Calorimetry Calorimetry - - 1 1 Mauricio Barbi University of Regina TRIUMF Summer Institute July 2007
Calorimetry Calorimetry -- 11
Mauricio BarbiUniversity of Regina
TRIUMF Summer InstituteJuly 2007
Some Literature
1. “Detector for Particle Radiation”, Konrad Kleinknecht, Cambridge University Press
2. “Introduction to Experimental Particle Physics”, Richard Fernow, Cambridge University Press
3. “Techniques in calorimetry”, Richard Wigmans, Cambridge University Press4. Particle Data Group (PDG): http://pdg.lbl.gov/
Thanks to Michele Levin (INFN and PaviaUniversity) for letting me use some of his material and examples in these lectures
Principles of CalorimetryPrinciples of Calorimetry(Focus on Particle Physics)(Focus on Particle Physics)
Lecture 1:Lecture 1:i. Introductionii. Interactions of particles with matter (electromagnetic)iii. Definition of radiation length and critical energy
Lecture 2:i. Development of electromagnetic showersii. Electromagnetic calorimeters: Homogeneous, sampling.iii. Energy resolution
Lecture 3:i. Interactions of particle with matter (nuclear) ii. Development of hadronic showers iii. Hadronic calorimeters: compensation, resolution
Introductionàà http://http://en.wikipedia.org/wiki/Calorimeteren.wikipedia.org/wiki/Calorimeter:
– A calorimeter is a device used for calorimetry– Calorimetry is the science of measuring the heat generated or absorbed in a chemical reaction
or physical process.
à The word Calorimeter comes from the Latin calor meaning heat, and from the Greek metrymeaning to measure.
à A primitive calorimeter was invented by Benjamin Thompson (17th century): “When a hot object is set within the water, the system's temperature increases. By measuring the
increase in the calorimeter's temperature, factors such as the specific heat (the amount of heat lost per gram) of a substance can be calculated.” (http://www.bookrags.com/Calorimeter)
Bomb calorimeter
IntroductionSpecific heat is the amount of heat per unit mass required to raise the temperature by one Kelvin:
Q = heat added (energy)c = specific heatm = mass∆T = change in temperature
tcmQ ∆=
0.20.84Glass0.190.79Granite0.492.05Ice (-10 C)
14.186Water0.582.4Alcohol(ethyl)
0.0330.14Mercury0.09250.387Zinc0.03210.134Tungsten0.05580.233Silver0.03050.128Lead0.03010.126Gold0.0920.38Brass
0.09230.386Copper0.02940.123Bismuth0.2150.9Aluminum
c in cal/gm Kc in J/gm KSubstance
How to measure the energy of a particle?
Let’s consider that we have a calorimeter with 1 liter of water as absorber. Using the formula and table from previous slide, let’s solve the following problems?
What is the effect of a 1 GeV particle (e.g., at LHC) in the calorimeter?
This is a far too small temperature change to be detected in the calorimeter.
New techniques of detection are needed in particle physics.
Introduction
KcM
ET
water
14108.3 −×=×
=∆
IntroductionStill at Still at http://http://en.wikipedia.org/wiki/Calorimeteren.wikipedia.org/wiki/Calorimeter:à In particle (and nuclear) physics, a calorimeter is a component of a
detector that measures the energy of entering particles
IntroductionMain goals:ð Provide information to fully reconstruct the 4-vector pµ= (E,p) of a particleð Complementary to tracking detectors at very high energies:
ð Provide particle ID based on different energy deposition pattern for different particles species (e/p, etc)ü Though neutrinos are not directly detected, they can be identified from the missing
energy needed for energy conservation to hold
ð Segmentation of th calorimeter can also provide space coordinates of particles. Time information also possible with high resolution achievable
ð Usually important in removing background (cosmic rays, beam spills, etc)
energymissingmeasureddirectly
==
+=
miss
vis
missvis
EE
EEE
pp
? pEE
E∝∝ :chambers drifiting;
1)( :rsCalorimeteσ
IntroductionBasic principles:ð Sensitive to both charged
(e±, µ±, p±, etc) and neutral particles (γ, p0, etc)
ð Total energy absorptionü Particle is “completely destroyed”
Destructive processð The mechanism evolves as:ü Entering particle interact with matter
ü Energy deposition by development of showers of decreasingly lower-energy particles produced in the interactions of particle with matter
ü Electromagnetic showers à produced by electromagnetic processes
ü Hadronic showers à produced by hadronic processes (+ EM components)
ü The energy of the particles produced in the showers is converted into ionization or excitation of the matter which compounds the calorimeterà energy loss
ð The calorimeter response is proportional to the energy of the enteringparticle (note the statistical process in the previous item)
IntroductionCalorimeter is a complicate device: ð Particle has to be completely absorbed in order to have its
energy fully detectedØ Depends on detector material, its size and geometry
ð Several things happen during this processØ Showers are product of competing physics interactions between particle and
matter ü Again, this depends on detector material
ð Particle ID and energy measurement through development of showers or (with exception of muons)Ø Statistical processes à fluctuations à detector resolutionØ Depends on the energy of the particle, calorimeter uniformity, etcØ Detector material, its size and geometry to fully contain the showers
ð Different calorimeter types for different physics goalsØ Faster response? Better energy resolution? Spatial coordinates? Hadronic
particles? EM particles? Etc…..
Introductionq More about EM interaction of particle with matter in this
lecture
q Development of showers andenergy resolution in the next lecture
detec to rs absorbers
d
EM shower in a sampling calorimeter
eK
eL
e
γ
γ
θ
atomAtomic electron
φ
Free electron
Compton scattering
IntroductionSome applications of calorimetry in particle physics
Ø Basic mechanism used in calorimetry in particle physics to measure energy
Ø Cherenkov light
Ø Scintillation light
Ø Ionization charge
IntroductionNeutrino physicsØ Super-Kamiokande (SK) - JapanØ Measurement of neutrino oscillationsØ Water as active materialØ Energy measurement through Cherenkov
radiation
~12K PMTs50K metric ton of water
IntroductionUltra high energy cosmic rayØ The Pierre Auger Observatory (world’s largest calorimeter)Ø Measure charged particles with E > 1019 eVØ Atmosphere as the calorimeterØ Surface detectors to
measure energy and shower profile
3000 Km2
Air shower
16K water Cherenkov detectors
IntroductionCollider experimentsØ ZEUS at HERA e-p collider, GermanyØ Study the proton structure and confront QCD predictionsØ Uranium-scintillator sampling calorimeterØ Energy measured using scintillating light
Rear calorimeter
Central tracking
Forward calorimeter
Barrel calorimeter
IntroductionCollider experimentsØ ATLAS at LHC p-p collider, SwitzerlandØ Search for Higgs, SUSY particles, CP violation, QCD, etcØ Liquid Argon/Pb (EM) and Cu (or W) (Hadron) sampling CalorimeterØ Energy measured using ionization in the liquid argon
Solenoid Forward Calorimeters
Muon DetectorsElectromagnetic Calorimeters
EndCap Toroid
Barrel Toroid Inner Detector Hadronic Calorimeters Shielding
Interactions of Particles with MatterWe have seen that the calorimeter is based on absorptionØ It is important to understand how particles interact with matterØ Several physics processes involved, mostly of electromagnetic natureØ Energy deposition, or loss, mostly by ionization or excitation of matter
One can initially separate the interactions into two classes
Ø Electromagnetic (EM) processes (this lecture):Ø Main photon interactions with matter: Ø Compton scatteringØ Pair ProductionØ Photoelectric effect
Ø Main electron interactions with matter:Ø BremsstrahlungØ IonizationØ Cherenkov radiation (not covered in this lecture)
Ø Hadronic processes (next lecture): more complicate business than EMà nuclear interactions between hadrons (charged or neutral) and matter
Interactions of Particles with MatterInteractions of PhotonsInteractions of Photons
For a beam of photons traversing a layer of material (Beer-Lambert’s law):
a = µ/? is called mass absorption coefficient.
Also,
? = a-1 [g/cm2] = photon mass attenuation length
( )X?µµx eIeII(X) −− == 00
][cmµ
]cmg[?xX
]cmg [?
[cm]x
I
-1
2
3
0
t coefficien absorptionlinear
thicknessmass
material theofdensity
layer theof thickness
intensity beam initial
=
==
=
==
?XeII(X) −= 0?XeP −−= 1
Probability that the photon will interact in thickness X of material
?µx
Interactions of Particles with MatterInteractions of PhotonsInteractions of PhotonsPhoton attenuation length for different elemental absorbers versus photon energy
Note the different patterns for different elements à different response to photons as a function of the photon energy
Why? à Next slide
http://pdg.lbl.gov
Interactions of Particles with MatterInteractions of PhotonsInteractions of PhotonsCross-section for photon absorptionTotal cross-section s for photon absorption is related to the total mass attenuation length ?:
Several processes contribute to the total cross-section:
The “+…” in the above expression includes: Ø Rayleigh scattering, where the atom is neither ionized or excitedØ Photonuclear absorption
ANA
?s
1=
number sAvogrado'mol 10 99(47) 141 6.022N
]molg[ material theof mass AtomicA1-23
A ==
=
productionpair epair
scatteringCompton Compeffect ricPhotoelectp.e.
-+=
==
+++=
e
...ssss pairCompp.e. Therefore, different processes contributes with different attenuations:
Aii N
As
?1
=
... pair, Comp, p.e.,=i
http://pdg.lbl.gov
Interactions of Particles with MatterInteractions of PhotonsInteractions of PhotonsCross-section for photon absorption
à Since a calorimeter has to fully absorb the energy of an interacting photon:à Important to understand the cross-sections as a function of the photon energy in
different materialà Will ultimately define the geometry and composition of a calorimeter
à The cross-section calculations are difficult due to atomic effects, but there are fairly good approximations:à Depend on the absorber materialà Depend on the photon energy
Let’s then visit some of the processes cited in the previous slide
Interactions of Particles with MatterInteractions of PhotonsInteractions of PhotonsPhotoelectric effect
à Can be considered as an interaction between a photon and an atom as a whole
à Can occur if a photon has energy Eγ > Eb(Eb = binding energy of an electron in the atom).
Ø The photon energy is fully transferred to the electron
Ø Electron is ejected with energy T = Eγ - Eb
à Discontinuities in the cross-section due to discreteenergies Eb of atomic electrons(strong modulations at Eγ=Eb; L-edges, K-edges, etc)
à Dominating process at low γ’s energies ( < MeV ).à Gives low energy electrons
−+ +→+ e)(Xion (X) atomγ
e-
X+X
p.e. cross-section in Pb
Eγ
Kleinknecht
Interactions of PhotonsInteractions of PhotonsPhotoelectric effect
à Cross-section:
Let (reduced photon energy)
For eK < e < 1 ( eK is the K-absorption edge):
For e >> 1 (“high energy” photons):
s p.e goes with Z5/e
Interactions of Particles with Matter
2cmE
ee
?=
eTh
Kp.e. sZa
es 54
7
21
32
=
eZaprs e
Kp.e.
14 542=
p.e. cross-section in Pb
Eγ
eK
eL
e = 1eK
radiuselectron Classical r
constant) structure (fine,137
1
)(Thomson 38
e
2
=
=
=
a
prs eeTh
Interactions of Particles with MatterInteractions of PhotonsInteractions of PhotonsCompton scattering
à A photon with energy Eγ,in scatters off an(quasi-free) atomic electron
à A fraction of Eγ,in is transferred to the electron
à The resulting photon emerges with Eγ,out < Eγ,in
and at different direction
Using conservation of energy and momentum:
The energy of the outgoing photon is:
, where
Eγ
)E(EEEcm
? ?,out?,in?,out?,in
e −−=2
1cos
2cm
Ee
e
?,in=?)e(
EE ?,in
?,out cos11 −+=
eK
eL
e
γ
γ
θ
atomAtomic electron
φ
Free electron−+ +→+ e)(Xion (X) atomγ
Interactions of Particles with MatterInteractions of PhotonsInteractions of PhotonsCompton scattering
à The energy transferred to the electron:
Two extreme cases of energy loss:à θ ≈ 0 : Eγ,out ≈ Eγ,in ; Te ≈ 0
ð No energy transferred to the electron
à Backscattered at θ = p :
Compton edge
?)e(?)(e
cmEET e?,out?,ine cos11cos12
2
−+−
=−=
1221
2
>>→+
= , for ecm
e
EE e?,in
?,out
eK 1for ,22
1121
221
2 2
,,
22 >>−=
−→
+=
+= ε
ε γγcmEE
eeE
eecmT e
inin?,inee
Eγ
e = 1eK
Eγ,
out/ E
γ,in Coherent scattering
(Rayleigh)
Incoherent scattering(electron is removed from atom)
Eγ ,in [MeV]
http://www.mathcad.com/Library/LibraryContent/MathML/compton.htm
Interactions of Particles with MatterInteractions of PhotonsInteractions of Photons
Compton scatteringTotal Compton cross-section per electron given by Klein-Nishina (QED) (1929):
.
Two extreme cases:
e << 1 :
à Backward-forward symmetry in θ distribution
e >> 1 :
à θ distribution peaks in the forward direction
Cross-section per atom:
( )( )
++
−++
+−
++
+
= 222
2131
21ln21
21ln1
21121
2ee
e)(e
eee
e)(e
eprs e
eComp
( )εσσ 21−= eTh
eComp
( )
+= ε
εσσ 2ln
211
83 e
TheComp
eComp
atomicComp Zσσ ≈
Includes coherent and incoherent scattering
Incoherent scattering only
http://www.mathcad.com/Library/LibraryContent/MathML/compton.htm
Interactions of PhotonsInteractions of PhotonsPair Production
à An electron-positron pair can be created when (and only when) a photon passes by the Coulombfield of a nucleus or atomic electron à this isneeded for conservation of momentum.
Threshold energy for pair production atEγ = 2mc2 near a nucleus.Eγ = 4mc2 near an atomic electron
à Pair production is the dominant photon interaction process at high energies. Cross-section from production in nuclear field is dominant.
First cross-section calculations made by Bethe and Heitler using Born approximation (1934).
Interactions of Particles with Matter
nucleus eenucleus? +→+ −+
Z
e+
e-
γ + e-à e+ + e- + e-
γ + nucleusà e+ + e- + nucleus
Interactions of Particles with MatterInteractions of PhotonsInteractions of PhotonsPair Production (Attenuation length)The interesting energy domain is that of several hundred MeV or more, . The cross- section per nucleus is:
à Does not depend on the energy of the photon, but
à Mass attenuation length for pair creation (check few slides ago):
or
Accurate to within a few percent down to energies as low as 1 GeV
X0 is called radiation length and corresponds to a layer thickness of material where pair creation has a probability P = 1 – e-7/9 ≈ 54%
≈
31
22 183ln
97
4Z
aZrs enpair
31
137
Ze >>
2Zs npair ∝
===3
1220
0 183ln4
1 where,
1971
ZaZrNA
XX
sA
N?
eA
npair
Anpair
079
X?npair =
Interactions of Particles with MatterInteractions of PhotonsInteractions of PhotonsPair Production
Photon pair conversion probability
P=54%
097
1 XX
eP−
−=
http://pdg.lbl.gov
Interactions of Particles with MatterInteractions of PhotonsInteractions of PhotonsPair Production (Attenuation Length)Along with Bremsstrahlung (more later), pair production is a very important process in the development of EM showers à X0 is a key parameter in the design of a calorimeter
There are more complicate expressions for X0 in the literature:
(PDG, http://pdg.lbl.gov)
Lrad is similar to the expression for X0 in the previous slide L’rad replaces 183Z-1/3 by 1194Z-2/3
f(z) is an infinite sum which can be approximate to
Where a = aZPDG also gives a fitting function:
( )[ ]radradA
e LZf(Z))LZA
NarX ′+−=− 221
0 4
−+−+
+= 642
22 00200083003690202060
11
a.a.a..a
af(Z)
+
= 20287ln1
716cm
g
Z)Z(Z
AX
Interactions of Particles with MatterInteractions of PhotonsInteractions of PhotonsPair Production
For compound mixtures:
Where,
wj = weight fraction of each element in the compound
j = “jth” element
http://pdg.lbl.gov
∑=j j
j
X
w
X0
1
Interactions of Particles with MatterInteractions of PhotonsInteractions of PhotonsSummary
http://pdg.lbl.gov
productionpair pair
scatteringCompton Compeffect ricPhotoelectp.e.
-
pairCompp.e.
ee
...ssss
+=
==
+++=
Rayleighscattering
Compton
Pair production
Photoeletric effect
Michele Livan
Energy range versus Z for more likely process:
Interactions of Particles with MatterInteractions of ElectronsInteractions of ElectronsIonization (Fabio Sauli’s lecture)
For “heavy” charged particles (M>>me: p, K, p, µ), the rate of energy loss (or stopping power) in an inelastic collision with an atomic electron is given by the Bethe-Block equation:
δ(ß?) : density-effect correction
C: shell correction
z: charge of the incident particle
ß = vc of the incident particle ; γ = (1-ß2)-1/2
Wmax: maximum energy transfer in one collision
I: mean ionization potential
−−−
=−
gcm
MeVZC
dßI
Wcmßz
AZ
cmrNdxdE e
eeA 2)(22
ln2 22
max222
2
222 βγ
γβπ
http://pdg.lbl.gov
Interactions of Particles with MatterInteractions of ElectronsInteractions of ElectronsIonizationFor electrons and positrons, the rate of energy loss is similar to that for “heavy”charged particles, but the calculations are more complicate:à Small electron/positron massà Identical particles in the initial and final stateà Spin ½ particles in the initial and final states
k = Ek/mec2 : reduced electron (positron) kinetic energyF(k,ß,γ) is a complicate equation
However, at high incident energies (ß≈1)à F(k) ≈ constant(next slide)
−−−
+=−
gcm
MeVZC
kF
cmI
)(kkßA
ZcmrpN
dxdE
e
eeA 2),,(2
2ln
12
22
2
222 δγβ
Interactions of ElectronsInteractions of ElectronsIonizationAt this high energy limits (ß≈1), the energy loss for both “heavy” charged particles and electrons/positrons can be approximate by
Where,
The second terms indicates that the rate of relativistic rise for electrons is slightly smaller than for heavier particles
Interactions of Particles with Matter
−+
∝− B?A
Icm
dxdE e ln
2ln2
2
A Belectrons 3 1.95heavy charged particles 4 2
Interactions of ElectronsInteractions of ElectronsBremsstrahlung (breaking radiation)
A particle of mass mi radiates a real photon while being decelerated in the Coulomb field of a nucleus with a cross section given by:
à Makes electrons and positrons the only significant contribution to this process for energies up to few hundred GeV’s.
Interactions of Particles with Matter
EE
mZ
dEd
i
ln2
2
∝σ mi
2 factor expected since classically radiation2
2
=∝
ii m
Fa
32
1037 ×≈
=
e
µ
µ
em
m
dEds
dEds
Interactions of ElectronsInteractions of ElectronsBremsstrahlung
The rate of energy loss for high energy electrons ( k >> 137/Z1/3 ), is giving by:
Recalling from pair production
à
The radiation length X0 is the layer thickness that reduces the electron energy by a factor e (≈63%)
Interactions of Particles with Matter
EZA
NaZr
dxdE A
e
≈−
31
183ln4 22
=3
1220
183ln4
1
ZaZrNA
Xe
A
00
0
Xx
eEE(x)XE
dxdE −
=⇒−=
Interactions of ElectronsInteractions of ElectronsBremsstrahlung
Radiation loss in lead.
Interactions of Particles with Matter
http://pdg.lbl.gov
Interactions of ElectronsInteractions of ElectronsBremsstrahlung and Pair production
à Note that the mean free path for photons for pair production is very similar to X0
for electrons to radiate Bremsstrahlung radiation:
à This fact is not coincidence, as pair production and Bremsstrahlung have very similar Feynman diagrams, differing only in the directions of the incidentand outgoing particles (see Fernow for details and diagrams).
In general, an electron-positron pair will each subsequently radiate a photon by Bremsstrahlung which will produce a pair and so forth à shower development.
Interactions of Particles with Matter
079
X?pair =
Interactions of ElectronsInteractions of ElectronsBremsstrahlung (Critical Energy)Another important quantity in calorimetry is the so called critical energy. One definition is that it is the energy at which the loss due to radiation equals that due to ionization. PDG quotes the Berger and Seltzer:
Interactions of Particles with Matter
( ) ionc
Bremcc )(E
dxdE)(E
dxdE
.ZMeVE =+
≈ when21
800http://pdg.lbl.gov
http://pdg.lbl.govOther definition à Rossi
Summary of the basic EM interactionsSummary of the basic EM interactions
Interactions of Particles with Matter
e+ / e-
§ Ionisation
§ Bremsstrahlung
§ Photoelectric effect
§ Compton effect
§ Pair production
E
E
E
E
E
γ
dE
/dx
dE
/dx
σ
σ
σ
Z
Z(Z+1)
Z5
Z
Z(Z+1)
Calorimeters?Curiosity à Primitive calorimeter invented by Benjamin Thompson (17th century):
“We owe the invention of this device to an observation made just before the turn of the nineteenth century by the preeminent scientist Benjamin Thompson ( Count Rumford). While supervising the construction of cannons, Rumford noticed that as the fire chamber was bored out, the metal cannons would heat up. He observed that the more work the drill exerted in the boring process, the greater the temperature increase. To measure the amount of heat generated by this process, Count Rumford placed the warm cannon into a tub of water and measured the increase in the water's temperature. In doing so, he simultaneously invented the science of calorimetry and the first primitive calorimeter. In simplest terms, a modern calorimeter is a water-filled insulated chamber. When a hot object is set within the water, the system's temperature increases. By measuring the increase in the calorimeter's temperature, a scientist can calculate such factors as the specific heat (the amount of heat lost per gram) of a substance. Another application of calorimetry is the determination of the calorific value of certain fuels--that is, the amount of energy obtained when fuel is burned. Engineers burn the fuel completely within a calorimeter system and then measure the temperature increase within the device. The amount of heat generated by this burning is indicative of the fuel's calorific value. “ (http://www.bookrags.com/Calorimeter)