1. Gaseous Particle Detectors:
By Archana SHARMA
CERN Geneva Switzerland
March 2009
Troisieme Cycle
EPFL Lausanne, Switzerland

2. 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

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: 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.

4. 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

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-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

6. 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

7. 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

8. 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

9. 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

10. 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?

11. Bethe-Bloch Formula Projectile force
Change of momentum of target/projectile
Energy transferred

12. 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

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

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 parameters
Dec 2008
Alfons Weber

15. Bethe-Bloch Formula Simple approximations for
From relativistic kinematics
Inelastic collision
Results in the following expression

16. 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)

17. 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)

18. Different Materials

19. Different Materials (2)

20. Average Ionisation Energy
Few eV to few tens of eV

21. Density Correction depends on material with
x = log10(p/M)
C, δ0, x0 material dependant constants

22. Particle Range/Stopping Power

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 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

25. Straggling Energy Loss Is a statistical process
Simple parameterisation
Landau function

26. Straggling
Dec 2008
Alfons Weber

27. 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

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

29. Electrons Electrons are different light Bremsstrahlung
Pair production

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

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

32. 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

33. 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.

34. 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

35. 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

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

37. 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!

38. 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.

39. 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?

40. 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

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

42. 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

43. 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

44. 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

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 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

47. Cerenkov Radiation Moving charge in dielectric medium
Wave front comes out at certain angle
slow
fast

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

49. 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

50. 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

51. Transition Radiation (3)
Consider relativistic particle traversing a boundary from material (1) to material (2)
Total energy radiated
Can be used to measure g

52. From Interactions to Detectors
From the Particle Adventure

55. Multiwire Proportional Chamber

56. Multiwire Proportional Chamber
and derivatives

57. 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

58. 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