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Calorimetry I Electromagnetic Calorimeters 6.1 Allgemeine Grundlagen Funktionsprinzip – 1

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Calorimetry I Electromagnetic Calorimeters 6.1 Allgemeine Grundlagen Funktionsprinzip – 1 Calorimetry I Electromagnetic Calorimeters 6.1 Allgemeine Grundlagen Funktionsprinzip – 1 !IntroductionIn der Hochenergiephysik versteht man unter einem Kalorimeter einen Detektor, welcher die zu analysierenden Teilchen vollständig absorbiert. Da- durch kann die Einfallsenergie des betreffenden Teilchens gemessen werden. Calorimeter: ! Die allermeisten Kalorimeter sind überdies positionssensitiv ausgeführt, um dieDetector Energiedeposition for energy measurement ortsabhängig via total absorption zu messen of particles und sie ... beim gleichzeitigen DurchgangAlso: most calorimeters von mehreren are position Teilchen sensitive den to measure individuellen energy depositionsTeilchen zuzuordnen. depending on their location ... ! Ein einfallendes Teilchen initiiert innerhalb des Kalorimeters einen Teilchen- schauerPrinciple of (eine operation: Teilchenkaskade) aus Sekundärteilchen und gibt so sukzessive seineIncoming ganze particle Energie initiates and particle diesen shower Schauer ... ab. DieShower Zusammensetzung Composition and shower dimensions und die depend Ausdehnung on eines solchen SchauersSchematic ofhängen vonparticle der type Art and des detector einfallenden material ... Teilchens ab (e±, Photon odercalorimeter Hadron). principle Energy deposited in form of: heat, ionization, particle cascade (shower) excitation of atoms, Cherenkov light ... Different calorimeter types use different kinds of theseBi lsignalsd rec toh tmeasures: Gro totalbes energy Sch e...ma incident particle Important:eines Teilchenschauers in einem (homogenen) Kalorimeter Signal ~ total deposited energy detector volume [Proportionality factor determined by calibration] M. Krammer: Detektoren, SS 05 Kalorimeter 2 Introduction Energy vs. momentum measurement: σ 1 σ Calorimeter: E Gas detector: p p [see below] E ⇠ pE [see above] p ⇠ e.g. ATLAS: e.g. ATLAS: σE 0.1 σp 4 5 10− pt E ⇡ pE p ≈ · · i.e. σE/E = 1% @ 100 GeV i.e. σp/p = 5% @ 100 GeV At very high energies one has to switch to calorimeters because their resolution improves while those of a magnetic spectrometer decreases with E ... Shower depth: E Calorimeter: L ln Shower depth nearly energy independent [see below] ⇠ Ec i.e. calorimeters can be compact ... [Ec: critical energy] Compare with magnetic spectrometer: σp/p p/L2 Detector size has to grow quadratically to maintain⇠ resolution Introduction Further calorimeter features: Calorimeters can be built as 4π-detectors, i.e. they can detect large for small θ particles over almost the full solid angle ⇥ 2 ⇥ 2 ⇥ 2 Magnetic spectrometer: anisotropy due to magnetic field; remember: ( p/p) =( pt/pt) +( θ/sin θ) Calorimeters can provide fast timing signal (1 to 10 ns); can be used for triggering [e.g. ATLAS L1 Calorimeter Trigger] Calorimeters can measure the energy of both, charged and neutral particles, if they interact via electromagnetic or strong forces [e.g.: γ, μ, Κ0, ...] Magnetic spectrometer: only charged particles! Segmentation in depth allows separation of hadrons (p,n,π±), from particles which only interact electromagnetically (γ,e) ... ... Electromagnetic Showers Reminder: Dominant processes at high energies ... Photons : Pair production Electrons : Bremsstrahlung X0 Pair production: 7 2 2 183 Bremsstrahlung: ⇥pair 4 αre Z ln 1 ⇡ 9 Z 3 ✓ ◆ 2 dE Z 2 183dE E 7 A =4αNA r E ln = = [X0: radiation length] e 1 2 dx A · Zdx3 X0 9 NAX0 [in cm or g/cm ] Absorption x/X0 coefficient: ➛ E = E0e− NA 7 ρ After passage of one X0 electron µ = n⇥ = ρ ⇥pair = has only (1/e)th of its primary energy ... A · 9 X0 [i.e. 37%] Abbildung 8.2: Entwicklung eines elektromagnetischen Sch • Nur die Prozesse werden ber • Electromagnetic ShowersAuf derAnalytic Strecke Shower Model Electromagnetic shower • ¨ucksichtigt ( Reminder: Das Photon materialisiert nachSimple shower model: [from Heitler] Dominant processes • X at high energiesF ... Only two dominant interactions: Folgende Gr 0 ¨ur • Pair verliertproduction dasK and Bremsstrahlung ... PhotonsF : Pair production γ ¨ur E> =Kern).➛ + + − Electrons : Bremsstrahlung γ + Nucleus Nucleuse + e + e Electromagnetic Shower E [PhotonsX0 absorbed via pair production]+ K • ϵ [Monte Carlo Simulation] Zahl der Teilchen im Schauer K • ≤ tritt kein Energieverlust durch Ionisation/Anregunge + Nucleus auf. ➛ Nucleus + e + γ Lage des Schauermaximumsϵ • Pair¨oßen production: sind bei der Beschreibung eines Schauers von Interesse[Energy loss of electrons via Bremsstrahlung]→ Wir messen die longitudinalenLongitudinalverteilung Komponenten des Schauers des Schauersverlieren im Raum in die S Elektronen Energie e − → Use • 7 183 K Transversale Breite des Schauers⇥ 4 αr2Z2 ln Bremsstrahlung:Shower developmentdurch Bremsstrahlung governed by die X H0 ... Simplification: pair e 1 K ⇡ 9 Z 3 + ✓ ◆ After a distance2 X0 electrons remain with auers (MonteEγ = Carlo Ee ≈ Simulation) E0/2 dE Z 183dE E+ e + Nach Durchlaufen der Schichtdicke 7 A X only (1/e)th of their2 primary energy ... [Ee looses half the energy] =4αNA re E ln 1 = e len Teilchen = [X0: radiation length] E + [in cm or g/cm2] dx0 A · + − Zdx3 X0 + 9 NAX0 ,dieEnergievonPositronundElektronbetrPhoton produces1 e e -pair after 9/7X0 ≈ X0 ...e Ee ≈ E0/2 γ − [Energy shared by e+/e–] Absorption x/X= 0 coefficient: ➛ E = E0e− Assume: E NA 7 ρ E After passage of one 0X0 electron ... with initial particle energy E0 µ = n⇥ = ρ ⇥pair = E has> E onlyc : no(1/e) energyth of2 its primaryloss by energy ionization/excitation ... A · 9 X0 ± =E < Ec : energy loss only[i.e. via 37%] ionization/excitation E 1 2 ¨alfte seiner Energie nur durch Ionisation/Anregung. t betr t = ¨agt in unserem einfachen Modell die Zahl der schnel- x N X ( t 0 )=2 ¨agt : 156 t , trahlungsl ¨angen: 20 27. Passage of particles through matter 10 GeV 1.2 Bremsstrahlung y d 100 GeV / M 1 TeV P L σ 0.8 d 10 TeV y ) A / A 100 TeV N 0.4 0 X ( 1 PeV 10 PeV 0 0 0.25 0.5 0.75 1 y = k/E Figure 27.11: The normalized bremsstrahlung cross section kdσLP M /dk in lead versus the fractional photon energy y = k/E.Theverticalaxishasunits Electromagnetic Showers of photons per radiation length. 200 Copper −2 Further basics: X0 = 12.86 g cm 100 Ec = 19.63 MeV ) g V l n e 70 a u ot l Critical Energy [see above]: M h ( T a Rossi: r 0 t 50 s X E s Ionization per X0 × ≈ m 40 = electron energy s e x r dE dE m b d e / t (E ) = (E ) 30 r c c c E B a x dx dx d Brems Ion E Ionization 20 Brems = ionization Approximations: 10 2 5 10 20 50 100 200 Gas 710 MeV Sol/Liq 610 MeV E = Ec = Electron energy (MeV) c Z +0.92 Z +1.24 Figure 27.12: Two definitions of the critical energy Ec. with: dE dE Z E incomplete,dE and near y =0,wheretheinfrareddivergenceisremovedbyE dE E · = & c =const. dx dx ≈ 800 MeV the interferencedx of bremsstrahlungX dx amplitudes⇡ X from nearby scattering centers Brems Ion Brems 0 Ion 0 ✓ ◆ ✓ ◆ February 2, 2010 15:55 Transverse size of EM shower given by 21 MeV RM = X0 RM : Moliere radius radiation length via Molière radius Ec Ec : Critical Energy [Rossi] [see also later] X0 : Radiation length Some Useful 'Rules of Thumbs' Problem: Calculate how much Pb, Fe or Cu 180A g is needed to stop a 10 GeV electron. Radiation length: X0 = 3 2 2 Pb : Z = 82 , A = 207, ρ = 11.34 g/cm Z cm 3 Fe : Z = 26 , A = 56, ρ = 7.87 g/cm 3 Cu : Z = 29 , A = 63, ρ = 8.92 g/cm 550 MeV Critical energy: Ec = [Attention: Definition of Rossi used] Z E 1.0 e– induced shower Shower maximum: t =ln − max 1.0 γ induced shower Ec − 0.5 −{ Longitudinal energy containment: L(95%) = tmax +0.08Z +9.6[X0] Transverse Energy containment: R(90%) = RM R(95%) = 2RM Design of a Calorimeter • TransverseSimplified modelShower [Heitler containment]: shower development governed by X0 ‣- RM(Pb) ≈ 1.6 cm ⎫ e loses [1 - 1/e] = 63% ofuse energy high-Z in material 1 Xo (Brems.) the mean free path of⎬ a is 9/7 Xo (pair prod.) ‣ RM(C) ≈ 22 cm γ Lead%%absorbers%in%cloud%chamber% ⎭ • LongitudinalAssume: shower containment (and realistic compactness) E > Ec : no energy loss by ionization/excitation ‣ L(95% in Pb) ≈ 26 X0 → L ≈ 13 cm ⎫ E < Ec : energy loss only via ionization/excitationuse high-Z material ⎬ ‣ L(95% in C) ≈ 17 X0 → L ≈ 170 cm Simple shower model: ⎭ • Signalt generation and measurement After shower max is reached: • 2 particles after t [X0] use low-Zonly ionization,material Compton, photo-electric • chargeeach with collection energy from E/2 ionisationt ‣ → (mean free path of electrons) • Stops if E < critical energy ε ‣ light collection from scintillationC → transparent medium (low- or high-Z) • Number of particles N = E/εC • Homogeneous• Maximum ator sampling calorimeter cost, performance, detector integration… Roman Kogler 30 Calorimetry Electromagnetic Showers Typical values for X0, Ec and RM of materials used in calorimeter X0 [cm] Ec [MeV] RM [cm] Pb 0.56 7.2 1.6 Scintillator (Sz) 34.7 80 9.1 Fe 1.76 21 1.8 Ar (liquid) 14 31 9.5 BGO 1.12 10.1 2.3 Sz/Pb 3.1 12.6 5.2 PB glass (SF5) 2.4 11.8 4.3 Electromagnetic Shower Profile ElectromagneticLongitudinal shower Shower profiles Shape (longitudinal) 8.1 Electromagnetic calorimeters 235 Depth [X0] 600 Longitudinal profile 5000 MeV Energy deposit of electrons as a function of depth in a Parametrization: block of copper; integrals normalized to same value [EGS4* calculation] [Longo 1975] ] 400 0 Depth of shower maximum increases dE α ⇥t X logarithmically with energy = E0 t e− dt [MeV/ E t t ln( 0/Ec) d max / / α,β : free parameters 2000 MeV E tα : at small depth number of d 200 secondaries increases ... 1000 MeV –βt Energy deposit per cm [%] e : at larger depth absorption dominates ... 500 MeV Numbers for E = 2 GeV (approximate): 0 α = 2, β = 0.5, tmax = α/β 0 5 10 15 20 t [X0] Depth [cm] More exact *EGS = Electron Gamma Shower [Longo 1985] 100 with: α 1 ⇥t dE (⇥t) − e− α 1 E0 = E0 ⇥ ➛ tmax = − =ln + Ceγ Ceγ = 0.5 [γ-induced] dt · · Γ(α) ⇥ Ec10 − lead ✓] ◆ 0 Ceγ = 1.0 [e-induced] [Γ: Gamma function] X − iron aluminium 1 [MeV/ 6 t d / E d 0.1 0.01 0 5152025303510 t [X0] Fig.
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