Particle Detection with Drift Chambers (Particle Acceleration and Detection)

456 Pages·2008·11.88 MB·English

by  Walter Blum

Particle Detection with Drift Chambers
Particle Acceleration and Detection
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· ·
Walter Blum Werner Riegler Luigi Rolandi
Particle Detection
with Drift Chambers
123
WalterBlum WernerRiegler
MPIfu¨rPhysik CERN
Werner-Heisenberg-Institut 1211Geneve23
Fo¨hringerRing6 Switzerland
80805Mu¨nchen [email protected]
Germany
[email protected]
LuigiRolandi
CERN
1211Geneve23
Switzerland
[email protected]
ISBN:978-3-540-76683-4 e-ISBN:978-3-540-76684-1
LibraryofCongressControlNumber:2007940836
(cid:2)c 2008Springer-VerlagBerlinHeidelberg
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Preface to the First Edition
Adriftchamberisanapparatusformeasuringthespacecoordinatesofthetrajectory
ofachargedparticle.Thisisachievedbydetectingtheionizationelectronsproduced
bythechargedparticleinthegasofthechamberandbymeasuringtheirdrifttimes
andarrivalpositionsonsensitiveelectrodes.
Whenthemultiwireproportionalchamber,or‘Charpakchamber’asweusedto
callit,wasintroducedin1968,itsauthorshadalreadynotedthatthetimeofasignal
couldbeusefulforacoordinatedetermination,andfirststudieswithadriftcham-
berweremadebyBressani,Charpak,RahmandZupancˇicˇ in1969.Whenthefirst
operational drift-chamber system with electric circuitry and readout was built by
Walenta,HeintzeandSchu¨rleinin1971,anewinstrumentforparticleexperiments
hadappeared.Abroadstudyofthebehaviourofdriftingelectronsingasesbeganin
laboratorieswheretherewasinterestinthedetectionofparticles.
Diffusionanddriftofelectronsandionsingaseswereatthattimewell-established
subjects in their own right. The study of the influence of magnetic fields on these
processes was completed in the 1930s and all fundamental equations were con-
tained in the article by W.P. Allis in the Encyclopedia of Physics [ALL56]. It
did not take very long until the particle physicists learnt to apply the methods of
theMaxwell–Boltzmannequationsandoftheelectron-swarmexperimentsthathad
been developed for the study of atomic properties. The article by Palladino and
Sadoulet [PAL75] recorded some of these methods for use with particle-physics
instruments.
F.SauligaveanacademictrainingcourseatCERNin1975/76,inordertoinform
agrowingnumberofusersofthenewdevices.Hepublishedlecturenotes[SAU77],
whichwereamajorsourceofinformationforparticlephysicistswhobegantowork
withdriftchambers.
When the authors of this book began to think about a large drift chamber for
theALEPHexperiment,werealizedthattherewasnosingletexttointroduceusto
thosequestionsaboutdriftchambersthatwouldallowustodeterminetheirultimate
limits of performance. We wanted to have a text, not on the technical details, but
on the fundamental processes, so that a judgement about the various alternatives
for building a drift chamber would be on solid ground. We needed some insight
v
vi PrefacetotheFirstEdition
into the consequences of different geometries and how to distinguish between the
behaviour of different gases, not so much a complete table of their properties. We
wantedtounderstandonwhattrajectoriestheionizationelectronswoulddrifttothe
proportionalwiresandtowhatextentthetrackswouldchangetheirshape.
Pathstotheliteraturewerealsorequired–justafewessentialones–sothatan
entrypointtoeveryimportantsubjectexisted;theywouldnothavetobeacompre-
hensivereviewof‘everything’.
In some sense we have written the book that we wanted at that time. The text
also contains a number of calculations that we made concerning the statistics of
ionization and the fundamental limits of measuring accuracy that result from it,
geometrical fits to curved tracks, and electrostatics of wire grids and field cages.
SeveralexperimentsthatweundertookduringtheconstructiontimeoftheALEPH
experimentfoundtheirwayintothebook;theydealmainlywiththedriftanddiffu-
sionofelectronsingasesundervariousfieldconditions,butalsowiththestatistics
oftheionizationandamplificationprocesses.
Thebookisnonethelessincompleteinsomerespects.Weareawarethatitlacks
achapteronelectronicsignalprocessing.Alsosomeofthecalculationsarenotyet
backedupindetailbymeasurementsastheywilleventuallyhavetobe.Especially
theparameterN oftheionizationprocesswhichgovernstheachievableaccuracy
eff
shouldbeaccuratelyknownandsupportedbymeasurementswithinterestinggases.
We hope that workers in this field will direct their efforts to such questions. We
wouldwelcomecommentsaboutanyotherimportantomissions.
It was our intention to make the book readable for students who are interested
in particle detectors. Therefore, we usually tried to explain in some detail the ar-
gumentsthatleaduptoafinalresult.Onemaysaythatthebookrepresentsacross
betweenamonographandanadvancedtextbook.Thosewhorequireacompendious
catalogueofexistingorproposeddriftchambersmayfindusefultheproceedingsof
thetriannualViennaWireChamberConferences[VIE]oroftheannualIEEESym-
posiaonInstrumentationforNuclearScience[IEE].
Partsofthematerialhavebeenpresentedinsummerschoolsandguestlectures,
andwethankH.D.Dahmen(HerbstschuleMariaLaach),E.Fernandez(Universita
Autonoma,Barcelona)andL.Bertocchi(ICTP,Trieste)fortheirhospitality.
We thank our colleagues from the ALEPH TPC group, and especially J. May
andF.Ragusa,formanystimulatingdiscussionsontheissuesofthisbook.Weare
alsoobligedtoH.Spitzer(Hamburg)whoreadandcommentedonanearlyversion
of the manuscript. Special thanks are extended to Mrs. Heininger in Munich who
producedmostofthedrawings.
Geneva W.Blum
1April1993 L.Rolandi
Preface to the Second Edition
Thefirsteditionhascontinuouslyservedmanystudentsandresearchersinthefield.
Now we have enlarged and improved the book, essentially in three ways: (1) The
chapter on electronic signal processing was added, and (2) the chapter on the cre-
ation of the signal was rewritten and based on the principle of current induction.
This was made possible because our team was complemented with a new young
co-author(W.R.).(3)Alsotherearevariousmodernizationsthroughoutthebookin-
cludingsomeoftherecentchamberscapabletomeasuretracksatveryhighfluences
thatonecouldnotimagine15yearsago.Fourofthechapterswereleftuntouched.
Thedevelopmentofdriftchambersinthelast15yearswasdrivenbytheideathat
theirperformanceshouldbepushedtowardsthelimitsofthelawsofphysics.The
concept of the book matches very well this trend because it is the basic principles
ofdriftchambersratherthantheirtechnicaldesignsolutionsthatareinfocus.The
mostmoderndesignsolutions,amongthemtheonesdevelopedfortheexperiments
of the Large Hadron Collider, can be found e.g. in the proceedings of the IEEE
Symposia[IEE]andoftheViennaWireChamberConferences[VIE].
During the last two decades, the development and optimization of drift cham-
bershasincreasinglyreliedonsimulationprograms,whichinsomesense’encode’
thephysicsprocessesdescribedinthisbook.TheprogramGARFIELD,writtenby
Rob Veenhof, is the most widely used tool for drift chamber simulation. It allows
calculation of electric fields, electron and ion drift lines, induced signals, electro-
staticwiredisplacementsandmanymorefeaturesofdriftchambers.Forcalculation
oftheprimaryionizationoffastparticlesingases,theprogramHEED,writtenby
Igor Smirnov, is widely used. A very popular program for calculation of electron
transport properties in different gas mixtures is the program MAGBOLTZ, writ-
tenbySteveBiagi.MAGBOLTZandHEEDaredirectlyinterfacedtoGARFIELD,
whichthereforeallowsacompletesimulationofthedriftchamberprocesses,from
thepassageofthechargedparticletothedetectoroutputsignal.Clearlyathorough
understanding of driftchambers, which issubject of thisbook, isanecessary pre-
conditionforefficientuseofthesesimulationprograms.
Despite the development of the fine grained silicon detectors which now out-
perform the wire chambers near the interaction point, the large detector volumes
vii
viii PrefacetotheSecondEdition
surrounding modern experiments have to rely on drift chambers because of their
simplicity and also because their measurement accuracy in relation to their size is
better than it is in any other instrument. Time Projection Chambers with electron
drift lengths up to 2.5m are the most important tools for studying heavy ion col-
lisions, because of their very low material budget, channel number economy and
particle identification capabilities. TPCs are also studied as principle detectors for
futureelectroncolliders.36yearsafterthefirstworkingdriftchamber,theseinstru-
mentsarestillgoingstrong.
Geneva W.Blum
April2008 W.Riegler
L.Rolandi
References
[ALL56] W.P.Allis,Motionsofionsandelectrons,inHandbuchderPhysik,ed.byS.Flu¨gge
(Springer,Berlin1956)Vol.XXI,p.383
[IEE] Thesymposiaareusuallyheldinthefallofeveryyearandarepublishedinconsec-
utivevolumesoftheIEEETransactionsinNuclearScienceinthefirstissueofthe
followingyear
[PAL75] V.PalladinoandB.Sadoulet,Applicationofclassicaltheoryofelectronsingasesto
driftproportionalchambers,Nucl.Instrum.Methods128,323(1975)
[SAU77] F.Sauli,Principlesofoperationofmultiwireproportionalanddriftchambers,Lec-
turesgivenintheacademictrainingprogrammeofCERN1975–76(CERN77-09,
Geneva1977),inExperimentalTechniquesinHighEnergyPhysics,ed.byT.Ferbel
(Addison-Wesley,MenloPark1987)
[VIE] The Vienna Wire Chamber Conferences were held in February of the years 1978,
1980,1983,1986,1989,1992,1995,1998,2001,2004,2007,andtheywerepublished
mostlythesameyearsinNuclearInstrumentsandMethodsinthefollowingvolumes:
135,176,217,A252,A283,A323,A367,A419,A478,A535.Since2001they
arecalled ViennaConferenceonInstrumentation.
Contents
1 GasIonizationbyChargedParticlesandbyLaserRays ............ 1
1.1 GasIonizationbyFastChargedParticles ....................... 1
1.1.1 IonizingCollisions................................... 1
1.1.2 DifferentIonizationMechanisms ....................... 3
1.1.3 AverageEnergyRequiredtoProduceOneIonPair ........ 4
1.1.4 TheRangeofPrimaryElectrons........................ 7
1.1.5 TheDifferentialCross-sectiondσ/dE................... 7
1.2 CalculationofEnergyLoss .................................. 9
1.2.1 ForceonaChargeTravellingThroughaPolarizableMedium 9
1.2.2 ThePhoto-AbsorptionIonizationModel................. 11
1.2.3 BehaviourforLargeE................................ 15
1.2.4 Cluster-SizeDistribution.............................. 15
1.2.5 IonizationDistributiononaGivenTrackLength .......... 16
1.2.6 VelocityDependenceoftheEnergyLoss ................ 24
1.2.7 TheBethe–BlochFormula ............................ 29
1.2.8 EnergyDepositedonaTrack–RestrictedEnergyLoss .... 32
1.2.9 LocalizationofChargeAlongtheTrack ................. 35
1.2.10 AMeasurementofN ............................... 37
eff
1.3 GasIonizationbyLaserRays ................................ 38
1.3.1 ThenthOrderCross-SectionEquivalent ................. 38
1.3.2 RateEquationsforTwo-PhotonIonization ............... 39
1.3.3 DependenceofLaserIonizationonWavelength........... 42
1.3.4 Laser-BeamOptics................................... 44
References..................................................... 46
2 TheDriftofElectronsandIonsinGases.......................... 49
2.1 AnEquationofMotionwithFriction .......................... 49
2.1.1 CaseofENearlyParalleltoB ......................... 52
2.1.2 CaseofEOrthogonaltoB ............................ 52
2.2 TheMicroscopicPicture..................................... 53
2.2.1 DriftofElectrons .................................... 53
ix
x Contents
2.2.2 DriftofIons ........................................ 56
2.2.3 InclusionofMagneticField ........................... 64
2.2.4 Diffusion .......................................... 67
2.2.5 ElectricAnisotropy .................................. 70
2.2.6 MagneticAnisotropy ................................. 72
2.2.7 ElectronAttachment ................................. 75
2.3 ResultsfromtheCompleteMicroscopicTheory ................. 79
2.3.1 DistributionFunctionofVelocities...................... 79
2.3.2 Drift ............................................... 81
2.3.3 InclusionofMagneticField ........................... 82
2.3.4 Diffusion ........................................... 83
2.4 Applications............................................... 83
2.4.1 Determinationofσ(ε)andλ(ε)fromDriftMeasurement .. 83
2.4.2 Example:Argon–MethaneMixture ..................... 85
2.4.3 Experimental Check of the Universal Drift Velocity
forLargeωτ........................................ 88
2.4.4 AMeasurementofTrackDisplacementasaFunction
ofMagneticField.................................... 89
2.4.5 AMeasurementoftheMagneticAnisotropyofDiffusion... 89
2.4.6 Calculated and Measured Electron Drift Velocities
inCrossedElectricandMagneticFields ................. 92
References..................................................... 94
3 ElectrostaticsofTubes,WireGridsandFieldCages................ 97
3.1 PerfectandImperfectDriftTubes............................. 98
3.1.1 PerfectDriftTube.................................... 99
3.1.2 DisplacedWire...................................... 99
3.2 WireGrids ................................................105
3.2.1 The Electric Field of an Ideal Grid of Wires Parallel
toaConductingPlane ................................105
3.2.2 Superposition of the Electric Fields of Several Grids
andofaHigh-VoltagePlane ...........................108
3.2.3 Matching the Potential of the Zero Grid and of the
ElectrodesoftheFieldCage ...........................110
3.3 AnIonGateintheDriftSpace................................112
3.3.1 CalculationofTransparency ...........................113
3.3.2 Setting of the Gating Grid Potential with Respect
totheZero-GridPotential .............................118
3.4 FieldCages ...............................................118
3.4.1 TheDifficultyofFreeDielectricSurfaces................119
3.4.2 IrregularitiesintheFieldCage .........................121
References.....................................................124