2 Chapter I 5th March 20091.1 Introduction1.2 Units and Definitions, Radiation Sources1.3 Interaction of Radiation with MatterChapter II 12th March 20092.1 General Characteristics of gas detectors, Electronics for HEP detectors2.2: Transport Properties2.3: Wire-based DetectorsTool
3 Electromagnetic Interaction of Particles with Matter If particle’s velocity is greater than the speed of light in the medium -> Cherenkov Radiation. When crossing the boundary between media, ~1% probability of producing a Transition Radiation X-ray.From Riegler Lecture 2: IntroductionInteraction with atomic nucleus. Particle undergoes multiple scattering. Could emit a bremsstrahlung photon.Interaction with atomic electrons. Particle loses energy; atoms are excited or ionized.
4 Cross-sectionMaterial with atomic mass A and density ρ contains n atomsA volume with surface S and thickness dx contains N=nSdx atomsSdxProbability, p of incoming particle hitting an atomProbablity that a particle hits exactly one atom between x and (x + dx)Average collisions/cmMean free path l
5 Differential Cross-section Differential cross-section is the cross-section from an incoming particle of energy E to lose an energy between E and E’Total cross-sectionProbability (P(E)) that a particle of energy, E, loses between E’ and E’ + dE’ in a collisionAverage number of collisions/cm causing an energy loss between E’ and E’+dE’Average energy loss per cm
6 Stopping PowerLinear stopping power (S) is the differential energy loss of the particle in the material divided by the differential path length. Also called the specific energy loss.Bethe-Bloch FormulaStopping Power of muons in CopperPDG, Ch 27 p 3.Particle Data GroupEnergy loss through ionization and atomic excitation
7 Stopping PowerLinear stopping power (S) is the differential energy loss of the particle in the material divided by the differential path length. Also called the specific energy loss.Bethe-Bloch FormulaStopping Power of muons in CopperPDG, Ch 27 p 3.Particle Data GroupEnergy loss through ionization and atomic excitation
8 Bethe-Bloch FormulaDescribes how heavy particles (m>>me) lose energy when travelling through a materialExact theoretical treatment difficultAtomic excitationsScreeningBulk effectsPhenomenological description
9 Bethe-Bloch Formula m – electronic mass v – velocity of the particle (v/c = b)N – number density of atomsI – ‘Effective’ atomic excitation energy – average value found empiricallyGas is represented as a dielectric medium through which the particle propagatesAnd probability of energy transfer is calculated at different energies – Allison CobbPDG, Ch 27 p 3.Particle Data Group
10 A very rough Bethe-Bloch Formula X or Y? zebyrθxZeConsider particle of charge ze, passing a stationary charge ZeAssumeTarget is non-relativisticTarget does not moveCalculateMomentum transferEnergy transferred to targetX or Y?
11 Bethe-Bloch Formula Projectile force Change of momentum of target/projectileEnergy transferred
12 Bethe-Bloch Formula Consider α-particle scattering off Atom Mass of nucleus: M=A*mpMass of electron: M=meBut energy transfer isEnergy transfer to single electron is
13 Bethe-Bloch FormulaEnergy transfer is determined by impact parameter bIntegration over all impact parametersbdbze
14 Bethe-Bloch Formula Calculate average energy loss There must be limits Dependence on the material is in the calculation of the limits of the impact parametersDec 2008Alfons Weber
15 Bethe-Bloch Formula Simple approximations for From relativistic kinematicsInelastic collisionResults in the following expression
16 Bethe-Bloch Formula This was a very simplified derivation IncompleteJust to get an idea how it is doneThe (approximated) true answer iswithε screening correction of inner electronsδ density correction (polarisation in medium)
17 Energy Loss Function 1.6 1.5 1.4 To mips 1.3 Rel Fermi Plateau 1.2 1.1 Relativistic RisebgMinimum ionizing particles (mips)
23 Energy-loss in Tracking Chambers The Bethe Bloch Formula tool for Particle Identification
24 Straggling Mean energy loss Actual energy loss will scatter around the mean valueDifficult to calculateparameterization exist in GEANT and some standalone software librariesForm of distribution is important as energy loss distribution is often used for calibrating the detector
25 Straggling Energy Loss Is a statistical process Simple parameterisationLandau function
27 δ-rays Energy loss distribution is not Gaussian around mean. In rare cases a lot of energy is transferred to a single electronIf one excludes δ-rays, the average energy loss changesEquivalent of changing Emax
28 Restricted dE/dxSome detectors only measure energy loss up to a certain upper limit EcutTruncated mean measurementδ-rays leaving the detector
29 Electrons Electrons are different light Bremsstrahlung Pair production
30 Multiple ScatteringParticles not only lose energy … but also they also change direction
31 Multiple ScatteringAverage scattering angle is roughly Gaussian for small deflection anglesWithAngular distributions are given by
32 Correlation bet dE/dx and MS Multiple scattering and dE/dx are normally treated to be independent from eachNot truelarge scatter large energy transfersmall scatter small energy transferDetailed calculation is difficult, but possibleAllison & Cobb
33 Range Integrate the Bethe-Bloch formula to obtain the range Useful for low energy hadrons and muons with momenta below a few hundred GeVPDGRadiative Effects important at higher momenta. Additional effects at lower momenta.
34 Photon and Electron Interactions Electrons: bremsstrahlungPresence of nucleus required for the conservation of energy and momentumeeγpnCharacteristic amount of matter traversed for these interactions is the radiation length (X0)Photons: pair productionPDGepnγe
35 Radiation LengthMean distance over which an electron loses all but 1/e of its energy through bremsstralungEnergy Loss in Leadalso7/9 of the mean free path for electron-positron pair production by a high energy photonpdg
36 Energy Loss by electrons A charged particle of mass M and charge q=Z1e is deflected by a nucleus of charge Ze (charge partially shielded by electrons)The deflection accelerates the charge and therefore it radiates bremsstrahlungElastic scattering of a nucleus is described byPartial screening of nucleus by electronsRiegler/PDG
37 Electron Critical Energy Energy loss through bremsstrahlung is proportional to the electron energyIonization loss is proportional to the logarithm of the electron energyCritical energy (Ec) is the energy at which the two loss rates are equalPDGElectron in Copper: Ec = 20 MeVMuon in Copper: Ec = 400 GeV!
38 Energy Loss by electrons Contributing Processes photo electric cross sectionStrong dependence of ZAt high energies ~ Z5Energy Loss by electronsContributing ProcessesAtomic photoelectric effectRayleigh scatteringCompton scattering of an electronPair production (nuclear field)Pair production (electron field)Photonuclear interactionLight element: CarbonHeavy element: LeadPDGAt low energies the photoelectric effect dominates; with increasing energy pair production becomes increasingly dominant.
39 Photon Pair Production Probability that a photon interaction will result in a pair productionDifferential Cross-sectionTotal Cross-sectionPDGWhat is the minimum energy for pair production?
40 Electromagnetic cascades A high-energy electron or photon incident on a thick absorber initiates an electromagnetic cascade through bremsstrahlung and pair productionLongitudinal Shower ProfileLongitudinal development scales with the radiation lengthPDGElectrons eventually fall beneath critical energy and then lose further energy through dissipation and ionizationMeasure distance in radiation lengths and energy in units of critical energy
41 Electromagnetic cascades Visualization of cascades developing in the CMS electromagnetic and hadronic calorimetersFrom CMS outreach site
42 Muon Energy LossFor muons the critical energy (above which radiative processes are more important than ionization) is at several hundred GeV.Pair production, bremsstrahlung and photonuclearIonization energy lossMean range
43 Muon Energy LossCritical energy defined as the energy at which radiative and ionization energy losses are equal.Muon critical energy for some elementsFrom PDG
44 Muon TomographyLuis Alvarez used the attenuation of muons to look for chambers in the Second Giza PyramidHe proved that there are no chambers presentRiegler Lectures – thought it was a neat illustration
45 X-Ray Radiography for airport security Riegler Lectures – thought it was a neat illustration
46 Signals from Particles in a Gas Detector Signals in particle detectors are mainly due to ionisationAnd excitation in a sensitive medium – gasAlso:Direct light emission by particles travelling faster than the speed of light in a mediumCherenkov radiationSimilar, but not identicalTransition radiation
47 Cerenkov Radiation Moving charge in dielectric medium Wave front comes out at certain angleslowfast
48 Cerenkov Radiation (2)How many Cherenkov photons are detected?
49 Transition RadiationTransition radiation is produced, when a relativistic particle traverses an inhomogeneous mediumBoundary between different materials with different diffractive index n.Strange effectWhat is generating the radiation?Accelerated chargesDec 2008Alfons Weber
50 Transition Radiation (2) Before the charge crosses the surface, apparent charge q1 with apparent transverse vel v1After the charge crosses the surface, apparent charges q2 and q3 with apparent transverse vel v2 and v3
51 Transition Radiation (3) Consider relativistic particle traversing a boundary from material (1) to material (2)Total energy radiatedCan be used to measure g
52 From Interactions to Detectors From the Particle Adventure
57 Key Points: Lecture 1-3 Energy loss by heavy particles Multiple scattering through small anglesPhoton and Electron interactions in matterRadiation LengthEnergy loss by electronsCritical EnergyEnergy loss by photonsBremsstrahlung and pair productionElectromagnetic cascadeMuon energy loss at high energyCherenkov and Transition Radiation
58 Exercise: Lecture 1-3 Estimate the range of 1 MeV alphas in Aluminium MylarArgonIndicate major interaction processes in:1 MeV g in Al10 MeV g in Argon100 keV g in Iron