Computational Accelerator Physics 2002 Proceedings of the Seventh International Conference on Computational Accelerator Physics, Michigan, USA, 15-18 ... (Institute of Physics Conference Series)

361 Pages·2005·21.6 MB·English

by  M Berz

Computational Accelerator Physics 2002
Proceedings of the Seventh International Conference on
Computational Accelerator Physics
Michigan, USA, 15–18 October 2002
Edited by
Martin Berz and Kyoko Makino
Institute of Physics Conference Series Number 175
Institute of Physics Publishing
Bristol and Philadelphia
Preface

This volume contains selected papers from the Seventh International Computational
Accelerator Physics Conference that took place 15–18 October, 2002 at Michigan State
University. Following a now well established tradition, the meeting succeeded the conference
in Darmstadt in 2000, and in turn will be followed by the conference in St. Petersburg, Russia
in 2004.

For the refereeing of the papers, we would like to acknowledge the help from a group of
sectional editors that assumed responsibility for certain groups of papers based on their
expertise. Their help was essential for the thorough refereeing and reviewing of the papers.
We would like to thank Bela Erdelyi, Alfredo Luccio, Stephan Russenschuck, Ursula van
Rienen, and Thomas Weiland for assuming responsibility of this important task.

The meeting would not have been possible without help from various sources. We are
grateful for financial support from the US Department of Energy, as well as from Tech-X and
Accel, who as representatives from the commercial world helped defray travel expenses of
graduate students who otherwise may not have been able to attend the meeting. Substantial
support was also provided by the MSU College of Natural Science and the Department of
Physics and Astronomy; specifically, we thank Lorie Neuman and Brenda Wenzlick for their
enthusiasm, professionalism, and seemingly never-ending patience.

Kyoko Makino and Martin Berz
Other titles in the series
The Institute of Physics Conference Series regularly features papers presented at
important conferences and symposia highlighting new developments in physics and
related fields. Previous publications include:
182 Light Sources 2004
Papers presented at the 10th International Symposium on the Science and Technology
of Light Sources, Toulouse, France
Edited by G Zissis
180 Microscopy of Semiconducting Materials 2003
Papers presented at the Institute of Physics Conference, Cambridge, UK
Edited by A G Cullis and P A Midgley
179 Electron Microscopy and Analysis 2003
Papers presented at the Institute of Physics Electron Microscopy and Analysis Group
Conference, Oxford, UK
Edited by S McVitie and D McComb
178 Electrostatics 2003
Papers presented at the Electrostatics Conference of the Institute of Physics,
Edinburgh, UK
Edited by H Morgan
177 Optical and Laser Diagnostics 2002
Papers presented at the First International Conference, London, UK
Edited by C Arcoumanis and K T V Grattan
174 Compound Semiconductors 2002
Papers presented at the 29th International Symposium on Compound
Semiconductors, Lausanne, Switzerland
Edited by M Ilegems, G Weimann and J Wagner
173 GROUP 24: Physical and Mathematical Aspects of Symmetries
Papers presented at the 24th International Colloquium, Paris, France
Edited by J-P Gazeau, R Kerner, J-P Antoine, S Métens and J-Y Thibon
172 Electron and Photon Impact Ionization and Related Topics 2002
Papers presented at the International Conference, Metz, France
Edited by L U Ancarani
171 Physics of Semiconductors 2002
Papers presented at the 26th International Conference, Edinburgh, UK
Edited by A R Long and J H Davies
Contents
Preface v
Persistent currents in superconducting filaments due to arbitrary field changes in the
transverse plane
M Aleksa, B Auchmann, S Russenschuck and C Völlinger 1
A simple parallelization of a FMM-based serial beam-beam interaction code
P M Alsing, V Boocha, M Vogt, J Ellison and T Sen 13
Accuracy analysis of a 2D Poisson-Vlasov PIC solver and estimates of the collisional
effects in space charge dynamics
A Bazzani, G Turchetti, C Benedetti, A Franchi and S Rambaldi 25
The COSY language independent architecture: porting COSY source files
L M Chapin, J Hoefkens and M Berz 37
Simulation issues for RF photoinjectors
E Colby, V Ivanov, Z Li and C Limborg 47
Enhancements to iterative inexact Lanczos for solving computationally large finite
element eigenmode problems
J F DeFord and B L Held 57
New numerical methods for solving the time-dependent Maxwell equations
H De Raedt, J S Kole, K F L Michielsen and M T Figge 63
Beam simulation tools for GEANT4 (and neutrino source applications)
V D Elvira, P Lebrun and P Spentzouris 73
Muon cooling rings for the ν factory and the µ+ µ- collider
Y Fukui, D B Cline, A A Garren and H G Kirk 83
Status of the Los Alamos Accelerator Code Group
R W Garnett 91
3D space-charge model for GPT simulations of high-brightness electron bunches
S B van der Geer, O J Luiten, M J de Loos, G Pöplau and U van Rienen 101
S-parameter-based computation in complex accelerator structures: Q-values and field
orientation of dipole modes
H-W Glock, K Rothemund, D Hecht and U van Rienen 111
viii
AHF booster tracking with SIMPSONS
D E Johnson and F Neri 121
Parallel simulation algorithms for the three-dimensional strong-strong beam-beam
interaction
A C Kabel 131
A parallel code for lifetime simulations in hadron storage rings in the presence of
parasitic beam-beam interactions
A C Kabel and Y Cai 143
Using macroparticles with internal motion for beam dynamics simulations
M Krassilnikov and T Weiland 151
The software ModeRTL for simulation of radiation processes in electron beam
technologies
V T Lazurik, V M Lazurik, G F Popov, Yu V Rogov 161
Computational aspects of the trajectory reconstruction in the MAGNEX large
acceptance spectrometer
A Lazzaro, A Cunsolo, F Cappuzzello, A Foti, C Nociforo, S Orrigo, V Shchepunov,
J S Winfield and M Allia 171
Study of RF coupling to dielectric loaded accelerating structures
W Liu, C Jing and W Gai 181
On the map method for electron optics
Z Liu 185
Aspects of parallel simulation of high intensity beams in hadron rings
A U Luccio and N L D’Imperio 193
High-order beam features and fitting quadrupole-scan data to particle-code models
W P Lysenko, R W Garnett, J D Gilpatrick, J Qiang, L J Rybarcyk, R D Ryne,
J D Schneider, H V Smith, L M Young and M E Schulze 203
Muon beam ring cooler simulations using COSY INFINITY
C O Maidana, M Berz and K Makino 211
Solenoid elements in COSY INFINITY
K Makino and M Berz 219
Experience during the SLS commissioning
M Muñoz, M Böge, J Chrin and A Streun 229
Tracking particles in axisymmetric MICHELLE models
E M Nelson and J J Petillo 235
ix
Beam dynamics problems of the muon collaboration: ν-factories and µ+-µ- colliders
D Neuffer 241
Simulation of electron cloud multipacting in solenoidal magnetic field
A Novokhatski and J Seeman 249
RF heating in the PEP-II B-factory vertex bellows
A Novokhatski and S Weathersby 259
Optimization of RFQ structures
A D Ovsiannikov 273
A multigrid based 3D space-charge routine in the tracking code GPT
G Pöplau, U van Rienen, M de Loos and B van der Geer 281
On the applicability of the thin dielectric layer model for wakefield calculation
S Ratschow, T Weiland and I Zagorodnov 289
COSY INFINITY’s EXPO symplectic tracking for LHC
M L Shashikant, M Berz and B Erdélyi 299
ORBIT: Parallel implementation of beam dynamics calculations
A Shishlo, V Danilov, J Holmes, S Cousineau, J Galambos, S Henderson 307
Vlasov simulation of beams
E Sonnendrücker and F Filbet 315
Space charge studies and comparison with simulations using the FNAL Booster
P Spentzouris, J Amundson, J Lackey, L Spentzouris and R Tomlin 325
Progress in the study of mesh refinement for particle-in-cell plasma simulations and
its application to heavy ion fusion
J-L Vay, A Friedman and D P Grote 333
_
Calculation of transversal wake potential for short bunches
I Zagorodnov and T Weiland 343
Author Index 353
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Published by Institute of Physics Publishing, wholly owned by the Institute of Physics, London
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Inst. Phys. Conf. Ser. No 175 1
Paper presented at 7th Int. Conf. Computational Accelerator Physics, Michigan, USA, 15–18 October 2002
©2004 IOPPublishing Ltd
Persistent Currents in Superconducting Filaments
Due to Arbitrary Field Changes in the Transverse Plane
MartinAleksa,BernhardAuchmann,
StephanRussenschuck,ChristineVo¨llinger
Abstract. Magnetic field changes in the coils of superconducting magnets are shielded
from the filaments’ core by so-called persistent currents which can be modeled by means
ofthecriticalstatemodel.Thispaperpresentsansemi-analytical2-dimensionalmodelofthe
filamentmagnetizationduetopersistentcurrentsforchangesofthemagnitudeofthemagnetic
inductionanditsdirectionwhiletakingthefielddependenceofthecriticalcurrentdensityinto
account.Themodeliscombinedwithnumericalfieldcomputationmethods(couplingmethod
betweenboundaryandfiniteelements)forthecalculationoffielderrorsinsuperconducting
magnets. The filament magnetization and the field errors in a nested multipole corrector
magnethavebeencalculatedasanexample.
1.Introduction
The Large Hadron Collider (LHC) [6], a proton-proton superconducting accelerator, will
consistofabout8400superconductingmagnetunitsofdifferenttypes,operatinginsuper-fluid
heliumatatemperatureof1.9K.Theappliedmagneticfield changesinducecurrentsinthe
filaments thatscreentheexternalfield changes(so-calledpersistentcurrents). Thefilaments
are made of type II hard superconducting material with the property that the magnetic
field penetrates into the filaments with a gradient that is proportional to the magnitude
of the persistent currents. Macroscopically, these currents (that persist due to the lack of
resistivityiffluxcreepeffectsareneglected)arethesourceofamagnetization ofthe
superconductingstrands. Onewaytocalculatethismagnetizationwouldbetomeshthecoil
withfinite elementsandsolvetheresultingnon-linearfield problemnumericallybymaking
useofameasured -curve.Thisapproachhastwomaindrawbacks:Thenumericalfield
computationhasto becombined with ahysteresismodel forhard superconductors, andthe
coil has to be discretizedwith highestaccuracy also accountingfor theexisting gradientof
thecurrentdensityduetothetrapezoidalshapeofthecables,theconductoralignmentonthe
windingmandrel,andtheinsulationlayers.Hence,weaimedforcomputationalmethodsthat
avoidthemeshingofthecoilbycombiningasemi-analyticalmagnetizationmodelwiththe
BEM-FEMcouplingmethod[5].
Inthestraightsectionofacceleratormagnetsthemagneticinductionisalmostperpendicularto
thefilament axis.Theeffectofamagneticinductionparalleltoasuperconductingfilament is
small(see[11])andhasthereforebeenneglectedhere.Amodeltocalculatethemagnetization
of the superconducting strands is presented, considering external fields that change their
magnitudeanddirection. Forthispurpose,themodelintroducedin[1]hasbeenextendedto
accountforfilament magnetizationsnon-paralleltotheoutsidefield. Asin[1],themodeldoes
notattempttodescribethemicroscopicfluxpinning,butappliesthecriticalstatemodel[2]
which states that any external field change is shielded from the filament’s core by layers
of screening currents at critical density . The model differs from other attempts to
describe a superconducting filament’s response to arbitrary field changes in the transverse
2
g
planeas, e.g., in[8]. It takesintoaccountthedependenceofthecriticalcurrentdensityon
theappliedexternalfiel andtheresultingfield distributioninthefilament cross-section. Asa
consequence,alsolowfield effectssuchasthepeak-shifting(asymmetryinthemagnetization
curveforvanishingexternalfield) arereproducedbythemodel.
Thedescribedmodeliscombinedwiththecoupledboundaryelement/finite elementmethod
(BEM-FEM)[5]whichavoidstherepresentationofthecoilinthefinite elementmeshsince
the coil is located in theiron-free BEM domain. The fields arising from current sources in
thecoilarecalculatedbymeansoftheBiot-Savartlaw,whilethesurroundingferromagnetic
ironyokehastobemeshedwithfinite elements. Hence,thediscretizationerrorsduetothe
finite-element partintheBEM-FEMformulationarelimitedtotheiron-magnetizationarising
fromtheyokestructure. Inordertoaccountforthefeed-backofthefilament magnetization
onthemagneticfield, an -iterationisperformed.
The magnetization model is based on the input function of the critical current
density, which represents the material properties of the superconductor, but is independent
of geometrical parameters such as the filament diameter or shape and the ratio of the
superconductor to total strand volume. The method reproduces the hysteretic behavior for
arbitraryturningpointsinthemagnet’sexcitationalcycleincludingminorloopsandrotating
externalfields.
2.The1-dimensionalmagnetizationmodel
Forabetterunderstandingofthemagnetizationmodel,letusfirst considerafield changeof
theform where and isthenominalfield strengthinsomedirection
perpendiculartotheaxisofacircularsuperconductingfilament, whichweshallcalla1-
dimensional field change. This field change induces a shielding-current layer of a relative
thickness called therelativepenetrationdepth, see Fig. 1. Itis measured onthescale of
the relative penetration parameter that is zero on the outside and one in the center of the
filament. Thecurrentsaredirectedastocreateamagneticinductionthatopposestheapplied
field changeontheconductorsurface,thusshieldingthefield changefromthefilament’score.
Thethicknessofthelayerdependsontheamplitudeoftheappliedfield sweep,onthefilament
radius,andonthecriticalcurrentdensityinthesuperconductingmaterial.
The generation of a shielding field can be modeled by the perfectly uniform dipole field
produced by two intersecting circles with opposite current densities shifted by the relative
distance ,
(1)
where istheshieldingfield, isthefilament radiusand aretherelativepenetration
parametersthatlimit theshieldingcurrentlayer,[3]. Such pairsofcirclesarenestedinside
concentric circles. This equation will later be used to find a differential equation for the
differential shielding . In Fig. 1 these nested pairs of circles are represented with
finite thickness, notwithstanding the continuous nature of the mathematical model, which
will be introduced in Sec. 3.1. Figure 1 (left) shows the cross-section of a filament after a
1-dimensional change of the external field from to . The nested circles each shield
a fraction of the outside field from the inside, thus increasing in the inner circles, as
represented in Fig. 1 (left bottom diagram). The figure also yields a vector representation
of the 1-dimensional field change and the corresponding shielding effect. The vector
indicates theshieldingmagnetic inductionasa functionofthe penetrationfromtheoutside
( ),where and ,totheinnerboundaryoftheshieldinglayer
3
g
(cid:3)(cid:4) (cid:6) (cid:2)(cid:3)(cid:4) (cid:6)
(cid:2)
(cid:13)(cid:14) (cid:15) (cid:13)(cid:16) (cid:15) (cid:8) (cid:8)
(cid:1) (cid:6)
(cid:5) (cid:5)
(cid:5) (cid:3)(cid:4) (cid:1) (cid:7) (cid:5) (cid:3)(cid:4)(cid:1) (cid:7)
(cid:8) (cid:8)
(cid:1) (cid:2) (cid:1) (cid:2) (cid:1) (cid:2) (cid:1) (cid:2)
(cid:13)(cid:10) (cid:15) (cid:13)(cid:17) (cid:15)
(cid:6)(cid:12)
(cid:11)
(cid:1) (cid:11) (cid:1)
(cid:8) (cid:6)(cid:12) (cid:7) (cid:6)(cid:12) (cid:8) (cid:6) (cid:1)
(cid:9) (cid:5)
(cid:10)
(cid:13)(cid:18) (cid:15) (cid:8) (cid:7) (cid:8) (cid:6) (cid:1)
(cid:9) (cid:5)
(cid:10)
(cid:8) (cid:6)(cid:12) (cid:7) (cid:6)(cid:12) (cid:6)
(cid:8) (cid:7) (cid:6)
Figure1. Circularsuperconductingfilamentinamagneticinduction offixeddirection,
fordifferentpenetrationstates. Theindividualgraphscontain: (a)Aschematicviewofthe
circularfilamentwithinscribedpairsofcircles. Orangecolorsindicatepositivecurrentsin
-direction,bluecolorsindicatenegativecurrents.Thecolorintensityrepresentstheabsolute
valueofthecurrentsatcriticaldensity ;(b)The componentofthemagnetic
inductionovertherelativepenetrationparameter ;(c)The componentof over ;(d)
Thevectorrepresentationoftheshieldingprobleminthe -plane; and denotethe
externalfieldvector andtheshieldingfieldvectoratpenetration , ,respectively;(e)
Theshieldingcurrentsatcriticaldensity inthecross-section.Left:Penetrationto
arelativepenetrationdepthof .Right:Fullpenetration( ).
( ),where .Theabsolutevalueof dependsinanon-linear
wayonthepenetrationparameter (see -relationinEq.(6)andontheappliedfield
change.
TherighthandsideofFig.1showsthesituationwherealargerfield changeisappliedtothe
filament surface.Theentirecross-sectioncontainsshieldingcurrentsofcriticaldensitywhich
are, however,unabletocompletelyshieldthefield fromtheinside. Thefield hasthusfully
penetrated the filament ( ). In the vector representation, points from the induction
at the filament surface to the value of the induction at the center of the filament
.
Fig.2(left)showsthecasewherethemagneticinductionoutsidethefilament isrampedupto
(previouslydenoted )andsubsequentlyreducedto . Anewlayerofshielding
currentsisgenerated,leavingtheremaininginnerlayersuntouched. Thenewfield changeis
again shielded from the filament’s core. The shielding vector is now to oppose the
new field change. It further has to fulfill continuity requirements on the outer ( ) and
innerboundaryofthenewcurrentlayer( ):
(2)
(3)