• R. Pakter, J.S. Moraes, F.B. Rizzato
  IF-UFRGS, Porto Alegre

A general equation for the centroid motion of free, continuous, intense beams propagating off-axis 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 off-axis 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).

• R. Pakter, F.B. Rizzato, W. Simeoni
  IF-UFRGS, Porto Alegre

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.

• A. BenIsmail, R. Duperrier, D. Uriot
  CEA/DSM/DAPNIA, Gif-sur-Yvette
• N. Pichoff
  CEA/DAM, Bruyères-le-Châtel

High-power 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 non-linear 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.

• N.E. Vasyukhin, Y. Senichev, R. Tölle
  FZJ, Jülich

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 beta-function 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.

• N.E. Vasyukhin, Y. Senichev, R. Tölle
  FZJ, Jülich

At present the superconducting proton linacs have obvious applications in energy range ~100-1000 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 half-wave and spoke cavity with quadrupoles and new schemes. In conclusion the table of major parameters for different structures is given.

• T. Ohkawa
  JAERI, Ibaraki-ken
• M. Ikegami
  KEK, Ibaraki

• T. Ieiri, Y. Ohnishi, M. Tobiyama
  KEK, Ibaraki

• K. Hanke, J. Sanchez-Conejo, R. Scrivens
  CERN, Geneva

• A. Adelmann, S.R.A. Adam, H. Fitze, R. Geus, M. Humbel, L. Stingelin
  PSI, Villigen

• J.C. Dooling, F.R. Brumwell, G.E. McMichael, S. Wang
  ANL, Argonne, Illinois

The Intense Pulsed Neutron Source (IPNS) Rapid Cycling Synchrotron (RCS) accelerates 3.2x 10¹² 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 2-4 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.

• W. Liu
  Illinois Institute of Technology, Chicago, Illinois
• W. Gai, J.G. Power, H. Wang
  ANL, Argonne, Illinois

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.

• J.F. Amundson, P. Spentzouris
  Fermilab, Batavia, Illinois

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 3-D space charge package Synergia.

• P. Spentzouris, J.F. Amundson
  Fermilab, Batavia, Illinois
• D.R. Dechow
  Tech-X, Boulder, Colorado

High precision modeling of space-charge effects is essential for designing future accelerators as well as optimizing the performance of existing machines. Synergia is a high-fidelity parallel beam dynamics simulation package with fully three dimensional space-charge capabilities and a higher-order optics implementation. We describe the Synergia framework and model benchmarks we obtained by comparing to semi-analytic results and other codes. We also present Synergia simulations of the Fermilab Booster accelerator and comparisons with experiment.

• O.A. Anderson
  LBNL, Berkeley, California

Previous solutions of the K-V 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.

• Z. Huang, D. Dowell, P. Emma, C. Limborg-Deprey, G.V. Stupakov, J. Wu
  SLAC, Menlo Park, California

• V.H. Ranjbar
  Fermilab, Batavia, Illinois

Several papers*,** have suggested possibility of using varying chromaticity to damp the head-tail instability. We test this by cycling the chromaticity sextupole magnets in the Tevatron near the synchrotron frequency to see if the head-tail stability threshold is increased. Further we compare the turn-by-turn 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.

• R.A. Kishek, G. Bai, S. Bernal, T.F. Godlove, I. Haber, P.G. O'Shea, B. Quinn, C. Tobin, M. Walter
  IREAP, College Park, Maryland
• M. Reiser
  University Maryland, College Park, Maryland

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 little-known regions of higher beam intensities using low-energy 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.

• K. Tian, Y. Cui, I. Haber, Y. Huo, R.A. Kishek, P.G. O'Shea, Y. Zou
  IREAP, College Park, Maryland
• M. Reiser
  University Maryland, College Park, Maryland

Understanding the dynamics of longitudinal space^- charge waves is very important for advanced accelerator research. Although analytical solutions of space-charge wave equations based on the cold fluid model exist in one dimension, there are few results for two-dimensional wave evolution. One-dimensional 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 space-charge 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 space-charge dominated beams in an R-Z 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.

• A.B. Sefkow, R.C. Davidson, P. Efthimion, E.P. Gilson
  PPPL, Princeton, New Jersey
• F.M. Bieniosek, J.E. Coleman, S. Eylon, W.G. Greenway, E. Henestroza, J.W. Kwan, P.K. Roy, D.L. Vanecek, W. Waldron, S. Yu
  LBNL, Berkeley, California
• D.R. Welch
  ATK-MR, Albuquerque, New Mexico

Heavy ion drivers for high energy density physics applications and inertial fusion energy use space-charge-dominated beams which require longitudinal bunch compression in order to achieve sufficiently high beam intensity at the target. The Neutralized Drift Compression Experiment-1A (NDCX-1A) at Lawrence Berkeley National Laboratory (LBNL) is used to determine the effective limits of neutralized drift compression. NDCX-1A 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 space-charge with background plasma. Accurately measuring the longitudinal compression of the beam pulse with high resolution is critical for NDCX-1A, and an understanding of the accessible parameter space is modeled using the LSP particle-in-cell (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.

• E. Startsev, R.C. Davidson, W.L. Lee
  PPPL, Princeton, New Jersey

In intense charged particle beams with large energy anisotropy, free energy is available to drive transverse electromagnetic Weibel-type instabilities. Such slow-wave transverse electromagnetic instabilities can be described by the so-called Darwin model, which neglects the fast-wave 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 space-charge-dominated, low-emittance 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.

• G. Franchetti, I. Hofmann, A. Orzhekovskaya, P.J. Spiller
  GSI, Darmstadt