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Type of presentation requested : Poster Classification : [D02] Nonlinear Dynamics  Resonances, Tracking, Higher Order 1135  Specific Design Peculiarities of Compact Pproton Synchrotron for Hadron Therapy A. Molodojentsev, KEK, Ibarakiken The report presents study of specific design peculiarities of the lowcycling proton synchrotron for hadron therapy, in particular the spacecharge effects of the lowenergy highintensity proton beam and the nonlinear particle motion caused by the magnetic field near the edge of the magnets of the compact synchrotron. The space charge of the beam can excite the highorder resonances without any magnetic field imperfection that will lead to the transverse emittance blowup. From the other side, the nonlinearities of the fringe fields become significant especially in the case of large amplitude of the particles. Combination of these effects in the case of the lowcycling compact synchrotron can limit the beam intensity of the medical machine. To avoid it the proper choice of main machine parameters should be based on accurate analysis of these effects. The detailed study of the space charge and fringe field effects for the compact proton synchrotron is performed by ACCSIM and COSY INFINITY codes. It is shown that the correct choice of the "bare" betatron tunes can improve the dynamic aperture of the synchrotron and minimize the blowup of the transverse emittances. The simulations are made for the compact proton synchrotron designed by Hitachi, Ltd. for the Proton Medical Center of the University of Tsukuba. Type of presentation requested : Poster Classification : [D02] Nonlinear Dynamics  Resonances, Tracking, Higher Order 1142  Fringe Field Effects and Dynamic Aperture of the 3 GeV JAERIKEK Synchrotron A. Molodojentsev, S. Machida, KEK, Ibarakiken Fringe fields of synchrotron magnets induce a variety of effects itself beginning from changing the linear properties of the focusing structure. The pseudomultipole nonlinearities of the fringe fields become more significant in the case of large amplitudes of the particles. As the result these effects can change the dynamic aperture of the synchrotron even without any magnetic field imperfections. Accurate simulation of these effects including amplitude dependent tune shift and chromaticity are performed for the 3GeV synchrotron by using the COSY INFINITY code. The fringe fields of the magnets are presented by the Enge functions. Sensitivity of the fringe field effects for different sets of the Enge coefficients is tested. The dynamic aperture of the synchrotron is estimated. The symplectic particle tracking predicts regions of the betatron tunes near the design values where the fringe field effects are most critical. Optimization of the working point provides improving the dynamic aperture of the synchrotron. Type of presentation requested : Poster Classification : [D02] Nonlinear Dynamics  Resonances, Tracking, Higher Order 851  Measurements of Mechanical Triplet Vibrations in RHIC* C. Montag, R. Bonati, J.M. Brennan, J. Butler, P. Koello, BNL, Upton, Long Island, New York Mechanical vibraions of the RHIC interaction region triplets has been identified as the dominant source of orbit jitter for frequencies up to 20 Hz. Detailed measurementws are reported that were performed in order to characterize these effects. We discuss its impact on beam dynamics and possible cures. * Work performed under the auspices of the U.S. Department of Energy. Type of presentation requested : Poster Classification : [D02] Nonlinear Dynamics  Resonances, Tracking, Higher Order 855  Modulated BeamBeam Interactions as a Possible Source of Emittance Growth in RHIC * C. Montag, W. Fischer, T. Satogata, BNL, Upton, Long Island, New York During RHIC Au operations in mid2001, lowfrequency (up to 20 Hz) beam orbit oscillations were present, with amplitudes on the order of 10 percent of the transverse beam size. These oscillations, created by mechanical vibrations in triplet quadrupole assemblies, drive tune and beambeam offset modulations, and may drive transverse emittance growth, thus degrading performance during RHIC colliding beam stores. This paper presents the current status and results of simulation studies to determine associated growth mechanisms and rates. * Work performed under the auspices of the U.S. Department of Energy. Type of presentation requested : Poster Classification : [D02] Nonlinear Dynamics  Resonances, Tracking, Higher Order 904  Analysis of MultiTurn Beam Position Measurements in the CERN PS A.S. Mueller, M.E. Angoletta, M. Giovannozzi, M. Martini, E. Metral, G. Metral, R. Steerenberg, CERN, Geneva The observation of betatron oscillations following a deflection by a kicker pulse offers the possibility to study various machine parameters. The decoherence and recoherence of a bunch's centreofcharge signal, for example, is governed by chromaticity, momentum spread and transverse nonlinearities. The multiturn acquisition system of the CERN PS is able to store beam position information of about 2000 turns. A careful analysis of such data can be used to extract estimates of the parameters involved, as well as to reconstruct the beam dynamics in phase space. Experimental results are compared to existing models. Type of presentation requested : Poster Classification : [D02] Nonlinear Dynamics  Resonances, Tracking, Higher Order 487  Study of Offset Collisions and Beam Adjustment in the LHC Using a StrongStrong Simulation Model B. Muratori, CERN, Geneva The bunches of the two opposing beams in the LHC do not always collide headon. The beambeam effects cause a small, unavoidable separation under nominal operational conditions. During the beam adjustment and when the beams are brought into collision the beams are separated by a significant fraction of the beam size. A result of small beam separation can be the excitation of coherent dipole oscillations or an emittance increase. These two effects are studied using a strongstrong multiparticle simulation model. The aim is to identify possible limitations and to find procedures which minimize possible detrimental effects. Type of presentation requested : Poster Classification : [D02] Nonlinear Dynamics  Resonances, Tracking, Higher Order 523  Consequences of Beambeam Interactions on the Detection of Lepton Pairs Produced by Gammagamma Collisions in the LHC B. Muratori, W. Herr, CERN, Geneva; D. Bocian, INP, Cracow The observation of electronpositron pairs produced in gammagamma collision at the LHC can be used to determine the luminosity of the proton proton collisions. The observation of the leptons may be obscured by direct and long range beambeam effects and we have evaluated these consequences in calculations and simulations to estimate the feasibility of the method and possible uncertainties. Type of presentation requested : Poster Classification : [D02] Nonlinear Dynamics  Resonances, Tracking, Higher Order 598  Application of a New Class of Symplectic Integrators to AcceleratorTracking L. Nadolski, LBNL, Berkeley; J. Laskar, IMCCNRS, Paris The dynamics of particle accelerator beams is commonly described by a Hamiltonian of the form H=A+B where A and B are integrable. Using Lie formalism, we give an overview of a new class of symplectic integrator [1] particularly well adapted when B is viewed as a perturbation of A. These integrators with positive step size can be constructed with a remainder of arbitrary order n in A and order 2 in B. Moreover a corrector step can be added to the integration scheme in many cases such that the remainder becomes actually of order 4 in B. A comparison with the fourthorder standard Forest and Ruth's [2] is performed showing in general a one order magnitude improvement in computation precision for the same cost. The easy construction of these integrators is sketched for the main magnetic elements of an electron storage ring. [1] J. Laskar, P. Robutel, ``High order symplectic integrators for perturbed Hamiltonian systems'', Celestial Mechanics, vol. 80, pp. 3962 (2001). [2] E. Forest, R.D. Ruth, ``Fourthorder symplectic integration'', Physica D, vol. 43(1), pp. 105117 (1990). Type of presentation requested : Poster Classification : [D02] Nonlinear Dynamics  Resonances, Tracking, Higher Order 1619  New Approach to Beam Dynamics Optimization Problem D. Ovsyannikov, SPbSU, St.Petersburg In the works [1],[2] mathematical methods of optimization of beam dynamics in accelerating and focusing structures were developed. Optimization problems of the charged particle beam dynamics were treated as a control problem of trajectory ensemble of dynamical system. In this paper another approach to optimization problems is considered. It is based on the investigation of special partial differential equations. [1] Ovsyannikov D.A. (1996). “Mathematical Methods of Optimization of Charged Partical Beams Dynamics”. Proceedings of European Partical Accelerator Conf., Barselona, Spain, Vol.2, p.13821384. [2] Ovsyannikov D.A., Modeling and Optimization Problems of Charged Particle Beams Dynamics, Proceedings of the 4th European Control Conference, Brussels, 1997, pp. 390394. Type of presentation requested : Poster Classification : [D02] Nonlinear Dynamics  Resonances, Tracking, Higher Order 1480  The SNS Ring Dipole Magnetic Field Auality I. Papaphilippou, J. Jackson, A. Jain, Y.Y. Lee, W. Meng, J. Wei, BNL, Upton, Long Island, New York The large acceptance and compact size of the SNS ring implies the use of short, large aperture dipole magnets with significant end field errors, which can be locally compensated with iron bumps and yoke chamfers. Special care has to be taken to the accurate evaluation of the fringefield effect to beam dynamics. To this end, the ring dipole magnetic field was modeled using 3D simulations and compared with long and short coil measurements. The impact of the dipole magnetic field quality to the dynamics of the SNS ring is discussed and sorting installation strategies are proposed. Type of presentation requested : Poster Classification : [D02] Nonlinear Dynamics  Resonances, Tracking, Higher Order 742  Dynamic Behavior of Charged Particle Beams in Curvilinear Magnetic Field Z. Parsa, BNL, Upton, Long Island, New York; V. Zadorozhny, IK NASU, Ukraine We study the stationary equilibrium orbits of compensate charge particle beams in curvilinear magnetic filed. Dynamics of charge particles in curvilinear coordinate system and how to choose an electric field to construct Brilluen's flow will be discussed. Type of presentation requested : Poster Classification : [D02] Nonlinear Dynamics  Resonances, Tracking, Higher Order 948  Linear and Nonlinear Corrections in the RHIC Interaction Regions F. Pilat, P. Cameron, V. Ptitsyn, BNL, Upton, Long Island, New York; J.P. Koutchouk, CERN, Geneva A method has been developed to measure operationally the linar and nonlinear effects of the interaction region triplets, that gives access to the multipolar content through the action kick, by applying closed orbit bumps and analysing tune and orbit shifts. This technique has been extensively tested and used during the RHIC operations in 2001. Measurements were taken at 3 different interaction regions and for different focusing at the interaction point. Nonlinear effects up to the dodecapole have been measured as well as the effects of linear, sextupolar and octupolar corrections. An analysis package for the data processing has been developed that through a precise fit of the experimental tune shift data (measured by a phase lock loop technique to better than 0.00001 resolution) determines the multipole content of an IR triplet. The experimental results have been compared to a model of RHIC that includes the measured magnet errors in the interaction region magnets. Type of presentation requested : Poster Classification : [D02] Nonlinear Dynamics  Resonances, Tracking, Higher Order 1181  Measurements of Tune Shifts with Amplitude at the ESRF A. Ropert, L. Farvacque, ESRF, Grenoble Together with the reduction of thirdorder resonances driving terms, the minimisation of tune shifts with amplitude is an important lattice design issue for synchrotron light sources. Since the beginning of ESRF operation, the tuning of harmonic sextupoles has been further refined to better match this objective and improve machine performance. The experimental detuning with amplitude has been determined from the analysis of turnbyturn BPM measurements for several sets of sextupoles and compared with predictions from the model. The limitations arising from the different contributions to beam decoherence, from nonlinear beam dynamics,... are discussed. Type of presentation requested : Poster Classification : [D02] Nonlinear Dynamics  Resonances, Tracking, Higher Order 899  On the Mechanisms of Particle Acceleration K. Sadoyan, ARUS, Yerevan A concept which rejects the existence of both magnetic monopoles and electric charges in nature is proposed. Electromagnetism is represented as a unified localized process inside a material vacuum. The electric field reflects dynamic aspects of the process while the magnetic field  kinematical ones. As an attribute of materiality of the vacuum it is considered the dissipative character of the processes occurring in it. The dissipativity of electromagnetic processes is evidenced by the redshift of spectral lines of the distant stars. The Habble's constant characterizes the rate of photon attenuation in the Universe. On the basis of equivalence between the inertial and gravitational masses the relative density of the material vacuum substance is established; this density is by a factor of 2 x 10^13 greater than the nuclear density. The motion in the vacuum is described by the laws of Continuum Mechanics. It is proved that the maximum velocity of nuclear motion in the vacuum is determined by the binding energy of nucleons in the nucleus and its formfactor. The anomalously high content of Li, Be and B nuclei in the cosmic rays is considered as a result of effective acceleration of heavy nuclei in strong gravitational fields with their subsequent highvelocity collapse into highenergy light nuclei. The mechanisms of particle acceleration in the electromagnetic and gravitational fields, as well as in the nuclear processes are analyzed and possibilities for the realisation of those mechanisms in the Earth's conditions are considered. Type of presentation requested : Poster Classification : [D02] Nonlinear Dynamics  Resonances, Tracking, Higher Order 1036  Beam Decoherence due to Combination of Wake Force and Nonlinearity in SPring8 Storage Ring J. Schimizu, K. Soutome, M. Takao, Hitoshi Tanaka, JASRI/SPring8, Hyogo Topup operation is planned in the SPring8 storage ring to maintain the high brilliance of synchrotron radiation during several bunch operation where beam lifetime is extremely short due to Touschek effect. To realize the topup operation, we began to investigate the beam loss at invacuum IDs during beam injection, but simulation results could not explain the measured beam loss evolution. To understand particle behavior from a beam injection state to equilibrium state determined by radiation effects, we have performed a simple experiment to observe the beam decoherence, i.e., temporal variation of the damping of beam coherent motion generated by a single horizontal kicker. We found that the beam decoherence much depends on chromaticities, the sign of amplitudedependent tune shift and beam current. This suggests that short range wake force and nonlinearity of ring parameters play an important role in the observed phenomenon. By taking wake force into account, we could see that simulation shows good agreements with the experimental data. In this paper, we will show our present analysis results on observed beam decoherence in the SPring8 storage ring. 