Calorimetry I Electromagnetic Calorimeters

Transcription

1 Calorimetry I Electromagnetic Calorimeters

2 Introduction Calorimeter: Detector for energy measurement via total absorption of particles... Also: most calorimeters are position sensitive to measure energy depositions depending on their location... Principle of operation: Incoming particle initiates particle shower... Shower Composition and shower dimensions depend on particle type and detector material... Energy deposited in form of: heat, ionization, excitation of atoms, Cherenkov light... Different calorimeter types use different kinds of these signals to measure total energy... Important: Signal ~ total deposited energy incident particle [Proportionality factor determined by calibration] Schematic of calorimeter principle particle cascade (shower) detector volume

3 Introduction Energy vs. momentum measurement: Calorimeter: [see below] E E p 1 E Gas detector: [see above] p p p e.g. ATLAS: E E p 0.1 E i.e. σe/e = 100 GeV e.g. ATLAS: p p p t i.e. σp/p = 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: Calorimeter: [see below] L ln E E c [Ec: critical energy] Shower depth nearly energy independent i.e. calorimeters can be compact... Compare with magnetic spectrometer: p/p p /L 2 Detector size has to grow quadratically to maintain resolution

4 Introduction Further calorimeter features: Calorimeters can be built as 4π-detectors, i.e. they can detect particles over almost the full solid angle Magnetic spectrometer: anisotropy due to magnetic field; remember: Calorimeters can provide fast timing signal (1 to 10 ns); can be used for triggering [e.g. ATLAS L1 Calorimeter Trigger] ( p/p) 2 =( p t/p t ) 2 +( /sin ) 2 Calorimeters can measure the energy of both, charged and neutral particles, if they interact via electromagnetic or strong forces [e.g.: γ, μ, Κ 0,...] Magnetic spectrometer: only charged particles! large for small θ Segmentation in depth allows separation of hadrons (p,n,π ± ), from particles which only interact electromagnetically (γ,e)......

5 Electromagnetic Showers Reminder: Dominant processes at high energies... Photons : Pair production Electrons : Bremsstrahlung X0 Pair production: pair 7 4 re 2 9 Z2 ln 183 Z 1 3 Absorption coefficient: = 7 A 9 N A X 0 µ = n = N A A pair [X0: radiation length] [in cm or g/cm 2 ] = 7 9 X 0 Bremsstrahlung: de dx =4 N A E = E 0 e x/x 0 Z 2 A r2 e E ln 183 Z 1 3 After passage of one X0 electron has only (1/e) th of its primary energy... [i.e. 37%] = E X 0

6 Electromagnetic shower X0 neti Electromagnetic Shower [Monte Carlo Simulation]

7 Electromagnetic Showers 200 Further basics: 100 Copper X 0 = g cm 2 E c = MeV Critical Energy [see above]: de dx (E c) Brems = de dx (E c) Ion de/dx X 0 (MeV) Rossi: Ionization per X 0 = electron energy Brems E Total Ionization Exact bremsstrahlung Approximations: E Gas c = de dx Brems 710 MeV Z de dx Ion E Sol/Liq c = Z E 800 MeV 610 MeV Z Brems = ionization Electron energy (MeV) Figure 27.12: Two definitions of the critical energy. with: de dx Brems = E X 0 & de dx Ion E c X 0 =const. Transverse size of EM shower given by radiation length via Molière radius [see also later] R M = 21 MeV E c X 0 RM : Moliere radius Ec : Critical Energy [Rossi] X0 : Radiation length

8 Some Useful 'Rules of Thumbs' Radiation length: Critical energy: [Attention: Definition of Rossi used] Shower maximum: X 0 = 180A Z 2 E c = 550 MeV Z t max =ln E E c g cm 2 { Problem: Calculate how much Pb, Fe or Cu is needed to stop a 10 GeV electron. Pb : Z = 82, A = 207, ρ = g/cm 3 Fe : Z = 26, A = 56, ρ = 7.87 g/cm 3 Cu : Z = 29, A = 63, ρ = 8.92 g/cm 3 e induced shower γ induced shower Longitudinal energy containment: Transverse Energy containment: L(95%) = t max +0.08Z +9.6 [X 0 ] R(90%) = R M R(95%) = 2R M

9 Design of a Calorimeter Transverse Shower containment R M(Pb) 1.6 cm R M(C) 22 cm use high-z material Longitudinal shower containment (and realistic compactness) L(95% in Pb) 26 X 0 L 13 cm L(95% in C) 17 X 0 L 170 cm Signal generation and measurement charge collection from ionisation light collection from scintillation Homogeneous or sampling calorimeter cost, performance, detector integration use high-z material use low-z material (mean free path of electrons) transparent medium (low- or high-z)

10 Electromagnetic Showers Typical values for X0, Ec and RM of materials used in calorimeter X0 [cm] Ec [MeV] RM [cm] Pb Scintillator (Sz) Fe Ar (liquid) BGO Sz/Pb PB glass (SF5)

11 Longitudinal Shower Shape Depth [X0] Energy deposit per cm [%] Energy deposit of electrons as a function of depth in a block of copper; integrals normalized to same value [EGS4* calculation] Depth of shower maximum increases logarithmically with energy t max / ln( E 0/E c ) Parametrization: [Longo 1975] de dt = E 0 t e t α,β:free parameters t α : at small depth number of secondaries increases... e βt : at larger depth absorption dominates... Numbers for E = 2 GeV (approximate): α = 2, β = 0.5, tmax = α/β *EGS = Electron Gamma Shower Depth [cm]

12 Transversal Shower Shape Molière Radii Transverse profile at different shower depths... Up to shower maximum broadening mainly due to multiple scattering... Characterized by RM: [90% shower energy within RM] R M = 21 MeV E c X 0 Energy deposit [a.u.] Beyond shower maximum broadening mainly due to low energy photons... Radial distributions of the energy deposited by 10 GeV electron showers in Copper [Results of EGS4 simulations] Distance from shower axis [RM]

13 Homogeneous Calorimeters In a homogeneous calorimeter the whole detector volume is filled by a high-density material which simultaneously serves as absorber as well as as active medium... Signal Material Scintillation light BGO, BaF2, CeF3,... Cherenkov light Ionization signal Lead Glass Liquid nobel gases (Ar, Kr, Xe) Advantage: homogenous calorimeters provide optimal energy resolution Disadvantage: very expensive Homogenous calorimeters are exclusively used for electromagnetic calorimeter, i.e. energy measurement of electrons and photons

14 Homogeneous Calorimeters CMS electromagnetic calorimeter

15 Homogeneous Calorimeters CMS electromagnetic calorimeter Scintillator : PBW04 [Lead Tungsten] Photosensor : APDs [Avalanche Photodiodes] Number of crystals: ~ Light output: 4.5 photons/mev Barrel ECAL (EB) y = = Preshower (ES) z = 2.6 = 3.0 Endcap ECAL (EE)

16 Sampling Calorimeters Principle: Alternating layers of absorber and active material [sandwich calorimeter] Absorber materials: [high density] Iron (Fe) Lead (Pb) Uranium (U) [For compensation...] Active materials: Plastic scintillator Silicon detectors Liquid ionization chamber Gas detectors incoming particle passive absorber shower (cascade of secondaries) active layers Scheme of a sandwich calorimeter Electromagnetic shower

17 Sampling Calorimeters Advantages: By separating passive and active layers the different layer materials can be optimally adapted to the corresponding requirements... By freely choosing high-density material for the absorbers one can built very compact calorimeters... Sampling calorimeters are simpler with more passive material and thus cheaper than homogeneous calorimeters... Disadvantages: Only part of the deposited particle energy is actually detected in the active layers; typically a few percent [for gas detectors even only ~10-5 ]... Due to this sampling-fluctuations typically result in a reduced energy resolution for sampling calorimeters...

18 Sampling Calorimeters Possible setups Scintillators as active layer; signal readout via photo multipliers Absorber Scintillator Light guide Photo detector Scintillators as active layer; wave length shifter to convert light Scintillator (blue light) Wavelength shifter Charge amplifier Absorber as electrodes HV Ionization chambers between absorber plates Argon Active medium: LAr; absorber embedded in liquid serve as electrods Electrodes Analogue signal

19 Sampling Calorimeters Example: ATLAS Liquid Argon Calorimeter

20 Response and Linearity response = average signal per unit of deposited energy e.g. # photoelectrons/gev, picocoulombs/mev, etc A linear calorimeter has a constant response In general: Electromagnetic calorimeters are linear! All energy deposited through ionization/excitation of absorber Hadronic calorimeters are not (later)

21 Energy Resolution Calorimeter energy resolution determined by fluctuations Different effects have different energy dependence quantum, sampling fluctuations σ/e ~ E -1/2 shower leakage σ/e ~ constant or E-1/4 (*) electronic noise σ/e ~ E -1 structural non-uniformities σ/e = constant Add in quadrature: σ 2 tot= σ σ σ σ (*) different for longitudinal and transverse leakage example: ATLAS EM calorimeter

22 Energy Resolution Ideally, if all shower particles counted: In practice: absolute: relative: = a p E b ce E = p a b E E c p E E ~ N, σ ~ N ~ E E / N N N N = p 1 N a: stochastic term intrinsic statistical shower fluctuations sampling fluctuations signal quantum fluctuations (e.g. photo-electron statistics) b: noise term readout electronic noise Radio-activity, pile-up fluctuations c: constant term inhomogeneities (hardware or calibration) imperfections in calorimeter construction (dimensional variations, etc.) non-linearity of readout electronics fluctuations in longitudinal energy containment (leakage can also be ~ E -1/4 ) fluctuations in energy lost in dead material before or within the calorimeter

23 Homogeneous calorimeters: signal = sum of all E deposited by charged particles with E > E threshold If W is the mean energy required to produce a signal quantum (eg an electron-ion pair in a noble liquid or a visible photon in a crystal)! mean number of quanta produced is hni = E/W Intrinsic Energy Resolution n = E / W The intrinsic energy resolution is given by the fluctuations on n. E = p 1 r W = n E σ E / E = 1/ n = 1/ (E / W) i.e. in a semiconductor crystals (Ge, Ge(Li), Si(Li)) W = 2.9 ev (to produce e-hole pair)! 1 MeV γ = electrons! 1/ n = 0.17% stochastic term In addition, fluctuations on n are reduced by correlation r in the production of consecutive e-hole pairs: the Fano factor F FW σ E / E = (FW / E) E = E For GeLi γ detector F ~ 0.1! stochastic term ~ 0.05%/ E[GeV]

24 Example: CMS ECAL Resolution Relatively large size of sampling term (3%): PbWO4 rather weak scintillator 4500 photos / 1 GeV Fano factor of 2 for crystal / APD combination Still: sampling term 3 times smaller than for ATLAS ECAL!

25 Resolution of Sampling Calorimeters Sampling fluctuations: Additional contribution to energy resolution in sampling calorimeters due to fluctuations of the number of (low-energy) electrons crossing active layer... Increases linearly with energy of incident particle and fineness of the sampling... N ch / E E / E E c t abs Resulting energy resolution: N ch N ch / r Ec t abs E Nch Nmax tabs Choose: Ec small (large Z) tabs small (fine sampling) : charged particles reaching active layer : total number of particles = E/Ec : absorber thickness in X0 Reasoning: Energy deposition dominantly due to low energy electrons; range of these electrons smaller than absorber thickness tabs; only few electrons reach active layer... Fraction f ~ 1/tabs reaches the active medium... Semi-empirical: E E =3.2% s E c [MeV] t abs F E [GeV] where F takes detector threshold effects into account...

26 Resolution of Sampling Calorimeters Measure energy resolution of a sampling calorimeter for different absorber thicknesses.. Kanale GeV tabs : absorber thickness in X0 D : absorber thickness in mm Sampling contribution: E E =3.2% s E c [MeV] t abs F E [GeV] Sampling Fluctuations Sampling Fluktuationen Photo-electron Statistics + Leakage Photoelektron Statistik + Leakage Best choice: Ec small (large Z) tabs small (fine sampling) D [mm]