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Ketzer Lecture1 Sub Small.Pdf Modern Particle Detectors Bernhard Ketzer Helmholtz-Institut für Strahlen- und Kernphysik SFB 1044 School 2016 Boppard Plan of the Lecture 1. Introduction 2. Interaction of charged particles with matter 3. Ionization detectors 4. Position and momentum measurement / track reconstruction 5. Photon detection 6. Calorimetry 7. Detector systems Detectors B. Ketzer 2 1 Introduction Struktur und Entwicklung des Universums Detectors B. Ketzer 4 How to observe this? Accelerators Microscopes Binoculars Optical and radio telescopes Resolution: θ Detectors B. Ketzer 5 Old Particle Detectors Bernhard Ketzer Helmholtz-Institut für Strahlen- und Kernphysik SFB 1044 School 2016 Boppard Cloud Chamber C.T.R. Wilson (1910): Charges act as condensation nuclei in supersaturated water vapor (later: alcohol vapor diffusion cloud chamber) Alphas, Philipp 1926 Positron discovery, Carl Andersen 1933 V-particles, Rochester and Wilson, 1940ies Detectors B. Ketzer 7 Nuclear Emulsion M. Blau (1930s): Charges initiate a chemical reaction that blackens the emulsion (film made of Ag-halide, e.g. AgBr) Kaon Decay into 3 pions, 1949 C. Powell, Discovery of muon and pion, 1947 Cosmic Ray Composition Detectors B. Ketzer 8 Bubble Chamber D. Glaser (1952): Charges create bubbles in superheated liquid, e.g. propane or Hydrogen (Alvarez) Neutral Currents 1973 Discovery of the in 1964 − 훀 Charmed Baryon, 1975 Detectors B. Ketzer 9 The Giants ATLAS ALICE Very Large Structures • Engineering, Services, Cooling • Electronics But in the end: resolution limits are still defined by the LHCb fundamental detector physics processes … Detectors B. Ketzer 10 Resolution dE/dx particle ID resolution is defined by the fundamental properties of EM interactions of charged particles with matter, ‘Bethe Bloch’ curve + ‘Landau’ distribution Time of Flight Resolution with Resistive Plate Chambers (ALICE) is defined by the electron avalanche fluctuations together with the drift-velocity. [W. Riegler, priv. comm.] Detectors B. Ketzer 11 Alpha Mass Spectrometer Detectors B. Ketzer 12 A Typical Detector Setup Different components, measuring different aspects of reaction products: track, charge, energy, momentum, particle type, ... Tracking Electromagn. Hadron Muon chamber calorimeter calorimeter chamber γ e± Beam µ π±,p n Target Magnet Detectors B. Ketzer 14 Detection of Radiation Goal: Measurement of 4-momentum and position in space of particles Methods: • Position-sensitive detectors direction and position of momentum vector • Bending in magnetic field magnitude of p • Absorption in calorimeter energy • Cherenkov radiation, time of flight velocity β • Transition radiation γ • Energy loss β, γ • Characteristic decay of a particle, detection of secondaries m Detection by interaction with detector material: • electromagnetic interaction with ∆E<<E • interaction with ∆E~E (calorimtery) [Claus Grupen, Particle Detectors, Cambridge, 1996] Detectors B. Ketzer 15 Interactions of Charged Particles Processes for a charged particle passing through matter: 1. Inelastic collisions with atomic electrons energy loss excitation (soft collision) or ionization (hard collision) of hit atom deflection: small 2. Elastic collisions with nuclei deflection energy loss: negligible, since normally ma<<mb no excitation of hit atom 3. Emission of Bremsstrahlung important for e± 4. Emission of Cherenkov radiation / transition radiation in inhom. materials 5. Nuclear interactions Moderately relativistic heavy charged particles: µ, π, p, α, … (ma>me) -17 -16 2 energy loss almost entirely throughB. Ketzer process 1.: σ~10 -10 cm Detectors 17 Electromagnetic Interaction of Particles with Matter Z2 electrons, q=-e0 M, q=Z1 e0 Interaction with the Interaction with the atomic electrons. The atomic nucleus. The In case the particle’s velocity is larger incoming particle particle is deflected than the velocity of light in the medium, loses energy and the (scattered) causing the resulting EM shockwave manifests atoms are excited or multiple scattering of itself as Cherenkov Radiation. When the ionized. the particle in the particle crosses the boundary between material. During this two media, there is a probability of the scattering a order of 1% to produce an X ray photon, Bremsstrahlung called Transition radiation. photon can be emitted. [W. Riegler, priv. comm.] Detectors B. Ketzer 18 Warm Up 1. What is the general relation between energy and momentum? 2. What approximations can be used? 3. What are and ? How are they calculated from , , ? 4. How large훽 are the훾 fluctuations in radioactive decay?퐸 푝 푚 5. What is a cross section? 6. What are typical values of cross sections? 7. How is it related to luminosity? 8. How do charged particles interact with matter? Detectors B. Ketzer 19 2 Electromagnetic Interactions of Charged Particles with Matter 2.1 Ionizing collisions 2.2 Calculation of mean energy loss 2.3 Fluctuations of energy loss 2.1 Collisions Interactions of a fast charged particle with speed = / and momentum = with matter 훽 푣 푐 푝 푀푐훽Occurrence훾 of random individual collisions In each collision the particle loses a random amount of energy Characterization by mean free path and collision cross section : 퐸 1 1 휆 휎 = = number density of electrons number of (primary) collisions per unit length 푛푒 푝 휆 푒 푝 푛 Number of encounters푛 휎 in 푛length described by Poisson distribution 퐿 ; = = = 푘! 휇 −휇 퐿 푃 푘 휇 푒 휇 퐿 푛푝 Detectors 푘 B. Ketzer 휆 21 Collisions Probability distribution d of free flight paths between collisions: 푓 푙 푙 d d 푙 d = 0; 1; = single exponential 푙 − 푙 푙 휆 푙 푓 푙 푙 푃 ∙ 푃 푒 ∙ 휆 휆 휆 Probability of having zero encounters along track length : 퐿 / 0; = Number of ionizing collisions 퐿 −퐿 휆 per cm track length, 푃 푒 measured at given value of inefficiency휆 of a perfect detector, 훾 which is capable of detecting even single electrons [V.K. Ermilova et al., Sov. Phys.-JETP 29, 861 (1969)] method to measure λ, np [K. Söchting, Phys. Rev. A, 20, 1359 (1979)] Detectors B. Ketzer 22 2.2 Mean energy loss 24 2 22 d4E πδz e ne 12 mcβγ Tmax 2 − = 2 ln −−β 2 22β 2 d2x ()4πε 0 mc I “Bethe equation” with ze charge of incoming particle Z n electron number density of material nN= ρ e eAA m electron mass β=v/c velocity of incoming particle γ relativistic factor Tmax maximum kinetic energy imparted to electron in single collision I mean excitation energy δ density effect correction Detectors B. Ketzer 23 Mean Energy Loss 24 2 22 d4E πδz e ne 12 mcβγ Tmax 2 − = 2 ln −−β 2 22β 2 d2x ()4πε 0 mc I • independent of mass of incident particle • depends only on velocity of inc. particle and on I main parameter −dE ∝ 1 • low energies dx β 2 • minimum at βγ ≈ 3 : “MIP” −dE ∝ ln βγ22 • high energies d x : relativistic rise −dE ∝z2 Z ⋅, fIβ • mass stopping power: ρdxA() () almost independent of material • density effect: polarization of atoms along track partly compensates relativistic rise Detectors B. Ketzer 24 Calculation of Energy Loss Quantum picture: energy loss caused by a number of discrete collisions per unit length, each with energy transfer f (E) dE probability of energy loss per unit path length 퐸 between E and E+dE and with electron density 푛푒 energy transfer in single collision 퐸d /d collision cross section differential in transferred energy 휎 퐸 number of primary collisions per unit Mean free path: path length 푛푝 probability of energy loss in Spectrum of energy transfer , + d per collision 퐸 퐸 퐸 need a model for collision cross section! [H. Bichsel, NIM A 562, 154 (2006)] Detectors B. Ketzer 25 Rutherford - Mott Model Simplest ansatz: hard collisions • Coulomb scattering of projectile with charge off free electrons • only valid for energy transfers typical atomic binding energies 푧푒 • in rest frame of projectile: electron scattering off heavy particle at rest ≫ 퐼 Mott cross section: for static potential (no recoil) Detectors B. Ketzer 26 Rutherford - Mott With , , p θ 2 θ 2 p′ q follows the cross section differential in transferred energy Exercise: show this… Detectors B. Ketzer 27 Rutherford - Mott Evaluation of integral Validity range of Mott CCS: I: mean excitation energy Therefore we arrive at Yields Bethe equation, except Contribution from • Factor 2 hard scattering! • instead of Detectors휖 퐼 B. Ketzer 28 Bethe – Fano Model Bethe, 1930: [H. Bethe, Ann. Phys. 5, 325 (1930)] • drop assumption of free electrons • derive expression for cross section double-differential in energy loss and momentum transfer for inelastic scattering on free atoms • use first Born approximation 퐸 풒 with Fano, 1963: [U. Fano, Ann. Rev. Nucl. Sci. 13, 1 (1963)] • extend method for solids • no calculations exist for gases Detectors B. Ketzer 29 Bethe – Fano Model [H. Bichsel, NIM A 562, 154 (2006)] Detectors B. Ketzer 31 Bethe – Fano Model [H. Bichsel, NIM A 562, 154 (2006)] Detectors B. Ketzer 33 Total Energy Loss Total energy loss: Bethe-Bloch formula Z Hard: Mott Soft nN=⋅⋅ρ eAA with independent of ε Detectors B. Ketzer 34 Total Energy Loss In principle, mean excitation energy can be calculated from atomic theory: 퐼 models needed for all but lightest atoms often used in practice: as phenomenological constant 퐼 Goal: Simplify cross section expression based on measured photo- absorption cross sections Photoabsorption Ionization Model … also called Fermi virtual photon (FVP) model Detectors B. Ketzer 35 Classical Calculation of Energy Loss Idea: Calculate dd Ex of a moving charged particle (other than e±) in a polarizable medium classical calculation: medium treated as continuum with ε = ε1 + iε2 later: quantum mechanical interpretation dd Ex longitudinal component of electric field Er () , t generated by the moving particle in the medium at its own position rv= t ⟺ dE = eE dx long [L. Landau, E.M. Lifshitz, Electrodynamics of continuous media, 1960] [W.W.M Allison, J.H. Cobb, Ann. Rev. Nucl. Part. Sci. 30, 253 (1980)] [W. Blum, W. Riegler, L. Rolandi, Particle Detection with Drift Chambers, Springer 2008] Detectors B.
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