Paper  Title  Page 

TPAT045  Equilibrium and Stability in the Transport of Intense OffAxis Beams in Periodic Focusing Systems  


Funding: Work supported by Brazilian agencies CNPq, CAPES, and FAPERGS.
A general equation for the centroid motion of free, continuous, intense beams propagating offaxis in solenoidal periodic focusing fields is derived.* The centroid equation is found to be independent of the specific beam distribution and may exhibit unstable solutions. A new Vlasov equilibrium for offaxis beam propagation is also obtained. Properties of the equilibrium and the relevance of centroid motion to beam confinement are discussed. The effects of a conducting pipe encapsulating the beam are also investigated.** It is shown that the charge induced at the pipe may generate chaotic orbits which can be detrimental to the beam transport.
*J.S. Moraes, R. Pakter, F.B. Rizzato, Phys. Rev. Lett., accepted for publication (2004). **J.S. Moraes, R. Pakter, F.B. Rizzato, Phys. Plasmas, accepted for publication (2004). 

TPAT046  Nonlinear Stability of Intense Mismatched Beams in a Uniform Focusing Field  2941 


Funding: Work supported by Brazilian agencies CNPq, CAPES, and FAPERGS. We investigate the nonlinear coupling between axisymmetric and elliptic oscillations in the dynamics of intense beams propagating in a uniform magnetic focusing field. It is shown that finite amplitude mismatched oscillations of an initially round beam may destabilize elliptic oscillations, heavily affecting stability and the shape of the beam. This is a potential mechanics for beam particle loss in such systems. Self consistent simulations are performed to verify the findings. 

TPAT047  A Space Charge Compensation Study of Low Energy Hydrogen Ion Beams  2947 


Funding: Work supported by the European CommunityResearch Infrastructure Activity under the FP6 "Structuring the European Research Area" programme (CARE, contract number RII3CT2003506395).
Highpower accelerators are being studied for several projects including accelerator driven neutron or neutrino sources. The low energy part of these facilities has to be carefully optimized to match the beam requirements of the higher energy parts. The complexity of high intensity beam dynamics in the low energy line is essentially due to the nonlinear space charge effects. The PIC code CARTAGO* has been developed in order to simulate the beam transport at low energy including the temporal evolution effects of the space charge compensation. This paper relates the structure and the numerical methods of a 2D (r,z) new version of the code. The effects of the longitudinal space charge, the image charge and external 2D (r,z) magnetic field were included. The results of H^{+} and H^{} beam transports using solenoid lenses are discussed. Space charge compensation degrees are given for each studied cases.
*A. Ben Ismail et al., in Space Charge Compensation in Low Energy Proton Beams, proceeding of the International Linear Accelerator Conference, Lübeck, 2004. 

TPAT048  The Transverse Nonlinear Tune Shift as Stabilising Factor in Halo Creation in Space Charge Dominated Beam  3004 


Funding: We acknowledge the support of the European CommunityResearch Infrastructure Activity under the FP6 "Structuring the European Research Area" program (CARE, contract number RII3CT2003506395). One of the most important problems for space charge dominated beam in the low energy part of superconducting linac is halo creation. Many authors show one of the key effects in halo creatiation is parametric resonance due to the mismatched betafunction oscillation (between core and particle). To estimate parametric resonance conditions the nonlinear tune shift for binomial distributed beam is described theoretically in this article. Simultaneously the beam dynamics simulation 3D PIC code was developed. The transverse oscillation frequencies compared with parametric resonance criteria. As a result the recommendation for space charge shift is concluded to minimize halo creation. 

TPAT049  Comparison of Beam Dynamic in Different Superconducting Options of Low Energy High Intense Linac  3058 


Funding: We acknowledge the support of the European CommunityResearch Infrastructure Activity under the FP6 "Structuring the European Research Area" program (CARE, contract number RII3CT2003506395). At present the superconducting proton linacs have obvious applications in energy range ~1001000 MeV. For the lower energy the comprehensive investigations are required. In this article the various variants of superconducting options from 3MeV up to 100MeV are discussed. The considered variants include both the conventional combination of halfwave and spoke cavity with quadrupoles and new schemes. In conclusion the table of major parameters for different structures is given. 

TPAT050  Beam Dynamics Design of the L3BT for JPARC  3091 


L3BT is beam transportation line from the linac to the 3GeV RCS which is the part of the accelerators for the HighIntensity Proton Accelerator Facility Project, JPARC.In this paper, especially results of the beam simulation of the injection section of the L3BT are presented. And the matching of rms envelopes and dispersion function for space charge dominated beams are also discussed.  
TPAT051  Asymmetrical Spectrum Observed at the KEKB High Energy Electron Ring  3176 


KEKB is a multibunch, highcurrent, electron/positron collider for B meson physics. The two beams collide at one interaction point (IP) with a finite horizontal crossing angle. The luminosity achieved at KEKB is the best in the world. In order to keep up the performance, the tune of a noncolliding bunch, placed just after a colliding bunchtrain, is continuously monitored. It was observed that an electron bunch showed an asymmetrical distribution biased to a higher tune in the vertical tunespectrum. We found that the asymmetrical spectrum was reinforced by the beambeam interaction, though the electron bunch did not collide. The asymmetry was reinforced moreover, as the electron bunch approached a bunchtrain further. These observations suggest that the asymmetry in the spectrum is not related to trappedions or fastions observed in an electron single beam, but related to ions produced by the beambeam interaction, which makes the particles scattered and they might yield new ions due to the collision with residual gas. We can imagine that the ions are accumulated along a bunchtrain and some ions survive after colliding bunches passed through in the electron ring. A quantitative analysis remains for future study.  
TPAT054  Dispersion Matching of a Space Charge Dominated Beam at Injection into the CERN PS Booster  3283 


In order to match the dispersion at injection into the CERN PS Booster, the optics of the injection line was simulated using two different codes (MAD and TRACE). The simulations were benchmarked versus experimental results. The model of the line was then used to rematch the dispersion. Experimental results are presented for different optics of the line. Measurements with varying beam current show the independence of the measured quantity of spacecharge effects.  
TPAT055  On Start to End Simulation and Modeling Issues of the Megawatt Proton Beam Facility at PSI  3319 


At the Paul Scherrer Institut (PSI) we routinely extract a one megawatt (CW) proton beam out of our 590 MeV Ring Cyclotron. In the frame of the ongoing upgrade program, large scale simulations have been undertaken in order to provide a sound basis to assess the behaviour of very intense beams in cyclotrons. The challenges and attempts towards massive parallel three dimensional startto end simulations will be discussed. The used state of the art numerical tools (mapping techniques, time integration, parallel FFT and finite element based multigrid Poisson solver) and their parallel implementation will be discussed. Results will be presented in the area of: space charge dominated beam transport including neighbouring turns, eigenmode analysis to obtain accurate electromagnetic fields in large the rf cavities and higher order mode interaction between the electromagnetic fields and the particle beam. For the problems investigated so far a good agreement between theory i.e. calculations and measurements is obtained.  
TPAT057  Observations of UHF Oscillations in the IPNS RCS Proton Bunch  3375 


Funding: This work is supported by the U.S. Department of Energy under contract no. W31109ENG38. The Intense Pulsed Neutron Source (IPNS) Rapid Cycling Synchrotron (RCS) accelerates 3.2x 10^{12} protons from 50 MeV to 450 MeV in a single bunch (h=1) at 30 Hz. The rf frequency varies from 2.21 MHz to 5.14 MHz during the 14.2 ms acceleration interval. To maintain stability of the bunch, phase modulation is introduced to the rf at approximately twice the synchrotron frequency (synchrotron tune is 0.0014). This phase modulation causes a parametric quadrupole oscillation to develop in the bunch, and as this occurs, the bunch spectrum shows a significant increase in high frequency content. Without phase modulation, the beam experiences an instability which results in the loss of a large fraction of the charge 24 ms prior to extraction. It is unclear if the stability imparted to the beam by phase modulation comes from the quadrupole oscillation or from the high frequency excitation. A longitudinal tracking code is presently being modified to include amplitude and phase modulation of the bunch. The numerical analysis will be used to compare growth rates with those observed in the machine. The results of this analysis will be important as we introduce second harmonic rf with a new third cavity in the RCS later in 2005. 

TPAT058  Calculation of Electron Beam Potential Energy from RF Photocathode Gun  3441 


Funding: U.S. Department of Energy. In this paper, we consider the contribution of potential energy to beam dynamics as simulated by PARMELA at low energies (10  30MeV). We have developed a routine to calculate the potential energy of the relativistic electron beam using the static coulomb potential in the rest frame (first order approximation as in PARMELA). We found that the potential energy contribution to the beam dynamics could be very significant, particularly with high charge beams generated by an RF photocathode gun. Our results show that when the potential energy is counted correctly and added to the kinetic energy from PARMELA, the total energy is conserved. Simulation results of potential and kinetic energies for short beams (~1 mm) at various charges (1  100 nC) generated by a high current RF photocathode gun are presented. 

TPAT059  Space Charge Experiments and Simulation in the Fermilab Booster  3453 


Funding: Scientific Discovery through Advanced Computing project, "Advanced Computing for 21st Century Accelerator Science and Technology," U.S. DOE/SC Office of High Energy Physics and the Office of Advanced Scientific Computing Research. We have studied space charge effects in the Fermilab Booster. Our studies include investigation of coherent and incoherent tune shifts and halo formation. We compare experimental results with simulations using the 3D space charge package Synergia. 

TPAT060  Overview of the Synergia 3D MultiParticle Dynamics Modeling Framework  3490 


Funding: Scientific Discovery through Advanced Computing project, "Advanced Computing for 21st Century Accelerator Science and Technology," U.S. DOE/SC Office of High Energy Physics and the Office of Advanced Scientific Computing Research. High precision modeling of spacecharge effects is essential for designing future accelerators as well as optimizing the performance of existing machines. Synergia is a highfidelity parallel beam dynamics simulation package with fully three dimensional spacecharge capabilities and a higherorder optics implementation. We describe the Synergia framework and model benchmarks we obtained by comparing to semianalytic results and other codes. We also present Synergia simulations of the Fermilab Booster accelerator and comparisons with experiment. 

TPAT061  Accurate Iterative Analysis of the KV Equations  3535 


Funding: Supported in part by the U.S. Department of Energy under Contract No. DEAC0376SF00098. Previous solutions of the KV equations have either yielded poor accuracy or have been complex and difficult to follow. We describe a new approach, simple in concept, easy to use, with accuracy substantially improved over previous treatments. The results are given in the same form as the smooth approximation but include a few correction terms obtained from the field gradient integrated along the axis of a quadrupole cell. The input quantities–quadrupole field, beam current, and emittance–yield the average beam radius, the maximum envelope excursion, and the depressed and undepressed tunes. For all values of the input parameters, the results are much closer to the exact values from simulations than are results from the smooth approximation. For example, with the parameters adjusted for an exact phase advance of 83.4 degrees and 50% tune depression, both tunes are in error by less than 0.5%–over 22 times better than the smooth approximation. The error in maximum radius is 0.04%, improved by a factor of 80. The new method and its application to a wide range of cases will be presented. 

TPAT062  Uncorrelated Energy Spread and Longitudinal Emittance for a Photoinjector Beam  3570 


Longitudinal phase space properties of a photoinjector beam are important in many areas of highbrightness beam applications such as bunch compression, transversetolongitudinal emittance exchange, and highgain freeelectron lasers. In this paper, we discuss both the rf and the space charge contributions to the uncorrelated energy spread of the beam generated from a laserdriven rf gun. We compare analytical expressions for the uncorrelated energy spread and the longitudinal emittance with numerical simulations and recent experimental results.  
TPAT065  Damping Transverse Instabilities in the Tevatron Using AC Chromaticity  3665 


Funding: Operated by Universities Research Association Inc. under Contract No. DEAC0276CH03000 with the U.S. Department of Energy.
Several papers*,** have suggested possibility of using varying chromaticity to damp the headtail instability. We test this by cycling the chromaticity sextupole magnets in the Tevatron near the synchrotron frequency to see if the headtail stability threshold is increased. Further we compare the turnbyturn evolution of a bunch slice in the presence of varying chromaticity to a model previously developed.
*W.H. Cheng, A. M. Sessler, and J. S. Wurtele, Phys. Rev. Lett. 78, 4565 (1997). **T. Nakamura in Proceedings of the 1995 IEEE Particle Accelerator Conference (IEEE, Dallas, 1995), Vol. 5, p. 3100. 

TPAT066  Significance of Space Charge and the Earth Magnetic Field on the Dispersive Characteristics of a Low Energy Electron Beam  3691 


Funding: This work is funded by U.S. Dept. of Energy grant numbers DEFG0294ER40855 and DEFG0292ER54178.
The combination of energy spread and space charge provides a rich domain for interesting beam dynamics that are currently not well understood. The University of Maryland Electron Ring (UMER) [1] is a small scaled ring designed to probe the littleknown regions of higher beam intensities using lowenergy electrons. As such, design, commissioning and operation of UMER present many challenges, some quite novel. For example the UMER beam energy of 10 keV makes the beam very sensitive to the Earth magnetic field, which we can fortunately use to assist in bending the beam. This paper presents a systematic simulation study of the interaction of space charge and energy spread, with and without the earth magnetic field.
*"Commissioning of the University of Maryland Electron Ring (UMER)," S. Bernal, et al., this conference. 

TPAT067  Study of Longitudinal SpaceCharge Wave Dynamics in SpaceCharge Dominated Beams  3712 


Funding: Work supported by the U.S. Department of Energy, Office of Science. Understanding the dynamics of longitudinal space^{} charge waves is very important for advanced accelerator research. Although analytical solutions of spacecharge wave equations based on the cold fluid model exist in one dimension, there are few results for twodimensional wave evolution. Onedimensional theory predicts two eigen solutions, given an initial perturbation. One is called the fast wave, which moves toward the beam head in the beam frame and the other is termed the slow wave, which moves backward in the beam frame. In this paper, we report experimental results of space charge wave studies conducted on a 2.3 meter long straight beam line at the University of Maryland. An energy analyzer is used to directly measure the energy of spacecharge waves at the end of the transport line, which demonstrates the decomposition of an initial current perturbation into a slow wave and a fast wave. A PIC code, WARP [1], is used to simulate this experiment and the behavior of longitudinal waves in spacecharge dominated beams in an RZ geometry. Simulations shown here also demonstrate if the initial current and velocity perturbation strengths are chosen properly, only fast or slow waves could be selectively generated. 

TPAT068  A Fast Faraday Cup for the Neutralized Drift Compression Experiment  3765 


Funding: Research supported by the U.S. Department of Energy. Heavy ion drivers for high energy density physics applications and inertial fusion energy use spacechargedominated beams which require longitudinal bunch compression in order to achieve sufficiently high beam intensity at the target. The Neutralized Drift Compression Experiment1A (NDCX1A) at Lawrence Berkeley National Laboratory (LBNL) is used to determine the effective limits of neutralized drift compression. NDCX1A investigates the physics of longitudinal drift compression of an intense ion beam, achieved by imposing an initial velocity tilt on the drifting beam and neutralizing the beam's spacecharge with background plasma. Accurately measuring the longitudinal compression of the beam pulse with high resolution is critical for NDCX1A, and an understanding of the accessible parameter space is modeled using the LSP particleincell (PIC) code. The design and preliminary experimental results for an ion beam probe which measures the total beam current at the focal plane as a function of time are summarized. 

TPAT069  Numerical Studies of Electromagnetic Instabilities in Intense Charged Particle Beams with Large Energy Anisotropy  3780 


Funding: Research supported by the U.S. Department of Energy. In intense charged particle beams with large energy anisotropy, free energy is available to drive transverse electromagnetic Weibeltype instabilities. Such slowwave transverse electromagnetic instabilities can be described by the socalled Darwin model, which neglects the fastwave portion of the displacement current. The Weibel instability may also lead to an increase in the longitudinal velocity spread, which would make the focusing of the beam difficult and impose a limit on the minimum spot size achievable in heavy ion fusion experiments. This paper reports the results of recent numerical studies of the Weibel instability using the Beam Eigenmode And Spectra (bEASt) code for spacechargedominated, lowemittance beams with large tune depression. To study the nonlinear stage of the instability, the Darwin model is being developed and incorporated into the Beam Equilibrium Stability and Transport(BEST) code. 

TPAT070  Intensity and BunchShape Dependent Beam Loss Simulation for the SIS100  3807 


We have studied the combined influence of magnet nonlinearities, space charge and bunch shapes consistent with different RF scenarios on the longterm loss in the planned SIS100 synchrotron of the FAIR project. The simulation is a 3D tracking with "frozenin" space charge calculation employing the MICROMAP code. Comparing a oneharmonic RF scenario with an alternative doubleharmonic scenario we find that for the same absolute beam loss roughly twice the number of particles can be stored in the doubleRF system. Moreover, a barrier bucket RF scenario is found to be loss free. This is due to the fact that loss is caused here by spacecharge induced periodic resonance crossing, which is absent for the strictly flat bunch profile of the barrier case. 