length and of the resulting multiple reflection issues. Simulations, issues related to RF phase noise and first experimental results from laboratory models as well as from a wire-compensator prototype installed in the CERN Super Proton Synchrotron (SPS) are presented.
THPC082	Wire Excitation Experiments in the CERN SPS	3176
	U. Dorda, J.-P. Koutchouk, R. Tomas, J. Wenninger, F. Zimmermann CERN, Geneva R. Calaga, W. Fischer BNL, Upton, Long Island, New York
	In order to study the effect of long range interaction and its wire compensation experimentally, current carrying wires are installed in the CERN Super Proton Synchrotron (SPS). In this paper we summarize the main results of the 2007 wire excitation results at 26, 37 and 55 GeV including wire-current-, beam-wire distance and chromaticity scans. A strong dependence on the chromaticity and indications of a threshold effect at 37 and 55 GeV was found. The results are compared to simulation, to a simple analytic scaling law and to experimental results from RHIC. Wire-driven resonances have been observed through the Fourier spectrum of experimental BPM data and compared to simulations.
THPC083	Simulation Studies of Space-charge Effects in the LENS Nonlinear Transport Lines	3179
	M. Hess, A. Bogdanov IUCF, Bloomington, Indiana
	The upgraded IUCF LENS beamline is designed to deliver a square shaped 13 MeV proton beam at 25 mA with a relatively uniform density using two octupole magnets for nonlinear focusing in both transverse directions. The space-charge effects in the LENS beamline (without nonlinear focusing) can vary the beam profile by roughly 8%-13% compared to a zero current beam. In this paper, we show the results of simulation studies of the LENS beamline which incorporate the effects of space-charge, as well as, nonlinear focusing from the octupole magnets. The simulations utilize self-consistent methods for computing the space-charge fields, since the beam density distribution can be nonlinear. We also show simulation results for beam currents in excess of 25 mA, which may be useful for future upgrades of LENS.
THPP008	Hamiltonian Approach to the Dynamics of Particles in Non-scaling FFAG Accelerators	3392
	B. D. Muratori, S. L. Smith, S. I. Tzenov STFC/DL/ASTeC, Daresbury, Warrington, Cheshire
	Starting from first principle the Hamiltonian formalism for the description of the dynamics of particles in non-scaling FFAG machines has been developed. The stationary reference (closed) orbit has been found within the Hamiltonian framework. The dependence of the path length on the energy deviation has been described in terms of higher order dispersion functions. The latter have been used subsequently to specify the longitudinal part of the Hamiltonian. It has been shown that higher order phase slip coefficients should be taken into account to adequately describe the acceleration in non-scaling FFAG accelerators.