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**Gaseous Particle Detectors:**

By Archana SHARMA CERN Geneva Switzerland March 2009 Troisieme Cycle EPFL Lausanne, Switzerland

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Chapter I 5th March 2009 1.1 Introduction 1.2 Units and Definitions, Radiation Sources 1.3 Interaction of Radiation with Matter Chapter II 12th March 2009 2.1 General Characteristics of gas detectors, Electronics for HEP detectors 2.2: Transport Properties 2.3: Wire-based Detectors Tool

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**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: Introduction Interaction with atomic nucleus. Particle undergoes multiple scattering. Could emit a bremsstrahlung photon. Interaction with atomic electrons. Particle loses energy; atoms are excited or ionized.

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Cross-section Material with atomic mass A and density ρ contains n atoms A volume with surface S and thickness dx contains N=nSdx atoms S dx Probability, p of incoming particle hitting an atom Probablity that a particle hits exactly one atom between x and (x + dx) Average collisions/cm Mean free path l

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**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-section Probability (P(E)) that a particle of energy, E, loses between E’ and E’ + dE’ in a collision Average number of collisions/cm causing an energy loss between E’ and E’+dE’ Average energy loss per cm

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Stopping Power Linear 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 Formula Stopping Power of muons in Copper PDG, Ch 27 p 3. Particle Data Group Energy loss through ionization and atomic excitation

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Stopping Power Linear 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 Formula Stopping Power of muons in Copper PDG, Ch 27 p 3. Particle Data Group Energy loss through ionization and atomic excitation

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Bethe-Bloch Formula Describes how heavy particles (m>>me) lose energy when travelling through a material Exact theoretical treatment difficult Atomic excitations Screening Bulk effects Phenomenological description

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**Bethe-Bloch Formula m – electronic mass**

v – velocity of the particle (v/c = b) N – number density of atoms I – ‘Effective’ atomic excitation energy – average value found empirically Gas is represented as a dielectric medium through which the particle propagates And probability of energy transfer is calculated at different energies – Allison Cobb PDG, Ch 27 p 3. Particle Data Group

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**A very rough Bethe-Bloch Formula X or Y?**

ze b y r θ x Ze Consider particle of charge ze, passing a stationary charge Ze Assume Target is non-relativistic Target does not move Calculate Momentum transfer Energy transferred to target X or Y?

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**Bethe-Bloch Formula Projectile force**

Change of momentum of target/projectile Energy transferred

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**Bethe-Bloch Formula Consider α-particle scattering off Atom**

Mass of nucleus: M=A*mp Mass of electron: M=me But energy transfer is Energy transfer to single electron is

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Bethe-Bloch Formula Energy transfer is determined by impact parameter b Integration over all impact parameters b db ze

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**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 parameters Dec 2008 Alfons Weber

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**Bethe-Bloch Formula Simple approximations for**

From relativistic kinematics Inelastic collision Results in the following expression

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**Bethe-Bloch Formula This was a very simplified derivation**

Incomplete Just to get an idea how it is done The (approximated) true answer is with ε screening correction of inner electrons δ density correction (polarisation in medium)

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**Energy Loss Function 1.6 1.5 1.4 To mips 1.3 Rel Fermi Plateau 1.2 1.1**

Relativistic Rise bg Minimum ionizing particles (mips)

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Different Materials

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**Different Materials (2)**

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**Average Ionisation Energy**

Few eV to few tens of eV

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**Density Correction depends on material with**

x = log10(p/M) C, δ0, x0 material dependant constants

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**Particle Range/Stopping Power**

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**Energy-loss in Tracking Chambers**

The Bethe Bloch Formula tool for Particle Identification

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**Straggling Mean energy loss**

Actual energy loss will scatter around the mean value Difficult to calculate parameterization exist in GEANT and some standalone software libraries Form of distribution is important as energy loss distribution is often used for calibrating the detector

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**Straggling Energy Loss Is a statistical process**

Simple parameterisation Landau function

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Straggling Dec 2008 Alfons Weber

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**δ-rays Energy loss distribution is not Gaussian around mean.**

In rare cases a lot of energy is transferred to a single electron If one excludes δ-rays, the average energy loss changes Equivalent of changing Emax

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Restricted dE/dx Some detectors only measure energy loss up to a certain upper limit Ecut Truncated mean measurement δ-rays leaving the detector

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**Electrons Electrons are different light Bremsstrahlung**

Pair production

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Multiple Scattering Particles not only lose energy … but also they also change direction

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Multiple Scattering Average scattering angle is roughly Gaussian for small deflection angles With Angular distributions are given by

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**Correlation bet dE/dx and MS**

Multiple scattering and dE/dx are normally treated to be independent from each Not true large scatter large energy transfer small scatter small energy transfer Detailed calculation is difficult, but possible Allison & Cobb

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**Range Integrate the Bethe-Bloch formula to obtain the range**

Useful for low energy hadrons and muons with momenta below a few hundred GeV PDG Radiative Effects important at higher momenta. Additional effects at lower momenta.

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**Photon and Electron Interactions**

Electrons: bremsstrahlung Presence of nucleus required for the conservation of energy and momentum e e γ p n Characteristic amount of matter traversed for these interactions is the radiation length (X0) Photons: pair production PDG e p n γ e

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Radiation Length Mean distance over which an electron loses all but 1/e of its energy through bremsstralung Energy Loss in Lead also 7/9 of the mean free path for electron-positron pair production by a high energy photon pdg

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**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 bremsstrahlung Elastic scattering of a nucleus is described by Partial screening of nucleus by electrons Riegler/PDG

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**Electron Critical Energy**

Energy loss through bremsstrahlung is proportional to the electron energy Ionization loss is proportional to the logarithm of the electron energy Critical energy (Ec) is the energy at which the two loss rates are equal PDG Electron in Copper: Ec = 20 MeV Muon in Copper: Ec = 400 GeV!

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**Energy Loss by electrons Contributing Processes**

photo electric cross section Strong dependence of Z At high energies ~ Z5 Energy Loss by electrons Contributing Processes Atomic photoelectric effect Rayleigh scattering Compton scattering of an electron Pair production (nuclear field) Pair production (electron field) Photonuclear interaction Light element: Carbon Heavy element: Lead PDG At low energies the photoelectric effect dominates; with increasing energy pair production becomes increasingly dominant.

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**Photon Pair Production**

Probability that a photon interaction will result in a pair production Differential Cross-section Total Cross-section PDG What is the minimum energy for pair production?

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**Electromagnetic cascades**

A high-energy electron or photon incident on a thick absorber initiates an electromagnetic cascade through bremsstrahlung and pair production Longitudinal Shower Profile Longitudinal development scales with the radiation length PDG Electrons eventually fall beneath critical energy and then lose further energy through dissipation and ionization Measure distance in radiation lengths and energy in units of critical energy

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**Electromagnetic cascades**

Visualization of cascades developing in the CMS electromagnetic and hadronic calorimeters From CMS outreach site

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Muon Energy Loss For muons the critical energy (above which radiative processes are more important than ionization) is at several hundred GeV. Pair production, bremsstrahlung and photonuclear Ionization energy loss Mean range

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Muon Energy Loss Critical energy defined as the energy at which radiative and ionization energy losses are equal. Muon critical energy for some elements From PDG

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Muon Tomography Luis Alvarez used the attenuation of muons to look for chambers in the Second Giza Pyramid He proved that there are no chambers present Riegler Lectures – thought it was a neat illustration

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**X-Ray Radiography for airport security**

Riegler Lectures – thought it was a neat illustration

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**Signals from Particles in a Gas Detector**

Signals in particle detectors are mainly due to ionisation And excitation in a sensitive medium – gas Also: Direct light emission by particles travelling faster than the speed of light in a medium Cherenkov radiation Similar, but not identical Transition radiation

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**Cerenkov Radiation Moving charge in dielectric medium**

Wave front comes out at certain angle slow fast

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Cerenkov Radiation (2) How many Cherenkov photons are detected?

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Transition Radiation Transition radiation is produced, when a relativistic particle traverses an inhomogeneous medium Boundary between different materials with different diffractive index n. Strange effect What is generating the radiation? Accelerated charges Dec 2008 Alfons Weber

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**Transition Radiation (2)**

Before the charge crosses the surface, apparent charge q1 with apparent transverse vel v1 After the charge crosses the surface, apparent charges q2 and q3 with apparent transverse vel v2 and v3

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**Transition Radiation (3)**

Consider relativistic particle traversing a boundary from material (1) to material (2) Total energy radiated Can be used to measure g

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**From Interactions to Detectors**

From the Particle Adventure

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**Multiwire Proportional Chamber**

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**Multiwire Proportional Chamber**

and derivatives

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**Key Points: Lecture 1-3 Energy loss by heavy particles**

Multiple scattering through small angles Photon and Electron interactions in matter Radiation Length Energy loss by electrons Critical Energy Energy loss by photons Bremsstrahlung and pair production Electromagnetic cascade Muon energy loss at high energy Cherenkov and Transition Radiation

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**Exercise: Lecture 1-3 Estimate the range of 1 MeV alphas in Aluminium**

Mylar Argon Indicate major interaction processes in: 1 MeV g in Al 10 MeV g in Argon 100 keV g in Iron

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