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Calorimetry - 1Calorimetry - 1Mauricio Barbi

University of Regina

TRIUMF Summer InstituteJuly 2007

Some Literature

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 Livan (INFN and Pavia University) 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

Introduction http://en.wikipedia.org/wiki/Calorimeterhttp://en.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.

The word Calorimeter comes from the Latin calor meaning heat, and from the Greek metry meaning to measure.

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 = massT = change in temperature

TmQc

0.20.84Glass0.190.79Granite0.492.05Ice (-10 C)

14.186Water0.582.4Alcohol(ethyl)

0.0920.38Brass0.09230.386Copper0.02940.123Bismuth

0.2150.9Aluminumc 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

ETwater

14108.3

IntroductionStill at http://en.wikipedia.org/wiki/CalorimeterStill at http://en.wikipedia.org/wiki/Calorimeter: In particle (and nuclear) physics, a calorimeter is a component of

a detector that measures the energy of entering particles

IntroductionMain goals:Main goals: Provide information to fully reconstruct the 4-vector p= (E,p) of a particle Complementary to tracking detectors at very high energies:

Provide particle ID based on different energy deposition pattern for different particles species (e/π, etc)

Though neutrinos are not directly detected, they can be identified from the missing energy needed for energy conservation to hold

Segmentation of the calorimeter can also provide space coordinates of particles. Time information also possible with high resolution achievable

Usually important in removing background (cosmic rays, beam spills, etc)

energymissingmeasureddirectly

miss

vis

missvis

EE

EEE

pp

ΔpEE

E :chambers drifiting;1)( :rsCalorimete

IntroductionBasic principles:

Sensitive to both charged (e±, ±, π±, etc) and neutral particles (, π0, etc) Total energy absorption

Particle is “completely destroyed” Destructive process

The mechanism evolves as: Entering particle interact with matter Energy deposition by development of showers of decreasingly lower-energy

particles produced in the interactions of particle with matter Electromagnetic showers produced by electromagnetic processes Hadronic showers produced by hadronic processes (+ EM components)

The energy of the particles produced in the showers is converted into ionization or excitation of the matter which compounds the calorimeter energy loss

The calorimeter response is proportional to the energy of the entering particle (note the statistical process in the previous item) σ(E)/E=A/E-1/2

IntroductionCalorimeter is a complicate device:

Particle has to be completely absorbed in order to have its energy fully detected

Depends on detector material, its size and geometry

Several things happen during this process Showers are product of competing physics interactions between particle and

matter Again, this depends on detector material

Particle ID and energy measurement through development of showers (with exception of muons)

Statistical processes fluctuations detector resolution Depends on the energy of the particle, calorimeter uniformity, etc Detector material, its size and geometry to fully contain the showers

Different calorimeter types for different physics goals Faster response? Better energy resolution? Spatial coordinates? Hadronic

particles? EM particles? Etc…..

Introduction More about EM interaction of particle with matter in this

lecture

Development of showers and energy resolution in the next lecture

detectors absorbers

d

EM shower in a sampling calorimeter

εK

εL

e

atomAtomic electron

Free electron

Compton scattering

IntroductionSome applications of calorimetry in particle physics

Basic mechanism used in calorimetry in particle physics to measure energy

Cherenkov light

Scintillation light

Ionization charge

IntroductionNeutrino physics Super-Kamiokande (SK) - Japan

Measurement of neutrino oscillations Water as active material Energy measurement through Cherenkov radiation

~12K PMTs50K metric ton of water

IntroductionUltra high energy cosmic ray The Pierre Auger Observatory (world’s largest calorimeter)

Measure charged particles with E > 1019 eV Atmosphere as the calorimeter Surface detectors to measure energy and shower profile

3000 Km2

Air shower

16K water Cherenkov detectors

IntroductionCollider experiments ZEUS at HERA e-p collider, Germany

Study the proton structure and confront QCD predictions Uranium-scintillator sampling calorimeter Energy measured using scintillating light

Rear calorimeter

Central tracking

Forward calorimeter

Barrel calorimeter

IntroductionCollider experiments

ATLAS at LHC p-p collider, Switzerland Search for Higgs, SUSY particles, CP violation, QCD, etc Liquid Argon/Pb (EM) and Cu (or W) (Hadron) sampling Calorimeter Energy measured using ionization in the liquid argon

Solenoid Forward CalorimetersMuon DetectorsElectromagnetic Calorimeters

EndCap Toroid

Barrel Toroid Inner Detector Hadronic Calorimeters Shielding

Interactions of Particles with MatterWe have seen that the calorimeter is based on absorption It is important to understand how particles interact with matter Several physics processes involved, mostly of electromagnetic nature Energy deposition, or loss, mostly by ionization or excitation of matter

One can initially separate the interactions into two classes Electromagnetic (EM) processes (this lecture):

Main photon interactions with matter: Compton scattering Pair Production Photoelectric effect

Main electron interactions with matter: Bremsstrahlung Ionization Cherenkov radiation (not covered in this lecture)

Interactions of Particles with MatterInteractions of PhotonsInteractions of Photons

For a beam of photons traversing a layer of material (Beer-Lambert’s law):

α = /ρ is called mass absorption coefficient.

Also,

λ = α-1 [g/cm2] = photon mass attenuation length

Xρμμx eIeII(X) 00

][cmμ

]cmg[ρxX

]cmg [ρ

[cm]xI

-1

2

3

0

t coefficien absorptionlinear

thicknessmass

material theofdensity

layer theof thicknessintensity beam initial

λXeII(X) 0λXeP 1

Probability that the photon will interact in thickness X of material

ρx

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 different response to photons as a function of the photon energy

Why? Next slide

http://pdg.lbl.gov

Interactions of Particles with MatterInteractions of PhotonsInteractions of PhotonsCross-section for photon absorptionTotal cross-section σ for photon absorption is related to the total mass attenuation length λ:

Several processes contribute to the total cross-section:

The “+…” in the above expression includes: Rayleigh scattering, where the atom is neither ionized or excited Photonuclear absorption

ANA

λσ 1

number sAvogrado'mol 10 99(47) 141 6.022N

]molg[ material theof mass AtomicA1-23

A

productionpair epair

scatteringCompton Compeffect ricPhotoelectp.e.

-

e

...σσσσ pairCompp.e. Therefore, different processes contributes with different attenuations:

Aii N

λ 1

... pair, Comp, p.e.,i

http://pdg.lbl.gov

Interactions of Particles with MatterInteractions of PhotonsInteractions of PhotonsCross-section for photon absorption

Since a calorimeter has to fully absorb the energy of an interacting photon: Important to understand the cross-sections as a function of the photon energy in

different material Will ultimately define the geometry and composition of a calorimeter

The cross-section calculations are difficult due to atomic effects, but there are fairly good approximations:

Depend on the absorber material 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

Can be considered as an interaction between a photon and an atom as a whole

Can occur if a photon has energy E > Eb

(Eb = binding energy of an electron in the atom).

The photon energy is fully transferred to the electron Electron is ejected with energy T = E - Eb

Discontinuities in the cross-section due to discrete energies Eb of atomic electrons (strong modulations at E=Eb; L-edges, K-edges, etc)

Dominating process at low ’s energies ( < MeV ). Gives low energy electrons

e)(Xion (X) atom

e-

X+X

p.e. cross-section in Pb

E

Kleinknecht

Interactions of PhotonsInteractions of PhotonsPhotoelectric effect

Cross-section:

Let (reduced photon energy)

For εK < ε < 1 ( εK is the K-absorption edge):

For ε >> 1 (“high energy” photons):

σp.e goes with Z5/ε

Interactions of Particles with Matter

2cmEε

e

γ

eTh

Kp.e. σZα

εσ 54

7

21

32

εZαπrσ e

Kp.e.

14 542

p.e. cross-section in Pb

E

εK

εL

ε = 1εK

constant) structure (fine,137

1

)(Thomson 38

e

2

α

πrσ eeTh

Interactions of Particles with MatterInteractions of PhotonsInteractions of PhotonsCompton scattering

A photon with energy E,in scatters off an (quasi-free) atomic electron

A fraction of E,in is transferred to the electron

The resulting photon emerges with E,out < E,in and at different direction

Using conservation of energy and momentum:

The energy of the outgoing photon is:

, where E

)E(EEEcmθ γ,outγ,in

γ,outγ,in

e 2

1cos

2cmE

εe

γ,inθ)ε(

EE γ,in

γ,out cos11

εK

εL

e

atomAtomic electron

Free electron e)(Xion (X) atom

1for ,22

1121

221

2 2

,,

22

cmEE

εεE

εεcmT e

ininγ,inee

Interactions of Particles with MatterInteractions of PhotonsInteractions of PhotonsCompton scattering

The energy transferred to the electron:

Two extreme cases of energy loss: 0 : E,out E,in ; Te 0 No energy transferred to the electron

Backscattered at = π :

Compton edge

θ)ε(θ)(εcmEET eγ,outγ,ine cos11

cos122

1221

2

, for εcmε

EE eγ,in

γ,out E

ε = 1εK

E,

out /

E,

in

Coherent scattering(Rayleigh)

Incoherent scattering(electron is removed from atom)

E,in [MeV]

Interactions of Particles with MatterInteractions of PhotonsInteractions of PhotonsCompton scatteringTotal Compton cross-section per electron given by Klein-Nishina (QED) (1929):

.

Two extreme cases:

ε << 1 : Backward-forward symmetry in distribution

ε >> 1 :

distribution peaks in the forward direction

Cross-section per atom:

222

213121ln

2121ln1

211212

εεε)(

εε

εεε)(

εεπrσ e

eComp

21 eTh

eComp

2ln

211

83 e

TheComp

eComp

atomicComp Z

Includes coherent and incoherent scattering

Incoherent scattering only

Interactions of PhotonsInteractions of PhotonsPair Production

An electron-positron pair can be created when (and only when) a photon passes by the Coulomb field of a nucleus or atomic electron this is needed for conservation of momentum.

Threshold energy for pair production at E = 2mc2 near a nucleus. E = 4mc2 near an atomic electron

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 eenucleusγ

Z

e+

e-

+ e- e+ + e- + e-

+ nucleus 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:

Does not depend on the energy of the photon, but

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 183ln974

ZαZrσ e

npair

31

137

2Zσ npair

3

1220

0 183ln4

1 where,1971

ZαZrNAX

AN

λe

A

npair

Anpair 07

9 Xλnpair

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 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, for elements up to U, can be approximate to

Where a = αZPDG also gives a fitting function:

e LZf(Z))LZA

NαrX 2210 4

6422

2 002000830036902020601

1 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

Xw

X 0

1

Interactions of Particles with MatterInteractions of PhotonsInteractions of PhotonsSummary

http://pdg.lbl.gov

productionpair pair

scatteringCompton Compeffect ricPhotoelectp.e.

-

pairCompp.e.

ee

...σσσσ

Rayleigh scattering

Compton

Pair production

Photoeletric effect

Michele Livan

Energy range versus Z for more likely process:

Calorimeters?Curiosity 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)

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