Скачать 396.75 Kb.

Type of presentation requested : Poster Speaker : Dr. Hitoshi Tanaka Classification : [D02] Nonlinear Dynamics  Resonances, Tracking, Higher Order 859  Measurement of Resonance Driving Terms F. Schmidt, M. Hayes, R. Tomas, CERN, Geneva In 2001 a series of experiments have been performed at the CERN SPS at an energy of 26 GeV to measure resonance driving terms. Theory predicts that these terms can be determined by harmonic analysis of BPM data recorded after applying single kicks. This analysis works equally well for linear and nonlinear diagnostics of accelerators. Results of the experiments are presented, including a direct measurement of resonance driving terms and a comparison to the theory. Type of presentation requested : Poster Classification : [D02] Nonlinear Dynamics  Resonances, Tracking, Higher Order 360  Some Features of Beam Dynamics in Superconducting Linac Based on Quarter and Halfwave Cavities Y. Senichev, A. Bogdanov, A. Lehrach, R. Maier, R. Tölle, E. Zaplatin, FZJ, Jülich Superconducting Injector LINAC for COSY has to accelerate the protons and deuterium particles that differ in mass by a factor of 2. There are two preferable types of linear accelerator structures appropriate for this purpose: the multigap structure with internal synchronization of gaps, such as an Alvarez structure and the system with external synchronizing of the different groups of structures with few gaps, for instance the superconducting coaxial cavities. For our purpose the superconducting cavity is more appropriate. We consider two options of linear accelerator based on the superconducting quarter and halfwave resonators. In both options the accelerator consists of two parts. In first and second parts we use the resonators with 160 MHz and 320 MHz frequencies correspondingly. Simultaneously the resonators are subdivided into families with the same relative velocity. We optimize the number of resonators in each group and each family. We discuss how to optimize for protons and deuterium particles simultaneously. We analyze the 6dimensional beam dynamics in the real field calculated by MAFIA. The quarterwave cavity technology is quite developed, but due to the dipole component of magnetic and electrical fields the beam is unstable in the transverse plane. We have developed the special method to compensate this effect. In the halfwave resonators such problem does not exist due to the field symmetry. For the transverse plane we examine the single, doublet and triplet systems. We investigate the parametric resonance arising in the longitudinal plane due to the drift space needed for the focusing elements and determine the space limitation. Type of presentation requested : Poster Classification : [D02] Nonlinear Dynamics  Resonances, Tracking, Higher Order 970  BeamBased Global Correction of Nonlinear Field Errors J. Shi, University of Kansas, Lawrence In the scheme of the global compensation of field errors based on the minimization of nonlinearities in oneturn maps, the nonlinear terms in the oneturn map are minimized orderbyorder with a few groups of correctors and, consequently, the nonlinearity of the system can be significantly reduced. One potential advantage of this global correction scheme is that it allows an optimization of the correction during the commissioning of an accelerator if a oneturn map can be extracted from beam measurements. Such beambased optimization is especially important when there is significant uncertainty in the magnet measurement or a significant change in the multiples of magnets after a certain period of operation. As a measured oneturn map always contains experimental errors or uncertainties, the sensitivity of the beambased global compensation to the experimental uncertainties in the measured oneturn maps was studied. Type of presentation requested : Poster Classification : [D02] Nonlinear Dynamics  Resonances, Tracking, Higher Order 1586  StrongStrong BeamBeam Simulation for LHC J. Shi, L. Jin, University of Kansas, Lawrence, KS; W. Herr, CERN, Geneva Beambeam effects in LHC were studied with including multipole field errors in the lattice and headon and longrange beambeam interactions. The study was conducted with tracking of one million particles over 100 thousand turns by using the particleincell method. The effect of the wirecompensation of the longrange beambeam interactions and emittance growth due to headon collisions with possible offset were studied. Type of presentation requested : Poster Classification : [D02] Nonlinear Dynamics  Resonances, Tracking, Higher Order 195  Orbit Hamiltonian, Synchrotron Oscillations and SynchroBetatron Coupling T. Suzuki, KEK, Ibarakiken A Hamiltonian formalism is developped for synchrotron oscillations and synchrobetatron coupling. The orbit length is chosen as an independent variable, and the canonical variables are the arrival time and minus the total energy. A standingwave picture with a periodic deltafunction is shown to play an important role. We also study the effect of changing magnetic fields (betatron acceleration ) for synchrotron oscillations in the Hamiltonian formalism. The present work is based on a previous paper by the author (KEK 9610 ), but the errors are corrected and the contents are much extended. Type of presentation requested : Poster Classification : [D02] Nonlinear Dynamics  Resonances, Tracking, Higher Order 659  Simple Calculation Method of Distributed Momentum Acceptance along a Storage Ring Hitoshi Tanaka, J. Schimizu, K. Soutome, M. Takao, JASRI/SPring8, Hyogo Momentum acceptance (MA) plays an important role to enlarge beam lifetime under the condition where electronelectron scattering is dominant in total beam loss. In this case, MA is generally not constant along a storage ring due to distributed energy dispersion. To optimize lattice parameters, it is therefore important to calculate the distributed MA and estimate the "effective MA" which can be used as a typical value for the estimation of Touschek lifetime. We then developed a simple calculation method for the distributed MA by using first order phase space distortion, nonlinear dispersion up to 4th order of dp/p, and dynamic aperture data at one point in the ring. The calculated MA by this method well explains the experimental data in the SPring8 storage ring. In this paper, we will present our calculation method and comparison between the calculation and experimental data. Type of presentation requested : Poster Speaker : Dr. Hitoshi Tanaka Classification : [D02] Nonlinear Dynamics  Resonances, Tracking, Higher Order 854  Analysis of Nonlinear Resonances using an AC Dipole in the CERN SPS R. Tomas, F. Schmidt, CERN, Geneva; M. Bai, BNL, Upton, Long Island, New York AC dipoles in accelerators are used to excite coherent betatron oscillations at a drive frequency close to the tune. In principle these oscillations last arbitrarily long without significant emittance growth if the AC dipole is adiabatically turned on and off. Therefore the AC dipole seems to be an adequate tool for nonlinear diagnostics provided the particle motion is well described in presence of the AC dipole and nonlinearities. A powerful tool to study these nonlinearities is the Normal Form technique. In this article it is shown how this technique can be generalized to include forced oscillations due to an AC dipole. This new approach is applied to data from a recent experiment at SPS in which nonlinearities have been studied in conjunction with AC dipole excitations. Type of presentation requested : Poster Classification : [D02] Nonlinear Dynamics  Resonances, Tracking, Higher Order 686  Experimental Study on the Higher Order Nonlinear Resonance at Taiwan Light Source T.S. Ueng, J. Chen, K.T. Hsu, K.H. Hu, SRRC, Hsinchu The higher order nonlinear resonances of transverse betatron oscillation were studied experimentally at the SRRC's storage ring. The turnbyturn method and phase space maps were used to analyze the experimental data. The instantaneous tune was extracted to study the tune variation from the different betatron amplitude and different machine conditions. The linear coupling due to the difference resonance at around the 6th order nonlinear resonance has also been investigated. Type of presentation requested : Poster Classification : [D02] Nonlinear Dynamics  Resonances, Tracking, Higher Order 1156  Beam Injection and Longitudinal Emittance Control in the JKJ 50 GeV Synchrotron T. Uesugi, E. Ezura, Y. Hashimoto, Y. Mori, C. Ohmori, A. Schnase, A. Takagi, M. Yoshii, KEK, Ibarakiken; F. Tamura, M. Yamamoto, JAERI, Ibarakiken In high intensity proton synchrotrons such as those of the JAERIKEK joint hadron(JKJ) project, it is important to make peak spacecharge density as low as possible. In the case of the 50 GeV synchrotron of the JKJ, it is required that the longitudinal emittance of an injected beam is enlarged more than 10 eVs before acceleration keeping with the bunching factor more than 0.3, which corresponds to the spacecharge tune shift of 0.16. In this paper, the scheme of the longitudinal beam manipulation in the JKJ 50 GeV synchrotron is described with simulation studies. Type of presentation requested : Poster Classification : [D02] Nonlinear Dynamics  Resonances, Tracking, Higher Order 1211  Non Linear Beam Dynamics for the Octupole Compensated Lattice of DAFNE C. Vaccarezza, D. Alesini, G. Benedetti, S. Bertolucci, M.E. Biagini, C. Biscari, R. Boni, M. Boscolo, A. Clozza, G. Delle Monache, G. Di Pirro, A. Drago, A. Gallo, A. Ghigo, S. Guiducci, M. Incurvati, C. Ligi, F. Marcellini, G. Mazzitelli, C. Milardi, L. Pellegrino, M.A. Preger, R. Ricci, C. Sanelli, F. Sannibale, M. Serio, M. Serio, F. Sgamma, A. Stecchi, A. Stella, M. Vescovi, M. Zobov, INFNLNF, Frascati (Roma); P. Raimondi, SLAC, Stanford Octupole magnets have been installed in DAFNE to compensate an octupolelike component measured in the wiggler magnets, providing a knob to control the tune dependence on amplitude and Landau damping. DAFNE operation with octupoles and comparison with simulations are presented. Type of presentation requested : Poster Classification : [D02] Nonlinear Dynamics  Resonances, Tracking, Higher Order 1610  FirstOrder Averaging Principles for Maps with Applications to Beam Dynamics in Particle Accelerators * M. Vogt, J.A. Ellison, UNM, Albuquerque; H.S. Dumas, UC, Cincinnati We extend the method of averaging at first order to slowly evolving, discretetimedependent systems defined by iterative maps. The validity of the averaging approximation is demonstrated using a generalized Besjes inequality. We study both cases of neartoloworder resonance and farfromloworderresonance. We apply our results to localized perturbations of an otherwise linear lattice. In particular we discuss the weakstrong beambeam effect. Work supported by US D.O.E. grant DEFG0399ER41104 Type of presentation requested : Poster Classification : [D02] Nonlinear Dynamics  Resonances, Tracking, Higher Order 1681  Explicit Symplectic Integrators for Modeling 3D Magnetic Field Elements Y.K. Wu, DFELL, Durham A variety of insertion devices (IDs), wigglers and undulators, linearly or elliptically polarized, have become widely used as high brightness radiation sources at modern light source rings. In addition, long wigglers with high magnetic fields have been proposed as radiation damping sources for the next generation linear collider damping rings. Like the insertion devices, the modeling of the threedimensional effects of the magnetic fringe fields is critical for the future high energy accelerators including future Hadron colliders and Neutrino Factory and Muon Colliders with large aperture magnets. Since the early 1990's, the elementbyelement tracking based on explicit symplectic integrators has been successfully applied for the design and optimization of third generation light sources. However, the elementbyelement tracking has been limited to the magnetic elements with twodimensional fields, such as dipoles, quadrupoles, and magnetic multipoles with an impulse boundary due to the lack of explicit symplectic models for 3D magnetic devices. This situation has been changed with our recent work of explicit symplectic integrators for general 3D magnetic field Hamiltonians. With this type of integrators, particle motion in 3D magnetic devices can be integrated as yet another magnetic element in a kickcode at any given order. Consequently, this explicit symplectic model allows the detailed analysis of the beam dynamics in the next generation of accelerators, from light source rings to high energy physics rings, in which 3D field elements play a significant role in beam dynamics. Type of presentation requested : Poster Classification : [D02] Nonlinear Dynamics  Resonances, Tracking, Higher Order 1113  Dynamic Aperture of the PoPFFAG Proton Synchrotron M. Yoshimoto, T. Adachi, M. Aiba, S. Machida, Y. Mori, R. Muramatsu, J. Nakano, C. Ohmori, I. Sakai, Y. Sato, M. Sugaya, A. Takagi, R. Ueno, T. Yokoi, M. Yoshii, Y. Yuasa, KEK, Ibarakiken; K. Koba, FNAL, Batavia The Proof of Principle (PoP)Fixed Field Alternating Gradient (FFAG) synchrotron, which is the world first FFAG proton synchrotron, was constructed at KEK, and the various beam experiments have been carried out. Among them, measurements of dynamic aperture is one of the critical items. In the PoPFFAG synchrotron, a horizontal acceptance of more than 10000pi mmmrad is expected from beam tracking simulation, although the magnetic field in the FFAG synchrotron intrinsically has strong higher order components in order to satisfy the zero chromaticity condition. The beam trajectories in the horizontal phase space in the PoPFFAG synchrotron are measured to verify the large horizontal dynamic aperture experimentally. We have developed a beam position monitor, especially for that measurement, with which the beam position and the angle can be obtained simultaneously. Type of presentation requested : Poster Classification : [D02] Nonlinear Dynamics  Resonances, Tracking, Higher Order 1514  RMS Dynamics via Localized Modes M. Zeitlin, A. Fedorova, IPME RAS, St. Petersburg Computational methods based on the exact fast convergent expansions in highlocalized waveletlike bases are used for construction of solutions for a few nonlinear rmslike (envelope) dynamical problems which can be used for description and modeling important features of collective type behaviour in momentum approximation and are related to description of different spacecharge effects in high intensity transport systems in accelerators and plasma physics problems. Our method is based on the generalization of variationalwavelet approach which allows to consider both polynomial and rational type of nonlinearities without perturbations or/and linearization [1]. All dynamical variables are represented as expansions in the bases of maximally localized modes and are parametrised by a number of solutions of reduced standard algebraical problems which can be solved by scalar or parallel algorithms. Best convergence properties and minimal cost of algorithms lead to saving CPU time and hdd space as on the level of scalar as on the level of parallel algorithms inside. 1. A.Fedorova, M.Zeitlin, Seven papers in PAC01 Proc., arXiv preprints: physics/0106022, 0106010, 0106009, 0106008, 0106007, 0106006, 0106005. Type of presentation requested : Poster Classification : [D02] Nonlinear Dynamics  Resonances, Tracking, Higher Order 1875  Oscillations of Mismatched Beams in Fodo Channels O.A. Anderson, LBNL, Berkeley Designers of accelerators for Heavy Ion Inertial Fusion face various challenges because of the strong space charge. Among other things, they need simple, accurate tools for calculating quantities such as the phase advances sigma0 and sigma given the lattice and beam parameters. In conjuction with the KV beam model, the smooth approximation [1] is often used. It is simple but not very accurate in many cases. Although Struckmieir and Reiser [2] showed that the stable oscillation frequencies of unbalanced beams could be obtained accurately, they actually used a hybrid approach where sigma0 and sigma were given exactly in advance. Starting instead with basic quantities?quadrupole dimensions and field strength, beam charge and emittance?the smooth approximation formulas give substantial errors (10% or more). We previously described an integration method [3] for matched beams that yields fairly simple thirdorder formulas for sigma0, sigma, beam radius and ripple. Here we extend the method to include smallamplitude mismatch oscillations. We derive a simple modification of the smooth approximation formulas and show that it improves the accuracy of the predicted envelope frequencies by a factor of five. [1] M. Reiser, Particle Accelerators 8, 167 (1978). [2] J. Struckmeier and M. Reiser, Particle Accelerators 14, 227 (1984). [3] O.A. Anderson, Particle Accelerators 52, 133 (1996). Type of presentation requested : Poster Classification : [D03] High Intensity  Incoherent Instabilities, Space Charge, Halos, Cooling 1483  Equilibrium Beam Distribution and Halo in the LHC R.W. Assmann, F. Schmidt, F. Zimmermann, CERN, Geneva; M.P. Zorzano, INTA, tbd The equilibrium LHC beam distribution at large amplitudes is a crucial input to the collimation and machine protection design, as well as to background studies. Its estimation requires a knowledge of the diffusion rates at which beam particles are transported to large transverse or longitudinal amplitudes. Important known mechanisms of particle diffusion include Touschek scattering, synchrotron radiation, intrabeam scattering, the nonlinear motion due to the long range beam beam collisions at top energy, persistent current field errors during injection and at the start of acceleration, Coulomb scattering on residual gas, and beam gas bremsstrahlung. The expected contributions from the different sources are summarized and the corresponding equilibrium beam distribution is calculated. The scattering process in the collimator jaws is included, quantifying the overpopulation of the halo close to the jaws due to "inward scattering". The result is compared to simple estimates based on typical beam lifetimes in existing proton rings. Type of presentation requested : Poster Classification : [D03] High Intensity  Incoherent Instabilities, Space Charge, Halos, Cooling 961  Comparison of Space Charge Simulations by Different Multiparticle Tracking Codes J. BeebeWang, N.L. D'Imperio, A.U. Luccio, BNL, Upton, Long Island, New York; S. Machida, KEK, Ibarakiken Space charge in high intensity beams is an important issue in accelerator physics. Due to the complexity of the problems, the most effective way of investigating its effect is by computer simulations. In recent years, many space charge simulation methods have been developed and incorporated in various 2D or 3D multiparticle tracking codes. It has become necessary to benchmark these methods against each other, and against experimental results. As a part of a global effort, we present some comparison of the space charge calculations done in the PIC codes ORBIT++, ORBIT and SIMPSONS, with discussion of the relevant differences. Type of presentation requested : Poster Classification : [D03] High Intensity  Incoherent Instabilities, Space Charge, Halos, Cooling 676  Longitudinal Beam Echos in Intense Ion Beams O. BoineFrankenheim, GSI, Darmstadt; A. AlKhateeb, Yarmouk University, Irbid, Jordan Temporal echos have already proven to be a sensitive probe for diffusion processes in stored high energy particle beams (see eg. [1,2]). If impedances can be neglected the echo response is due to the free drifting motion of the beam ions (ballistic echo). In order to measure diffusion rates in high phase space density beams at low and intermediate energies (like eg. in the GSI cooler storge ring ESR) the effect of the space charge impedance must be included into the VlasovFokkerPlanck framework. This requires a selfconsistent analytical approach that will be outlined. The transition from the ballistic beam echo to the selfconsistent echo in a space charge dominated beam is analyzed. As an application of the analytic theory we determine and compare the numerical diffusion in different selfconsistent particle simulation schemes (ParticleInCell and direct Vlasov) using longitudinal beam echos [1] L.K. Spentzouris, J.F. Ostiguy, and P.L. Colestock, Phys. Rev. Lett. 76, 620 (1996) [2] O. Bruening, T. Linnecar, F. Ruggiero, W. Scandale, E. Shaposhnikova, D. Stellfield, Proceedings of the EPAC 96, p.1332 Type of presentation requested : Poster Classification : [D03] High Intensity  Incoherent Instabilities, Space Charge, Halos, Cooling 382  Emission and Control of H+ Ions near an Electronphoton Conversion Target A. Compant La Fontaine, D. Guilhem, J.L. Lemaire, C. Quine, CEA, BruyeresleChatel A highintensity relativistic electron beam is focused on a tantalum target that converts the electrons into photons via the bremsstrahlung process. The Xray emission, directed along the beam axis, is used for radiographic purposes. The energy deposited by the beam focused on a small spot size, causes local vaporisation of the target and production of ions. A beam charge neutralisation then occurs, cancelling the average radial electrical field. Therefore, the beam pinches due to the remaining azimuthal magnetic field. The ions are subsequently accelerated downstream in the strong axial electric field induced by the electron beam. Thus, the displacement of the waist from the target along with the ions leads to an increase of the spot size at the target and would result in a degradation of the sharpness of the radiographic image. The H+ light ions, issued from hydrogen atoms contaminating the target, where identified on the PIVAIR accelerator facility, with a timeof flight diagnostic placed in front of the target. The H+ ions produced by ionisation of the H atoms desorbed from the target by the electron beam, is then calculated, and their transport is implemented in the M2V MaxwellVlasov PIC code. In this paper, we compare the experimental ionic current, measured on the timeofflight diagnostic with this abinitio model, by computing the H+ current collected on this foil. The calculated mean velocity of the ions is in agreement with the experimental result and the plateau of the ion current is closed to the ChildLangmuir theoretical limit. We also present the new selfbiased target converter designed in order to counteract the ionic motion. We report on the successfull tests and beam size control along the pulse. Type of presentation requested : Poster Classification : [D03] High Intensity  Incoherent Instabilities, Space Charge, Halos, Cooling 847  A Deuteron Linac for Production of Medicine Radioisotope Molybdenum99 P. Demchenko, Y. Gussev, M. Shulika, KIPT, Kharkov Production of a medicine radioisotope of molybdenum99 using a high current deuteron linear accelerator had been investigated. Molybdenum99 is a generator of a technetium99m that is a very important radionuclide for medicine diagnostics. It was shown that irradiation of a natural molybdenum target by deuteron with energy of 15MeV and an average beam current of 1mA gave a molybdenum99 yield about 1.6Ci/h. As a result of numerical simulation, a radiofrequency accelerating channel of a high current deuteron linac had been calculated. The accelerating channel consists of an ion injector with output energy 100keV, an initial accelerating section with radiofrequency quadrupole focusing (RFQ) and output energy 2MeV, and two sections with alternating phase focusing (APF) and output energy 15MeV. The sections with alternating phase focusing are based on the interdigital Htype structures with drift tubes. An operative frequency of the accelerating channel is 152,5MHz. The details are given of a beam forming in the ion injector, of a particle dynamics and the beam phase space parameters in accelerating sections, and also the features of a beam matching when the beam is moving through the sections with different types of symmetry of accelerating electric fields. Type of presentation requested : Poster Speaker : Dr. P.O. Demchenko Classification : [D03] High Intensity  Incoherent Instabilities, Space Charge, Halos, Cooling 881  Beams Dynamics End to End Simulations in IFMIF Linac R. Duperrier, CEA, GifsurYvette; R. Ferdinand, N. Pichoff, D. Uriot, CEA, GifsurYvette The IFMIF project (International Fusion Material Irradiation Facility) requests two linacs designed to accelerate 125 mA CW deuteron beams up to 40 MeV. After extraction and transport, the deuteron beams with strong internal space charge forces have to be captured, bunched, accelerated and transport to targets for the production of high neutrons flux. This paper presents the reference design linac for this project. It is a combination of RFQ and DTL. Beams dynamics end to end calculations with errors studies and cavities design are detailed. Type of presentation requested : Poster Classification : [D03] High Intensity  Incoherent Instabilities, Space Charge, Halos, Cooling 1312  Beams Dynamics End to End Simulations with Errors Studies through the ESS linac R. Duperrier, CEA, GifsurYvette; N. Pichoff, D. Uriot, CEA, GifsurYvette The ESS project (European Spallation Source) aims to deliver high power beams for matter studies. Both protons and H have to be accelerated and guided to the different spallation targets. Two 50 mA H branches are funelled with one 100 mA H+ beam at around 20 MeV. The H front end is constituted by a chopper lines between two RFQs and DTLs. The H+ front end is composed by one RFQ and one DTL. The two species are transported through the same linac up to 1.334 GeV. This commpon part is composed by SDTL and CCL from 20 to 185 MeV and followed by a SCL (SuperConducting Linac) to reach the final energy. This paper presents beams dynamics end to end calculations with errors studies through the ESS linac. Type of presentation requested : Poster Speaker : Dr Nicolas PICHOFF Classification : [D03] High Intensity  Incoherent Instabilities, Space Charge, Halos, Cooling 1184  Electron Cooling of Ion Beams with Large Momentum Spread H. Fadil, Y. Iwashita, A. Noda, T. Shirai, ICR, Kyoto; T. Furukawa, Chiba University; M. Beutelspacher, M. Grieser, MPIK, Heidelberg; M. Muramatsu, K. Noda, NIRS, Chiba City; S. Shibuya, SHI A novel method for the reduction of electron cooling time for an ion beam with large momentum spread has been studied and experimentally tested at the TSR and HIMAC rings. A constant external force is applied to the beam using an induction accelerator, and the beam is rapidly shifted toward the stable point of the cooling force. The cooling time of a carbon ion beam (C6+ 73.3 MeV) with momentum shift of 1% was measured at TSR. We have observed a reduction from 2.5sec cooling time without induction accelerator to 0.6sec when applying an induction voltage of 0.4V. Also, we have investigated the maximum limit of the induction accelerator voltage where the ion beam becomes no longer captured by the electron cooling force. The dependence of such a limit on the electron density was measured using the HIMAC electron cooler and a newly constructed induction accelerator for Ar18+ ions. Type of presentation requested : Poster Classification : [D03] High Intensity  Incoherent Instabilities, Space Charge, Halos, Cooling 1635  Complex Emittance Dynamics in SpaceCharge DominatedHigh Brightness Beams A. Fedorova, M. Zietlin, IPME RAS, St. Petersburg We present numericalanalytical approach to nonlinear rational envelope dynamics of spacecharge dominated high brightness beam systems, which can provide understanding of the instability phenomena such as emittance growth, mismatch, halo formation etc related to complicated behaviour of underlying hidden nonlinear modes outside of perturbative torilike KAM regions. We calculate the exact fast convergent representations for solutions in highlocalized waveletlike bases functions, which correspond to underlying hidden (coherent) nonlinear eigenmodes [1]. The constructed solutions correspond to the full multiresolution expansion in all internal underlying scales and give expansion into slow modes and fast oscillating modes. So, we give contribution to dynamics as from coarse scales of resolution as from finest ones to obtain all information about complex dynamics of interaction of hidden nonlinear eigenmodes, which leads to the understanding of fullydeveloped instability processes. Because our approach started from variational formulation we can control evolution of instability on the pure algebraical level of reduced algebraical system of equations. This helps to control stability/unstability scenario of evolution in parameters space. We demonstrate advantages of this approach regarding perturbative ones. 1.A.Fedorova, M.Zeitlin, Seven papers in PAC01 Proc., arXiv preprints: physics/0106022, 0106010, 0106009, 0106008, 0106007, 0106006, 0106005. Type of presentation requested : Poster Classification : [D03] High Intensity  Incoherent Instabilities, Space Charge, Halos, Cooling 968  Halfinteger Resonance Crossing and Spacecharge Limit* A.V. Fedotov, BNL, Upton, Long Island, New York; I. Hofmann, GSI, Darmstadt We study the influence of space charge on the crossing of the secondorder resonance and the associated spacecharge limit in highintensity rings. Twodimensional simulation studies are compared with the envelope models which agree in the finding of an increased intensity limit due to the coherent frequency shift. We also discuss the effect on realistic beams with multiturn injection painting, effects of coupling and highorder resonances, and issues of the envelope instability in highintensity rings. *SNS is managed by UTBattelle, LLC, under contract DEAC0500OR22725 for the U.S. Department of Energy. SNS is a partnership of six national laboratories: Argonne, Brookhaven, Jefferson, Lawrence Berkeley, Los Alamos, and Oak Ridge. Type of presentation requested : Poster Classification : [D03] High Intensity  Incoherent Instabilities, Space Charge, Halos, Cooling 974  Exploring Transverse Beam Stability in the SNS in the Presence of Space Charge* A.V. Fedotov, M. Blaskiewicz, J. Wei, BNL, Upton, Long Island, New York; V.V. Danilov, J.A. Holmes, A. Shishlo, ORNL, Oak Ridge The highest possible intensity in the machine is typically determined by the onset of coherent beam instabilities. Understanding the contribution of various effects to the damping and growth of such instabilities in the regime of strong space charge is thus of crucial importance. In this paper we explore transverse beam stability by numerical simulations using recently implemented models of transverse impedance and threedimensional space charge. Results are discussed with application to the SNS accumulator ring. *SNS is managed by UTBattelle, LLC, under contract DEAC0500OR22725 for the U.S. Department of Energy. SNS is a partnership of six national laboratories: Argonne, Brookhaven, Jefferson, Lawrence Berkeley, Los Alamos, and Oak Ridge. Type of presentation requested : Poster Classification : [D03] High Intensity  Incoherent Instabilities, Space Charge, Halos, Cooling 44  Intrabeam Scattering Measurements in RHIC* W. Fischer, R. Connolly, S. Tepikian, K. Zeno, J. van Zeijts, BNL, Upton, Long Island, New York RHIC in gold operation shows significant intrabeam scattering due to the high charge state of the stored ions. Intrabeam scattering leads to longitudinal and transverse emittance growth. The longitudinal emittance growth causes debunching in operation; the transverse emittance growth contributes to the reduction of the beam and luminosity lifetimes. Longitudinal and transverse growth rates were measured with different intensities below and above transition. Measured growth rates are compared with computations. *Work supported by U.S. DOE under contract No DEAC0298CH10886 Type of presentation requested : Poster Classification : [D03] High Intensity  Incoherent Instabilities, Space Charge, Halos, Cooling 762  Effect of Lattice Random Errors on a Space Charge Dominated Beam G. Franchetti, I. Hofmann, GSI, Darmstadt The effect of random errors in linear accelerators raises some fundamental questions on error propagation and transformation into emittance growth due to the action of space charge. In this paper we carry out a generic study of this problem by using 2D computer simulation in a periodic quadrupole channel. In the limit of no or very weak space charge random focusing errors lead to the wellknown square root law of mismatch accumulation with distance. In the presence of sufficiently strong space charge the parametric (in some case also higher order) resonances of particles with the mismatch motion lead to a continuous damping of mismatch. This has the effect that the average value of the rms emittance (over an error ensemble) grows linearly with distance. Quantitative laws on the rms emittance evolution as function of error strength, and using a large number of error sets, are presented. Type of presentation requested : Poster Classification : [D03] High Intensity  Incoherent Instabilities, Space Charge, Halos, Cooling 455  The Electron Gun with Variable Beam Profile for Optimization of Electron Cooling A.V. Ivanov, A.V. Bubley, A.D. Goncharov, E.S. Konstantinov, S.G. Konstantinov, A.M. Kryuchkov, V.M. Panasyuk, V.V. Parkhomchuk, V.B. Reva, B.A. Skarbo, B.M. Smirnov, B.N. Sukhina, M.A. Tiunov, M.N. Zakhvatkin, BINP, Novosibirsk; X.D. Yang, IMP, Lanzhou The electron cooling of the intensive ion beams shows the problems connected with the development of the instabilities inside cooled core of the beam. To avoid this, the usage of the hollow electron beams was proposed. The density of the electron beam at central part can be decreased at many times without losses of the cooling of whole ion beam. As results the recombination losses in the core of the stored ion beam can be made less and the intensive ion beam will interact with low intensive electron beam that can decrease undesirable coherent oscillations. The electron gun with the possibilities of the variation of the electron beam profile was designed for CSR cooler (IMP, China) and consists of the cathode, control electrode and anode. The variation of the potential sign of the control electrode permits to change the beam profile from disk to ring in the crosssection. The gun parameters were calculated using UltraSAM code. The results of the microperveance and the electron beam profiles measurements are presented. For the electron beam profiles measurements the interaction of the electron beam with crossed wire and with the residual gas was used. The results are in good agreement with calculations. Type of presentation requested : Poster Classification : [D03] High Intensity  Incoherent Instabilities, Space Charge, Halos, Cooling 626  Stability Analysis of Intense Ion Beams in the NIRS Sring V. Kapin, M. Kanazawa, T. Murakami, K. Noda, S. Yamada, NIRS, Chiba City; E. Syresin, JINR, Dubna, Moscow Region; S. Shibuya, Sumitomo Heavy Industries, Tokyo A small ring (Sring) with circumference of 25 m has been proposed at NIRS. It will produce an ion beam with intensity higher 5 billions particle per second, the injection energy of 6 MeV/u, energy of 128 MeV/u for charge to mass ratio of 0.5 and bunch length of 101000 ns. The main peculiarities of Sring are the low energy after deceleration and the small circumference. A feature of Sring is a large relative length of the cooling section, which occupies 3.6% of the ring circumference. This value is 35 times higher than in the usual ion storage rings. A maximum intensity of cooled ion beam can be restricted by the ion beam instabilities. The application of intense electron beam for fast cooling of ion beam in the Sring is limited socalled effect of electron heating. The stability analysis includes the following effects: tune shift, longitudinal and transverse beam instabilities, space charge effects in the electron cooling system, dipole transverse instability due to interaction with ionization electrons. Beam dynamics including spacecharge effects has been simulated using ACCSIM and WinAGILE codes. Results of analytical estimations, stability analysis and numerical simulations are presented. Type of presentation requested : Poster Classification : [D03] High Intensity  Incoherent Instabilities, Space Charge, Halos, Cooling 607  