CERN Accelerator School Magnets

494 Pages·2010·28.43 MB·English

CERN–2010–004
30November2010
ORGANISATION EUROP(cid:131)ENNE POUR LA RECHERCHE NUCL(cid:131)AIRE
CERN
EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH
CERN Accelerator School
Magnets
Bruges, Belgium
16–25 June 2009
Proceedings
Editor: D. Brandt
GENEVA
2010
ISBN978–92–9083–355-0
ISSN 0007–8328
Copyright c CERN,2010
(cid:13)
CreativeCommonsAttribution3.0
KnowledgetransferisanintegralpartofCERN’smission. CERNpublishesthisreportOpenAccessunderthe
CreativeCommonsAttribution3.0license(http://creativecommons.org/licenses/by/3.0/)inorder
topermititswidedisseminationanduse.
Thisreportshouldbecitedas:
ProceedingsoftheCAS–CERNAcceleratorSchool: Magnets,Bruges,Belgium,16–25June2009,
editedbyD.Brandt,CERN-2010-004.
Acontributioninthisreportshouldbecitedas:
[Authorname(s)],inProceedingsoftheCAS–CERNAcceleratorSchool: Magnets,Bruges,Belgium,
16–25June2009,editedbyD.Brandt,CERN-2010-004,pp. [firstpage]–[lastpage]
Abstract
These proceedings present the lectures given at the twenty-third specialized course organized by the CERN
Accelerator School (CAS), the topic being ‘Magnets’. The course was held in Bruges, Belgium, from 16 to
25 June 2009. This is the first time this topic has been selected for a specialized course. Taking into account
thenumberofrelatedapplicationscurrentlyinuseinacceleratorsaroundtheworld,but,evenmoreimportant,
the worrying decrease in the corresponding expertise in the different laboratories, it was recognized that such
a topic should definitively be incorporated into the CAS series of specialized courses. The specific aim of the
course was to introduce the participants to the basics of resistive magnet design and its underlying theoretical
concepts.
ThefirstpartoftheschooldealtwithbasicintroductorycoursessuchasMaxwell’sequationsformagnets,
beamoptics,physicsandmeasurementofmagneticmaterials,thedifferenttypesofresistivemagnetsandtheir
respective performance, an introduction to numerical field computation, and a core lecture on basic magnet
design.
The second part of the course focused more on quality control, the different measurement systems with
their electronics, calibration techniques and respective applications as well as the question of stability and
reproducibility.
For the first time, in addition to the actual lectures, a Case Study was proposed to the participants. This
consistedofeighthoursofaguidedpracticalexercise, wheretheparticipantshadtoproposetheirowndesign
for a magnet fulfilling the boundary conditions corresponding to a combined-function magnet developed for
theALBASynchrotronLightSourceinBarcelona,Spain. ThisCaseStudywasenthusiasticallyreceivedbythe
participants, who praised both the proposed approach and the amount of practical information acquired from
thisexercise.
iii
iv
Foreword
The aim of the CERN Accelerator School (CAS) to collect, preserve, and disseminate the knowledge ac-
cumulated in the world’s accelerator laboratories applies not only to general accelerator physics, but also to
relatedsub-systems,equipment,andtechnologies. Thiswideraimisachievedbymeansofspecializedcourses.
The topic of the 2009 course was Resistive Magnets and was held at the Novotel Brugge Centrum, Bruges,
Belgium,from16to25June2009.
Thiswasthefirsttimethat‘ResistiveMagnets’wasthetopicofaCASspecializedcourse. Themotivation
forselectingthistopicwastwofold: first,resistivemagnetsrepresentanessentialcomponentofanyaccelerator
and, secondly, a slow but constant decrease in the existing expertise in the different laboratories was a clear
indicationoftheneedforsuchtraining.
The present course was made possible by the active collaboration provided by the firm IBA (Louvain-la-
Neuve, Belgium) and many individuals. In particular, the contributions of the Local Organizing Committee
composed of Micheline Desmedt (IBA) and Dirk Vandeplassche (SCK-CEN) were most valuable. Similarly,
thehelpofLouisWalckiers(CERN)inidentifyingcontactstoproposepossiblevenueswashighlyappreciated.
The generous financial support provided by Dr. Yves Jongen (IBA Chief Research Officer Managing Di-
rector) allowed CAS to offer scholarships to highly deserving young students, who would not have been able
toattendtheschoolotherwise.
Asfarasthecourseisconcerned,itisworthmentioningthat,forthefirsttimeatCAS,a‘CaseStudy’was
proposed to the participants. It consisted of eight hours of a guided practical exercise, where the participants
had to propose their own solution for the design of a magnet fulfilling the boundary conditions corresponding
to a combined-function magnet developed for the ALBA Synchrotron Light Source in Barcelona, Spain. This
Case Study proved to be extremely successful and similar practical approaches will certainly be considered
for future specialized courses. The impressive success of the Case Study is most definitely related to the
outstanding contributions of our colleagues Dieter Einfeld (ALBA- CELLS) and Davide Tommasini (CERN)
whoinvestedsomuchenergyandenthusiasminpreparing,running,andevaluatingtheexercise.
As always, the backing of the CERN management, the guidance of the CAS Advisory and Programme
Committees, the attention to detail of the Local Organizing Committee and the management and staff of the
NovotelBruggeCentrumensuredthattheSchoolwasheldunderoptimumconditions. Specialthanksmustgo
tothelecturersforthepreparation,presentation,andwritingupoftheirtopics.
Finally,theenthusiasmoftheparticipantswhocamefrommorethan20differentcountrieswasconvincing
proofoftheusefulnessandsuccessofthecourse.
It is my pleasure and privilege to thank all those persons who helped in making the course a success,
includingBarbaraStrasserandtheCERNDesktopPublishingServicefortheirdedicationandcommitmentto
theproductionofthisdocument.
DanielBrandt
CERNAcceleratorSchool
v
Thursday 25 June Manufacturing & Calibration of Measurement Systems II M. Buzio Hall Probes: Physics, Measurements & Applications S. Sanfilippo Stability & Reproducibility N. Marks Case Study: Summing Up
Tuesday Wednesday 23 June 24 June Metrology & Coils and Wires Alignment I A. Lestrade L. Walckiers Dielectric Electronics for nsulation & High Measurement Voltage Issues Systems I I D. Tommasini P. Arpaia C O F F E E Metrology & Alignment II A. Lestrade Case Study III Dielectric nsulation & High Voltage Issues II D. Tommasini L U N C H Harmonic Coils L. Walckiers Case Study II Electronics for Measurement Systems II P. Arpaia T E A Seminar Manufacturing & Medical Calibration of Applications Measurement Systems I Y. Jongen M. Buzio DinnerDinner
I I

GRAMME Magnets ne 2009, Bruges, Belgium Sunday Monday 21 June 22 June Permanent Magnets including Wigglers & Undulators III J. Bahrdt Specification & Quality Control, Manufacturing & E Acceptance Test I X D. Einfeld C Specification & Quality Control, U Manufacturing & Acceptance Test II R D. Einfeld S Introduction Case Study I O D. Einfeld/ D. Tommasini N Case Study I Exhibition Dinner Dinner
PRO16-25 JuSaturday 20 June Injection & xtraction Magnets I M. Barnes Permanent Magnets including Wigglers & Undulators I J. Bahrdt Injection & xtraction Magnets II M. Barnes Permanent Magnets including Wigglers & Undulators II J. Bahrdt Solenoids A. Dael Seminar An Accelerator Driven System: MYRRHA D. Vandeplassche Discussion Session Special Dinner
E E

Thursday Friday 18 June 19 June Overview of Magnetic Field Measurement Computations Methods using FEM L. Bottura S. Russenschuck Beam Optics Basic Magnet II Design III D. Brandt T. Zickler C O F F E E Physics & Basic Magnet Measurements of Design Magnetic Materials IV III S. Sgobba T. Zickler Magnet Types & SC Magnets Performances I II A. Dael L. Bottura L U N C H Foundation of SC Magnets Numerical Field II Computation II S. Russenschuck L. Bottura Basic Magnet Eddy Currents Design I T. Zickler G. Moritz T E A Basic Magnet Discussion Design Introduction II T. Zickler Dinner Dinner

Wednesday 17 June Maxwell Equations for Magnets I A. Wolski Beam Optics I D. Brandt Maxwell Equations for Magnets II A. Wolski Physics & Measurements of Magnetic Materials I S. Sgobba Magnet Types & Performances I A. Dael Foundation of Numerical Field Computation I S. Russenschuck Physics & Measurements of Magnetic Materials II S. Sgobba Welcome Drink Dinner
Time 08:30 09:30 10 :30 11:00 12:00 12:00 13:00 14:30 15:30 15:30 16:30 17:00 18:00 20:00

vi
Contents
Foreword
D.Brandt ...................................................................................... v
Maxwell’sequationsformagnets
A.Wolski ....................................................................................... 1
Physicsandmeasurementsofmagneticmaterials
S.Sgobba ..................................................................................... 39
Basicdesignandengineeringofnormal-conducting,iron-dominatedelectromagnets
Th. Zickler .................................................................................... 65
Eddycurrentsinacceleratormagnets
G.Moritz .................................................................................... 103
Injectionandextractionmagnets: kickermagnets
M.J.Barnes,L.Ducimetière,T.Fowler,V.Senaj,L.Sermeus ...................................... 141
Injectionandextractionmagnets: septa
M.J.Barnes,J.Borburgh,B.Goddard,M.Hourican ............................................. 167
Permanentmagnetsincludingundulatorsandwigglers
J.Bahrdt ..................................................................................... 185
Specifications,qualitycontrol,manufacturing,andtestingofacceleratormagnets
D.Einfeld .................................................................................... 231
Dimensionalmetrologyandpositioningoperations: basicsforaspatiallayoutanalysisofmeasurement
systems
A.Lestrade ................................................................................... 273
Dielectricinsulationandhigh-voltageissues
D.Tommasini ................................................................................ 335
Magneticmeasurementwithcoilsandwires
L.Walckiers .................................................................................. 357
Fabricationandcalibrationofsearchcoils
M.Buzio ..................................................................................... 387
Hallprobes: physicsandapplicationtomagnetometry
S.Sanfilippo .................................................................................. 423
Magnetstabilityandreproducibility
N.Marks ..................................................................................... 463
ListofParticipants .............................................................................. 485
vii

Maxwell’s equations for magnets
A.Wolski
UniversityofLiverpool,Liverpool,UKandtheCockcroftInstitute,Daresbury,UK
Abstract
Magnetostatic fields in accelerators are conventionally described in terms of
multipoles. We show that in two dimensions, multipole fields do provide so-
lutions of Maxwell’s equations, and we consider the distributions of electric
currents and geometries of ferromagnetic materials required (in idealized sit-
uations) to generate specified multipole fields. Then, we consider how to de-
termine the multipole components in a given field. Finally, we show how the
two-dimensional multipole description may be extended to three dimensions;
this allows fringe fields, or the main fields in such devices as undulators and
wigglers,tobeexpressedintermsofasetofmodes,whereeachmodeprovides
asolutiontoMaxwell’sequations.
1 Maxwell’sequations
Maxwell’sequationsmaybewrittenindifferentialformasfollows:
divD~ = ρ, (1)
divB~ = 0, (2)
∂D~
curlH~ = J~+ , (3)
∂t
∂B~
curlE~ = . (4)
− ∂t
The fields B~ (magnetic flux density) and E~ (electric field strength) determine the force on a particle of
chargeq travellingwithvelocity~v (theLorentzforceequation):
F~ = q E~ +~v B~ .
×
(cid:16) (cid:17)
TheelectricdisplacementD~ andmagneticintensityH~ arerelatedtotheelectricfieldandmagneticflux
densityby
D~ = εE~,
B~ = µH~.
The electric permittivity ε and magnetic permeability µ depend on the medium within which the fields
exist. Thevaluesofthesequantitiesinvacuumarefundamentalphysicalconstants. InSIunits:
µ0 = 4π 10−7Hm−1,
×
1
ε = ,
0 µ c2
0
wherecisthespeedoflightinvacuum. Thepermittivityandpermeabilityofamaterialcharacterizethe
response of that material to electric and magnetic fields. In simplified models, they are often regarded
as constants for a given material; however, in reality the permittivity and permeability can have a com-
plicated dependence on the fields that are present. Note that the relative permittivity ε and the relative
r
permeabilityµ arefrequentlyused. Thesearedimensionlessquantities,definedby
r
ε µ
ε = , µ = . (5)
r r
ε µ
0 0
1
A. WOLSKI
Thatis,therelativepermittivityisthepermittivityofamaterialrelativetothepermittivityoffreespace,
andsimilarlyfortherelativepermeability.
The quantities ρ and J~ are respectively the electric charge density (charge per unit volume) and
electriccurrentdensity(J~ ~nisthechargecrossingunitareaperpendiculartounitvector~nperunittime).
·
Equations (2) and (4) are independent of ρ and J~, and are generally referred to as the ‘homogeneous’
equations;theothertwoequations,(1)and(3)aredependentonρandJ~,andaregenerallyreferredtoas
the ‘inhomogeneous’ equations. The charge density and current density may be regarded as sources of
electromagneticfields. Whenthechargedensityandcurrentdensityarespecified(asfunctionsofspace,
and,generally,time),onecanintegrateMaxwell’sequations(1)–(3)tofindpossibleelectricandmagnetic
fields in the system. Usually, however, the solution one finds by integration is not unique: for example,
the field within an accelerator dipole magnet may be modified by propagating an electromagnetic wave
through the magnet. However, by imposing certain constraints (for example, that the fields within a
magnetareindependentoftime)itispossibletoobtainauniquesolutionforthefieldsinagivensystem
ofelectricchargesandcurrents.
MostrealisticsituationsaresufficientlycomplicatedthatsolutionstoMaxwell’sequationscannot
be obtained analytically. A variety of computer codes exist to provide solutions numerically, once the
charges,currents,andpropertiesofthematerialspresentareallspecified,see,forexample,Refs.[1–3].
Solving for the fields in realistic (three-dimensional) systems often requires a reasonable amount of
computingpower; somesophisticatedtechniqueshavebeendevelopedforsolvingMaxwell’sequations
numerically with good efficiency [4]. We do not consider such techniques here, but focus instead on
the analytical solutions that may be obtained in idealized situations. Although the solutions in such
casesmaynotbesufficientlyaccuratetocompletethedesignofarealacceleratormagnet,theanalytical
solutions do provide a useful basis for describing the fields in real magnets, and provide also some
importantconnectionswiththebeamdynamicsinanaccelerator.
An important feature of Maxwell’s equations is that, for systems containing materials with con-
stant permittivity and permeability (i.e., permittivity and permeability that are independent of the fields
present), the equations are linear in the fields and sources. That is, each term in the equations involves
a field or a source to (at most) the first power, and products of fields or sources do not appear. As a
consequence, theprincipleofsuperpositionapplies: ifB~ andB~ aresolutionsofMaxwell’sequations
1 2
withthecurrentdensitiesJ~ andJ~ ,thenthefieldB~ = B~ +B~ willbeasolutionofMaxwell’sequa-
1 2 T 1 2
tions, withthesourcegivenbythetotalcurrentdensityJ~ = J~ +J~ . Thismeansthatitispossibleto
T 1 2
representcomplicatedfieldsassuperpositionsofsimplerfields. Animportantandwidelyusedanalysis
technique for accelerator magnets is to decompose the field (determined from either a magnetic model,
orfrommeasurementsofthefieldinanactualmagnet)intoasetofmultipoles. Whileitisoftentheideal
toproduceafieldconsistingofasinglemultipolecomponent,thisisneverperfectlyachievedinpractice:
themultipoledecompositionindicatestheextenttowhichcomponentsotherthanthe‘desired’multipole
arepresent. Multipoledecompositionsalsoproduceusefulinformationformodellingthebeamdynam-
ics. Although the principle of superposition strictly only applies in systems where the permittivity and
permeabilityareindependentofthefields,itisalwayspossibletoperformamultipoledecompositionof
the fields in free space (e.g., in the interior of a vacuum chamber), since in that region the permittivity
and permeability are constants. However, it should be remembered that for nonlinear materials (where
thepermeability,forexample,dependsonthemagneticfieldstrength),thefieldinsidethematerialcom-
prising the magnet will not necessarily be that expected if one were simply to add together the fields
correspondingtothemultipolecomponents.
SolutionstoMaxwell’sequationsleadtoarichdiversityofphenomena,includingthefieldsaround
chargesandcurrentsincertainsimpleconfigurations,andthegeneration,transmissionandabsorptionof
electromagnetic radiation. Many existing texts cover these phenomena in detail; see, for example, the
authoritative text by Jackson [5]. Therefore, we consider only briefly the electric field around a point
chargeandthemagneticfieldaroundalongstraightwirecarryingauniformcurrent: ourmainpurpose
2
2