Moderne Teilchendetektoren Theorie und Praxis 2
Dr. Bernhard Ketzer
Technische Universität München
SS 2013
Schedule
• Tag der Physik: Wednesday, July 17, 14:00
 start lecture at 12:00
• Oral exams (part I + II)
• August 5 – 7, 2013
• September 16 – 18, 2013
Teilchendetektoren - B. Ketzer
11 Particle Identification
11.1 Introduction
11.2 PID by Difference in Interaction
11.3 Time-of-Flight Measurement
11.4 Interactions of Charged Particles in Dielectric Revisited
11.5 Measurement of Energy Loss
11.6 Cherenkov Radiation
11.7 Transition Radiation
Particle Detectors – B. Ketzer
PAI Model
Idea: Calculate dE dx 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
dE dx ⟺ longitudinal component of electric field E ( r ,t ) generated
by the moving particle in the medium at its own position r = vt
dE
= eElong
dx
[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]
PAI Model
Quantum picture: energy loss caused by a number of discrete collisions per
unit length, each with energy transfer E = ω (single photon exchange)
∞
dE
= − ∫ E f ( E ) dE
dx
0
f (E) dE probability of energy transfer per unit path
between E and E+dE
and with f ( E ) = N dσ dE
∞
dE
dσ
= − ∫ EN
 dω
dx
dE
0
N electron density
E = ω energy transfer in single collision
p = k
PAI Model
Therefore: differential cross section per electron and energy loss dE
−1
2
dσ
α σγ ( E ) 
2
4 2 2
ln (1 − β ε1 ) + β ε 2 
=
2


dE β π EZ
Energy loss by ionization
α σ γ ( E )  2mc 2 β 2 
ln 
+ 2

β π EZ
E


α 1 E σ γ ( E′)
dE ′
+ 2
2 ∫
β π E 0 Z
α 1  2 ε1 
+ 2
 β − 2 Θ
β π N c 
ε 
with
Rutherford scattering (for E >> EK)
 δ electrons
• Optical region: σγ = 0
 Cherenkov radiation
• Transition radiation for thin radiators
ε1, ε2 : real and imaginary part of dielectric constant (for real photons)
=
Θ arg (1 − ε1β 2 + iε 2 β 2 )
angle in pointer representation of complex number
σγ : atomic cross section of medium for absorption of photon with energy E
N : electron density in the medium
11.5 Measurement of Energy Loss
Restricted energy loss:
dE
−
dx
4π
( 4πε 0 )
T <Tcut
2
z 2 e 4 ne
mc 2 β 2
 1 2mc 2 β 2γ 2Tcut β 2 
Tcut
−
+
ln
1


2
I
2  Tmax
 2
 δ
− 
 2 
approaches normal Bethe-Bloch equation for 𝑇cut → 𝑇max
Transforms into average total number of e- ion pairs nT along path length x:
x
dE
= nTW
dx
But: actual energy loss fluctuates with a long tail (Landau distribution)
mean value of energy loss is a bad estimator
 use truncated mean of N pulse height measurements along the track:
1
At=
Nt
Nt
∑ Ai
i =1
Ai ≤ Ai +1 for i =
1, , N
Nt =
t ⋅ N , t ∈ [ 0,1]
Particle Detectors – B. Ketzer
Measurement of Energy Loss
Particle Detectors – B. Ketzer
Measurement of Energy Loss
Particle Detectors – B. Ketzer
Measurement of Energy Loss
Resolution (empirical):
N = number of samples
Δ𝑥 = sample length (cm)
p = gas pressure (atm)
Particle Detectors – B. Ketzer
Example: ALICE TPC
Particle Detectors – B. Ketzer
Example: FOPI GEM-TPC
• Sum up charge in 5 mm
steps
• Truncated mean: 0-70%
• Momentum from TPC +
CDC
• PID using dE/dx:
• Resolution ~ 14-17%
• No density correction
First dE/dx measurement
with GEM-TPC!
[F. Böhmer, TUM]
Particle Detectors – B. Ketzer
Example: FOPI GEM-TPC
• Sum up charge in 5 mm
steps
• Truncated mean: 0-70%
• Momentum from TPC +
CDC
• PID using dE/dx:
• Resolution ~ 14-17%
• No density correction
First dE/dx measurement
with GEM-TPC!
[F. Böhmer, TUM]
Particle Detectors – B. Ketzer
11.6 Cherenkov Radiation
11.6.1 Properties of Cherenkov Radiation
11.6.2 Threshold Counters
11.6.3 Imaging Counters
Particle Detectors – B. Ketzer
11.6.1 Properties of Cherenkov
Radiation
1. Prompt emission of light pulse
c
2. Velocity threshold for radiation v = β c > ≡ vthr
n
3. Cherenkov cone half angle
cos θ C =
1
βn
classically:
• polarization of molecules by charged particle
• relaxation
• emission of radiation
• coherent wave front, if v > vthr
Properties of Cherenkov Radiation
[K. Kleinknecht, Detektoren für Teilchenstrahlung,
Teubner, Stuttgart (1992)]
Material
n-1
γt (Thres.)
Glass
0.46-0.75
1.22-1.37
Scintillator
0.58
1.29
Plexiglass
0.48
1.36
Water
0.33
1.52
Aerogel
0.025-0.075
4.5-2.7
Pentan (STP)
1.7•10-3
17.2
CO2 (STP)
4.3•10-4
34.1
He (STP)
3.3•10-5
123
C4F10
1.53•10-3
18.3
Properties of Cherenkov Radiation
Number of emitted photons (z = charge of incoming particle)
dNγ
d 2 Nγ
z 2α
= =
sin 2 θ C const.
dω dx c
2
d Nγ
dλ dx
=
2π z α
2
λ2
dNγ
sin 2 θ C
For singly charged particles (z=1):
d 2 Nγ
dEdx
dE
= 370sin 2 θ C ( E ) eV −1cm −1
E
dλ
E
θC determined by n = n( E )
Properties of Cherenkov Radiation
Number of detected photoelectrons: Frank-Tamm equation
z 2α
N pe L
=
c
2
E
sin
ε
(
)
θ C ( E ) dE
∫
ε = efficiency of light collection and conversion
L = path length in radiator
Typical variation of n with E small  define quality factor
z 2α
-1
d
,
N
30,180
cm
N0 =
E
ε
∈
[
]
0
c ∫
typically
⇒ N pe ≈ L N 0 sin 2 θ C
Particle Detectors – B. Ketzer
11.6.2 Threshold Counters
Simplest form: yes / no information
based on whether particle velocity
v = βc >
c
≡ vthr
n
Enhancement: use number of observed photoelectrons to
discriminate between particle species
(or to set probabilities)
N pe
L
360 eV −1cm −1 ε coll sin 2 θ C
∫ ε det ( E ) dE
≈ 90 cm -1 sin 2 θ C
Careful design:
ε coll = 0.9
∫ε
Particle Detectors – B. Ketzer
det
dE = 0.27 eV for bi-alkali
Threshold Counters
Consider 2 particle species: mA < mB
Choose n such that for a given momentum p particles of species B are
1
exactly at threshold: n =
βB
for species A
Particle Detectors – B. Ketzer
Threshold Counters
Example: K / π separation at p = 1(5) GeV/c
Robust counter:
Rejection of species B: no signal  minimize electronic and other noise!
In practice: combination of several threshold counters
Particle Detectors – B. Ketzer
Threshold Counters
Setup: threshold counter with Silica aerogel
PMT
particle
thin foil
aerogel
Particle Detectors – B. Ketzer
BELLE ACC
Aerogel Cherenkov Counter
[Belle collab., Nucl. Instr. Meth. A 453, 321 (2000)]
Particle Detectors – B. Ketzer
11.6.3 Imaging Counters
Measure angle of emission for individual Cherenkov photons  v
Low-energy photon  angle not measurable directly by detector, only position
 imaging necessary to determine angle from position
• Differential Cherenkov Detectors: DISC, CEDAR
• Ring-Imaging Cherenkov Counters: RICH
• Detector of Internally Reflected Cherenkov Light: DIRC
Particle Detectors – B. Ketzer
Differential Cherenkov Detector
Selection of a small region of the emission angle
• by a variable diaphragm (ring aperture) or
• by varying the gas pressure at fixed diaphragm,
and imaging to photocathode via a mirror system
Important: correction of chromatic aberration (dispersion in the gas)
DISC: directional isochronuous self collimating
CEDAR: Cherenkov differential counter with achromatic ring focus
Particle Detectors – B. Ketzer
Differential Cherenkov Counter
[C. Bovet et al., CERN 82-13]
Particle Detectors – B. Ketzer
Differential Cherenkov Counter
[C. Bovet et al., CERN 82-13]
Particle Detectors – B. Ketzer
Differential Cherenkov Counter
COMPASS CEDAR
Particle Detectors – B. Ketzer
Differential Cherenkov Counter
Advantage: 30 – 40 × higher momenta than threshold counter,
π / K separation up to p ~ 500 GeV/c possible
Disadvantage: only useful for particles incident parallel to optical axis
 very limited acceptance,
 not useful for diverging particles, e.g. from an interaction point
Particle Detectors – B. Ketzer
Ring-Imaging Cherenkov Counter
RICH [Seguinot, Ypsilantis, 1977]
Large acceptance:
• proximity focusing  thin radiator (solid, liquid)
• mirror focusing
 gaseous radiator
Focusing onto position-sensitive photodetector
Particle Detectors – B. Ketzer
RICH
Imaging:
mirror
direct
COMPASS RICH1
Particle Detectors – B. Ketzer
PID with RICH Detector
COMPASS RICH1
Particle Detectors – B. Ketzer
RICH
Resolution for particle velocity:
with
average single photoelectron resolution,
defined by optics, detector resolution, dispersion
of radiator gas
C other contributions, e.g. track reconstruction,
alignment, multiple scattering, hit-ambiguities,
background hits, hits by other tracks
Particle Detectors – B. Ketzer
RICH
Separation in units of σ :
(well above threshold)
In practice:
depending on size, radiator, photodetector
Momentum range for separation:
• ~ 20% above threshold for lighter species up to imaging limit p( Nσ )
• can be tuned by choosing index of refraction n !
Example:
Fused silica: n = 1.474  3σ π / K separation from 0.15 GeV/c to 4.2 GeV/c
C5F12:
n = 1.0017  3σ π / K separation from 3 GeV/c to 18 GeV/c
Particle Detectors – B. Ketzer
RICH
Central element: position-sensitive photon detector
• MWPC with TEA, TMAE
• MWPC with CsI photocathode
• MA-PMT  lenses required to minimize dead area
COMPASS RICH1: MWPC with CsI photo cathodes
Cooling plates
Readout electronics
CsI photo cathode
Anode wires
Spacer frame
Cathode wires
Collection wires
Quartz glass window
Frame
11.6.3 Imaging Counters
Measure angle of emission for individual Cherenkov photons  v
Low-energy photon  angle not measurable directly by detector, only position
 imaging necessary to determine angle from position
• Differential Cherenkov Detectors: DISC, CEDAR
• Ring-Imaging Cherenkov Counters: RICH
• Detector of Internally Reflected Cherenkov Light: DIRC
Particle Detectors – B. Ketzer
DIRC
Detector of Internally Reflected Cherenkov Light [I. Adam et al., NIM A 538, 281 (2005)]
 collection and imaging of the totally internally reflected light
(rather than transmitted light)
Optical material: quartz (SiO2), high-purity fused Silica
• radiator
• light guide
 transport photons outside particle path
Readout:
• PMT (BaBar 11000)
• MCP
Particle Detectors – B. Ketzer
DIRC
Principle:
BaBar DIRC
[I. Adam et al., Nucl. Instr. Meth. A 538, 281 (2005)]
Particle Detectors – B. Ketzer
BaBar DIRC Performance
300 ns
time window
8 ns
time window
e+e-µ+µ-
Particle Detectors – B. Ketzer
11.7 Transition Radiation Detector
v
u
Emission of radiation by a particle if β′ = =
v
changes abruptly
cn
• direction of v  synchrotron radiation
• absolute value of v  Bremsstrahlung
• Index of refraction n  transition radiation
Classical electrodynamics:
Consider particle traversing boundary between 2 materials with n1≠n2:
• transverse range of electromagnetic field different inside the 2 materials
y0 ∝ β ′γ ′ (relativistic expansion in 2-D model)
• rearrangement of fields
y
 time-dependent change of electromagnetic field
 radiation (indep. of velocity, i.e. no threshold!)
x
ze,β
• ~half of total energy in 2-20 keV range (X-rays)
• opening angle θ∼1/γ  forward direction
n n2
1
Transition Radiation Detector
Energy radiated by particle (charge ze) crossing vacuum-medium boundary:
W=
α z2
3
ωp ⋅ γ , ωp =
Typical photon energy:
nZe 2
εε 0 me
=
ω
1
ω p ⋅ γ
4
about half of total energy emitted in
0.1 ωpγ < ω < ωpγ  2-20 keV for ωp=20 eV
Number of photons per interface: ∝ α
 many transitions necessary: foil stack (100-1000 foils), foam/fibre material
γ dependence of emitted energy due to hardening of spectrum rather than
due to an increase of flux
Opening angle:
 emission along particle trajectory for large γ
Reabsorption of emitted radiation:
• lower for higher photon energies  X-ray TR used in detectors
• lower for small Z  low Z material: Li, PP, PE
Transition Radiation Spectrum
3 regions of emission spectrum:
i) large TR photon energy:
 large drop in intensity
ii) medium energies:
 logarithmic decrease with ω
ii) small energies:
 yield almost constant
Multilayer structure  interference
amplitudes for radiation at 1→2 and 2→1
of the same order of magnitude with
different sign
Absorption in radiator  lower cut-off in frequency spectrum
[PDG, K. Nakamura et al., J. Phys. G 37, 075021 (2010)]
Transition Radiation
Minimal thickness of radiatior material given by formation zone
distance along particle trajectory in given medium,
after which separation between particle and photon
is ~ λ
 loss of coherence, decoupling of particle and photon
Bulk of TR energy is emitted around last maximum:
l2 = thickness of foil
Particle Detectors – B. Ketzer
Transition Radiation Detector
Highly relativistic particle
 TR emitted along particle trajectory
 Signal from TR cannot be separated
in time and space from ionization signal,
i.e. superposition of Eγ and dE/dx
Pulse height spectrum
Detector:
• Radiator: low absorption of X-rays  low Z
• Actice medium:
high absorption of X-rays  high Z
• low ionization loss
 gaseous detector, e.g. MWPC or DC with Kr, Xe
[C.W. Fabjan et al., Rep. Progr. Phys. 43, 1003 (1980)]
Transition Radiation Detector
Detection methods:
i) Total energy deposition: Q method
 separation of TR and ionization signal through pulse height
but: Landau tail of ionization signal!
separation possible for γ > 1000,
i.e. for e- with p > 0.6 GeV/c
for π with p > 140 GeV/c
ii) Cluster counting: N method
• Measure distribution of charge density along particle track
• Cluster distribution due to ionization follows Poisson distribution
 smaller tails than Landau distribution
 less overlap with TR signal
Particle Detectors – B. Ketzer
ALICE TRD
• 18 TRD supermodules
• 540 drift chambers
• length, diam. ~ 7m
Particle Detectors – B. Ketzer
ATLAS TRT
Combination of Central Tracker and
TR for electron identification
End-cap
Detecting element:
straw tube 4 mm diam., 30 µm W/Au wire
fast gas: Xe/CO2/O2 (70/27/3)
C-fiber shell
Radiator
Straws
Tension plate
Layers of straws
& radiators
HV &
signal
Particle Detectors – B. Ketzer
readout
Overview PID Detectors
[C. Lippmann, arxiv.org/abs/1101.3276]
Particle Detectors – B. Ketzer
Overview PID Detectors
Particle Detectors – B. Ketzer