Paper  Title  Page 

TPAP056  Electron Beam Stability Requirements for LinacRing ElectronIon Colliders  3363 


Funding: Work performed under the auspices of the U.S. Department of Energy. In recent years, linacring electronion colliders have been proposed at a number of laboratories around the world. While the linacring approach overcomes the beambeam tuneshift limitation on the electron beam, it also introduces noise into the ion beam, via the beambeam interaction with electron bunches of slightly fluctuating intensity and transverse size. The effect of these fluctuations is studied using a linearized model of the beambeam interaction. Upper limits for the rms jitter amplitudes of electron beam parameters for various linacring electronion colliders are presented. 

TPAT005  Start to End Error Study for the SPIRAL2 Linac  934 


Funding: CEA The possibility of a high intensity accelerator at GANIL, producing secondary beams of unprecedented intensity, is considered. The proposed driver for the SPIRAL2 project aims to accelerate a 5 mA deuteron beam up to 20 A.MeV and a 1 mA ion beam for q/A = 1/3 up to 14.5 A.MeV. It is a continuous wave regime linac, designed for a maximum efficiency in the transmission of intense beams and a tunable energy. This paper presents the error sensitivity study which has been performed for this linac in order to define the tolerances for the construction. The correction scheme and the expected losses are described. 

TPAT006  Impact of Optics on CSRRelated Emittance Growth in Bunch Compressor Chicanes  1015 


The dependence of emittance growth due to Coherent Synchrotron Radiation (CSR) in bunch compressor chicanes on optics has been noticed and empirically studied in the past. We revisit the subject, suggesting a model to explain slice emittance growth dependence on chicane optics. A simplified model to calculate projected emittance growth when it is mainly caused by transverse slice centroid offsets is presented. It is then used to find optimal compensation of centroid kicks in the single chicanes of a twostage compression system by adjusting the phase advance of the transport in between and the ration of the compression factors.  
TPAT007  RF Defocusing in SuperConducting Structure with Constant Geometry  1042 


Due to higher accelerating gradient in the superconducting linac the RF defocusing factor plays significant role in the beam dynamics. Together with the space charge it is a main reason for the stability loss. Usually it is estimated in frame of the travelling wave formalism with synchronous motion. However, the superconducting cavity is desirable to have the constant geometry, when synchronous motion is absent. In this case the quasisynchronous phase velocity is adjusted by RF phasing. In this paper we investigate RF defocusing factor in absent of synchronism between the beam and the accelerating structure.  
TPAT008  Numerical Dispersion Error Reduction in EM Calculations for Accelerators  1114 


Funding: Deutsches ElektronenSynchrotron DESY In this contribution novel numerical algorithms with no dispersion along the beam axis are investigated. This property is of interest for the longtime calculation of electromagnetic fields in accelerators. Instead of increasing the spatial stencil of the Yee scheme the compared methods modify the timestepping algorithm.The results are compared on several test examples. As a practical application the electromagnetic field of a very short bunch inside a cavity is calculated. 

TPAT010  Practical Definitions of Beam Lifetimes in an Electron Storage Ring  1216 


Derived are simple definitions of beam lifetimes in an electron storage ring. They are defined in terms of measured beam lifetime and its time derivative. They are practical rather than theoretical. The only condition required is suppression or saturation of the radiative polarization.  
TPAT011  Impedance Analysis of Longitudinal Bunch Shape Measurements at PLS  


We measured the longitudinal bunch shape by streak camera at 2.5 GeV Pohang Light Source. The impedances estimated by a series R+L model indicate a resistance R= 960 ohm, an inductance L= 80 nH and a longitudinal impedance Z/n= 0.53 ohm. The scaling law for the bunch lengthenig is expressed as I^{0}.22. The effects of insertion device in the ring on the ring impedance, particularly the vertical height of invacuum undulator are also presented.  
TPAT014  A Novel Technique for Multiturn Injection in a Circular Accelerator Using Stable Islands in Transverse Phase Space  1377 


By applying a timereversal to the multiturn extraction recently proposed a novel approach to perform multiturn injection is proposed. It is based on the use of stable islands of the horizontal phase space generated by means of sextupoles and octupoles. A particle beam can be injected into stable islands of phase space, and then a slow tune variation allows merging the beam trapped inside the islands. The results of numerical simulations will be presented and discussed in details, showing how to use the proposed approach to generate hollow bunches.  
TPAT015  Simulations of ErrorInduced Beam Degradation in Fermilab's Booster Synchrotron  1458 


Funding: Work supported by the University Research Association, Inc. under U.S. Department of Energy (DOE) contract No. DEAC0276CH03000, and by DOE grant No. DEFG0204ER41323 to NIU, and by DOE grant No. DEFG0291ER40685 to University of Rochester. Individual particle orbits in a beam will respond to both external focusing and accelerating forces as well as internal spacecharge forces. The external forces will reflect unavoidable systematic and random machine errors, or imperfections, such as jitter in magnet and radiofrequency power supplies, as well as magnet translation and rotation alignment errors. The beam responds in a selfconsistent fashion to these errors; they continually do work on the beam and thereby act as a constant source of energy input. Consequently, halo formation and emittnace growth can be induced, resulting in beam degradation and loss. We have upgraded the ORBITFNAL package and used it to compute effects of machine errors on emittance dilution and halo formation in the existing FNALBooster synchrotron. This package can be applied to study other synchrotrons and storage rings, as well. 

TPAT017  Transverse Impedance of Elliptical Tapers  1535 


Funding: Work supported by the U.S. DOE. The geometric impedance of smallgap undulator chambers is of paramount importance for modern light sources because it may drive transverse single bunch instabilities. Analytical expressions are derived for the transverse impedance assuming a slowly tapered vacuum chamber with a confocal elliptical crosssection. The analytical results are confirmed by numerical simulations with the GdfidL Electromagnetic Field simulator and they yield the correct asymptotic limits for both round and flat chambers. 

TPAT018  Stability of Barrier Buckets with Short or Zero Barrier Separations  1589 


A barrier bucket with small separation between the rf barriers (relative to the barrier widths) or even zero separation has its synchrotron tune decreasing rather slowly towards the boundary of the bucket. As a result, large area at the bucket edges can become unstable under the modulation of rf voltage and rf phase. Application is made to those barrier buckets used in the process of momentum mining on the issues of bunchdistribution distortion and particle loss.  
TPAT019  Discussions on the Cancellation Effect on a Curved Orbit  1631 


Funding: Work supported by DOE Contract DEAC0584ER40150.
The canonical formulation and the cancellation effect for bunch dynamics under collective interaction on a curved orbit were presented in Ref. [*]. Some possible controversial representations of the cancellation effect were later addressed by Geloni et al.** In this study, we discuss all the points raised in Ref. [**] based on our canonical treatment, and show how these points can be perceived from the view point of the cancellation picture.
*R. Li and Ya. S. Derbenev, Jefferson Laboratory Report No. LJABTN02054, 2003. **G. Geloni et al., DESY Report No. DESY 03165, 2003. 

TPAT022  Future Plans for the Small Isochronous Ring  1778 


Funding: Work supported by NSF Grant #PHY0110253 and DOE Contract DEAC0584ER40150. The Small Isochronous Ring has been operational at Michigan State University since December 2003. It is used for experimental studies of the beam dynamics in highintensity isochronous cyclotrons and synchrotrons at the transition energy. The operational experience with SIR has proven that the ring can be successfully used to study space charge effects in accelerators. The low velocity of beam particles in the ring allowed us to achieve a high accuracy of longitudinal profile measurements that is difficult to achieve in fullsize accelerators. The experimental data obtained in the ring was used for validation of multiparticle, spacecharge codes CYCO and WARP3D. Inspired by the solid performance of SIR in the isochronous regime, we consider options for expanding the scope of the beam physics studied in the ring. In this paper, we outline possible future experiments and discuss required modifications of the ring optics and hardware. 

TPAT023  Tests of a 3D Self Magnetic Field Solver in the Finite Element Gun Code MICHELLE  1814 


Funding: Work supported by ONR. We have recently implemented a prototype 3d self magnetic field solver in the finiteelement gun code MICHELLE. The new solver computes the magnetic vector potential on unstructured grids. The solver employs edge basis functions in the curlcurl formulation of the finiteelement method. A novel current accumulation algorithm takes advantage of the unstructured grid particle tracker to produce a compatible source vector, for which the singular matrix equation is easily solved by the conjugate gradient method. We will present some test cases demonstrating the capabilities of the prototype 3d self magnetic field solver. One test case is self magnetic field in a square drift tube. Another is a relativistic axisymmetric beam freely expanding in a round pipe. 

TPAT026  Synergia: An Advanced ObjectOriented Framework for Beam Dynamics Simultation  1925 


Synergia is a 3D, parallel, particleincell beam dynamics simulation toolkit. At heart of the software development effort is the integration of two extant objectoriented accelerator modeling frameworks–Impact written in Fortran 90 and mxyptlk written in C++–so that they may be steered by a third, a more flexible human interface framework, written in Python. Recent efforts are focused on the refactoring of the ImpactFortran 90 codes in order to expose more looselycoupled interfaces to the Python interface framework.  
TPAT027  Measurement of Transverse Echoes in RHIC  1955 


Funding: Work supported by U.S. DOE under contract No DEAC0298CH10886. Beam echoes are a very sensitive method to measure diffusion, and longitudinal echo measurements were performed in a number of machines. In RHIC, for the first time, a transverse beam echo was observed after applying a dipole kick followed by a quadrupole kick. After application of the dipole kick, the dipole moment decohered completely due to lattice nonlinearities. When a quadrupole kick is applied at time T after the dipole kick, the beam recohered at time 2T thus showing an echo response. We describe the experimental setup and measurement results. In the measurements the dipole and quadrupole kick amplitudes, amplitude dependent tune shift, and the time between dipole and quadrupole kick were varied. In addition, measurements were taken with gold bunches of different intensities. These should exhibit different transverse diffusion rates due to intrabeam scattering. 

TPAT028  TRACK: The New Beam Dynamics Code  2053 


Funding: This work was supported by the U.S. Department of Energy, Office of Nuclear Physics, under Contract No. W31109ENG38.
The new raytracing code TRACK was developed* to fulfill the special requirements of the RIA accelerator systems. The RIA lattice includes an ECR ion source, a LEBT containing a MHB and a RFQ followed by three SC linac sections separated by two stripping stations with appropriate magnetic transport systems. No available beam dynamics code meet all the necessary requirements for an endtoend simulation of the RIA driver linac. The latest version of TRACK was used for endtoend simulations of the RIA driver including errors and beam loss analysis.** In addition to the standard capabilities, the code includes the following new features: i) multiple charge states ii) realistic stripper model; ii) static and dynamic errors iii) automatic steering to correct for misalignments iv) detailed beamloss analysis; v) parallel computing to perform large scale simulations. Although primarily developed for simulations of the RIA machine, TRACK is a general beam dynamics code. Currently it is being used for the design and simulation of future proton and heavyion linacs at TRIUMF, Fermilab, JLAB and LBL.
*P.N. Ostroumov and K.W. Shepard. Phys. Rev. ST. Accel. Beams 11, 030101 (2001). **P.N. Ostroumov, V. N. Aseev, B. Mustapha. Phys. Rev. ST. Accel. Beams, Volume 7, 090101 (2004). 

TPAT029  RIA Beam Dynamics: Comparing TRACK to IMPACT  2095 


Funding: This work was supported by the U.S. Department of Energy, Office of Nuclear Physics, under Contract No. W31109ENG38. In order to benchmark the newly developed beam dynamics code TRACK we have performed comparisons with well established existing codes. During code development, codes like TRANSPORT, COSY, GIOS and RAYTRACE were used to check TRACK's implementation of the different beam line elements. To benchmark the endtoend simulation of the RIA driver linac, the simulation of the lowenergy part (from the ion source to the entrance of the SC linac) was compared with PARMTEQ and found to agree well. For the simulation of the SC linac the code IMPACT is used. Prior to these simulations, the code IMPACT had to be updated to meet the special requirements of the RIA driver linac. Features such as multiple charge state acceleration, stripper simulation and beam collimation were added to the code. IMPACT was also modified to support new types of rf cavities and to include fringe fields for all the elements. This paper will present a comparison of the beam dynamics simulation in the RIA driver linac between the codes TRACK and IMPACT. A very good agreement was obtained which represents another validation of both codes. 

TPAT030  Transverse Beam Matching Application for SNS  2143 


Funding: 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. An automated transverse beam matching application has been developed for the Spallation Neutron Source (SNS) beam transport lines. The application is written within the XAL Java framework and the matching algorithm is based on the simplex optimization method. Other functionalities, such as emittance calculated from profile monitor measurements (adopted from a LANL Fortran code), profile monitor display, and XAL online model calculation, are also provided by the application. Test results obtained during the SNS warm linac commissioning will be reported. A comparison between the emittances obtained from this application and an independent Trace3D routine will also be shown. 

TPAT031  Painting SelfConsistent Beam Distributions in Rings  2194 


Funding: 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. We define selfconsistent beam distributions to have the following properties: 1) timeindependence or periodicity, 2) linear space charge forces, and 3) maintainance of their defining shape and density under all linear transformations. The periodic condition guarantees zero spacechargeinduced halo growth and beam loss during injection. Some selfconsistent distributions can be manipulated into flat, or even pointlike, beams, which makes them interesting to colliders and to heavyion fusion. This paper presents methods for painting 2D and 3D selfconsistent distributions and for their manipulation to produce flat and pointlike beams. 

TPAT032  Transverse Stability Studies of the SNS Ring  2254 


Funding: 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. Detailed studies of the transverse stability of the SNS ring have been carried out for realistic injection scenarios. For coasting beam models and single harmonic impedances, analytic and computational results including phase slip, chromaticity, and space charge are in excellent agreement. For the dominant extraction kicker impedance and bunched beams resulting from injection, computationally determined stability thresholds are significantly higher than for coasting beams. At this time, we have no analytic model to treat the bunched beam case, but we present a formulation that provides an approach to this problem. 

TPAT033  Experimental Characterizations of 4D Transverse PhaseSpace of a Compressed Beam  2263 


Funding: Work supported by U.S. DOE. Coherent synchrotron radiation can significantly distort beam phase spaces in longitudinal direction and bending plane through a bunch compressor. A tomography technique is used to reconstruct transverse phase space of electron beam. Transverse 4D phase spaces are systematically measured at UCLA/ATF compressor and their characteristics with different bunch compression conditions are analyzed. 

TPAT034  Manipulations of Double Electron Beams within One RF Period for Seeded SMLWFA Experiment  2312 


Funding: Work supported by U.S. DOE. Although seeded SMLWFA only requires one electron beam to initiate the laser wakefield, it would be highly desirable to have a second electron beam traveling after the first one to probe the accelerated electrons. To create and preserve significant amount of wakefield in the STELLA SMLWFA experiment, the first ebeam needs to be tiny (<40 microns FWHM) in size and short in length within the plasma. To probe the wakefield which is damped within 10 ps for certain plasma density, the separation between the first and second beams needs to be within one RF period and the second ebeam must have smaller energy spread and smaller size. Design of double beams in one RF period to meet the strict requirements and the preliminary beam study at BNLATF facility are presented. The scheme of double beams with ATF bunch compressor is also discussed. 

TPAT035  Coherent Synchrotron Radiation from an Electron Beam in a Curved Waveguide  2390 


Funding: Research supported by the office of Naval Research and the Joint Technology Office. The radiation emitted by a pulsed electron beam as it travels on a circular trajectory inside a waveguide is calculated using a 3D simulation. Forwardpropagating wave equations for the fields in the waveguide are calculated by a perturbation of the Maxwell equations where the radius of curvature is large compared to the dimensions of the waveguide. These are integrated selfconsistently with the distribution of charge in the beam to provide the complete fields (electric and magnetic) for all times during the passage of the beam through the waveguide and therefore are applicable to sections of any length or combinations thereof. The distribution of electrons and their momentum are also modified selfconsistently so that the results may be used to estimate the effect of the radiation on the beam quality (emittance and energy spread). 

TPAT036  Ferroelectric Plasma Source for Heavy Ion Beam Charge Neutralization  2452 


Funding: Research supported by the U.S. Department of Energy. Plasmas are employed as a medium for charge neutralizing heavy ion beams to allow them to focus to a small spot size. Calculations suggest that plasma at a density of 1100 times the ion beam density and at a length ~ 0.11 m would be suitable. To produce 1 meter plasma, largevolume plasma sources based upon ferroelectric ceramics are being considered. These sources have the advantage of being able to increase the length of the plasma and operate at low neutral pressures. The source will utilize the ferroelectric ceramic BaTiO3 to form metal plasma. The drift tube inner surface of the Neutralized Drift Compression Experiment (NDCX) will be covered with ceramic. High voltage (~ 15 kV) is applied between the drift tube and the front surface of the ceramic by placing a wire grid on the front surface. A prototype ferroelectric source 20 cm long produced plasma densities ~ 5x1011 cm3. The source was integrated into the experiment and successfully charge neutralized the K ion beam. Presently, the 1 meter source is being fabricated. It will be characterized and integrated into NDCX for charge neutralization experiments. Experimental results will be presented. 

TPAT037  Simulating the LongDistance Propagation of Intense Beams in the Paul Trap Simulator Experiment  2491 


Funding: Research supported by the U.S. Department of Energy. The Paul Trap Simulator Experiment (PTSX) makes use of a compact Paul trap configuration with quadrupolar oscillating wall voltages to simulate the propagation of intense charged particle beams over distances of many kilometers through magnetic alternatinggradient transport systems. The simulation is possible because of the similarity between the transverse dynamics of particles in the two systems. Onecomponent pure cesium ion plasmas have been trapped that correspond to normalized intensity parameters s < 0.8, where s is the ratio of the square of the plasma frequency to twice the square of the average transverse focusing frequency. The PTSX device confines the plasma for hundreds of milliseconds, which is equivalent to beam propagation over tens of kilometers. Results are presented for experiments in which the amplitude of the oscillating confining voltage waveform has been modified as a function of time. A comparison is made between abrupt changes in amplitude and adiabatic changes in amplitude. The effects of varying the frequency are also discussed. A barium ion source and a laser system have been installed and initial measurements made with this system are presented. 

TPAT038  Chaos in TimeDependent SpaceCharge Potentials  2515 


We consider a spherically symmetric, homologously breathing, spacechargedominated beam bunch in the spirit of the particlecore model. The question we ask is: How does the time dependence influence the population of chaotic orbits? The static beam has zero chaotic orbits; the equation of particle motion is integrable up to quadrature. This is generally not true once the bunch is set into oscillation. We quantify the population of chaotic orbits as a function of space charge and oscillation amplitude (mismatch). We also apply a newly developed measure of chaos, one that distinguishes between regular, sticky, and wildly chaotic orbits, to characterize the phase space in detail. We then introduce colored noise into the system and show how its presence modifies the dynamics. One finding is that, despite the presence of a sizeable population of chaotic orbits, halo formation in the homologously breathing beam is much less prevalent than in an envelopematched counterpart wherein an internal collective mode is excited.  
TPAT039  WaveletBased Poisson Solver for Use in ParticleinCell Simulations  2601 


Funding: Work of B.T., D.M. and C.L.B. is supported by Air Force contract FA9471040C0199. Work of I.V.P. is supported by the U.S. Department of Energy contract DEAC0376SF00098.
We report on a successful implementation of a waveletbased Poisson solver for use in 3D particleincell simulations. One new aspect of our algorithm is its ability to treat the general (inhomogeneous) Dirichlet boundary conditions. The solver harnesses advantages afforded by the wavelet formulation, such as sparsity of operators and data sets, existence of effective preconditioners, and the ability simultaneously to remove numerical noise and further compress relevant data sets. Having tested our method as a standalone solver on two model problems, we merged it into IMPACTT to obtain a fully functional serial PIC code. We present and discuss preliminary results of application of the new code to the modelling of the Fermilab/NICADD and AES/JLab photoinjectors.
Corresponding author: B.T. (bterzic@nicadd.niu.edu) 

TPAT040  Actual Stationary State for Plasma Lens  2619 


The electrostatic plasma lens (PL) provides an attractive and unique tool for manipulating highcurrent heavy ion beams. The fundamental concept of the PL is based on the use of magnetically insulated electrons and equipotentialization of magnetic field lines. Rigorous application of PL is, however, limited. The reason is the estimation behaviour of electrons for complicated magnetic fields runs into severe difficults.We show that there are specific conditions that admit steadystate of a longitudinal motion, and consider a question of it stability. These results are needed to develop an optimized PL with minimal spherical aberation, in party by optimization of the magnetic field conficuration in the lowmagneticfield range.  
TPAT041  On the VlasovMaxwell Equations  2654 


There are many interesting physical question which based on of the solution VlasovMaxwell Equation (VME). However, the procedure of solve is very difficult and hard. But it is often preferable, on physical grounds, to a common point of view. Such point of view maybe a structure of some solution. We define and discuss the notaion of structure for the distribution function and prove, the structure of the Lorentz force represent the structure of the one. At the time of the discovery of the integrable systems the question of VME integrability had been considered. Moreover, as example, we consider, by means of this approach, the relation integrability and dispersion with a spectra of Vlasov's operat.  
TPAT042  Progress on a Vlasov Treatment of Coherent Synchrotron Radiation from Arbitrary Planar Orbits  2699 


Funding: Support from DOE grants DEAC0276SF00515 and DEFG0299ER1104 is gratefully acknowledged.
We study the influence of coherent synchrotron radiation (CSR) on particle bunches traveling on arbitrary planar orbits between parallel conducting plates (shielding). The time evolution of the phase space distribution is determined by solving the VlasovMaxwell equations in the time domain. This provides lower numerical noise than the macroparticle method, and allows the study of emittance degradation and microbunching in bunch compressors. We calculate the fields excited by the bunch in the lab frame using a formula simpler than that based on retarded potentials.* We have developed an algorithm for solving the Vlasov equation in the beam frame using arc length as the independent variable and our method of local characteristics (discretized PerronFrobenius operator).We integrate in the interaction picture in the hope that we can adopt a fixed grid. The distribution function will be represented by Bsplines, in a scheme preserving positivity and normalization of the distribution. The transformation between lab and beam frame is carefully treated. Here we report on our implementation of the algorithm for a chicane bunch compressor with linear energy chirp and take steps to treat the nonlinear case.
*"Vlasov Treatment of Coherent Synchrotron Radiation from Arbitrary Planar Orbits" to be published in the Proceedings of ICAP04, St. Petersburg, R. Warnock, G. Bassi and J. A. Ellison. 

TPAT043  The MICHELLE 2D/3D ES PIC Code: Advances and Applications  


Funding: Office of Naval Research, Naval Research Laboratory.
MICHELLE is a new 2D/3D steadystate and timedomain particleincell (PIC) code* that employs electrostatic and now magnetostatic finiteelement field solvers. The code has been used to design and analyze a wide variety of devices that includes multistage depressed collectors, gridded guns, multibeam guns, annularbeam guns, sheetbeam guns, beamtransport sections, and ion thrusters. Latest additions to the MICHELLE/Voyager tool are as follows: 1) a prototype 3D self magnetic field solver using the curlcurl finiteelement formulation for the magnetic vector potential, employing edge basis functions and accumulating current with MICHELLE's new unstructured grid particle tracker, 2) the electrostatic field solver now accommodates dielectric media, 3) periodic boundary conditions are now functional on all grids, not just structured grids, 4) the addition of a global optimization module to the user interface where both electrical parameters (such as electrode voltages)can be optimized, and 5) adaptive mesh refinement improvements. Applications illustrating these latest additions will be presented, including a relativistic sheet beam gun, a relativistic MIG gun, and a depressed collector optimization example.
*John Petillo, et al., IEEE Trans. Plasma Sci., vol. 30, no. 3, June 2002, pp. 12381264. 

TPAT072  LongTerm Simulation of BeamBeam Effects in the Tevatron at Collision Energy  3871 


The weakstrong beambeam effect is expected substantially to contribute to the degradation of beam lifetimes in the Tevatron at collision energy. We have expanded an existing multiprocessor code (which previously was applied to the Tevatron at injection energy* to include chromatic and nonlinear lattice effects as well as a fullycoupled treatment of the lattice in different approximations.** We obtain lifetime predictions by doing temporal statistics on the tracking results of a weighted macroparticle distribution and fitting it to a class of solutions for the diffusion equation. We present typical results of parameter scans.
*A. Kabel, Y. Cai, B. Erdelyi, T. Sen, M. Xiao; Proceedings of PAC03. **A. Kabel, this Conference. 