*List of Abstracts by Sessions*

- Modeling Challenges in Next-Generation Accelerators
- Status of Computational Accelerator Physics
- Computing in the 21st Century

- Advanced Accelerator Design & Control
- Modeling of High-Intensity Beam Phenomena
- Advances in Electromagnetic Modeling
- Advanced Algorithms & Methods
- New Software Environments & Libraries
- Graphic Interfaces & Advanced Visualization
- Modeling Advanced Accelerator Concepts
- Beam-Beam Simulations
- Computing Wakefield Effects
- Particle & Field Simulations

**S-Tu01: ****MODELING CHALLENGES IN THE NEXT LINEAR COLLIDER **
__Tor Raubenheimer __, SLAC

The Next Linear Collider (JLC/NLC) is a future linear collider having a center-of-mass energy of 1 TeV and a luminosity in excess of 10**34. To achieve the beam energy, the collider uses novel X-band rf sources and accelerator structures, while, to obtain the high luminosity, the collider must generate and preserve long trains of bunches having very small emittances. To design and optimize the components and to ensure the beam performance, extensive computer simulation and calculation is being used. One can separate the modeling into five distinct classes: First, electromagnetic field calculations which are needed to design the L-band, S-band, and X-band accelerator structures, calculate wakefields and impedances in the linacs and damping rings, and model the rf transport components. Second, full beam-field simulations, typically particle-in-cell calculations, used to model and design the rf klystrons, the particle sources, and understand the behavior of the beams during collision where the fields can become enormous. Third, beam tracking simulations where the complicated beam interactions are represented in a simplified form. This catagory includes the effect of the wakefields, beam-ion/beam-electron instabilities, generation of beam-halos, generation and transport of muon or synchrotron radiation backgrounds, and simulation of operational and tuning procedures. Next, there are codes needed for the magnet lattice and beam transport design which one would like to build into the beam control system and finally there are the codes used for the engineering design including the heat transport, magnet design, vacuum calculations, etc. These modeling tasks and requirements will be reviewed and the computer codes utilized will be discussed.

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Work supported by USDOE contract DE-AC03-76SF00515.

**S-Tu02: ****MODELING CHALLENGES FOR THE LHC **
__Francesco Ruggiero __, CERN

The CERN Large Hadron Collider (LHC) has a design energy of 7 TeV per beam and an unprecedented design luminosity of 10^34 cm^-2 s^-1. For cost optimization it makes use of the existing injector chain and has to be accommodated in the LEP tunnel. Such design objectives are accompanied by several technological and beam dynamics challenges, ranging from the 8.3 T superconducting magnets operating in superfluid helium at 1.9 K to the large number of low emittance, intense proton bunches to be injected at 450 GeV, safely accelerated and collided at top energy. In this talk we present an overview of accelerator physics issues specific to the design and operation of the LHC and address the corresponding modeling challenges. These include a realistic description of the unavoidable imperfections in superconducting magnets, producing non-linear field errors and affecting long-term single particle stability, as well as feedback systems, Landau octupoles and a careful optimization of the beam enclosure, to avoid single- or multi-bunch instabilities and to minimize the energy lost by the beam to its cold surroundings. In particular we review simulation codes currently used to investigate the possible fast build-up of an electron cloud, triggered by photoelectrons accelerated towards the positively charged proton bunches, and future developments required to properly model the effects of the beam-beam interaction.

**S-Tu03: ****MODELING CHALLENGES FOR THE MUON COLLIDER **
__H.G. Kirk, __R.C. Fernow, R.B. Palmer, BNL

A critical issue for the development of the muon collider concept is the ability to collect a large diffuse muon beam and rapidly reduce its phase space volume. Such a process is a necessary prerequisite for subsequent acceleration and achieving high luminosity within a collider. We discuss these issues and describe the modeling necessary to achieve a level of confidence that the overall scenario is viable and that an optimum set of parameters can be selected.

**S-Tu04: ****THE DOE GRAND CHALLENGE IN COMPUTATIONAL ACCELERATOR PHYSICS **
Salman Habib, Ji Qiang,
__Robert Ryne __, LANL

Kwok Ko, Zenghai Li, Brian McCandless, Wanjun Mi, Cho-Kuen Ng, Mikhail Saparov, Vinay Srinivas, Yong Sun, Michael Wolf, SLAC

Gene Golub, STANFORD U, Viktor Decyk, UCLA

Future particle accelerators will play a major role in solving problems of international importance. Proposed projects include the accelerator transmutation of waste (ATW), accelerator-based conversion of plutonium (ABC), accelerator production of tritium (APT), and accelerator-driven energy production (ADEP, or the "Energy Amplifier" concept). The next generation of accelerators will also be crucial to advances in basic and applied science, in areas such as high energy physics, materials science, and biological science, through projects such as the Next Linear Collider (NLC) and the Spallation Neutron Source (SNS). The design of accelerators for all of these projects will require a major advance in numerical modeling capability, due to extremely stringent beam control and beam loss requirements, and the presence of highly complex three-dimensional accelerator components. As part of the U.S. Department of Energy High Performance Computing and Communications program, a Computational Accelerator Physics "Grand Challenge" was approved in 1997. The primary goal of this project is to develop an advanced, parallel modeling capability, based on High Performance Computing and Communications resources and state-of-the-art numerical methods and algorithms, that will enable the design, optimization, and numerical validation of future accelerators for the above-mentioned projects. In this talk we will describe the beam dynamics and electromagnetics codes that are being developed as part of the Grand Challenge. We will briefly describe the algorithms, and their parallel implementation, using a variety of programming approaches including C++ with MPI, Fortran 90 with MPI, and High Performance Fortran. The codes are now supporting accelerator design efforts of several DOE projects through resources provided by the National Energy Research Scientific Computing Center (NERSC) at Lawrence Berkeley National Laboratory and the Advanced Computing Laboratory (ACL) at Los Alamos National Laboratory. In particular, we will present results of large scale electromagnetics simulations of accelerator structures and components for the NLC and SNS projects using new 3D parallel codes based on unstructured grids. We will also present results of beam halo simulations for the APT project using a new 3D parallel Particle-In-Cell code.

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Work supported by the U.S. Department of Energy, Office of Energy Research, Division of Mathematics, Information, and Computational Sciences, Division of High Energy Physics, and Office of Defense Programs.

**Plenary Session S-Th: Status of Computational Accelerator Physics **

**S-Th01: ****MODELING OF PLASMA ACCELERATORS: MEETING THE CHALLENGE **
__W.B. Mori __, UCLA

Plasma-based accelerators offer the promise of producing linear accelerators with gradients greatly exceeding 1GeV/m. This promise has resulted in an active basic research experimental program. To date low currents of preinjected or high currents of self-trapped electrons have been accelerated over mm distances. Computer simulations have been an integral part of this research effort, both for interpreting these experiments and for guiding future research directions. Some of the goals for the next generation of experiments are to controllably accelerate ~10^8 electrons while maintaining good beam quality and to extend the acceleration length to cm and meter distances. To accurately model these experiments presents great computational challenges. To meet these challenges, a mix of computational techniques will be required, including moving window, parallelization, fully explicit PIC, ponderomotive guiding center, and quasi-static PIC and fluid algorithms. In this talk I will review the role of computer simulations in recent experiments and discuss the challenges of accurately modeling future experiments.

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Work supported by DOE grants DE-FG03-90ER40727 and DE-FG03-98DP00211, NSF grant DMS-9722121 and LLNL contract W-7405-ENG-48.

**S-Th02: ****SIMULATIONS OF BEAM-BEAM INTERACTION IN LINEAR COLLIDERS **
__Pisin Chen __, SLAC

Because of the ultra-intense beam fields accompanying the colliding e+e- beams at the interaction point in linear colliders, the beam dynamics is highly nonlinear and computer simulations is indispensible for reliable estimates of the beam-beam effects. In additon the intense radiation so triggered, by the name "beamstrahlung", and its subsequent "coherent pair creation" process, require quantum electrodynamics (QED) for proper treatments. The beamstrahlung photons can also collide hadronically, and produce so-called "minijets", via quantum chromodynamic (QCD) processes. Monte Carlo simulations are needed to track these very important detector backgrounds. In this paper we review the essential physics behind these beam-beam effects, and the existing codes and their sample results.

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Work supported by USDOE contract DE-AC03-76SF00515.

**S-Th03: ****NUMERICAL COMPUTATIONS OF WAKEFIELDS AND IMPEDANCES BY THE FIT METHOD **
__Thomas Weiland __, TU-Darmstadt

**S-Th04: ****NEW METHOD FOR KLYSTRON MODELING**** **
__Yong Ho Chin __, KEK

We have developed a new method for an accurate and full-scale simulation of a klystron using the MAGIC code. MAGIC is the 2.5-D or 3-D, fully electromagnetic and relativistic particle-in-cell code for self-consistent simulation of plasma. It solves the Maxwell equations directly at particle presence by the finite difference method in time. It requires only the geometrical structure of the cavity and assumes no model for the beam-cavity interaction. In 2.5-D simulations, two-arm output couplers are approximated by a conductor which has the same complex scattering matrix with the actual 3-D ones. Advantages of MAGIC are its accuracy and generality. Even an electron gun can be simulated with results in good agreements with those of EGUN. Simulation results can be imported/exported from one section of klystron to another, allowing a consistent simulation of the entire klystron without loss of physics. Simulation results for the KEK XB72K No. 8 and No. 9 klystrons and the SLAC XL-4 klystron show excellent agreements with measurements.

**Plenary Session S-Fr: Computing in the 21st Century **

**S-Fr01: ****OVERVIEW OF NERSC **
__Horst Simon __, NERSC

**S-Fr02: ****CHALLENGES OF FUTURE HIGH-END COMPUTING **
__David Bailey __, NERSC

**S-Fr03: ****THE HYBRID TECHNOLOGY, MULTI-THREADED (HTMT) SYSTEM **
__Tom Sterling __, CALTECH

**S-Fr04: ****VIRTUAL REALITY IN THE 21ST CENTURY **
__Rick Stevens __, ANL

**S-Fr05: ****EXOTIC COMPUTER DEVICE TECHNOLOGIES **
__Creon Levit __, NASA-AMES

**Focused Session F-Tu: Advanced Accelerator Design & Control **

**F-Tu01: ****MERLIN - AN (OBJECT-ORIENTATED) SIMULATION TOOL FOR LINEAR COLLIDERS **
__Nicholas Walker __, DESY

The next generation of e+e- linear colliders will be "fly-by-wire" machines: the tight tolerances on alignment and field quality required to maintain the nanometer beam sizes at the interaction point will require active stabilisation using beam-based feedback systems. The simulation code Merlin has been developed at DESY over the last two years specifically to model the time-dependent behaviour of the luminosity of the TESLA linear collider, with particular emphasis on ground motion effects, tuning and orbit feedback systems. While Merlin was developed with these particular goals in mind, it is a general accelerator simulation tool which could be applied to other machines. The general nature of Merlin is specifically supported by its flexible input language MerlinScript, which is a powerful script language which supports both procedural and object-orientated programming. Finally, Merlin is completely written in C++, and has been developed to allow a large amount of code reuse for other accelerator related projects.

**F-Tu02: ****EXPERIENCE WITH THE CLASSIC LIBRARY FOR MAD VERSION 9**** **
__F. Christoph Iselin __, CERN

The CLASSIC library has been implemented to a large percentage, and it has been used successfully for implementing a new version of MAD written in C++. The talk focuses on the features and availability of the CLASSIC library. It will shows how the library can be used in a large accelerator design program like MAD. Some new developments of the latter are presented, like sophisticated matching features with simultaneous matching of two rings.

**F-Tu03: ****LEGO - A CLASS LIBRARY FOR ACCELERATOR DESIGN AND SIMULATION**** **
__Yunhai Cai __, SLAC

An object-oriented class library of accelerator design and simulation is designed and implemented in a simple and modular fashion. All physics of single-particle dynamics is implemented based on the Hamiltonian in the local frame of the component. Sympletic integrators are used to approximate the integration of the Hamiltonian. A differential algebra class is introduced to extract a Taylor map up to arbitrary oder. Analysis of optics is done in the same way both for the linear and nonlinar cases. Recently, Monte Carlo simulations of synchrotron radiation has been added to the library. The code is used to design and simulate the lattices of the PEP-II and SPEAR3. And it is also used for the commissioning of the PEP-II. Some examples of how to use the library will be given.

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Work supported by USDOE contract DE-AC03-76SF00515.

**F-Tu04: ****THE STANDARD EXCHANGE FORMAT (SXF) FOR ACCELERATOR DESCRIPTION **
__F. Pilat __, C.G. Trahern, J. Wei, BNL, R. Talman, N. Malitsky, CORNELL

H. Grote, CERN, J. Holt, W. Wan, FNAL

The SXF (Standard eXchange Format), triggered initially by the needs of the US-LHC Collaboration, is an accelerator description that has been developed for the purpose of easy exchange of modeling information among laboratories. An SXF lattice description is an ascii listing that contains one named, flat, ordered list of elements, similar to a MAD sequence describing the entire machine. Unlike the MAD sequence, SXF can describe not only design information but also the individual characteristics of elements, such as errors, apertures, corrector settings, etc. whose knowledge is needed for a fully instantiated model of the machine. SXF parsers have been developed for MAD8 and MAD9 (via DOOM), Teapot, Teapot++, COSY and the FNAL beamline class libraries. The SXF format is used for LHC and RHIC modeling. The use of SXF as a machine format as an interface with the conrols system is presently discussed as well as a lattice represention for database development.

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Work supported by the U.S. Department of Energy.

**F-Tu05: ****THE ACCELERATOR DESCRIPTION EXCHANGE FORMAT**** **
__N. Malitsky __, R. Talman, CORNELL U

The Accelerator Description eXchange Format (ADXF) is in response to the Iselin-Keil-Talman letter (1), which calls for a new accelerator description standard aimed to provide connectivity between a variety of beam-dynamics programs and heterogeneous data sources. ADXF represents a flat and complete description of the current accelerator state. It has been designed as the additional independent fully-instantiated layer to existing design data structures, in particular the Standard Input Format (SIF). Though the ADXF preserves all SIF element types its open model provides a mechanism for introducing elements with arbitrary attributes. The proposed specification is based on the Extensible Markup Language (XML), an industrial standard for processing Web documents and application-neutral data.

(1) C. Iselin, E. Keil, R. Talman, 21 January, 1998.

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Work supported by the U.S. Department of Energy.

**F-Tu06: ****MATLAB-LIKE ENVIRONMENT FOR ACCELERATOR MODELING AND SIMULATIONS**** **
__Hiroshi Nishimura __, LBNL

TracyM is an interactive and programmable environment for accelerator design, simulation and modeling studies built on top of O-Matrix that is one of the MATLAB-like environments available on Windows. It wraps the C++ class library Goemon for the use in the O-Matrix environment. O-Matrix was chosen for its better connectivity to external function calls. It allows a single DLL to support multiple external functions instead of requiring a separate DLL for each individual external function. It provides a list structure to describe the lattice configuration, various kinds of mathematics routines that cover flexible parameter fittings, and graphics routines. As all the CPU- intensive calculations are done in the C++ layer, there is no run-time penalty. A standard set of GUI is also supported by an external program that communicates with TracyM by using a WIN32 shared memory and a pipe.

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This work was supported by the Director, Office of Energy Research, Office of Basic Energy Sciences, Material Sciences Division, U. S. Department of Energy, under Contract No. DE-AC03-76SF00098.

**F-Tu07: ****EXPERIENCE WITH BEAM PHYSICS COMPUTATION IN A CONTROL SYSTEM ENVIRONMENT **
__E.S. McCrory __, A.J. Braun, G.P. Goderre, J.A. Holt, J-F. Ostiguy, L. Michelotti, W. Wan, FNAL

Beam physics computation codes are being incorporated into the Fermilab control system in two ways: (1) Redirection of the control system so that real beamline devices are controlled and read out via a computational model, unbeknownst to the program requesting this information, and (2) on-line models, used to make conventional beam-physics calculations so a user can easily perform these calculations and can directly compare model predictions with real machine behavior. This paper concentrates on the techniques involved with the redirection of the control system console to a computational model. This model, referred to as the open-access model (OAM), must exactly mimic the behavior of the control system and of the actual devices in the machine in order to make the test of the controls application meaningful. The Fermilab Main Injector (FMI) project, scheduled to be in commissioning at the time of this conference, has relied heavily on these mechanisms.

**F-Tu08: ****EXPANSION OF THE CONTROL SYSTEM CONSTRUCTED BY OOP METHOD **
__Hiroshi Yoshikawa __, Hironao Sakaki, Yuichi Itoh, Yasushi Terashima and Hideaki Yokomizo, JSRRI

An exemplification of expanding the control system of a 1 GeV electron linac is described, and the merit of OOP method is estimated. This linac is the injector for the 8 GeV synchrotron radiation storage ring. Through the operation for 2 years, this linac is expanded two beam transport lines in this summer for the injection to a medium energy storage ring( NewSUBARU) and for the fundamental researches aiming SASE. The work in order to correspond with this expansion of control system has been^[$B!!^[(Bestablished only in three weeks by two programmers. Compiling is not at all necessary, when the device that is the same kind that it already works is added, even man-machine process. Almost all devices are new types, but 30 percent of this work was editing of text^[$B!!^[(Bfiles, 40 percent was editing and compiling, and 30 percent was test. Details of this work and not at all necessary, when the device that is the same kind that it already works is added, even man-machine process. Almost all devices are new types, but 30 percent of this work was editing of text^[$B!!^[(Bfiles, 40 percent was editing and compiling, and 30 percent was test. Details of this work and characteristics of our modeling of machine class which enabled to ease this modification will be described.

**F-Tu09: ****A SIMPLE REAL-TIME BEAM TUNING PROGRAM FOR THE KEKB INJECTOR LINAC **
__J.W. Flanagan __, K. Oide, KEK

A simple real-time beam tuning program has been developed for use at the KEK B-Factory injector linac. The program features the ability to adjust an arbitrary combination of parameters (e.g. magnet currents and RF phases) in order to optimize an arbitrary combination of monitor values (e.g. the ratio of a downstream beam current to gun current). Based on the downhill-simplex method, it requires no knowledge of beamline details. An additional "persistence" parameter is used to adjust the treatment of pulse-to-pulse variations of monitor values while mapping the parameter-space terrain, and controls the peak-holding performance in the presence of both statistical fluctuations and long-term drift. Preliminary results from the commissioning of the KEKB injector linac and plans for the future are discussed.

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Work supported by the Japanese Ministry of Education, Science, Sports and Culture (Monbusho) and the Japan Society for the Promotion of Science.

**F-Tu10: ****A UNIVERSAL POSTPROCESSING TOOLKIT FOR ACCELERATOR SIMULATION AND DATA ANALYSIS **
__Michael Borland __, ANL

The Self-Describing Data Sets (SDDS) toolkit comprises about 80 generally-applicable programs sharing a common data protocol. At the Advanced Photon Source (APS), SDDS performs the vast majority of operational data collection and processing, most data display functions, and many control functions(1). Further, a number of accelerator simulation codes use SDDS for all postprocessing and data display. This has three principle advantages: First, simulation codes need not provide customized postprocessing tools, thus simplifying development and maintenance. Second, users can enhance code capabilities without changing the code itself, by adding SDDS-based pre- and post-processing. Third, multiple codes can be used together more easily, by employing SDDS for data transfer and adaptation. Given its broad applicability, the SDDS file protocol is surprisingly simple, making it quite easy for simulations to generate SDDS-compliant data. This paper discusses the philosophy behind SDDS, contrasting it with some recent trends, and outlines the capabilities of the toolkit. The bulk of the paper consists examples of using SDDS for accelerator simulation.

(1) M. Borland, "Applications Toolkit for Accelerator Control and Analysis", Proc. 1997 PAC, Vancouver, Canada, to be published.

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Work supported by U.S. Department of Energy, Office of Basic Energy Sciences, under Contract No. W-31-109-ENG-38.

**F-Tu11: ****SUMMARY OF PANEL DISCUSSION ON ADVANCED ACCELERATOR DESIGN AND CONTROL **
__Jeff Corbett __, SLAC

A Panel Discussion was held at the 1998 International Computational Accelerator Physics Conference to discuss topics in Advanced Accelerator Design and Control Software. This paper reviews the findings and recommendations of the panel.

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Work sponsored by the U.S. Department of Energy, Office of Basic Sciences, Division of Chemical Sciences under Contract DE-AC03-76SF00515.

**Focused Session C-Tu: Modeling of High Intensity Beam Phenomena **

**C-Tu01: ****MODELS AND SIMULATION OF BEAM HALO DYNAMICS IN HIGH POWER PROTON LINACS **
__Thomas P. Wangler __, LANL

The threat of beam loss that causes radioactivation in high-power proton linacs is increased significantly by the formation of beam halo. Numerical multiparticle simulation studies have identified the nonlinear and time dependent space-charge forces, especially those that occur in rms mismatched beams, as a major source of halo growth. The predictions of the simulation codes must be compared with independent models to provide physical understanding and to confirm the validity of the simulation results. We compare particle-core model predictions for both transverse and longitudinal halo-particle dynamics with computer simulations.

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Work supported by U.S Department of Energy

**C-Tu02: ****ECHOES IN HIGH-ENERGY STORED BEAMS **
__P.L. Colestock__, L.K. Spentzouris, FNAL

Beam echoes have emerged as a useful tool for studying weak diffusion processes in high-energy stored beams. Although formlly a nonlinear process, they lend themselves to a fully analytic treatment using perturbation methods, and may exactly solved when wakefields are negligible. They are also readily modelled with particle simulations. Although a number of echo types may be produced, thus far only longitudinal echoes have been studied experimentally. In this paper we review the physics of echo formation and show how they may be used to study diffusion in both beams and corresponding particle simulations.

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Work supported by U.S Department of Energy

**C-Tu03: ****A MULTIGRID-BASED APPROACH TO MODELING A HIGH CURRENT SUPERCONDUCTING LINAC FOR WASTE TRANSMUTATION **
__Paolo Pierini __, INFN

High current proton accelerators are nowadays planned for various applications that make use of the resulting large flux of spallation neutrons. The INFN has started funding a study of the feasibility of a (greater than) 40 MW CW linac for nuclear waste trasmutation and energy production (a.k.a. the "Energy Amplifier" concept). A safe and reliable operation of similar machines will require proper control of the beam losses. Accurate simulations codes are required in order to assess that the beam losses are maintained to a safe level. As a part of the INFN program, an "ad hoc" code development activity has started, making use of the recent programming techniques and of numerical algorithms. The code in development deals, for now, with the beam dynamics in the high energy part of the proposed machine, composed by superconducting RF (elliptical) cavities placed between the long drifts of a quadrupole doublet array. The cavities are treated with an on-axis field distribution, either provided in analytical form or as tabular data. Space charge is evaluated with a fast Poisson solver, that uses a 3D multigrid algorithm. V Cycle or full multigrid algorithms appear to be promising in terms of speed and memory requirements, and can be readily modified for parallel computers. Checks with standard direct point-to-point calculations are in progress. A major effort has been put in using a modular approach for the data and program design. The code conforms to the F90 syntax and, where possible, makes use of safe programming criteria (controlled scoping of variables through MODULEs and PRIVATE/PUBLIC qualifiers, explicit procedure INTERFACES with INTENT declaration, dynamic allocation of all the data structure for the beam line, the particles and the space charge meshes). Preliminary results of this ongoing work will be presented in this contribution.

**C-Tu04: ****SIMULATION AND OBSERVATION OF THE LONG TIME EVOLUTION OF THE LONGITUDINAL INSTABILITY IN A STORAGE RING **
__Oliver Boine-Frankenheim __, GSI

Storage rings are a unique tool to observe the rise and the saturation of the longitudinal instability in space charge dominated beams with high resolution. Kinetic simulations are mandatory to interpret the experimental data and to understand the underlying physical phenomena. In the simulations the longitudinal dynamics of space charge dominated, coasting beams interacting with the ring environment is modeled in the framework of the Vlasov-Fokker-Planck equation. The long time character of the collective phenomena pose high demands on the numerical integration method. Two different numerical codes (Particle-In-Cell (PIC) in cylindrical geometry, direct `noise-free' integration on a grid in the longitudinal phase space) are used to simulate the long time evolution of the experimental observables, like the momentum spread and the self-bunching amplitudes. The effect of electron cooling on the instability evolution is analyzed. The simulation noise inherent to PIC codes is used to predict the Schottky noise spectrum, which is an important experimental observable. The PIC code can be used to find correlations between the Schottky noise spectrum and the momentum spread.

**C-Tu05: ****ANALYTICAL MODEL OF HALO FORMATION**** **
__R.L. Gluckstern __, U of MD

An analytical model for halo formation has been constructed based on a beam in a focusing channel which is "breathing" due to a mismatch with the channel. For a 2-D KV beam, an integral of motion can be obtained assuming the dominance of the parametric resonance (breathing mode frequency is twice the frequency of individual particles within the beam). These results correspond to the "peanut diagram" in particle phase space in all respects. The model is then extended to other 2-D distributions, as well as 3-D distributions involving both longitudinal and transverse breathing modes. Numerical simulations are then used to determine the behavior of the longitudinal and transverse halos which occur, and their dependence on the initial phase space distribution, the bunch charge and shape, and the amplitude of the mismatch.

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Work supported by the U.S. Department of Energy

**C-Tu06: ****ASPECTS OF LONGITUDINAL HALO DYNAMICS INCLUDING NONLINEAR RF FIELDS **
__John J. Barnard __, Steven M. Lund, LLNL, Robert D. Ryne, LANL

In order to minimize beam loss, careful attention must be paid to mechanisms which give rise to halo, both longitudinal and transverse. In this paper, we focus on the production of longitudinal halo arising from longitudinal beam mismatches. Emphasis will be placed on those aspects of halo formation that are unique to the longitudinal case. In particular, we will describe the influence of the non-linear sinusoidal focusing field, which distorts the traditional "peanut diagram" of the longitudinal phase space. Further, under some circumstances the non-linearity can suppress the two-to-one resonance of particle oscillation with the envelope mismatch mode that drives the halo formation. Comparisons will be shown of 3D PIC simulations with Core/Test Particle models.

**C-Tu07: ****HALO FORMATION IN 3-D BUNCHES WITH SELF-CONSISTENT STATIONARY DISTRIBUTIONS **
__A.V. Fedotov __, R.L. Gluckstern, U of MD, S.S. Kurennoy, R.D. Ryne, LANL

We have constructed, analytically and numerically, a new class of self-consistent 6-D phase space stationary distributions. The beam is then mismatched longitudinally and/or transversely, and we explore the formation of longitudinal and transverse halos in 3-D axisymmetric beam bunches. The longitudinal phase space clearly shows the typical "peanut" diagram observed in 2-D calculations. We find that the longitudinal halo forms first for comparable longitudinal and transverse mismatches because the longitudinal tune depression is more severe than the transverse one for elongated bunches. Of particular importance is the coupling between longitudinal and transverse motion and its effect on halo formation.

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Work supported by the U.S. Department of Energy

**C-Tu08: ****NEW METHODS IN WARP**** **
__David P. Grote __and Alex Friedman, LLNL, Irving Haber, NRL

New methods and capabilities have recently been introduced into WARP, a multi-dimensional particle-in-cell code developed for the study of space-charge dominated beams(1). We describe: (a) a 2D3V "slice" model (WARPxy) with two novel capabilities: the optional use of 3D applied fields (which can be calculated using the WARP3d solver), and an "exact" treatment of a bent beam pipe, via coordinate transformations; (b) a multigrid fieldsolver which offers internal conductors in 2D and 3D; and (c) serial optimizations for cache-based machines which yielded a 20-30% speedup. (Other developments are described in ref. 2).

(1) D. P. Grote, A. Friedman, and I. Haber, AIP Conf. Proc. 391 (1996 Comp. Accel. Phys. Conf.), 51-58 (1997).

(2) D. P. Grote et. al., this conference.

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Work performed under the auspices of the U.S. Department of Energy by LLNL under contract W-7405-ENG-48.

**C-Tu09: ****UNIQUE FEATURES OF THE UNIVERSITY OF MARYLAND ELECTRON RING AND THE NECESSITY OF PIC CODE SIMULATION**
__R.A. Kishek __, S. Bernal, M. Reiser, and M. Venturini, U of MD, I. Haber, NRL

Abstract. The Maryland Electron Ring [1] is designed to explorethe transport of beams with much higher space charge than other circular machines. In addition, the ringfunctions as a testbed for design and simulation codes. Applications such as Heavy Ion Fusion and High Intensity Colliders require the preservation of beam quality during transport over large distances. This paper describes the application of self-consistent particle-in-cell code simulations using the WARP suite [2] to the E-ring lattice. The model used includes the nonlinear details of the external magnetic fields, a cylindrical external conductor, and the dispersive effects of the circular lattice on a beam with a non-zero energy spread.

(1) M. Reiser, et. al., Fusion Engineering and Design 32-33, 293 (1996).

(2) M. Venturini and M. Reiser, "RMS Envelope Equation in the Presence of Space Charge and Dispersion," Phys. Rev. Lett., in print (1998).

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Research Supported by Department of Energy.

**Focused Session F-We1: Advances in Electromagnetic Modeling **

**F-We11: ****HIGH PRECISION MODE CALCULATION USING THE PERFECT BOUNDARY APPROXIMATION TECHNIQUE **
P. Thoma,
__T. Weiland __, TU-Darmstadt

The exact modeling of very complicated, three dimensional structures is essential for precise numerical field calculation. To overcome the limited discretization accuracy of the Finite Integration Theory (FIT) on a Cartesian grid applied to arbitrarily shaped surfaces, several approaches are made. The advantage of the Perfect Boundary Approximation Technique (PBA) compared to other extending methods, like the introduction of local sub-grids or irregular non-orthogonal grids, is, that despite of the continued use of cartesian meshes, curved boundaries are perfectly approximated. although the boundaries not necessarily have to coincide with the mesh cells, the exact boundary shape is taken into account, resulting in a second order algorithm. The PBA technique, implemented in MAFIA, is applied to typical accelerator components. It turns out that the PBA technique is more than one order of magnitude faster than the conventional method if many non Cartesian metallic boundaries appear inside the modeled structure.

**F-We12: ****A RIGOROUS ANALYSIS OF CAVITY RESONATORS BY FINITE ELEMENT METHOD **
__Z. Cendes __, I. Bardi, and L. Walling, ANSOFT CORP.

The finite element method is applied to analyze the resonance frequencies and the unloaded quality factor of closed cavities. A new concept of eigenvalue analysis is used to find the expected resonancies in the given frequency range. The algorithm is based on the Lanczos algorithm and provides a more broadband response. Called ALPS (Adaptive Lanczos-Pade Sweep), the new procedure is able to find all resonances in a wide frequency range. It identifies the less dominant resonances and hence detects subtleties in the frequency response more easily. The solution time is almost the same as the solution time of one frequency analysis. Applying the finite element method, it is possible to analyze very complicated lossy structures with high accuracy. The analysis takes even the roughness of the walls into account. This factor could influence the unloaded quality factor as much as 30 percent. The analysis can be done by the High Frequency Structure Simulator (HFSS) software of Ansoft Corporation to take the advantage of the graphical user interfaces to solve the problem in an easy and fast way.

**F-We13: ****AN ADVANCED ELECTROMAGNETIC EIGENMODE SOLVER FOR VACUUM ELECTRONICS DEVICES - CTLSS **
__Simon J. Cooke __(1), Alfred A. Mondelli (1), Baruch Levush (2), John J. Petillo (1), Eric Nelson (3), David P. Chernin (1) and Thomas M. Antonsen, Jr. (4),

(1) SAIC, (2) NRL, (3) LANL, (4) U of MD

The first module of the Cold-Test and Large-Signal Simulation (CTLSS) code, a next generation design tool for vacuum electronics devices, is presented. The prototype is a three-dimensional, finite-difference, frequency-domain code solving for eigenfrequencies and fields discretised on a structured grid. An adaptation [1] of the Jacobi-Davidson algorithm [2] is used to determine the eigenmodes. This algorithm has proven effective in solving real problems, involving sharp-edged structures, with energy-absorbing materials having large dielectric constants and loss tangents >100%. Degenerate modes are also readily determined. 3D electromagnetic codes have experienced difficulty handling moderate to large loss tangents in complex cavities [3]. This talk will present the algorithm for eigenmode solution and features of CTLSS useful for vacuum electronic device and component design. Analysis of both closed cavities and periodic structures will be presented. Since the algorithm may be seeded with an approximate (coarser grid) solution, the overall execution time is moderate. Initial tests indicate below 0.1% frequency accuracy for all modes computed. This code is at present being generalised to include an unstructured mesh for the conformal representation of structures using a finite element model. The cold-test fields will feed forward into a large-signal simulation model, based on the CHRISTINE code [4].

[1] S.J. Cooke and B. Levush, "Eigenmodes of Microwave Cavities Containing High- Loss Dielectric Materials," Proceedings, PAC97 (Vancouver, BC, 1997).

[2] G.L.G. Sleijpen and H.A. van der Vorst, "A Jacobi-Davidson Iteration Method for Linear Eigenvalue Problems," SIAM J. Matrix Anal. 17, 401-425 (1996).

[3] D. Schmitt, R. Schuhmann, and T. Weiland, "The Complex Subspace Iteration fo r the Computation of Eigenmodes in Lossy Cavities," Int. J. Numerical Modeling: Electr onic Network, Devices and Fields 8, 385-398 (1995).

[4] T.M. Antonsen, Jr. and B. Levush, "CHRISTINE: A Multifrequency Parametric Si mulation Code for Traveling Wave Tube Amplifiers," NRL Memo Report NRL/FR/6840-97-9845 (1997).

**F-We14: ****ON SOLVINGING MAXWELLIAN EIGENVALUE PROBLEMS FOR ACCELERATING CAVITIES **
__Peter Arbenz __, ETH-Zurich

We investigate algorithms for solving large sparse symmetric matrix eigenvalue problems resulting from finite element discretizations of steady state electromagnetic fields in accelerating cavities. The methods have been applied to an analytically computable model cavity and to the old and the new design of the accelerating cavities for the PSI 590 MeV ring cyclotron. The solutions of this kind of eigenvalue problems can be polluted by so-called spurious modes if the divergence-free condition is not treated properly. The two methods used for the finite element formulation provide a scheme to suppress spurious modes: (A) using penalty terms and (B) applying a mixed method, with edge elements for the field representation and node elements for the Lagrange multiplier. Four different algorithms have been applied to solve the resulting large sparse matrix eigenvalue problems: (1) subspace iteration, (2) block Lanczos algorithm, (3) implicitly restarted Lanczos algorithm, and (4) Jacobi-Davidson algorithm. For both finite element formulations we compare the amount of work it takes each solver to compute a few of the smallest positive eigenvalues and corresponding eigenmodes to a given accuracy. Numerical results obtained on a multiprocessor HP Exemplar X-Class System are presented.

**F-We15: ****IMPROVED GDFIDL WITH GENERALIZED DIAGONAL FILLINGS AND REDUCED MEMORY AND CPU REQUIREMENTS**** **
__Warner Bruns __, TU-BERLIN

A new version of the Finite Difference code GdfidL implements generalized diagonal fillings for the discretization of the material distribution. The new algorithm allows 72 different types of material filling for each cell, whereas the common diagonal filling only allows 7 types. With the improved material filling, the discretization error for realistic geometries is reduced by a factor of three. The improved meshing is implemented both in the resonant solver and the time domain solver. Computed frequencies for some simple geometries are given to show the reduction in discretization error. GdfidL's organisation of the computational volume as a linked list has already reduced the resource requirements to about the half of other codes. A new organisation of the linked list reduces the requirements for time domain computations again by a factor of 0.7. The solvers and postprocessor now have a self decribing user interface. The command language is capable of handling user defined macros.

**F-We16: ****OPTIMIZED ORDER 2 (OO2) METHOD FOR HELMHOLTZ'S AND MAXWELL's HARMONIC EQUATIONS AND NON-CONFORMING MESHES **
Ph. Chevalier Y. Maday and
__F. Nataf __, CNRS

We introduce optimized second order interface conditions for Helmholtz's and Maxwell's equations. We are interested in showing convergence of the proposed algorithm for vanishing waves. We believe that this kind of waves impede the good convergence of Schwarz's algorithm with first order interface condition. We also make use of the QMR method that replaces the classical additive Schwarz method. We present numerical simulations for 2D Helmholtz's and 3D Maxwell's equations with industrial implementation. We also consider the important issue of the use of non conforming discretizations in the subdomains. It enables a rapid and genuinly parallel mesh generation. During the computation, it makes it possible to have local refinement without having to change the mesh in the neighbouring subdomains. The approach is related to the Mortar method but is more symmetric.

__________________________________________

Work partially supported by Thomson Tube Electronic

**Focused Session F-We2: Advanced Algorithms & Methods **

**F-We21: ****SELF-CONSISTENT MODEL FOR THE BEAMS IN ACCELERATORS**** **
__A. Novokhatski __and T. Weiland, TU-DARMSTADT

It is proposed to use ensembles of particles instead of "macro" particles for modeling the beams in accelerators. Each ensemble describes the dynamics of the real bunch, which interacts with linear forces. Ensemble parameters include first and second order moments of the bunch in the phase space. Self-consistent equations for these moments are derived from Vlasov equation. Examples of application of this model in different devices of accelerators are presented.

__________________________________________

Work supported in part by DESY, Hamburg

**F-We22: ****STOCHASTIC COLLISIONAL EFFECTS IN N-BODY PROBLEMS **
__Salman Habib __, Robert Ryne, and Ji Qiang, LANL

Within the next few years, computers will become powerful enough to allow simulations with realistic charge resolution, i.e., with particle numbers on the order of the number of particles in a single bunch (at least in some types of accelerators). Because of this fact, and because of the relevance to halo formation, it is important to quantitatively understand and predict effects due to intra-beam collisions. In this talk, I will review dynamical equations that include collisions such as the Landau/Fokker-Planck equation and describe their implementation in a particle-mesh N-body code. I will also discuss the presence of collisionality in ``collisionless'' N-body solvers.

**F-We23: ****MODELING BEAMS WITH ELEMENTS IN PHASE SPACE **
__Eric M. Nelson __, LANL

Conventional particle codes represent beams as a collection of macroparticles. An alternative is to represent the beam as a collection of current carrying elements in phase space. While such a representation has limitations, it may be less noisy than a macroparticle model, and it may provide insights about the transport of space charge dominated beams which would otherwise be difficult to gain from macroparticle simulations. The phase space element model of a beam is described, and progress toward an implementation is discussed. A simulation of an axisymmetric beam using 1d elements in phase space is demonstrated.

__________________________________________

Work supported by DOE, contract W-7405-ENG-36.

**F-We24: ****MODEL INDEPENDENT ANALYSIS OF BEAMLINE **
J. Irwin,
__C.X. Wang __, Y.T. Yan, K. Bane, Y. Cai, F. Decker, M. Minty, G. Stupakov , SLAC

We will discuss a new way to analyze (model) an accelerator beamline. Unlike the conventional beam-based machine modeling techniques which rely on fitting measurement data to certain machine model, our method does not depend on any particular machine model, therefore the name "Model Independent Analysis" (MIA). By analyzing the BPM matrix formed by the readings of a large number of pulses on a large number of BPMs, one can extract various beamline information with much better accuracy. In some sense, MIA is a statistical analysis (or data mining) of BPM readings.

__________________________________________

Work supported by DOE contract DE-AC03-76SF00515.

**F-We25: ****USING SYMBOLIC ALGEBRA FOR THE GENERATION OF ORBIT SIMULATION CODES FROM HAMILTONIANS **
Stefan Adam, Andreas Adelmann , PSI

As a part of the new research activity aiming at a detailed understanding of space charge effects in ring cyclotrons and in the corresponding injection beamlines at the Paul Scherrer Institute, we are currently developing a three dimensional space charge simulation code. Using the symbolic algebra system Maple, to derive the equation of motion and to cast them into Fortran we can establish the physical model on the high level of the Hamiltonian formalism. We start by defining the relativistic Hamiltonian for two simplified cases: the two-particle system and the motion of a single particle in a stable charge distribution. He mentioned models are foreseen to be extended to a more complex structure of the external magnetic fields and to various charge density distributions. For simulating small numbers of particles the Matlab system offers a powerful visualization and testing environment. Matlab's MEX-Interface allows us to use the Fortran subroutines produced by Maple in our simulation. For the two mentioned cases, the development steps from the Hamiltonian to the Fortran subroutine and to the resulting simulations are shown, as well as the general Maple and Matlab packages we have developed for this purpose.

**F-We26: ****IMPROVED A PRIORI ERROR BOUNDS FOR NUMERICAL INTEGRATION OF ORDINARY DIFFERENTIAL EQUATIONS **
Robert L. Warnock , SLAC

A fixed-point method is employed to bound rigorously the discretization error in numerical solution of the initial-value problem for systems of nonlinear (or linear) ordinary differential equations. The resulting analytic expressions for error bounds are both easier to evaluate and closer to the true error than formulas found in standard texts. The analysis applies to any explicit one-step method, for instance to the Taylor series integrator, the Runge- Kutta method, explicit symplectic integrators, etc. Both local and global errors are treated. A numerical example from accelerator physics is given, and relations to work of Berz, Lohner, and Zadunaisky. __________________________________________

Work supported by DOE contract DE-AC03-76SF00515.

**Focused Session C-We1: New Software Environments & Libraries **

**C-We11: ****SCICHAT - AN APPLICATION SERVER FOR COLLABORATIVE WORK **
__John R. Cary (1) __and Kelly G. Luetkemeyer, TECH-X CORP.

Tech-X Corporation has developed SciChat, an application server for scientific collaboration. Connections are made to the server through a Java client, that can either be an application or an applet served in a web page. Once connected, the client may choose to start or join a session. A session includes not only other clients, but also an application. Any client can send a command to the application. This command is executed on the server and echoed to all clients. The results of the command, whether numerical or graphical, are then distributed to all of the clients; thus, multiple clients can interact collaboratively with a single application. The client is developed in Java, the server in C++, and the middleware is the Common Object Request Broker Architecture. In this system, the Graphical User Interface processing is on the client machine, so one does not have the disadvantages of insufficient bandwidth as occurs when running X over the internet. Because the server, client, and middleware are object oriented, new types of servers and clients specialized to particular scientific applications are more easily developed.

(1) Also at the University of Colorado, Boulder

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Work supported by Tech-X Corporation.

**C-We12: ****A PYTHON INTERFACE TO WARP IN PARALLEL AND SERIAL ENVIRONMENTS **
__David P. Grote __, LLNL

The WARP(1) code is being developed and applied to simulate the creation and propagation of the high-current, space-charge dominated beams that are required for heavy-ion driven fusion energy (HIF). On serial computers, WARP makes use of the Basis(2) code development and interpreter system which provides interactive access to the runtime database and allows flexible steering of simulations. Because of the increasing size and complexity of the simulations required by the HIF program, it was deemed essential to port WARP to a parallel environment, and this has been accomplished. Since Basis was not easily portable to a parallel environment, Python(3), an object oriented interpreter, was chosen as a new interactive engine. Unlike Basis, Python does not provide an automatic system for generating the interface between the interpreter and the compiled code. Such a system was developed and will be described. With routines obtained to handle user input and output on multiple processors, Python can be used interactively as a front end to the physics code in a parallel processing environment. With this, we now have an interactive code with essentially the same user interface in both serial and parallel environments.

(1) D. P. Grote, et. al., "Three-Dimensional Simulations of High Current Beams in Induction Accelerators with WARP3d", Fus. Eng. Des. 32 (1996), pp 193.

(2) P. F. Dubois, The Basis System, LLNL Document M-225 (1988).

(3) http://www.python.org

__________________________________________

Work performed under the auspices of the U.S. Department of Energy by LLNL under contract W-7405-ENG-48.

**C-We13: ****THE FRAMEWORK OF UNIFIED ACCELERATOR LIBRARIES **
__N. Malitsky __, R. Talman, CORNELL U

The performance of an accelerator depends to a large extent on the quality of the theoretical algorithms and the level of their integration with the control system. An important and immediate accelerator task is to steer theoretical and experimental activities in a common direction toward the development of interoperable Accelerator Simulation Facilities and (later) intelligent model-based control systems. The framework of Unified Accelerator Libraries (UAL) addresses this problem by offering a single standard-based environment that facilitates compatible and independent implementation of accelerator applications and promotes sharing and standardization of the most effective approaches and solutions.

__________________________________________

Work supported by the U.S. Department of Energy.

**C-We14: ****PARTICLE ACCELERATOR SIMULATION USING C++ AND THE POOMA FRAMEWORK **
__Timothy J. Cleland __, William F. Humphrey, Graham A. Mark, Julian C. Cummings, Robert D. Ryne, Salman Habib, and Ji Qiang, LANL

A C++ program for the simulation of particle dynamics in high-intensity charged particle beams has been developed using the POOMA (Parallel Object- Oriented Methods and Applications) Framework. The simulation is based on an electrostatic model using a particle-in-cell approach with an FFT-based Poisson solver to model the inter-particle Coulomb forces. The particle trajectories are calculated as the beam travels through various accelerator beamline elements including drift chambers, quadrupole magnets, and RF cavities. An object-oriented software design was employed with abstractions for the particle beam, accelerator beamline, and the beamline elements. Using the template facilities of C++, the same code supports both 2D and 3D simulations. The POOMA Framework eased the development by encapsulating the parallelism through the use of its field and particle classes, particle-field interaction capabilities, and parallel FFT algorithms. This application is evaluated by comparing both the serial and parallel performance with an existing HPF implementation.

**C-We15: ****JPP: A PARTICLE TRACKING CODE WITH JAVA**** **
__Ryoichi Hajima __, U of TOYKO

A computer language Java fascinates a number of programmers in the world due to its superior features: simple, object-oriented, distributed, robust, architecture neutral, portable, multithreaded, involved graphics API and so on. It has been considered that a computer language running on interpreter such as Java is not suitable for scientific application where heavy calculation is required. There, however, are splendid ideas to overcome the performance limit of the interpreter, which are ``just-in-time'' compiler (JIT), ``native method.'' In this paper, JPP: a particle tracking code written in Java is presented. We will show object-oriented class hierarchy for accelerator component, design of GUI/CUI post-processor, performance comparison with C language.

**C-We16: ****IMPLEMENTATION OF OBJECT-ORIENTED DESIGN WITH FORTRAN LANGUAGE IN BEAM DYNAMICS STUDIES **
__J. Qiang __, R. Ryne and S. Habib, LANL

In this paper, object-oriented design has been implemented using Fortran language in beam dynamics studies. Using module and derived type in F90, we can emulate object concept in the object-oriented design. This gives Fortran code a better maintainability, reusability, and extensibility. The fundamental classes in our object-based particle-in-cell code include beam line element class, beam class, field class and geometry class. These classes are implemented using F90 language with message passing interface (MPI) and High Performance Fortran (HPF) in parallel computation. MPI has advantages of flexibility in treating irregular problems. HPF has advantages of programming ease and portability between parallel and serial machines by encapsulating the details of communication and using directive comments in the Fortran language.

**Focused Session C-We2: Graphic Interfaces & Advanced Visualization **

**C-We21: ****AN APPLICATION FRAMEWORK AND GRAPHIC USER INTERFACE FOR MULTIPLE ACCELERATOR CODES **
__Barrey W. Hill __, Hendy Martono, John Moore and James S. Gillespie, GILLESPIE ASSOC.

A multi-platform application framework is being developed for implementing a variety of optics codes under a single Graphic User Interface (GUI) shell. The object oriented framework provides the underlying infrastructure for beamline representations, and multi-platform capabilities for the integration of particle physics simulation and analysis codes. The framework architecture supports plug-in tools such as an interactive particle trajectory module, optimization algorithms and hypertext tutorials which interface with, and enhance the functionality of the installed simulation codes. Simulation codes are integrated into the framework by separating the computational physics code, which is implemented as a platform independent Computational Module, from the I/O requirements, which are replaced with an Application Module developed with the multi-platform GUI framework components. The framework provides a sophisticated beamline object model and a rich library of GUI components. Application dependent components can be derived from the more abstract framework components to support specific requirements of the different simulation codes. An overview of the Multi-Platform Shell for Particle Accelerator Related Codes (S.P.A.R.C.-MP) application framework is presented here with illustrations from a Windows NT/95 application that has been built using the S.P.A.R.C.-MP framework.

**C-We22: ****THE GUI FOR MAPA, AN OBJECT-ORIENTED APPLICATION FOR DESIGNING AND MODELING PARTICLE ACCELERATORS **
__David L. Bruhwiler __, John R. Cary and Svetlana G. Shasharina, TECH-X CORP.

The MAPA (Modular Accelerator Physics Analysis) application is an interactive accelerator modeling and design tool with an X/Motif GUI that runs on a variety of Unix platforms. MAPA has been developed in C++ and makes full use of object-oriented design methods. We present an overview of its features and describe how users can independently extend the capabilities of the entire application, including the GUI. For example, a user can define a new model for a focusing or accelerating element. If the appropriate form is followed, and the new element is "registered" with a single line in the specified file, then the GUI will fully support this user-defined element type after it has been compiled and then linked to the existing application. In particular, the GUI will bring up windows for modifying any relevant parameters of the new element type. At present, one can use the GUI for phase space tracking, finding fixed points and generating line plots for the Twiss parameters, the dispersion and the accelerator geometry. The user can define new types of simulations which the GUI will automatically support by providing a menu option to execute the simulation and subsequently rendering line plots of the resulting data.

[1] Also University of Colorado.

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Work supported by Tech-X Corp. and by DOE grant no. DE-FG03-96ER82292.

**C-We23: ****COM OBJECTS AND CLIENT/SERVER ARCHITECTURES: HOW TO CUSTOMIZE MODERN CAD TOOLS FOR USE IN ACCELERATOR COMPONENT DESIGN **
__John F. DeFord __, STAR

Client/server software architectures are essentially an extension of the object-oriented programming model to executable objects. Microsoft operating systems such as Windows NT provide support for client/server operating systems such as Windows NT provide support for client/server implementation via the Component Object Model (COM). A COM object can register itself in the system database, can access the database for information on other COM objects, and can invoke and use other COM objects. That this functionality is supported between independent executable objects provides a strong foundation for software component development, a $400M/yr industry (excluding Microsoft) that is projected to grow to over $3B/yr by 2002. Utilizing COM methodologies, modern mid-range CAD packages such as SolidWorks and SolidEdge can be customized for use in accelerator design without interaction with the parent company, and without the use of specialized application programming interfaces. This talk will discuss general approaches to such customization, and illustrate the concepts with examples from a current development project.

**C-We24: ****DYNAMIC VISUALIZATION OF INSTABILITIES IN TIME-DEPENDENT PIC SIMULATIONS **
__Stefan Illy __, ITP-KARLSRUHE

Visualizing the data obtained with time dependent simulation programs often requires an animated representation of the results to show the transient behavior in more detail. The required framerate of 2-20 frames/sec. cannot be reached with most visualization programs or graphics libraries even on modern computers, if the amount of data is too high. This problem can be solved by combining a large number of pixmaps created by the visualization software to an animation file that can be played at the requested framerate with special software. In my talk I will present methods and tools to create animation files; in addition I will present animated simulation results of a 2.5D time dependent particle-in-cell code that was developed for the investigation of beam instabilities in gyrotrons (powerful, high-frequency microwave tubes). The visualization program is based on the graphics library UNIRAS/agX and is implemented in C and the scripting language Tcl/Tk. The data stream supplied by the simulation program can be displayed in a series of colored contour plots that are stored in single pixmap files in a fully automated process. After this step the series of pixmaps is converted into an FLI animation file using `ppm2fli'. Players for the FLI format are available for most platforms.

**C-We25: ****MEASUREMENTS AND VISUALIZATION OF THE TRANSVERSE PHASE-SPACE TOPOLOGY AT LEP **
__Giulio Morpurgo __, CERN

The LEP Beam Orbit Measurement system (BOM) allows for the acquisition of the beam position at each Beam Position Monitor (BPM) for over 1000 consecutive turns. By synchronizing the acquisition with a kick given to the beam, we can investigate the behavior of the beam under different conditions. In particular, starting from the data of one BPM, we can apply a simple mathematical manipulation to build a "virtual" BPM, with a phase advance of 90 degrees. Plotting the real BPM against the virtual one, we can observe the evolution of the beam in the phase-space. An appropriate coloring technique is used, to help the User finding his way through the data. Fixed points in the phase-space can be put in evidence, as well as the beam behavior in their neighbourhood. Quantities like the tune, the beam detuning as function of the position amplitude and the beam damping can be studied in this way. Significant examples from real life will be shown.

**C-We26: ****USING 3-D PERSPECTIVES AS A VISUALIZATION TOOL FOR PHASE SPACE DATA **
__George H. Gillespie __, Barrey W. Hill, Michael C. Lampel, Nathan A. Brown, GILLESPIE ASSOC.

Two-dimensional projections of six-dimensional phase space data are routinely used in the analysis of accelerator beam dynamics phenomena. Plots of the distribution of particle coordinator and momenta in a given phase plane (e.g. x,x'), or for the coordinates of a beam cross section (i.e. x, y), are among the most commonly used projections. Computer-based visualizations of higher-dimensional projections of phase space data offer the possibility of providing improved insight into complex beam dynamics phenomena. In this presentation, we will illustrate one of these types of visualizations that uses interactive three-dimensional perspective displays.

**Focused Session F-Th1: Modeling Advanced Accelerator Concepts**

**F-Th11: ****SIMULATIONS OF THE SLAC E150 PLASMA LENS EXPERIMENT **
__Pisin Chen __and Shinichi Masuda, SLAC

We report our computer simulations on the first high beam energy and beam density plasma lens experiment to be performed at SLAC. A new PIC code SPLASH was developed for this purpose. All three regimes of beam-plasma interaction, namely the underdense and the overdense regimes for plasma self-focusing, and the superdense regime for beamstrahlung suppression, were studied. The results serve as a guidance for the experimental hardware design. We further simulate the stochastic emission of synchrotron radiation induced by the plasma focusing. Such signal is considered by the E150 as a means to directly diagnose the plasma lens focusing strength.

__________________________________________

Work supported by DOE contract DE-AC03-76SF00515.

**F-Th12: ****NUMERICAL STUDIES OF WAKE EXCITATION IN PLASMA CHANNELS**** **
__B. A. Shadwick __and J. S. Wurtele, UC BERKELEY and LBNL

The wake fields produced by an intense, short laser pulse propagating in a plasma channel with an arbitrary density profile is investiaged. Plasma channels, viewed as accelerating strutures, have many desirable features that are not shared by a homogeneous plasma. They are also becoming experimentally realizable. As part of an overall program to analyze plasma channels as accelerating structures, a new fluid simulation code has been developed with the primary purpose of producing fast tools to explore parameter space for both theoretical investigation of accelerator performance as well as the modeling and design of experiments. This code has flexible physics content, for example, the laser either be fully resolved temporally or treated as ponderomotive force. An important feature, from the accelerator design point of view, is capability to study of beam propagation dynamics. We present preliminary results consisting of a detailed analysis of the transverse structure of the wake for a wide range of experimentally accessible channel profiles and characteristics of the corresponding accelerated beam.

__________________________________________

Supported by the U. S. DOE under grant no. PDDEFG-03-95ER-40936.

** F-Th13: ** ** KINETIC MODELING OF INTENSE, SHORT LASER PULSES IN TENUOUS PLASMAS ** __ Thomas M. Antonsen Jr. __ , U of MD, Patrick Mora, ECOLE POLYTECHNIQUE

Fast time averaged equations have been derived for the motion of particles and the generation of electromagnetic wake fields under the action of the ponderomotive potential of an ultra-intense laser pulse propagating through a tenuous plasma. Based on these averaged equations, a new particle code has been designed which calculates the particle trajectories on the plasma period time scale as well as the evolution of the intense laser pulse. The code is capable of describing relativistic self focusing, cavitation and electron blowout, ponderomotive acceleration of electrons, and forward and near forward Raman scattering of the laser pulse. With this code the regime of total cavitation of the plasma is investigated. It is found that stable propagation over a long distance is possible in this regime, and that energetic electrons are produced with a simple characteristic dependence of their angle of deflection on energy. This new code allows for computationally efficient modeling of pulse propagation over great distances.

__________________________________________

Supported by the US Department of Energy and The National Science Foundation

**F-Th14: ****To Be Determined **
__Viktor Decyk __, UCLA

**Focused Session F-Th2: Beam-Beam Simulations **

**F-Th21: ****SIMULATIONS OF BEAM-BEAM TAILS IN E+E- STORAGE RINGS **
__John Irwin __, SLAC

The simulation of beam-beam tails in storage rings is quite challenging since the time scales for this motion (minutes) are so much longer than the damping times (milli-seconds). Straight forward tracking is almost bound to fail, except for rare computer-intensive efforts intended to confirm the results of other methods, because of the immense computing times required. I will discuss efforts to work around this two-time problem, and present simulation results obtained for the PEP-II collider.

__________________________________________

Work supported by DOE contract DE-AC03-76SF00515.

**F-Th22: ****BEAM-BEAM SIMULATIONS WITH THE GAUSSIAN CODE TRS**** **
__Miguel Furman __, LBNL

We present a description of the "soft-gaussian" beam-beam simulation code TRS and its application to the PEP-II asymmetric collider.

**F-Th23: ****ODYSSEUS: A DYNAMIC STRONG-STRONG BEAM-BEAM SIMULATION FOR STORAGE RINGS**** **
__E.B. Anderson __and J.T. Rogers, CORNELL U

We have developed a simulation of the beam-beam interaction in e+/e- storage ring colliders which is specifically intended to reveal the dynamic collective behavior of the colliding beams. This program is a true 6-dimensional strong-strong simulation in which the electromagnetic fields of longitudinal slices of the colliding beams are recalculated for each slice collision. Broadband wake fields are included and no constraints are placed on the distribution of particles in the beams. Information on tests of the code will be shown. Results will be presented including limiting beam-beam parameters for round and flat beams, deviations from the Gaussian distribution, effects of the beam-beam parameter on head-tail instability thresholds, and Landau damping rates. Possibilities for further improvements will be discussed.

**F-Th24: ****BEAM-BEAM SIMULATIONS WITH GUINEA-PIG**** **
__Daniel Schulte __, CERN

While the bunches in a linear collider cross once only, due to their small size they experience a strong beam-beam effect. Guinea-Pig is a code to simulate the impact of this effects on luminosity and background. A short overview over the program is given, with examples of its application to the background studies for TESLA, the top threshold scan and a possible luminosity monitor.

**Focused Session C-Th1: Computing Wakefield Effects**

**C-Th11: ****TRANSITION DYNAMICS OF THE WAKE FIELDS OF ULTRA SHORT BUNCHES**** **
__A. Novokhatski __, M. Timm, T. Weiland, TU-DARMSTADT

In the cavities and finite cell structures, ultra short bunches excite very high frequency electromagnetic fields. A fraction of these fields stay in the structure for a very long time. After several reflections another part leaves the structure. And the rest part is chasing the bunch. In a time, this field will catch the bunch and take its kinetic energy. The time and the distance, when and where the bunch is caught, is inversely proportional to the bunch length. The time and the distance can be very long for a very short bunch. The analyses of the wake fields in this transient region is given for the Linear Colliders accelerating structure.

__________________________________________

Work supported in part by DESY, Hamburg

**C-Th12: ****CALCULATIONS OF THE SHORT-RANGE LONGITUDINAL WAKEFIELDS IN THE NLC LINAC **
__K.L.F. Bane __, SLAC, A. Mosnier, CEA, A. Novokhatskii, TU-DARMSTADT, K. Yokoya, KEK

Using two frequency domain and one time domain numerical approaches, we calculate the short-range longitudinal wakefield of the NLC linac accelerating structure, and find that the results agree to 5%. In addition we obtain, through fitting, a simple formula for the short-range wakefield of a linac structure that can be useful in designing linear colliders. Finally, we demonstrate that for the NLC linac cavity the effects on the short-range wake of end conditions, tapering, and rounding of the irises are small.

**C-Th13: ****THE SURFACE ROUGHNESS WAKE FIELD EFFECT **
A. Novokhatski,
__M. Timm __, T. Weiland , TU-DARMSTADT

In the Linear Colliders FEL projects ultra short bunches are foreseen to be used. In addition to usual wake fields, coming from irregularities in the chamber, these bunches excite fields in transporting lines and undulators due to the surface roughness. This effect can be large for the extruded tubes, usually used in accelerators. Based on computer results it is shown, that the roughness wake field effect can be described by a simple model for the monopole and dipoles wakes of a tube with thin dielectric coating.

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Work supported in part by DESY, Hamburg

**C-Th14: ****WAKE OF A ROUGH BEAM WALL SURFACE**** **
K.L.F. Bane and
__G.V. Stupakov __, SLAC

One of the distinctive features in the designs of future e+/e- colliders and FEL's is a tendency toward ever shorter bunch lengths. Two examples are the Next Linear Collider (NLC) with an rms bunch length of 100 microns, and the Linac Coherent Light Source (LCLS), with one of 30 microns. For such short bunches, even the wall surface roughness can become a significant source of impedance. In this paper, we present an analytical model for the impedance of a perfect conductor with a rough surface. Using a small-angle approximation, we first find a general formula for the impedance of a small bump of arbitrary shape on the wall of a round beam pipe. Then modelling a rough surface as a random collection of such shapes, we express the impedance in terms of the spectral function of the surface. In a complimentary approach [1], a rough surface is modelled as a collection of bumps of different shapes, with the impedance computed numerically for each shape. In this model, the impedance of the surface is given in terms of a shape form factor and a packing factor of the bumps on the surface. We compare the results of both models and give numerical estimates for the impedance, due to this effect, of the beam chamber in the LCLS undulator.

[1] K.L.F. Bane, C.K. Ng and A.W. Chao. Estimate of the Impedance Due to Wall Surface Roughness. SLAC-PUB-7514 (1997).

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Work supported by the Department of Energy, contract DE-AC03-76SF00515.

**C-Th15: ****ON THE SLOW MICROWAVE INSTABILITY THRESHOLD FOR ELECTRON STORAGE RINGS **
__Boris Podobedov __and Sam Heifets, SLAC

The microwave instability is usually investigated via the Vlasov equation formalism. Full solution of the Vlasov equation for a general wake-field is only possible numerically and is cpu-intensive. Therefore, it is often useful to have some analytical expression for the instability threshold for the given wake-field. For the slow longitudinal microwave instability several criteria have been proposed by others. These criteria are based entirely on the amplitude dependence of the single particle oscillation frequency in the total (RF + wake) potential. In this paper we analytically show that such criteria are not general and that the true criterion must be related to the asymmetry of the potential well. We also consider the stability from the Fokker-Planck equation standpoint. We describe the relaxation of the distribution function to the steady state Haissinski and resonant solutions.

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Work supported by the Department of Energy, contract DE-AC03-76SF00515.

**Focused Session C-Th2: Particle & Field Simulations**

**C-Th21: ****ADVANCED ELECTRON MULTIPACTOR CODES **
__S. Humphries __and J. Gahl, U of NM, Daniel Rees, LANL

TRAK_RF [1] is a versatile simulation code for charged-particle orbits under the combined influence of electrostatic, magnetostatic and electromagnetic fields. The program was developed to study electron multipacting in high-power accelerators under development for the production of tritium. Field and orbit calculations are performed on a conformal mesh for high accuracy. The RF solution package handles both scattering and resonance solutions with the option for material losses. The code has exhibited good agreement with experiments in simulations of coaxial feeds. We have recently introduced contributions of angular dependence of the secondary emission coefficient (in addition to energy-dependence) for improved modeling of superconducting cavities. We have made progress on a three-dimensional multipactor code with structured mesh. The program has extensive interactive pre- and post-processing capabilities for ease of use. In the coming year we will create a new version of the two-dimensional code that combines particle-in-element techniques with time-domain electromagnetic solutions to model beam dynamics in high-power RF tubes.

[1] S. Humphries, Jr., accepted for publication, Particle Accelerators.

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Work support by Los Alamos National Laboratory under Contract No. DE-FG04-97AL77993.

**C-Th22: ****INVESTIGATIONS OF BEAM INSTABILITIES IN THE COMPRESSION REGION OF GYROTRONS USING KINETIC THEORY AND PARTICLE-IN-CELL SIMULATIONS **
__Stefan Illy __, Edith Borie, ITP-KARLSRUHE

Beam instabilities that arise in the compression zone of a gyrotron oscillator can degrade the beam quality and hence adversely affect the operating characteristics of these devices. We concentrated on a class of space charge instabilities that are related to unstable Bernstein modes. These are investigated both by simulations with a two-and-a-half-dimensional fully electromagnetic particle-in-cell code and by solving the linear dispersion equation (obtained with kinetic theory). Use of the code makes it possible to study effects that cannot be taken into account in the linear dispersion relation, such as the effect of static self-fields. The results of both methods indicate that space charge instabilities can influence the beam quality of gyrotron oscillators. In addition, the simulation strongly suggests that the instability is convective. The dependence of growth rate and frequency spectrum on beam parameters was calculated both with simulation and the analytic method and showed good agreement. A detailed analysis of the electromagnetic fields calculated in the simulation showed that the unstable waves are not, as frequently assumed in the past, purely electrostatic. Inclusion of velocity spread results in a narrowing of the frequency range over which the instability occurs but has little effect on the maximum growth rate at resonance.

**C-Th23: ****CALCULATION OF IMPEDANCE FOR MULTIPLE WAVEGUIDE JUNCTION USING SCATTERING MATRIX FORMULATION**** **
__V.A.Dolgashev __, BINP

A method of computing the electromagnetic characteristics of a complex 3D cavity consisting of series of waveguides with arbitrary cross section is derived. The scattering matrix formulation is used for the simulation. For calculations of modes in waveguide with arbitrary cross sections a finite element code SLANS is applied. The computer code based on the method is used to calculate scattering parameters, dispersion characteristics of periodical structures, resonances, longitudinal and transverse impedances. The method was originally developed for simulations of long range wake fields in accelerator structures and for calculations of RF windows. Advantages of the technology make possible to simulate long open cavities like accelerating structures and complex vacuum chambers. The method and some results are presented.

**C-Th24: ****THE 30 GHZ TRANSFER STRUCTURE FOR THE CLIC STUDY**** **
G. Carron,
__A. Millich __, L. Thorndahl , CERN

In the so-called 'Two-Beam Acceleration Scheme' the energy of a drive beam is converted to RF power by means of a 'Transfer Structure' which plays the role of power source. In the Transfer Structure the bunched drive beam is decelerated by the electromagnetic field which it induces and builds up by the coherent interaction of successive bunches with the chosen longitudinal mode. The CLIC Transfer Structure is original in that it operates at 30 GHz and uses teeth-like corrugations to slow down the hybrid TE mode to make it synchronous with the drive beam. The beam energy is transformed into RF power which travels along the structure and is collected by the output couplers. The 30 GHz RF power is then transported by means of two waveguides to two main linac disk-loaded accelerating structures. This report describes the CLIC Transfer Structure design, 3-D computer simulations, model construction and measurements as well as the prototype construction and testing with the low energy beam in the CLIC Test Facility. The result of this development is a compact, fully passive, relatively simple and low cost device which offers a readily scaleable solution to the problem of RF power extraction from high frequency bunched beams.

**C-Th25: ****FIELD FLATNESS AND NON-STATIONARY BEHAVIOR OF THE 4x7-CELL-TESLA-SUPERSTRUCTURE **
H.-W. Glock, D. Hecht,
__ U. van Rienen __, ROSTOCK U

A structure of 4 coupled 7-cell resonators has been proposed [1] to increase the effective gradient of TESLA. Each so-called "superstructure" is fed through a single input coupler. The sensi tivity of field flatness against geometrical deviations and the time dependence of the fields during fill- and re fill-time are studied by means of MAFIA calculations using an optimized grid. MAFIA results directly calculated of slightly perturbed structures will be compared with those of an analytical approach. Non-stationary fields are expanded in a set of eigenmodes calculated with MAFIA. For a short model the results of this procedure will be compared with fields directly calculated in time-domain.

[1] J. Sekutowicz, M. Ferrario, C. Tang: Superconducting Superstructure; LC97, Sept./Oct. 97, Zvenigorod, Russia

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Work supported in part by DESY

**L-Tu01: ****EFFICCIENT C++ LIBRARY FOR DIFFERENTIAL ALGEBRA **
__Svetlana G. Shasharina, John R. Cary __, TECH-X CORP.

We created a set of C++ classes for methods of the Differential Algebra. By using features of multiplication tables and pointer arithmetic, we achieved a good performance of multiplication of DA vectors: from 2 to 8 times faster than existing C++ codes. Our classes have reference counting for rapid and safe copying and expression templates technique to make addition as fast as hand-coded C.

**L-Tu02: ****A MULTI-PLATFORM GRAPHIC USER INTERFACE FOR THE MARYLIE CHARGED PARTICLE BEAM TRANSPORT CODE**** **
__Michael C. Lampel __, George H. Gillespie, Barrey W. Hill, Hendy C. Martono, John M. Moore, Kyle J. Ryan, GILLESPIE ASSOC., and Alex J. Dragt, U of MD

An advanced graphic user interface (GUI) is being developed for use with the particle optics program MARYLIE. MARYLIE is based on a Lie algebraic formulation of charged particle trajectory calculations and is particularly useful for particle tracking and the analysis of linear and nonlinear lattice properties. The GUI for MARYLIE uses the Multi-Platform Shell for Particle Accelerator Related Codes, a software framework developed specifically to support accelerator modeling and simulation. Transport element icons are selected from a palette and assembled into beamlines by graphical construction. Optical cells and lattices composed of element groups may be defined as sublines and any element or subline can be replicated using an alias element. The icon-based beamlines generate entries for the #beam, #menu, and #lines components of the MARYLIE Master Input File (MIF). Frequent computations, such as creating maps or generating particle distributions, are encapsulated interactive GUI commands which create corresponding entries in the #menu, #lines, and #labor components of the MIF. An icon-based description of procedural processes is being developed to support more complex MARYLIE analysis tasks that utilize the #lumps and #loops components. Progress on the development of this GUI for MARYLIE will be described and the software will be demonstrated.

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Work supported by Department of Energy Grant # DE-FG03-95ER81975

**L-Tu03: ****DESCRIPTION AND SIMULATION OF RHIC USING THE UNIFIED ACCELERATOR LIBRARY (UAL) **
__F. Pilat __, S. Tepikian, C.G. Trahern, BNL, N. Malitsky, CORNELL U

UAL, the Unified Accelerator Library** (1) is an object oriented and modular software environment for accelerator physics which includes an accelerator object model for the description of the machine, a collection of physics libraries and a Perl interface that provides a homogeneous shell for integrating and managing these components. We describe how this environment has been used to build a detailed model of RHIC and present as an application the study of dynamic stability of RHIC in the presence of helical dipoles and other unconventional magnets. Helical dipoles are used in the Siberian Snakes and Spin Rotators necessary to achieve polarized protons in RHIC.

(1) N.Malitsky, R.Talman, "Unified Accelerator Libraries", AIP 391, 1996

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Work supported by the Department of Energy

**L-Tu04: ****THE CERN/SL XDATAVIEWER: AN INTERACTIVE GRAPHICAL TOOL FOR DATA VISUALIZATION AND EDITING **
__Giulio Morpurgo __, CERN

As a result of many years of successive refinements, the CERN/SL Xdataviewer tool has reached its final stage. This graphical tool was especially developed to plot mono- or bi-dimensional arrays of data, and to interact with them, in many different ways. Many pages of graphical information can be handled by the program, in a loose hierarchy of Views, Graphs and Plots objects. Data can be displayed, and interacted with, both in graphical and in text format. Sophisticated built-in Zoom and Data Editing capability is implemented, as well as a flexible Data Output generation facility. A complete C Callable Interface is provided, including a mechanism for feeding back the Application Program with the selections made by the User in the Data Display part. The tool has been written in C language, making use of the standard X Window libraries (Xlib,Xt,Motif). It can be run as a stand alone process, communicating with the Application Program via a shared memory, or it can be embedded in the Application Program itself.

**L-Tu05: ****BEAM MATCHING AND NONLINEAR DELTA-F SIMULATION STUDIES OF HIGH INTENSITY BEAM PROPAGATION IN PERIODIC FOCUSING SYSTEMS **
__Peter H. Stoltz __, Ronald C. Davidson, W. Wei-li Lee, PPPL

This paper makes use of the nonlinear Vlasov-Poisson equations to describe the propagation of an intense, nonneutral ion beam through a periodic focusing solenoidal field in the thin-beam approximation. The nonlinear delta F-formalism is developed for numerical simulation applications by dividing the total distribution function into a zero-order part that propagates through the average focusing field plus a perturbation which evolves nonlinearly in the zero-order and perturbed field configurations. To illustrate the application of the technique to axisymmetric, matched-beam propagation, nonlinear delta F-simulation results are presented for the case corresponding to a thermal equilibrium distribution, and the oscillatory component of the coupling coefficient turns on adiabatically over several periods of the focusing lattice. For high intensity beams, adiabatic turn-on over about twenty lattice periods, the amplitude of the mismatch oscillation is reduced by about one order-of-magnitude compared to the case where the field oscillation is turned on suddenly. Quiescent, matched-beam propagation at high beam intensities is demonstrated over several hundred lattice periods.

**L-Tu06: ****TECHNIQUES FOR ROBUST NONLINEAR DELTA-F SIMULATIONS OF BEAMS**** **
__Alex Friedman __, John J. Barnard, and David P. Grote, LLNL

We describe means by which the range of applicability of delta-f methods (1,2) to beams may be enhanced, so as to faithfully describe a sharp-edged beam or a smooth beam whose edge moves by more than its scale length. As others have done, we follow a population of Lagrangian characteristic "marker" particles in the total (equilibrium plus perturbation) field. However, in contrast with usual practice, our marker distribution is not proportional to the physical particle distribution. We introduce "ghost" particles: a population of markers loaded into regions of phase space where the equilibrium f0 is zero or very small. Following a comment by Aydemir (2) (and in contrast with what we perceive to be common practice), we do not numerically evolve either delta-f or a "weight" w, but rather we use knowledge of the marker positions in phase space and of the functional form of f0 to evaluate delta-f anew at each timestep for each marker. This saves the solution of an ODE for each particle, with its attendant errors and possible timestep constraints. We describe the application of our formalism to the model problem of an oscillating displaced beam.

(1) S. E. Parker and W. W. Lee, Phys. Fluids B 5(1), 77-86 (1993).

(2) A. Y. Aydemir, Phys. Plasmas 1(4), 822-831 (1994).

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Work performed under the auspices of the U.S. Department of Energy by LLNL under contract W-7405-ENG-48.

**L-Tu07: ****DYNAMIC SPACE CHARGE CALCULATIONS FOR HIGH INTENSITY BEAMS IN RINGS **
__J. A. Holmes __, J. D. Galambos, D. Jeon, D. K. Olsen, ORNL,

M. Blaskiewicz, A. U. Luccio, and J. Beebe-Wang, BNL

Space-charge-induced emittance growth and halo generation could lead to unacceptably high beam loss in high intensity rings, such as the SNS. In such accelerators, uncontrolled losses to the walls as small as one part in 10**4 would lead to activation, making maintenance difficult. For this reason it is essential to understand the effects of space charge on beam dynamics, and halo generation in particular, in high intensity rings. We have undertaken the study of space charge dynamics in high intensity rings using a particle tracking approach, with self-consistent evaluation of the space charge forces through a particle-in-cell model. Because of the stringent loss requirements, it is necessary to thoroughly guarantee the reliability of these calculations to high precision through comparison with experiments and through convergence studies. In this paper we present the results of convergence studies in the parameters of the model, namely, the number of macroparticles, the resolution in the adopted FFT algorithm, the smoothing parameter, and the time step size. Although present calculations have been extended to more than 10**5 macroparticles on individual UNIX workstations, it will be necessary to increase another one to two orders of magnitude to obtain the necessary precision. To accomplish this, we are constructing a LINUX parallel computer from low cost components.

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Research on the Spallation Neutron Source is sponsored by the Division of Materials Science, U.S. Department of Energy, under contract number DE-AC05-96OR22464 with Lockheed Martin Energy Research Corporation for Oak Ridge National Laboratory.

**L-Tu08: ****PLASMA COMPENSATION OF BEAM-BEAM INTERACTION IN MUON COLLIDER **
__A.V. Yashin __, K.V. Lotov and A.N. Skrinsky, STANFORD U

One of the major factors limiting the luminosity of future colliders will be electromagnetic interaction of beams in the region of their collision. It's possible to diminish the degree of this interaction by injecting plasma into the colliding region or placing light metal (lithium) there. Prior to this paper the degree of compensation of fields in described method was investigated only in linear approximation and without taking into account focusing of beams by plasma. In this paper plasma compensation is studied in case of arbitrary densities of beams and plasma (nonlinear regime). It is shown that due to nonlinear effects degree of compensation depends on charge of beam particles. Optimal plasma thickness ensuring maximal compensation is found. The degree of compensation for ultimate parameters of muon collider is calculated. Analytical expression for the degree of compensation in the case of finite plasma thickness in linear approximation and criterion for applicability of the linear approximation are obtained.

**L-Tu09: ****MODELING ACCELERATION SCHEDULES FOR A RECIRCULATING HEAVY-ION ACCELERATOR **
__William M. Sharp __and David P. Grote, LLNL

The recent development of miniature inductive adders(1) has made it feasible to design programmable, high-repetition-rate pulsers with a substantially higher voltage than has been achieved using a conventional field-effect transistor (FET) architecture. Prototype pulsers using the new technology are being developed as part of a series experiments at Lawrence Livermore National Laboratory to test the concept of a recirculating induction accelerator. The pulsed-power circuitry originally designed to drive induction modules on this "small recirculator" used a parallel array of FETs with a voltage limit of about 500V to attain the needed precision and repetition rate. The new pulsers are expected to deliver a positive or negative pulse of 1.5KV, and if successful, this technology might lower the cost of the small recirculator by substantially reducing the number of induction modules. One question raised by the higher-voltage pulsers is whether applying larger-amplitude but less-frequent acceleration and control fields will seriously impair beam quality. Here, preliminary numerical work is reported to determine how gradually the head-to-tail velocity variation needed for longitudinal compression must be applied to a beam to avoid the initiation of betatron oscillation at the beam ends. The effects of using between four and thirty-four pulsers are compared using the fluid/envelope code CIRCE, and several schedules for acceleration and compression are examined for each configuration. The phase-space dynamics is also studied for selected schedules using the 3-dimensional particle-in-cell simulation code WARP3d.

(1) Developed by First Point Scientific, Inc.

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This work was performed under the auspices of the U. S. Department of Energy by Lawrence Livermore National Laboratory under contract no. W-7405-ENG-48.

**L-Tu10: ****MAP COMPUTATION FROM MAGNETIC FIELD DATA AND APPLICATION TO THE LHC HIGH GRADIEN T QUADRUPOLES**** **
__M. Venturini __, D. Abell, A. Dragt, U of MD

In many cases the most accurate information about fields in a magnet comes either from direct measurement or from a numerical computation done with a 3D electromagnetic code. In this paper we show how this information can be used to compute transfer maps with high accuracy. The resulting transfer maps take into account all effects of real beamline elements including fringe-field and multipole error effects. The method we employ automatically incorporates the smoothing properties of the Laplace Green function. Consequently, it is robust against both measurement and electromagnetic code errors. As an example, we apply the method to a study of end effects in the High Gradient Quadrupoles for the low-beta insertion in the Large Hadron Collider (LHC). The map computation for the quadrupoles has been carried out using MARYLIE's GENMAP routine and a newly written MARYLIE user-defined routine. For long-term tracking we used Cremona symplectification techniques as implemented in CTRACK.

**L-Tu11: ****FUNCTIONAL DEPENDENCE, BROAD-BAND FITTING, AND ANCILLARY CONDITIONS **
__David C. Carey __, FNAL

The ability to make multiple passes through a charged particle optical system, as a single step in a mathematical procedure, opens up new computational capabilities. At the simplest level, the functional dependence of any transfer matrix of any order, or any beam phase-space parameter can be plotted as a function of any other parameter used to describe the optical configuration. Secondly, broad-band fitting can be done on aberrations, where all orders are considered simultaneously according to their importance on the final phase-space beam distribution. Finally, ancillary conditions may be imposed in the calculation of functional dependences. For example, the dependence of a matrix element on a beam line parameter may be calculated and plotted, subject to constraints imposed on other matrix elements. The computer program TRANSPORT now has these capabilities. Additional examples will be given.

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Operated by Universities Research Association, Inc., under contract with the United States Department of Energy.

**L-Tu12: ****SELECTED MULTITASKING ASPECTS OF FREE ELECTRON LASER (FEL) SIMULATION CODES **
__Roman Tatchyn __, SLAC

In recent years, advancements in parallel computing resources have provided increased opportunities for the development of parallelized, or multitasked, Free Electron Laser (FEL) simulations based on realistic insertion device and particle beam field models. In recent work, for example, a linear undulator model with realistic field errors [1] was developed and incorporated into the 3-D FEL code MEDUSA, initially in serial form [2], and subsequently in an efficiently-parallelized version [3]. In this paper a summary of this work is given and selected aspects of the FEL simulation problem in relation to the development of multitasking codes and hardware architectures are discussed.

[1] R. Tatchyn, T. Cremer, "A fast analytical undulator model for realistic high-energy FEL simulations," NIM A 393, 114(1997).

[2] H. P. Freund, H..-D. Nuhn, R. O. Tatchyn, "Comparative simulations of the 1.5 Angstrom LCLS at SLAC using the non-wiggler-averaged code MEDUSA," SPIE Proceedings 2988, 127(1997).

[3] R. Tatchyn, H. Freund, "Multitasking Development of the MEDUSA 3-D FEL Simulation Code using a Realistic Permanent Magnet Undulator Model," presented at the 18th International FEL Conference, Williamsburg, VA, Aug. 17-21, 1998.

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This work was supported in part by the Department of Energy Offices of Basic Energy Sciences and High Energy and Nuclear Physics, and Department of Energy Contract DE-AC03-76SF00515. Selected calculations utilized resources of the National Energy Research Scientific Computing Center, which is supported by the Office of Energy Research of the U.S. Department of Energy.

**L-Tu13: ****TRANSIENT MAGNETIC FIELD ANALYSIS FOR THE LOCALIZATION OF ELECTRICAL FAULTS IN SUPERCONDUCTING COLLARED COILS**** **
__Piotr Komorowski __, Davide Tommasini , CERN

The follow-up of the construction of superconducting magnets for accelerators re quires a setting up of powerful diagnostic tools to detect weak electrical point s in the superconducting coils at various stages of their fabrication. In partic ular some electrical short circuits well detectable after collaring of the magne t often disappear after the coil is uncollared for repair; therefore it is prefe rable to localize this kind of electrical faults before disassembling the magnet . An R&D work on detection and localization of inter-turn short circuits i s being carried out at CERN in view of the series production of the LHC magnets. The diagnostic methods under study include pulse propagation, time domain refle ctometry and transient magnetic field analysis. In this paper special emphasis i s put on the analysis of the magnetic field distortions created by the short cir cuits during a pulsed discharge. A model of LHC dipole allowing the simulation o f different fault conditions in the coils has been implemented in ROXIE (static case) and in OPERA-2D (transient case). The model has been verified experimental ly on a dedicated short dipole magnet equipped with microswitches to trigger sho rt circuits in different areas of the coils.

**S-Tu14: ****NEW METHOD FOR CALCULATING THE LONGITUDINAL SINGLE-BUNCH STABILITY FOR ELECTRON BEAMS IN STORAGE RINGS **
__Boris Podobedov __and Sam Heifets, SLAC

Longitudinal microwave instability is often one of the limiting factors of storage ring performance. It is important to be able to calculate the threshold, the growth rate and the mode structure for this instability. These quantities are in principle defined by the dispersion relation of the linearized Vlasov equation. The latter, however, generally consists of an infinite system of coupled integral equations and hence is hard to solve. The detailed algorithm for truncation and approximate numerical solution of this system has been recently proposed by K. Oide and K. Yokoya. In this we describe a different algorithm where we transform the problem to a Fredholm equation which does not have double integrals and explicitly includes the single particle trajectories found from the perturbation theory. This gives better computational performance as well as clearer physical understanding of the results.

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Work supported by the Department of Energy contract DE-AC03-76SF00515

**S-Tu15: ****NEW APPROACH FOR CALCULATING THE BEAM DYNAMICS ABOVE THE LONGITUDINAL MICROWAVE INSTABILITY THRESHOLD **
__Boris Podobedov __, Sam Heifets and Robert Siemann, SLAC

Complex beam behavior above the microwave instability threshold has been reported in several experiments. Often the nonlinear stage of the evolution is observed to have two time scales - fast oscillations with some multiple of the synchrotron frequency modulated by a much slower varying envelope. It has been suggested earlier that such a behavior could be attributed to the relaxation oscillation between the two possible stationary solutions of the Fokker-Planck equation which are the Haissinski solution and the resonant solution. In this paper we describe a method for numerical calculation of beam dynamics based on this mechanism. The essence of the method is a repeated solution of the linearized Vlasov equation modifying the slowly varying zeroth fourier component of the distribution function at every step. This modification is defined self-consistently from the single particle hamiltonian with a harmonically varying perturbation caused by the unstable mode of the Vlasov equation.

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Work supported by the Department of Energy contract DE-AC03-76SF00515

**L-Tu16: ****ANALYSIS OF EMITTANCE GROWTH AND COMPLEX IMPEDANCE FOR COHERENT SYNCHROTRON RADIATION SHIELDED BY TWO PARALLEL PLATE**** **
__Ryoichi Hajima __, U of TOYKO

Emittance growth caused by coherent synchrotron radiation (CSR) and noninertial space charge force in magnetic bunch-compressors is a key issue for the design and construction of X-ray FELs. In the present study, a particle tracking code including intra bunch scattering due to CSR and noninertial space charge force is developed. The simulation code enable us to calculate distribution of electrons in full six-dimensional phase space along arbitrary beam transport line and to estimate energy loss and emittance growth arising from CSR force as well as usual space charge effect and aberrations. Calculated energy loss of electron bunch traveling through circular path shielded by two parallel plates shows good agreement with theoretical results from impedance analysis. The relationship between emittance growth and complex impedance is also presented.

**L-Tu17: ****CALCULATION OF EIGENMODES IN SUPERCONDUCTING CAVITIES ON AN APE-100 SUPERCOMPUTE R (SIMD) USING A SOFTWARE INTERFACE TO MAFIA**** **
F. Neugebauer, DESY,
__U. van Rienen__, ROSTOCK U

To design modern accelerators a profound knowledge of eigenmodes of RF-cavities is required. For normal conducting as well as for super conducting cavities MAFIA is a well established tool to determine the eigenmodes by numerical means. However, the 3-dimensional treatment of multi-cell cavities lacks from available computer power on a normal high end workstation. Therefore the present approach uses a parallel SIMD super computer (APE-100) to compute the numerical expensive part of the MAFIA-algorithm. The system matrix, incorporating geometry and material information, is transfered to the APE-100 during a normal MAFIA-session using a command provided by the MAFIA toolkit (MTK). The result of the diagonalization procedure is then read back to the MAFIA host where further data analysis and visualization can be done. As a first example the lowest eigenmodes of a pillbox resonator are computed on the APE-100. The results are compared with the analytic solution and with the results obtained from a usual MAFIA-session on a high end workstation.

**L-Tu18: ****CALCULATION OF THE COUPLING BETWEEN A WAVEGUIDE AND A SINGLE CELL RF CAVITY **
__Derun Li __, R.A. Rimmer and S. Kosta (1), LBNL

We report on calculations of the external Q using the MAFIA code in time domain. Applications of the method to a single cell RF cavity coupled to a rectangular waveguide through an iris on the cavity wall will be presented. Comparisons between the simulation and experimental results are given for a set of different coupling iris apertures. Preliminary results show good agreements between the simulations and the experiments. The method works more efficiently for high Q RF cavities with coupling strenghs close to critical.

(1) Visitor from R.D. University, India

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Work supported by the U.S. Department of Energy under contract DE-AC03-76SF00098.

**L-Tu19: ****INVESTIGATION OF THE IMPEDANCE AND HIGHER ORDER MODE LOSSES FOR PROPOSED BEAM PIPE CONFIGURATIONS FOR THE HERA LUMINOSITY UPGRADE PROJECT**** **
Martin Dohlus,
__Susan Wipf__, DESY

The impedance and wakefield effects and higher order mode losses have been investigated for the Luminosity Upgrade Project at HERA for three regions where only minimal heating can be tolerated. These are two versions of the beam pipe configuration at the interaction region of the experiment Zeus and also for a region where superconducting magnets are to be installed. As the structures are very long (up to 4.9m) it was not possible to calculate all modes up to the cut-off frequency directly, thus long term wake calculations (100nsecs) in the time domain were used to pinpoint potentially dangerous modes. The frequency and band-width information thus obtained could be used to obtain the impedance of these modes in the frequency domain. The calculations were carried out using the MAFIA programs.

**L-Tu20: ****DESIGN OF 2*2 DLDS RF COMPONENTS FOR JLC**** **
__J.Q. Wang __, Y.H. Chin, S. Kazakov, S. Yamaguchi and H. Tsutsui , KEK

We have studied a multi-mode Delay Line Distribution System (DLDS) as the RF power distribution system from klystrons to RF structures for linear colliders. In particular, a 2*2 DLDS has been proposed and studied at KEK for Japan Linear Collider(JLC). It has been proved that the 2*2 DLDS is simple, bus has a good transmission efficiency. We have designed RF components of a basic unit of a DLDS using the High Frequency Structure Simulation (HFSS) code. They include the TE01 extractor, the TE11 to TE01 convertor, and the TE11 to TE12 convertor for TE12 mode. A low power test model for the mode stability experiment in 55m long waveguide in DLDS is being developed. HFSS calculation of the system, which consists of TE01 extractor and TE11 to TE01 convertor, show that the transmission efficiency of each mode is better than 90%. Further study is underway.

**L-Tu21: ****ELECTROMAGNETIC MODELING OF FAST BEAM CHOPPER FOR SNS PROJECT **
__Sergey Kurennoy __, LANL

High current and stringent restrictions on beam losses in the designed linac and storage ring for the Spallation Neutron Source (SNS) require clean and fast - with the rise time from 2% to 98% less than 2.5 ns - beam chopping in its front end, at the beam energy 2.5 MeV. The development of new traveling-wave deflecting current structures, based on meander lines, is discussed. Three-dimensional time-domain computer simulations are used to study transient effects in the chopper and to optimize its design.

**L-Tu22: ****PISCESII: 2.5D RF CAVITY CODE WITH HIGH ACCURACY **
__Y. Iwashita __, KYOTO U

PISCES II calculates any Eigensolutions including dipole, quadrupole and so on, in any axisymmetric cavity with 2.5D Finite Element Method. Dipole and higher multipole solutions are obtained by hybrid elements. A periodic boundary condition can be handled for a long periodic structure. The accuracy of the frequency in a solution obtained from PISCES II is improved by use of higher order elements. The improvement on the Eigenvalue solver reduces the computation time.

**L-Tu23: ****FURTHER DEVELOPMENT OF A FINITE ELEMENT ELECTROMAGNETIC FIELD SOLVER **
__Eric M. Nelson __and Simon J. Cooke (1), LANL

Enhancements and modifications to a finite element electromagnetic field solver will be described. This includes extensions to handle lossy materials and quasi-periodic boundary conditions and to use tetrahedral elements. Test cases will be shown.

(1) Applied Physics Operation, Science Applications International Corporation, McLean VA 22102.

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Work supported by DOE, contract W-7405-ENG-36, and supported by ONR and administered by NRL, contracts N00014-97-C-2076 and N00173-98-MP-00127.

**L-Tu24: ****CONCEPTUAL DESCRIPTION OF A NOVEL FINITE ELEMENT GUN CODE **
__Eric M. Nelson__ and John J. Petillo (1), LANL

Los Alamos National Laboratory, MS B259, Los Alamos, NM 87545

A novel concept for a finite element based gun code is under development. Poisson's equation is solved using the finite element method on an unstructured grid. Curved conducting surfaces are represented well with quadratic elements. The use of such grids affects the ray tracing and charge deposition portions of the gun code. In this concept, rays are traced element by element using local coordinates in each element. Charge deposition involves an integral over ray trajectories (expressed in local coordinates) of linear charge density weighted by the finite element basis functions. The merits (good and bad) of this scheme relative to other schemes are discussed.

(1) Science Applications International Corporation, Suite 130, 20 Burlington Mall Road, Burlington, MA 01803

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Work supported by DOE, contract W-7405-ENG-36, and supported by ONR and administered by NRL, contracts N00014-97-C-2076 and N00173-98-MP-00127.

**L-Tu25: ****OMEGA3P: A PARALLEL EIGENSOLVER FOR MODELING LARGE, COMPLEX CAVITIES **
__Brian McCandless __, Zenghai Li, Vinay Srinivas, Yong Sun and Kwok Ko , SLAC

Omega3P is a parallel distributed-memory implementation of the finite element eigensolver Omega3 developed by SLAC's Numerical Modeling Group as part of the DOE Grand Challenge effort. The code is designed to model large, complex RF cavities with high accuracy that are beyond the capabilities of present-day software running on desktop computers. Omega3P utilizes existing parallel libraries, such as ParMETIS to partition the 3D mesh, and AZTEC to solve the sparse linear system. Communication between processors is handled by the MPI interface. A new hybrid algorithm is implemented to accelerate convergence for the eigenvalues. We will provide Omega3P results from the 512-CPU CRAY-T3E at NERSC on several applications: the NLC Damped and Detuned cell, the SNS RFQ cavity, and the TRISPAL accelerating cavity. Comparison between calculations and measurements on mode frequencies and Q-drop will be presented.

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Work supported by USDOE contract DE-AC03-76SF00515.

**L-Tu26: ****TAU3P: A PARALLEL TIME DOMAIN SOLVER TO SIMULATE LARGE RF STRUCTURES **
__Cho Ng __, Brian McCandless, Vinay Srinivas, Michael Wolf and Kwok Ko , SLAC

As part of the DOE Grand Challenge on Computational Accelerator Physics, the Numerical Modeling Group at SLAC is developing a 3D, time-domain field solver, Tau3P, that is capable of simulating LARGE RF structures with high accuracy. Based on the modified Yee algorithm, the solver utilizes an unstructured grid to model realistic geometries. It implements a broadband, matched waveguide termination so as to determine the transmission properties of a RF structure over a wide frequency range. The code is designed to be portable to MPP platforms (e.g. the CRAY-T3E at NERSC) for large scale simulations. We will present the initial results from calculations using the code in modeling various complex RF components for the NLC.

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Work supported by USDOE contract DE-AC03-76SF00515.

**L-Tu27: ****NUMERICAL METHODS FOR MICROWAVE TUBES SIMULATION **
Ph. Chevalier and
__F. Nataf__, ECOLE POLYTECHNIQUE

The microwaves tubes (Klystrons, travelling wave tubes, ...) are modeled by the Maxwell-Vlasov equations. In order to converge quickly to a periodic solution (amplification of a periodic signal) the solution is sought in the form of a truncated Fourier series in time. The resulting coupled non linear system of equations is solved by a special fixed point method. The frequencies used in tubes are very closed to the cavity resonant cavities. So, the use of the classical fixed point method (Vlasov then Maxwell) implies the computation of ill-posed problems. We propose to use a modified algorithm. We have implicited a part of the dielectric tensor by using approximate models.

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Work supported by Thomson Tube Electronic

**L-Tu28: ****PROGRESS IN PARALLELIZING XOOPIC**** **
__P. J. Mardahl __and J. P. Verboncoeur, UC BERKELEY

XOOPIC [1] (Object Oriented Particle in Cell code for X11-based Unix workstations) is presently a serial 2d 3v particle-in-cell plasma simulation. The present effort focuses on using parallel and distributed processing to optimize the simulation for large problems. The benefits include increased capacity for memory intensive problems, and improved performance for processor-intensive problems. The MPI library enables the parallel version to be easily ported to massively parallel, SMP, and distributed computers. The philosophy employed here is to spatially decompose the system into computational regions separated by 'virtual boundaries', objects which contain the local data and algorithms to perform the local field solve and particle communication between regions. This implementation reduces the impact of the parallel extension on the balance of the code. Specific implementation details such as the hiding of communication latency behind local computation will also be discussed, as well as code features and capabilities.

[1] J. P. Verboncoeur, A. B. Langdon, and N. T. Gladd, ``An object-oriented electromagnetic PIC code.'' Computer Physics Communications 87 (1995) 199-211. Codes available via http://ptsg.eecs.berkeley.edu.

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This work supported in part by AFSOR/AASERT F49620-94-1-0387, AFOSR/MURI F49620-95-1-0253.

**L-Tu29: ****PIC AND ENVELOPE EQUATION SIMULATIONS OF THE LBNL PLASMA LENS EXPERIMENT **
__E. Yu. Backhaus __, J. S. Wurtele, UC BERKELEY R. Govil, W. Leemans, LBNL

The 2D relativistic, fully electromagnetic Particle-in-cell code (XOOPIC) is used to simulate the recent LBNL plasma lens experiment. The experiment is also modeled with the envelope equation which includes the self-consistent evolution of the beam (i.e. "thick lens" effect), effects of nonlinear aberrations and full plasma return currents. (1), (2) The comparison of PIC and envelope equation results is presented, and the validity of the envelope equation is discussed. The finite plasma effect is investigated using the PIC code.

(1) E. Yu. Backhaus, D. Whittum and J. Wurtele, proceedings of 8th workshop on advanced accelerator concepts. (2) R. Govil and W. Leemans, proceedings of 8th workshop on advanced accelerator concepts.

(1) E. Yu. Backhaus, D. Whittum and J. Wurtele, proceedings of 8th workshop on advanced accelerator concepts.

(2) R. Govil and W. Leemans, proceedings of 8th workshop on advanced accelerator concepts.

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Work supported by DOE

**L-Tu30: ****A SIMULATION STUDY OF THERMAL-PHOTON AND RESIDUAL-GAS SCATTERING IN THE NLC BEAM DELIVERY SYSTEM**** **
__I. Reichel __, T. Raubenheimer, P. Tenenbaum, F. Zimmermann , SLAC

Without collisions, the largest contribution to the beam lifetime in LEP is Compton scattering off thermal photons. Even if only a few particles are scattered in a single pass, the potential background generated could make this effect important for the NLC as well. We used a version of the tracking program DIMAD, which was modified at CERN and includes a Monte Carlo simulation for the Compton scattering on thermal photons, to calculate the fraction of scattered particles that are lost and to determine the loss locations. We also studied particle losses due to other scattering processes, such as elastic and inelastic beam-gas scattering. For all these processes, the beneficial effect of additional collimators was investigated. We report the simulation results.

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Work supported by USDOE contract DE-AC03-76SF00515.