In this paper we present results of using parallel supercomputers to simulate
beam dynamics in next-generation high intensity ion linacs. Our approach uses a
three-dimensional space charge calculation with six types of boundary
conditions. The simulations use a hybrid approach involving transfer maps to
treat externally applied fields (including rf cavities) and parallel
particle-in-cell techniques to treat the space-charge fields. The large-scale
simulation results presented here represent a three order of magnitude
improvement in simulation capability, in terms of problem size and speed of
execution, compared with typical two-dimensional serial simulations. Specific
examples will be presented, including simulation of the spallation neutron
source (SNS) linac and the Low Energy Demonstrator Accelerator (LEDA) beam halo
experiment

Qiang, Ji

Ryne, Robert D.

English

arXiv

Ryne, Robert D

eScholarship - University of California

Large-Scale Simulation of Beam Dynamics in High Intensity Ion Linacs Using Parallel Supercomputers

In this paper we present results of using parallel supercomputers to simulate beam dynamics in next-generation high intensity ion linacs. Our approach uses a three-dimensional space charge calculation with six types of boundary conditions. The simulations use a hybrid approach involving transfer maps to treat externally applied fields (including rf cavities) and parallel particle-in-cell techniques to treat the space-charge fields. The large-scale simulation results presented here represent a three order of magnitude improvement in simulation capability, in terms of problem size and speed of execution, compared with typical two-dimensional serial simulations. Specific examples will be presented, including simulation of the spallation neutron source (SNS) linac and the Low Energy Demonstrator Accelerator (LEDA) beam halo experiment

RYNE, R.

QIANG, J.

UNT Digital Library

,‘A~~(j039’?l..-TITLE:AUTHOR(S):SUBMITTED .TO:LosNAT IONA LAhmimslLABORATORYLARGE-SCALE SIMULATION OF BEAM DYNAMICS IN HIGHINTENSITY ION LINACS USING PARALLELSUPERCOMPUTERSRobert D. RyneJi Qian.gLINAC 2000 ConferenceMonterey, CaliforniaAugust 21-25,2000LANSCE-ILANSCE-1Los Alamos National Laboratory, an affirmative action/equal opportunity employer, is operated by the University of California for the U.S. Department of Energyunder contract W-7405-ENG-36. By acceptance of this article, the publisher recognizes that the U.S. Government retains a nonexclusive, royalty-free ficense topublish or reproduce the published form of this contribution, or to allow othera to do so, for U.S. Government purposes. The Los Alamos National Laboratoryrequests that the publisher identify this article as work performed under the auspices of the U.S. Department of Energy.FomI NO. S36 R53T26XI 10/91DISCLAIMERThis report was prepared as an account of work sponsoredby an agency of the United States Government. Neitherthe United States Government nor any agency thereof, norany of their employees, make any warranty, express orimplied, or assumes any legal liability or responsibility forthe accuracy, completeness, or usefulness of anyinformation, apparatus, product, or process disclosed, orrepresents that its use would not infringe privately ownedrights. Reference herein to any specific commercialproduct, process, or service by trade name, trademark,manufacturer, or otherwise does not necessarily constituteor impiy its endorsement, recommendation, or favoring bythe United States Government or any agency thereof. Theviews and opinions of authors expressed herein do notnecessarily state or refiect those of the United StatesGovernment or any agency thereof.DISCLAIMERPortions of this document may be illegiblein electronic image products. Images areproduced from the best available originaldocument.>(.,LARGE-SCALE SIMULATION OF BEAM DYNAMICS IN HIGHINTENSITY ION LINACS USING PARALLEL SUPERCOMPUTERS*f~,~@~~~@BRobert D. Ryne and Ji Qiang, LANL, Los Alarnos, NM 87545, USADEC f 32Nl#lAbstractIn this paper we present results of using parallel supercom-puters to simulate beam dynamics in next-generation highintensity ion linacs. Our approach uses a three-dimensionalspace charge calculation with six types of boundary con-ditions. The simulations use a hybrid approach involvingtransfer maps to treat externally applied fields (includingrf cavities) and parallel particle-in-cell techniques to treatthe space-charge fields. The large-scale simulation resultspresented here represent a three order of magnitude im-provement in simulation capability, in terms of problemsize and speed of execution, compared with typical two-dimensional serial simulations. Specific examples will bepresented, including simulation of the spallation neutronsource (SNS) linac and the Low Energy Demonstrator Ac-celerator (LEDA) beam halo experiment.1 INTRODUCTIONThe high intensity of future accelerator-driven systemsplaces stringent requirements on the allowed beam loss,since very small fractional losses at high energy can pro-duce unacceptably high levels of radioactivity. Previousstudies suggest that the low density, large amplitude haloof the beam is a major issue for these systems [1, 2, 3].Large-scale simulations are an important tool for exploringthe beam dynamics, predicting the beam halo, and facilitat-ing design decisions aimed at controlling particle loss andmeeting operational requirements.The most widely used model for simulating intensebeams in ion rf linacs is represented by the Poisson-Vlasov equations. These equations are often solved us-ing a particle-in-cell (PIC) approach. In this paper we willdescribe a parallel simulation capability that combines thePIC method with techniques from magnetic optics, and wewill present results of using parallel supercomputers to sim-ulate beam dynamics in high intensity ion rf linacs.2 PHYSICAL MODEL ANDNUMERICAL METHODSIn the PIC approach a number of simulation particles,called macroparticles, are used to solve (indirectly) the evo-lution equations and model the charged particle dynamics.The motion of individual particles in the absence of radia-“ Work supported by the DOE Grand Challenge in Computational Ac-celerator Physics, Adwnced Computing for 21st Century AcceleratorScience and Technology Project, and the Los Alamos Aeeelerator CedeGroup using resources at the Advanced Computing Laboratory and theNational Energy Research Scientific Computing Center.tion can be described by Hamilton’s equations,- ----df dH d$ tlH—== ,z = –lIf’qljs ‘ndt 8pwhere H(1, I?,t) denotes the Hamiltonian of the system,and where ~ and F denote canonical coordinates and mo-menta, respectively. In the language of nrappirrgs we wouldsay that there is a (generally nordinear) map, M, corre-sponding to the Hamiltonian H, which maps initial phasespace variables, (i, into final variables, (f, and we write(f= J/@. (2)The potential in the Hamiltonian includes contributionsfrom both the external fields and the space-charge fields. Inthe Poisson-V1asov approach, discreteness effects are ne-glected and the space charge is represented by a smoothlyvarying mean field. TWically, the Hamiltonian can be writ-ten as a sum of two parts, H = H.zt + H8C, which corre-spond to the external and space-charge contributions. Sucha situation is ideally suited to multi-map symplectic split-operator methods [4]. A second-order-accurate algorithmfor a single step is given byM(T) = MI (7/2) M2(T) MI (7/2) , (3)where T denotes the step size, M 1 is the map correspond-ing to ll~zt and M2 is the map corresponding to H*C. Thisapproach can be easily generalized to higher order accuracyusing Yoshida’s scheme if desired [5].The electrostatic scalar potential generated by thecharged particles is obtained by solving Poisson’s equationV2V(r) = –p(r)/co. (4)where p is the charge density. We have developed aFourier-based transformation and an eigenfunction expan-sion method to handle six different boundary conditions:(1) open in all three dimensions; (2) open transversely andperiodic longitudinally; (3,4) round conducting pipe trans-versely and open or periodic longitudinally; (5,6) rectangu-lar conducting pipe transversely and open or periodic lon-gitudinally. A discussion of the numerical algorithms forsolving the Poisson’s equation with these different bound-ary conditions can be found in [8J.The charge density p on the grid is obtained by usinga volume-weighted linear interpolation scheme[6, 7]. Af-ter the potential and electric field is found on the grid, thesame scheme is used to interpolate the field at the particlelocations. During the course of the simulation each step in-volves the following: transport of a numerical distributionof particles through a half step based on M 1, solving Pois-son’s equation based on the particle positions and perform-ing a space-charge “kick” Mz, and performing transportthrough the remaining half of the step based on MI..3 APPLICATIONSWe have applied the above 3D parallel PIC approach to anearly design of the SNS linac and to the proposed LEDAbeam halo experiment. Our simulation of the SNS Iinacstarts at the beginning of the DTL. The code advances par-ticles through drift spaces, quadrupole fields and RF gaps.The dynamics inside the gaps is computed using externalfields calculated from the electromagnetic code SUPER-FISH [9], A schematic plot of the SNS Iinac configurationused in this study is shown in Figure I [10]. It consists ofthree types of RF structures: a DTL, a CCDTL, and a CCL.There are a total of 425 RF segments in the Iinac. Figure 2shows the rms transverse size (ZrmS,~rm~) and the maxi-mum transverse extent (zmQZ,ymoz) of the bunched beamin the linac with one set of errors. We see that the maxi-mum particle amplitude is well-below the aperture size ofthe linac. This margin is needed to operate the linac safelyand to avoid beam 10SSat the high energy end. The jumpin rms beam size between the DTL and CCDTL at 20 MeVis due to a change of focusing period from 8@Ato 12~A at805 MHz.‘T’;’pa%6QIJ2 Zpm805 MHz / I i‘“’sMHz /~ /— 12 p). lattice period —Figure 1: The SNS linac configuration2.5 -A *.,5,., --—Xmw —Y.. —Xmax —.,n,,.x2 -1~“-----””””’~r—–1,5 JI0 m m 24!4 em IcaK!r,eli Energy(M9v)Figure 2: Transverse beam size as a function of kinetic en-ergy in the SNS linacIn the LEDA beam halo experiment, a mismatchedhigh-intensity proton beam will be propagated through aperiodic focusing transport system and measurements willbe made of the beam profile. The goals of the experimentare two-fold: first, to study beam halo formation and testour physical understanding of the phenomena, and second,to evaluate our computational models and assess their pre-dictive capability through a comparison of simulation andexperiment. Fig. 3 gives a schematic plot of the layout ofthe experiment [11]. It consists of 52 alternating-focusingquadruple magnets with a focusing period of 41,96 cm.The gradients of the first four quadruple magnets can beadjusted to create a mismatch that excites the breathingmode or the quadruple mode. The transverse beam profilewill be measured using a beam-profile scanner. Fig. 4 andFig. 5 present simulation results of the transverse beam sizefor the breathing mode and the quadruple mode, plottedat the center of the drift spaces between quadruple mag-nets, as a function of distance. The plots include both therms beam size and the maximum particle extent in the sim-ulation. The physical parameters for the simulation were1=100 mA, E=6.7 MeV, and f=350 MHz. The simula-tion was performed using 100 million macroparticles witha 128x128x256 (x-y-z) space-charge grid.52 quadmpole FOOO IatiiceRFQ-? Ws Ws Ws w% Ws Ws Ws Ws WsEFigure 3: LEDA halo experiment layout‘1 ‘‘ Y.% —Xm --x--v% -*R0.2010 2 4 e 8 10 12dim”ca [m)Figure 4: Transverse beam size as a function of distancefor the breathing mode in the LEDA halo experimentFrom Fig. 4, the two transverse components of thebreathing mode are in phase, while the quadruple modein Fig. 5 has the two components out of phase. Evidently,it will be possible in the experiment to clearly excite ei-ther of the two modes. Furthermore, the debunching ofthe beam will not significantly alter the structure of the os-ciilations. Fig. 6 shows the accumtdated one-dimensional*1X.* —Yrn!s ------Xlnax -.+.Yn!a-e-0.8 -0 2 4 e 8 10Ois!a.ca (.]Figure 5: Transverse beam size as a timction of distancefor the quadruple mode in the LEDA halo experiment#wJo7COLW0e’WWzW@Xo4W3009WW0ZWWzlC.WX“ihatmg MYA —Ouad. pale * -------0../,,,,/I-am .o.mx 4.(04 4,W2 0 o.c02 0,034 0.W6 O.c@sx (cm)Figure 6: Accumulated density profile along z for thebreathing mode and the quadruple modedensity profiles (along $) for the breathing mode and thequadruple mode just after the magnet #49. The breath-ing mode is more peaked and has a larger extent than thequadruple mode. Measurements will be taken at this loca-tion. and will be compared with our simulations. The datain Fig. 6 are well-resolved over a range of about 6 decades.An important piece of information from a design stand-point is amount of charge beyond a specified radius or spa-tial location as a function of distance along the accelerator.This is shown graphically in Fig. 7 which shows the com-plement of the horizontal and vertical cumulative densityprofiles, at every step, when the quadruple mode is ex-cited. In other words, the contours describe the fraction ofcharge that would be intercepted by a scraper placed at thattransverse position.The above LEDA simulations used 100 millionmacroparticles and a 3D Poisson solver, and required only2 hours to execute on 256 processors. In contrast, beamdynamics simulations performed on serial computers typi-cally use 10,000 to 100,000 macroparticles and a 2D Pois-son solver. Even if the above large-scale calculations couldbe performed on a PC, they would require on the order of amonth to complete. In conclusion, while small-scale simu-100 million particle simulation of the LEDA halo experiment.Cumulative distributions of quadruple mode oscillations.1.0-L .001234~1.0-L .001234 5s 8 9 LoIccgikdii @h Z [m) 7Figure 7: Horizontal and vertical cumulative density pro-files of a quadruple mode mismatch in the LEDA haloexperiment.lations on serial computers are extremely valuable for rapiddesign and predicting rms properties, large-scale simula-tions are needed for high-resolution studies aimed at mak-ing quantitative predictions of the beam halo.4 ACKNOWLEDGMENTSWe thank the SNS Iinac design team and the LEDA beamhalo experiment team for helpful discussions. We alsothank S. Habib for helpful discussions and C. Thomas Mot-tershead for graphics support.[1][2][3][4][5][6][7][8][9]5 REFERENCESR. L. Gluckstem, Phys. Rev. Lett. 73, 1247 (1994),T. P.Wangler, K. R. Crandall, R. Ryne, and T. S. Wang, Phys.Rev. ST Accel. Beams 1,084201 (1998).J. Qiang and R. D. Ryne, Phys. Rev. ST. Accel. Beams 3,064201(2000).E. Forest et at., Phys. I,ett. A 158,99 (1991).H. Yoshida, Phys. Lett. A 150,262 (1990).R. W, Hockney and J. W. Eastwood, Computer SimulationUsing Particles, Adam Hilger, New York, 1988.C. K. Birdsall and A. B. Langdon, Plasma Physics Via Com-puter Simulation, McGraw-Hill Book Company, NY, 1985.J. Qiang and R. Ryne, “High Performance Particle-In-CellSimulation in a Proton Linac: to be submitted to PRST-AB.J. H. Billen and L. M. Young, “POISSON SUPERFISH’,LANL Report LA-UR-96-1834 (revised Jan. 8, 2000).[10] T. Bhatia et al,, “Beam Dynamics Design for the l-GeV 2-MW SNS Linac~’ LANL Report LA-UR-99-3802, 1999.[11] T. WangIer, “LEDA Beam Hato Experiment-Physics andConcept of the experiment;’ LA-UR-00-3181, 2000,

LARGE-SCALE SIMULATION OF BEAM DYNAMICS IN HIGH INTENSITY ION LINACS USING PARALLEL SUPERCOMPUTERS

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Large-Scale Simulation of Beam Dynamics in High Intensity Ion Linacs Using Parallel Supercomputers

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