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Electromagnetic Calorimeters Calorimetry I

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Page 1: Calorimetry I - particle.korea.ac.krparticle.korea.ac.kr/class/2011/phy603/Lecture9.pdfDie allermeisten Kalorimeter sind überdies positionssensitiv ausgeführt, um die Energiedeposition

Electromagnetic CalorimetersCalorimetry I

Page 2: Calorimetry I - particle.korea.ac.krparticle.korea.ac.kr/class/2011/phy603/Lecture9.pdfDie allermeisten Kalorimeter sind überdies positionssensitiv ausgeführt, um die Energiedeposition

M. Krammer: Detektoren, SS 05 Kalorimeter 2

6.1 Allgemeine GrundlagenFunktionsprinzip – 1

! In der Hochenergiephysik versteht man unter einem Kalorimeter einenDetektor, welcher die zu analysierenden Teilchen vollständig absorbiert. Da-durch kann die Einfallsenergie des betreffenden Teilchens gemessen werden.

! Die allermeisten Kalorimeter sind überdies positionssensitiv ausgeführt, umdie Energiedeposition ortsabhängig zu messen und sie beim gleichzeitigenDurchgang von mehreren Teilchen den individuellen Teilchen zuzuordnen.

! Ein einfallendes Teilchen initiiert innerhalb des Kalorimeters einen Teilchen-schauer (eine Teilchenkaskade) aus Sekundärteilchen und gibt so sukzessiveseine ganze Energie and diesen Schauer ab.

Die Zusammensetzung und die Ausdehnung eines solchen Schauers hängenvon der Art des einfallenden Teilchens ab (e±, Photon oder Hadron).

Bild rechts: Grobes Schemaeines Teilchenschauers ineinem (homogenen) Kalorimeter

Introduction

Calorimeter: Detector for energy measurement via total absorption of particles ...

Also: most calorimeters are position sensitive to measure energy depositionsdepending on their location ...

Principle of operation:

detector volume

incident particle

particle cascade (shower)

Incoming particle initiates particle shower ...Shower Composition and shower dimensions depend on particle type and detector material ...

Energy deposited in form of: heat, ionization,excitation of atoms, Cherenkov light ...Different calorimeter types use different kinds ofthese signals to measure total energy ...

Important:

Signal ~ total deposited energy [Proportionality factor determined by calibration]

Schematic of calorimeter principle

Page 3: Calorimetry I - particle.korea.ac.krparticle.korea.ac.kr/class/2011/phy603/Lecture9.pdfDie allermeisten Kalorimeter sind überdies positionssensitiv ausgeführt, um die Energiedeposition

Introduction

Energy vs. momentum measurement:σE

E∼ 1√

ECalorimeter:[see below]

Gas detector:[see above]

σp

p∼ p

e.g. ATLAS:σE

E≈ 0.1√

E

σp

p≈ 5 · 10−4 · pt

e.g. ATLAS:

i.e. σE/E = 1% @ 100 GeV i.e. σp/p = 5% @ 100 GeV

At very high energies one has to switch to calorimeters because their resolution improves while those of a magnetic spectrometer decreases with E ...

Shower depth:

Calorimeter:[see below]

L ∼ lnE

Ec

[Ec: critical energy]

Shower depth nearly energy independenti.e. calorimeters can be compact ...

Compare with magnetic spectrometer:Detector size has to grow quadratically to maintain resolution

σp/p ∼ p/L2

Page 4: Calorimetry I - particle.korea.ac.krparticle.korea.ac.kr/class/2011/phy603/Lecture9.pdfDie allermeisten Kalorimeter sind überdies positionssensitiv ausgeführt, um die Energiedeposition

Introduction

Further calorimeter features:

Calorimeters can be built as 4π-detectors, i.e. they can detect particles over almost the full solid angleMagnetic spectrometer: anisotropy due to magnetic field; remember:

Calorimeters can provide fast timing signal (1 to 10 ns); can be used for triggering [e.g. ATLAS L1 Calorimeter Trigger]

(σp/p)2 = (σpt/pt)2 + (σθ/sin θ)2

large for small θ

Calorimeters can measure the energy of both, charged and neutral particles, if they interact via electromagnetic or strong forces [e.g.: γ, μ, Κ0, ...]

Magnetic spectrometer: only charged particles!

Segmentation in depth allows separation of hadrons (p,n,π±), from particles which only interact electromagnetically (γ,e) ...

...

Page 5: Calorimetry I - particle.korea.ac.krparticle.korea.ac.kr/class/2011/phy603/Lecture9.pdfDie allermeisten Kalorimeter sind überdies positionssensitiv ausgeführt, um die Energiedeposition

µ = nσ = ρNA

A· σpair

Electromagnetic Showers

Reminder:

X0

Dominant processes at high energies ...

Photons : Pair productionElectrons: Bremsstrahlung

Pair production:

dE

dx=

E

X0

dE

dx= 4αNA

Z2

Ar2e · E ln

183Z

13

σpair ≈79

�4 αr2

eZ2 ln183Z

13

=79

ρ

X0

Bremsstrahlung:

E = E0e−x/X0

[X0: radiation length][in cm or g/cm2]

Absorption coefficient:

After passage of one X0 electronhas only (1/e)th of its primary energy ...

[i.e. 37%]

=79

A

NAX0

Page 6: Calorimetry I - particle.korea.ac.krparticle.korea.ac.kr/class/2011/phy603/Lecture9.pdfDie allermeisten Kalorimeter sind überdies positionssensitiv ausgeführt, um die Energiedeposition

Electromagnetic Showers

Transverse size of EM shower given by radiation length via Molière radius [see also later]

RM =21 MeV

EcX0 RM : Moliere radius

Ec : Critical Energy [Rossi]X0 : Radiation length

Critical Energy [see above]:

Further basics:

20 27. Passage of particles through matter

0

0.4

0.8

1.2

0 0.25 0.5 0.75 1y = k/E

Bremsstrahlung

(X0

NA/A

) yd

! LP

M/d

y

10 GeV

1 TeV

10 TeV

100 TeV

1 PeV10 PeV

100 GeV

Figure 27.11: The normalized bremsstrahlung cross section k d!LPM/dk inlead versus the fractional photon energy y = k/E. The vertical axis has unitsof photons per radiation length.

2 5 10 20 50 100 200

CopperX0 = 12.86 g cm"2

Ec = 19.63 MeV

dE/dx

# X

0 (M

eV)

Electron energy (MeV)

10

20

30

50

70

100

200

40

Brems = ionization

Ionization

Rossi:Ionization per X0= electron energy

Tota

l

Brem

s $ E

Exact

brem

sstr

ahlu

ng

Figure 27.12: Two definitions of the critical energy Ec.

incomplete, and near y = 0, where the infrared divergence is removed bythe interference of bremsstrahlung amplitudes from nearby scattering centers

February 2, 2010 15:55

dE

dx(Ec)

����Brems

=dE

dx(Ec)

����Ion

ESol/Liqc =

610 MeVZ + 1.24

Approximations:

dE

dx

����Brems

=E

X0

dE

dx

����Ion

≈ Ec

X0= const.

with:

&

�dE

dx

Brems

��dE

dx

Ion

≈ Z · E

800 MeV

EGasc =

710 MeVZ + 0.92

Page 7: Calorimetry I - particle.korea.ac.krparticle.korea.ac.kr/class/2011/phy603/Lecture9.pdfDie allermeisten Kalorimeter sind überdies positionssensitiv ausgeführt, um die Energiedeposition

Electromagnetic Showers

X0 [cm] Ec [MeV] RM [cm]

Pb 0.56 7.2 1.6

Scintillator (Sz) 34.7 80 9.1

Fe 1.76 21 1.8

Ar (liquid) 14 31 9.5

BGO 1.12 10.1 2.3

Sz/Pb 3.1 12.6 5.2

PB glass (SF5) 2.4 11.8 4.3

Typical values for X0, Ec and RM of materials used in calorimeter

Page 8: Calorimetry I - particle.korea.ac.krparticle.korea.ac.kr/class/2011/phy603/Lecture9.pdfDie allermeisten Kalorimeter sind überdies positionssensitiv ausgeführt, um die Energiedeposition

Abbildung

8.2: Entw

icklungeines

elektromagnetischen

Schauers(M

onteCarlo

Simulation)

•Nur

dieProzesse

!+

K!

K+

e ++

e !

e+

K!

K+

e+

!

werden

berucksichtigt(K

=Kern).

•Auf der

StreckeX

0verliert

dase !

durchBrem

sstrahlungdie

Halfte

seinerEnergie

E1

=

E02

•Das

Photon

materialisiert

nachX

0 , dieEnergie

vonPositron

undElektron

betragt

=

E12

•Fur

E>

"tritt

keinEnergieverlust

durchIonisation/A

nregungauf.

•Fur

E"

"verlieren

dieElektronen

Energie

nurdurch

Ionisation/Anregung.

FolgendeGroßen

sindbei der

Beschreibung

einesSchauers

vonInteresse:

•Zahl der

Teilchenim

Schauer

•Lage

desSchauerm

aximum

s

•Longitudinalverteilung

desSchauers

imRaum

•Transversale

Breite

desSchauers

Wir

messen

dielongitudinalen

Kom

ponentendes

Schauersin

Strahlungslangen:

t=

xX0

Nach

Durchlaufen

derSchichtdicke

t betragtin

unseremeinfachen

Modell die

Zahl derschnel-

lenTeilchen

N(t)

=2 t

,156

Simple shower model:[from Heitler]

Only two dominant interactions: Pair production and Bremsstrahlung ...

γ + Nucleus ➛ Nucleus + e+ + e−

[Photons absorbed via pair production]

e + Nucleus ➛ Nucleus + e + γ[Energy loss of electrons via Bremsstrahlung]

Electromagnetic Shower[Monte Carlo Simulation]

Shower development governed by X0 ...After a distance X0 electrons remain with only (1/e)th of their primary energy ...

Photon produces e+e−-pair after 9/7X0 ≈ X0 ...

Analytic Shower Model

Eγ = Ee ≈ E0/2

Simplification:

Ee ≈ E0/2

[Ee looses half the energy]

[Energy shared by e+/e–]

Assume:

E > Ec: no energy loss by ionization/excitation

E < Ec: energy loss only via ionization/excitation

Use

... with initial particle energy E0

Page 9: Calorimetry I - particle.korea.ac.krparticle.korea.ac.kr/class/2011/phy603/Lecture9.pdfDie allermeisten Kalorimeter sind überdies positionssensitiv ausgeführt, um die Energiedeposition

t =x

X0

N(t) = 2t

E =E0

N(t)= E0 · 2−t

t = log2(E0/E)

N(E0, Ec) = Nmax = 2tmax =E0

Ec

N(E0, E1) = 2t1 = 2 log2(E0/E1) =E0

E1

N(E0, E1) ∝ E0tmax ∝ ln(E0/Ec)➛

Simple shower model:[continued]

Shower characterized by:

Number of particles in shower Location of shower maximum Longitudinal shower distribution Transverse shower distribution

Longitudinal components; measured in radiation length ...

Number of shower particlesafter depth t:

... use:

Energy per particleafter depth t:

Total number of shower particleswith energy E1:

Number of shower particlesat shower maximum:

Shower maximum at:

8.1 Electromagnetic calorimeters 231

8.1 Electromagnetic calorimeters

8.1.1 Electron–photon cascades

The dominating interaction processes for spectroscopy in the MeV energyrange are the photoelectric and Compton e!ect for photons and ionisa-tion and excitation for charged particles. At high energies (higher than100 MeV) electrons lose their energy almost exclusively by bremsstrahlungwhile photons lose their energy by electron–positron pair production [1](see Sect. 1.2).

The radiation losses of electrons with energy E can be described by thesimplified formula:

!!

dE

dx

"

rad=

E

X0, (8.1)

where X0 is the radiation length. The probability of electron–positronpair production by photons can be expressed as

dw

dx=

1!prod

e!x/!prod , !prod =97X0 . (8.2)

A convenient measure to consider shower development is the distancenormalised in radiation lengths, t = x/X0.

The most important properties of electron cascades can be understoodin a very simplified model [2, 3]. Let E0 be the energy of a photon incidenton a bulk of material (Fig. 8.1).

After one radiation length the photon produces an e+e! pair; electronsand positrons emit after another radiation length one bremsstrahlungphoton each, which again are transformed into electron–positron pairs. Letus assume that the energy is symmetrically shared between the particles at

0

E 0 /2

E0

E 0/4 E 0/8 E 0/16

1 2 3 4 5 6 7 8 t [X0]

Fig. 8.1. Sketch of a simple model for shower parametrisation.

Analytic Shower ModelSketch of simpleshower development

Page 10: Calorimetry I - particle.korea.ac.krparticle.korea.ac.kr/class/2011/phy603/Lecture9.pdfDie allermeisten Kalorimeter sind überdies positionssensitiv ausgeführt, um die Energiedeposition

≈ (1 + t0) · E0

EcX0 ∝ E0

T =E0

Ec· X0 · F F < 1

T = X0

tmax−1�

µ=0

2µ + t0 · Nmax · X0

= X0 · (2tmax − 1) + t0 · E0

EcX0

= X0 · (2log2E0/Ec − 1) + t0 · E0

EcX0

Analytic Shower Model

Simple shower model:[continued]

Longitudinal shower distribution increases only logarithmically with theprimary energy of the incident particle ... Some numbers: Ec ≈ 10 MeV, E0 = 1 GeV ➛ tmax = ln 100 ≈ 4.5; Nmax = 100 E0 = 100 GeV ➛ tmax = ln 10000 ≈ 9.2; Nmax =10000

Relevant for energy measurement (e.g. via scintillation light): total integrated track length of all charged particles ...

with t0: range of electron with energy Ec

[given in units of X0]

Energy proportionalto track length ...

As only electrons contribute ...

[ with ]

Page 11: Calorimetry I - particle.korea.ac.krparticle.korea.ac.kr/class/2011/phy603/Lecture9.pdfDie allermeisten Kalorimeter sind überdies positionssensitiv ausgeführt, um die Energiedeposition

�θ2� ≈ (m/E)2 = 1/γ2

��θ2�3d ≈ 19.2 MeV/c

p

�x

X0

RM = �θ�x=X0 · X0 ≈ 21MeVEC

X0

Analytic Shower Model

Transverse shower development ...

16 27. Passage of particles through matter

Eq. (27.14) describes scattering from a single material, while the usual probleminvolves the multiple scattering of a particle traversing many di!erent layers andmixtures. Since it is from a fit to a Moliere distribution, it is incorrect to add theindividual !0 contributions in quadrature; the result is systematically too small. Itis much more accurate to apply Eq. (27.14) once, after finding x and X0 for thecombined scatterer.

Lynch and Dahl have extended this phenomenological approach, fittingGaussian distributions to a variable fraction of the Moliere distribution forarbitrary scatterers [35], and achieve accuracies of 2% or better.

x

splaneyplane

!plane

"plane

x /2

Figure 27.9: Quantities used to describe multiple Coulomb scattering. Theparticle is incident in the plane of the figure.

The nonprojected (space) and projected (plane) angular distributions are givenapproximately by [33]

12" !2

0

exp!"""#!

!2space

2!20

$"""% d" , (27.15)

1"2" !0

exp!"""#!

!2plane

2!20

$"""% d!plane , (27.16)

where ! is the deflection angle. In this approximation, !2space # (!2

plane,x + !2plane,y),

where the x and y axes are orthogonal to the direction of motion, andd" # d!plane,x d!plane,y. Deflections into !plane,x and !plane,y are independent andidentically distributed.

February 2, 2010 15:55

Opening angle for bremsstrahlung and pair production

Multiple scatteringdeflection angle in 2-dimensional plane ...

�θ2k� =

k�

m=1

θ2m = k�θ2�

Small contribution as me/Ec = 0.05

Multiple coulomb scattering

In 3-dimensions extra factor √2:

[β = 1]

��θ2� ≈ 13.6 MeV/c

p

�x

X0

[β = 1]

Assuming the approximate range of electrons to be X0 yields lateral extension: R =〈θ〉X0 ...

Molière Radius; characterizes lateral shower spread ...

Page 12: Calorimetry I - particle.korea.ac.krparticle.korea.ac.kr/class/2011/phy603/Lecture9.pdfDie allermeisten Kalorimeter sind überdies positionssensitiv ausgeführt, um die Energiedeposition

θ

�θ2k� =

k�

m=1

θ2m = k�θ2�

��θ 2k � =

�k�

m=1

�θm

�2

=k�

m=1

�θ 2m + 2

i�=j

�θi�θj =

k�

m=1

�θ 2m

Insertion – Multiple Scattering

b

τ = 2b/v

AtomAtomic number: Z

}

M,v

θ ≈ ∆pt

p�≈ ∆pt

p=

2Zze2

b

1pv

∆pt =2Zze2

bv

Reminder:[Derivation of energy loss ...]

pt

As θ ~ Z ➛ main influence from nucleus; contribution due electrons negligible ...

Proof:

θn

Here, the term ∑θiθj vanishes as successive interactions are statistically independent

Coulombscattering

Multiple Coulomb scattering

To calculate θk one needs toaverage over n independent collisions ...

Page 13: Calorimetry I - particle.korea.ac.krparticle.korea.ac.kr/class/2011/phy603/Lecture9.pdfDie allermeisten Kalorimeter sind überdies positionssensitiv ausgeführt, um die Energiedeposition

�θ2N � = N · �θ2� = N ·

� ∞

0P (b) [θ(b)]2 db

= 8π nxZ2z2e4

p2v2ln

bmax

bmin

N(b) = 2π b db dx · n

N =�

N(b)db

= E2s

�1pv

�2

z2 x

X0

X0 =1

4α n Z2r2e ln(183/Z

1/3)re =

e2

mec2

P (b) db =N(b)N

=1N

· 2π b db dx · n

≈ N

N

� bmax

bmin

� x

02π b · n

�2Zze2

bpv

�2

db dx

Es =�

αmec

2

➛ bmax/bmin ~ Z–⅔

=4π

α

�mec

2�2 1

p2v2· x z2 ·

�2Z2

�e2

mec

�2

nα lnζ

Z2/3

Insertion – Multiple Scattering

Probability for a single collision with impact parameter b:

n : particle densitydx, x : layer thicknessdb, b: impact parameterN(b) : average number of collisions N : total number of collisions

with

Estimation of bmin, bmax:

Atomic radius for bmax : bmax = aB ⋅Z–⅓

Nuclear size for bmin : bmin ~ A⅓ ~ Z⅓

Also:

,

Page 14: Calorimetry I - particle.korea.ac.krparticle.korea.ac.kr/class/2011/phy603/Lecture9.pdfDie allermeisten Kalorimeter sind überdies positionssensitiv ausgeführt, um die Energiedeposition

�θ� =21.2 MeV

Ee

�x

X0

�θ2� = E2s · 1

p2v2· z2 · x

X0

RM =21 MeV

EcX0

Es =�

α(mec

2) = 21.2 MeV

Analytic Shower Model

Deflection angle:[Molière-Theory]

with

Lateral shower spread: Main contribution must come from low energy electrons as〈θ〉~ 1/Ee, i.e. for electrons with E = Ec ...Assuming the approximate range of electrons to be X0 yields〈θ〉≈ 21 MeV/Ee ➛ lateral extension: R =〈θ〉X0 ...

θR

Lateral extension: R = x⋅tan θ ≈ x⋅ θ, if θ small ... x

Molière Radius:

Transverse shower development ...[continued]

Lateral shower spread characterized by RM !

[Scale Energy]

On average 90% of the shower energy containedin cylinder with radius RM around shower axis ...

[β = 1, c = 1]

Page 15: Calorimetry I - particle.korea.ac.krparticle.korea.ac.kr/class/2011/phy603/Lecture9.pdfDie allermeisten Kalorimeter sind überdies positionssensitiv ausgeführt, um die Energiedeposition

dE

dt= E0 · β · (βt)α−1e−βt

Γ(α)tmax =

α− 1β

= ln�

E0

Ec

�+ Ceγ➛

Electromagnetic Shower Profile

Longitudinal profile

dE

dt= E0 tαe−βt

8.1 Electromagnetic calorimeters 235

0

0.1

0.01

1

10

100

105 15 20 25 30 35t [X0]

dE / d

t [M

eV/X

0]

lead

iron

aluminium

0

500 MeV

1000 MeV

2000 MeV

5000 MeV

0

200

400

600

105 15 20t [X0]

dE / d

t [M

eV/X

0]

Fig. 8.4. Longitudinal shower development of electromagnetic cascades. Top:approximation by Formula (8.7). Bottom: Monte Carlo simulation with EGS4 for10 GeV electron showers in aluminium, iron and lead [11].

Figure 8.6 shows the longitudinal and lateral development of a 6 GeVelectron cascade in a lead calorimeter (based on [12, 13]). The lateral widthof an electromagnetic shower increases with increasing longitudinal showerdepth. The largest part of the energy is deposited in a relatively narrowshower core. Generally speaking, about 95% of the shower energy is con-tained in a cylinder around the shower axis whose radius is R(95%) = 2RMalmost independently of the energy of the incident particle. The depen-dence of the containment radius on the material is taken into account bythe critical energy and radiation length appearing in Eq. (8.11).

Parametrization:[Longo 1975]

α,β : free parameterstα : at small depth number of secondaries increases ...t–βt : at larger depth absorption dominates ...

Numbers for E = 2 GeV (approximate):α = 2, β = 0.5, tmax = α/β

More exact[Longo 1985]

[Γ: Gamma function]

with:

[γ-induced]

[e-induced]

Ceγ = −0.5Ceγ = −1.0

Page 16: Calorimetry I - particle.korea.ac.krparticle.korea.ac.kr/class/2011/phy603/Lecture9.pdfDie allermeisten Kalorimeter sind überdies positionssensitiv ausgeführt, um die Energiedeposition

1

!1

r/RM

e!

e+, e!

!

t

Abbildung 8.3: Schematische Entwicklung eines elektromagnetischen Schauers

/X0z

Abbildung 8.4: Longitudinalverteilung der Energiedeposition in einem elektromagnetischenSchauer fur zwei Primarenergien der Elektronen

/r RM

Abbildung 8.5: Transversalverteilung der Energie in einem elektromagnetischen Schauer inunterschiedlichen Tiefen gemessen

159

dE

dr= αe−

r/RM + βe−r/λmin

Electromagnetic Shower Profile

Transverse profile

Parametrization:

α,β : free parametersRM : Molière radiusλmin : range of low energetic photons ...

energy deposit [arbitrary unites]

r/RM r/RM

Inner part: coulomb scattering ...Electrons and positrons move awayfrom shower axis due to multiple scattering ...

Outer part: low energy photons ...Photons (and electrons) produced in isotropicprocesses (Compton scattering, photo-electric effect) move away fromshower axis; predominant beyond shower maximum, particularly in high-Z absorber media...

Shower gets wider at larger depth ...

Page 17: Calorimetry I - particle.korea.ac.krparticle.korea.ac.kr/class/2011/phy603/Lecture9.pdfDie allermeisten Kalorimeter sind überdies positionssensitiv ausgeführt, um die Energiedeposition

M. Krammer: Detektoren, SS 05 Kalorimeter 36

6.2.1 Elektromagnetische SchauerSchauerprofil – 2

Quelle: C . Grupen, Teilchendetektoren, B.I. W issenschaftsverlag, 1993

Longitudinale und transversale Schauerentwicklung einer durch 6!GeV/c Elektronenausgelösten elektromagnetischen Kaskade in einem Absorber aus Blei.Bild links: lineare Skala. – Bild rechts: hablogarithmische Skala

Electromagnetic Shower Profile

M. Krammer: Detektoren, SS 05 Kalorimeter 36

6.2.1 Elektromagnetische SchauerSchauerprofil – 2

Quelle: C . Grupen, Teilchendetektoren, B.I. W issenschaftsverlag, 1993

Longitudinale und transversale Schauerentwicklung einer durch 6!GeV/c Elektronenausgelösten elektromagnetischen Kaskade in einem Absorber aus Blei.

Bild links: lineare Skala. – Bild rechts: hablogarithmische Skala

lateral shower width [X0]

longitudinal shower depth [X0]

energy deposit [arbitrary unites]

lateral shower width [X0]

longitudinal shower depth [X0]

energy deposit [arbitrary unites]

Longitudinal and transversal shower profilefor a 6 GeV electron in lead absorber ...[left: linear scale; right: logarithmic scale]

Page 18: Calorimetry I - particle.korea.ac.krparticle.korea.ac.kr/class/2011/phy603/Lecture9.pdfDie allermeisten Kalorimeter sind überdies positionssensitiv ausgeführt, um die Energiedeposition

Electromagnetic shower profiles (longitudinal)

6

Longitudinal Shower Shape

Depth [cm]

Ene

rgy

depo

sit p

er c

m [%

]

Depth [X0]

Energy deposit of electrons as a function of depth in a block of copper; integrals normalized to same value

[EGS4* calculation]

Depth of shower maximum increases logarithmically with energy

*EGS = Electron Gamma Shower

tmax ∝ ln(E0/Ec)

Page 19: Calorimetry I - particle.korea.ac.krparticle.korea.ac.kr/class/2011/phy603/Lecture9.pdfDie allermeisten Kalorimeter sind überdies positionssensitiv ausgeführt, um die Energiedeposition

Scaling is NOT perfect

9

Pb Z = 82Fe Z = 26Al Z = 13

Longitudinal Shower Shape

Depth [X0]

Ene

rgy

depo

sit p

er c

m [%

]

LeadIronAluminum

Energy deposit of electrons as a function of depth for different materials[EGS4* calculation]

10 GeV electrons

Approximate scaling ....

Page 20: Calorimetry I - particle.korea.ac.krparticle.korea.ac.kr/class/2011/phy603/Lecture9.pdfDie allermeisten Kalorimeter sind überdies positionssensitiv ausgeführt, um die Energiedeposition

σ ∝ Z5, E−3

σ ∝ Z, E−1

σ increases with E, Zasymptotic at ∼ 1 GeV

Ec ∝1Z

Longitudinal Shower Shape

ElectronsPhotons

ZPhotons:

Photo-electric effect ...

Compton scattering ...

Pair production ...

Electrons:

Critical energy ...

In high Z materials particle multiplication ...

... down to lower energies

➛ longer showers

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Transversal Shower ShapeLateral profile

16

Radial distributions of the energy deposited by 10 GeV electron showers in Copper

[Results of EGS4 simulations]

Transverse profileat different shower depths ....

Distance from shower axis [RM]

Molière Radii

Ene

rgy

depo

sit [

a.u.

]

Up to shower maximum broadening mainly due to multiple scattering ...

Beyond shower maximum broadening mainly due to low energy photons ...

RM =21 MeV

EcX0

Characterized by RM:[90% shower energy within RM]

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Lateral profile

15

Transversal Shower Shape

Radial energy deposit profiles for 10 GeV electrons showering in Al, Cu and Pb[Results of EGS4 calculations]

10

1

0.1

0.010 1 2 3 4 5

Ene

rgy

depo

sit [

%]

Distance from shower axis [RM]

Most striking difference seen inslope of 'tail' or 'halo' ...

Halo

Material dependence:

Scaling almost perfect at low radii ...

Slope considerably steeper for high-Z material due to smaller mean free path for low-energy photons ...

Remark:

Even though calorimeters are intended to measure GeV, TeV their performance is determined by low energy particles ...

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Ec =550 MeV

Z

tmax = lnE

Ec

R(95%) = 2RM

R(90%) = RM

− 1.0{

Some Useful 'Rule of Thumbs'

X0 =180A

Z2

gcm2

− 0.5− 1.0

[Attention: Definition of Rossi used]

Radiation length:

Critical energy:

Shower maximum:e– induced shower

γ induced shower

Longitudinalenergy containment:

TransverseEnergy containment:

Problem:Calculate how much Pb, Fe or Cuis needed to stop a 10 GeV electron.

Pb : Z = 82 , A = 207, ρ = 11.34 g/cm3

Fe : Z = 26 , A = 56, ρ = 7.87 g/cm3

Cu : Z = 29 , A = 63, ρ = 8.92 g/cm3

L(95%) = tmax + 0.08Z + 9.6 [X0]

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Homogeneous Calorimeters

In a homogeneous calorimeter the whole detector volume is filled by ahigh-density material which simultaneously serves as absorber as well as as active medium ...

Advantage: homogenous calorimeters provide optimal energy resolution

Disadvantage: very expensive

Homogenous calorimeters are exclusively used for electromagneticcalorimeter, i.e. energy measurement of electrons and photons

Signal Material

Scintillation light BGO, BaF2, CeF3, ...

Cherenkov light Lead Glass

Ionization signal Liquid nobel gases (Ar, Kr, Xe)

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Homogeneous Calorimeters

Example: CMS Crystal Calorimeter

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Homogeneous Calorimeters

Chapter 4

Electromagnetic Calorimeter

4.1 Description of the ECALIn this section, the layout, the crystals and the photodetectors of the Electromagnetic Calor-imeter (ECAL) are described. The section ends with a description of the preshower detectorwhich sits in front of the endcap crystals. Two important changes have occurred to the ge-ometry and configuration since the ECAL TDR [5]. In the endcap the basic mechanical unit,the “supercrystal,” which was originally envisaged to hold 6!6 crystals, is now a 5!5 unit.The lateral dimensions of the endcap crystals have been increased such that the supercrystalremains little changed in size. This choice took advantage of the crystal producer’s abil-ity to produce larger crystals, to reduce the channel count. Secondly, the option of a barrelpreshower detector, envisaged for high-luminosity running only, has been dropped. Thissimplification allows more space to the tracker, but requires that the longitudinal vertices ofH " !! events be found with the reconstructed charged particle tracks in the event.

4.1.1 The ECAL layout and geometry

The nominal geometry of the ECAL (the engineering specification) is simulated in detail inthe GEANT4/OSCAR model. There are 36 identical supermodules, 18 in each half barrel, eachcovering 20! in ". The barrel is closed at each end by an endcap. In front of most of thefiducial region of each endcap is a preshower device. Figure 4.1 shows a transverse sectionthrough ECAL.

y

z

Preshower (ES)

Barrel ECAL (EB)

Endcap

= 1.653

= 1.479

= 2.6= 3.0 ECAL (EE)

Figure 4.1: Transverse section through the ECAL, showing geometrical configuration.

146

4.1. Description of the ECAL 147

The barrel part of the ECAL covers the pseudorapidity range |!| < 1.479. The barrel granu-larity is 360-fold in " and (2!85)-fold in !, resulting in a total of 61 200 crystals.The truncated-pyramid shaped crystals are mounted in a quasi-projective geometry so that their axes makea small angle (3o) with the respect to the vector from the nominal interaction vertex, in boththe " and ! projections. The crystal cross-section corresponds to approximately 0.0174 !0.0174! in !-" or 22!22 mm2 at the front face of crystal, and 26!26 mm2 at the rear face. Thecrystal length is 230 mm corresponding to 25.8 X0.

The centres of the front faces of the crystals in the supermodules are at a radius 1.29 m.The crystals are contained in a thin-walled glass-fibre alveola structures (“submodules,” asshown in Fig. CP 5) with 5 pairs of crystals (left and right reflections of a single shape) persubmodule. The ! extent of the submodule corresponds to a trigger tower. To reduce thenumber of different type of crystals, the crystals in each submodule have the same shape.There are 17 pairs of shapes. The submodules are assembled into modules and there are4 modules in each supermodule separated by aluminium webs. The arrangement of the 4modules in a supermodule can be seen in the photograph shown in Fig. 4.2.

Figure 4.2: Photograph of supermodule, showing modules.

The thermal screen and neutron moderator in front of the crystals are described in the model,as well as an approximate modelling of the electronics, thermal regulation system and me-chanical structure behind the crystals.

The endcaps cover the rapidity range 1.479 < |!| < 3.0. The longitudinal distance betweenthe interaction point and the endcap envelop is 3144 mm in the simulation. This locationtakes account of the estimated shift toward the interaction point by 2.6 cm when the 4 T mag-netic field is switched on. The endcap consists of identically shaped crystals grouped inmechanical units of 5!5 crystals (supercrystals, or SCs) consisting of a carbon-fibre alveolastructure. Each endcap is divided into 2 halves, or “Dees” (Fig. CP 6). Each Dee comprises3662 crystals. These are contained in 138 standard SCs and 18 special partial supercrystalson the inner and outer circumference. The crystals and SCs are arranged in a rectangular

Scintillator : PBW04 [Lead Tungsten]

Photosensor: APDs [Avalanche Photodiodes]

Number of crystals: ~ 70000Light output: 4.5 photons/MeV

Example: CMS Crystal Calorimeter

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Sampling Calorimeters

Simple shower model

! Consider only Bremsstrahlung and (symmetric) pair production

! Assume X0 ! !pair

! After t X0:

! N(t) = 2t

! E(t)/particle = E0/2t

! Process continues until E(t)<Ec

! E(tmax) = E0/2tmax = Ec

! tmax = ln(E0/Ec)/ln2

! Nmax " E0/Ec

5

Alternating layers of absorber and active material [sandwich calorimeter]

Absorber materials:[high density]

Principle:

Iron (Fe)Lead (Pb)Uranium (U)[For compensation ...]

Active materials:

Plastic scintillatorSilicon detectorsLiquid ionization chamberGas detectors

passive absorber shower (cascade of secondaries)

active layers

incoming particle

Scheme of asandwich calorimeter

Electromagnetic shower

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Sampling Calorimeters

Advantages:

By separating passive and active layers the different layer materials can be optimally adapted to the corresponding requirements ...

By freely choosing high-density material for the absorbers one can built very compact calorimeters ...

Sampling calorimeters are simpler with more passive material andthus cheaper than homogeneous calorimeters ...

Disadvantages:

Only part of the deposited particle energy is actually detected in theactive layers; typically a few percent [for gas detectors even only ~10-5] ...

Due to this sampling-fluctuations typically result in a reduced energy resolution for sampling calorimeters ...

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Sampling Calorimeters

Absorber Scintillator

Light guide

Photo detector

Scintillator(blue light)

Wavelength shifter

electrodes Absorber as

Charge amplifier

HV

Argon

Electrodes

Analoguesignal

Scintillators as active layer;signal readout via photo multipliers

Scintillators as active layer; wave length shifter to convert light

Active medium: LAr; absorberembedded in liquid serve as electrods

Ionization chambersbetween absorber plates

Possible setups

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Sampling Calorimeters

Example:ATLAS Liquid Argon Calorimeter

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Sampling Calorimeters

Example:H1 SpaCal[Spaghetti Calorimeter]

Lead matrix ...[Technical drawing]

4 SpaCal Supermodules

Lead-Fibre Matrix[Front view]

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Sampling Calorimeters

!"#!$#%!!& '!

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/566&8'8&0&/0-%'.654?'

!

4.2 The electromagnetic calorimeter concept

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F/+&+&6F(!0)!9(%%!0)!&'(!/(*(,&!)&3.-()!3)(!CTC!44VB!!

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!

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&'-)!&'-,!.(E-*(8!

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!

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Tungstenframe

Detectorslabs

max.: 1.6 m

Tungstenlayer

Sensors+ r/o electonics

‘Alveolar Structure’

Example: CALICE ElectromagneticCalorimeter

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Calorimetric Systems

FIGURE 5.16. Structure of a detector slab.The tungsten plate in the center (light grey) isenclosed by silicon sensor planes (light red) andPCBs (green) on both sides. The FE chip isintegrated in the PCB.

FIGURE 5.17. The mechanical structure forthe ECAL proposed by US institutes. Tung-sten planes (grey) of 200 kg weight are joinedto a module by rods (black). Hexagonal sensorplanes (green) are placed in between the tung-sten plates.

shower maximum using 12 mm2 pixels. More tests are needed to understand e.g. channel-by-channel variations.

The goal of the R&D is to fabricate a full-depth electromagnetic calorimeter prototypemodule. This will consist of 30 longitudinal layers, each consisting of an about 15 cm diam-eter silicon detector outfitted with a KPiX chip sandwiched between 2.5 mm thick tungstenradiator layers. The module will be fully characterized for electromagnetic response and res-olution in an electron beam, probably at SLAC in 2007. A first round of 10 silicon detectors,made from a 6 inch wafer, is purchased and tested in the laboratory. Several prototypes ofthe KPiX chip are successfully tested. A second, improved version, is under preparation. Thelight cable for signal transport inside the gap is being designed and preparations for bumpbonding are underway.

FIGURE 5.18. A silicon sensor pro-totype with hexagon pads.

FIGURE 5.19. The cross section of the ECAL. The silicon sensorsinterspersed between tungsten plates and readout by the KPiX FEchip bump bonded to metallic traces connected to each sensor cell.

ILC-Detector Concept Report 77

! "#

!

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!

4.3 Current status of the project

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4.4.1 General description

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Tungsten

Silicon Pads[5 x 5 mm2]

PCB

Read-out chip

1.4 mm

~ 3 mm

~ 3 mm

Aluminum protection

Heat shield

PCB with r/o-chips

Tungsten layer

Silicon matrices

Detectorslab

[embeddable?]

Sampling Calorimeters

Example: CALICE ElectromagneticCalorimeter

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! "#

!! !!!

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layers weighted by tungsten thickness0 10 20 30 40 50 60

energ

y w

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d h

its / e

vent [G

eV

]

0

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1

1.5

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2.5

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=1.5GeVbeam

run 230243, E

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run 230248, E

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run 230252, E

=6GeVbeam

run 300670, E

=10GeVbeam

run 300672, E

=20GeVbeam

run 300676, E

=30GeVbeam

run 300207, E

''''''''''' energy (GeV)

0 1 2 3 4 5 6 7

Rad

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(mm

)

10

15

20

25

30

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95% containment

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5'G&(! 3:5%*,5! 5%&! 7./0P! 5*! ,(6&D45'(6! 5%&! E')*D:I&5&D! E'):KD'5:*(! '(6! F&DA*DI'(E&! '(6! 5*! 5,(&! 5%&!

4:I,)'5:*(!:A!(&E&44'DCH!!$%&!%'6D*(!6'5'!5'G&(!3:5%!'(6!3:5%*,5!5%&!7./0!E'(!5%&(!K&!45,6:&6!3:5%!+D&'5&D!

E*(A:6&(E&!5*!&J5D'E5!5%&!F&DA*DI'(E&!'(6!4%*3&D!FD*F&D5:&4H!!$%&4&!6'5'!'D&!*A!+D&'5!:(5&D&45!:(!E*IF'D:(+!

3:5%! 4:I,)'5:*(4P! A*D! 3%:E%! 5%&! ,(6&D)C:(+! :(5&D'E5:*(! I*6&)! :4! I,E%! )&44! 3&))! ,(6&D45**6! 5%'(! A*D!

&)&E5D*I'+(&5:E!FD*E&44&4H!

!

$%&!E'):KD'5:*(!FD*E&6,D&! A*D! 5%&!/-./0! :4!I*D&!E*IF)&J! 5%'(! A*D! 5%&!7./0H! !/4!3&))! '4!,4:(+!I,*(!

K&'I4!5*!&45'K):4%!5%&!OQR!E'):KD'5:*(!5:)&SKCS5:)&P!5%&!M:RO!F%*5*4&(4*D4!&J%:K:5!'!4:+(:A:E'(5)C!(*(S):(&'D!

D&4F*(4&P! '(6! E'D&A,)! E'):KD'5:*(! *A! 5%:4! &AA&E5! :4! (&&6&6P! K'4&6! K*5%! *(! )'K! I&'4,D&I&(54! '(6! '! ):+%5!

:(T&E5:*(!4C45&IH!!Q5!:4!')4*!:IF*D5'(5!5*!:(E),6&!5%&4&!&AA&E54!:(5*!5%&!O*(5&!.'D)*!4:I,)'5:*(4H!!!

Sampling Calorimeters

! "#

!! !!!

!"#$%&' ()*+,' -"./%"0$/"12.' 13' /1/45' 6789' &2&%#:' 31%' +;' <&=' &5&>/%12.' ?5&3/@A' B"/C' 4' <4$.."42' 3"/'

.$D&%"ED1.&FG'%&.15$/"12'13'/C&'6789'31%'&5&>/%12.'?%"#C/@A'B"/C'F4/4'42F'H12/&'74%51''>1ED4%&FI''

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layers weighted by tungsten thickness0 10 20 30 40 50 60

energ

y w

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d h

its / e

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eV

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0

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Entries 30Mean 17.78RMS 9.518

=1.5GeVbeam

run 230243, E

=3GeVbeam

run 230248, E

=6GeVbeam

run 230252, E

=6GeVbeam

run 300670, E

=10GeVbeam

run 300672, E

=20GeVbeam

run 300676, E

=30GeVbeam

run 300207, E

''''''''''' energy (GeV)

0 1 2 3 4 5 6 7

Rad

ius

(mm

)

10

15

20

25

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35

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center

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E&4.$%&F' "2' /C&'789P76'6789G' ' /C&'F4/4'4%&' %&D%&.&2/&F'0:'D1"2/.'B"/C' ./4/"./">45' $2>&%/4"2/"&.'

42F'/C&'<68LQJ'H12/&'74%51''."E$54/"12'0:'/C&'C"./1#%4EI'R4%4E&/%".4/"12.'13'/C&'.C1B&%'D%13"5&.'

0:'/C&'31%E'>'/'!''&?*!'/@A''BC&%&'/''".'/C&'>451%"E&/&%'F&D/C'"2'%4F"4/"12'5&2#/C.A'4%&'45.1'.C1B2I'K"#C/,'

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!

12.3 The AHCAL data

! $%&!'(')*+,&!-./0!1/-./02!3'4!5&45&6!'5!.789!:(!;<<=!3:5%!#>?;@!*A!:54!:(5&(6&6!@B!)'C&D4!*A!

4E:(5:))'5:(+! 5:)&4!6,D:(+! 5%&! A:D45?4&E*(6!F&D:*6!*A!6'5'! 5'G:(+H!/!E')*D:I&5&D!3:5%! D*,+%)C!@HB! :(5&D'E5:*(!

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45'EG!A*D!5%&!4&E*(6!F&D:*6!3:5%*,5!:(ED&'4:(+!5%&!*L&D'))!6&F5%H!N'5'!3&D&!5'G&(!K*5%!3:5%!'(6!3:5%*,5!5%&!

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E*(A:6&(E&!5*!&J5D'E5!5%&!F&DA*DI'(E&!'(6!4%*3&D!FD*F&D5:&4H!!$%&4&!6'5'!'D&!*A!+D&'5!:(5&D&45!:(!E*IF'D:(+!

3:5%! 4:I,)'5:*(4P! A*D! 3%:E%! 5%&! ,(6&D)C:(+! :(5&D'E5:*(! I*6&)! :4! I,E%! )&44! 3&))! ,(6&D45**6! 5%'(! A*D!

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K&'I4!5*!&45'K):4%!5%&!OQR!E'):KD'5:*(!5:)&SKCS5:)&P!5%&!M:RO!F%*5*4&(4*D4!&J%:K:5!'!4:+(:A:E'(5)C!(*(S):(&'D!

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Energy Resolution

Ebeam = 1 GeV

Ebeam = 45 GeV

< 20%/√E

ECAL ‘Physics’ Prototype[CALICE]

Front EndElectronics

Structure 4.2

Structure 2.8 Structure 1.4

Active area

Event Display

[Pads: 10x10 mm2]

Example: CALICE ElectromagneticCalorimeter

Page 35: Calorimetry I - particle.korea.ac.krparticle.korea.ac.kr/class/2011/phy603/Lecture9.pdfDie allermeisten Kalorimeter sind überdies positionssensitiv ausgeführt, um die Energiedeposition

Homogeneous vs. Sampling Calorimeters28. Detectors at accelerators 57

Table 28.8: Resolution of typical electromagnetic calorimeters. E is in GeV.

Technology (Experiment) Depth Energy resolution Date

NaI(Tl) (Crystal Ball) 20X0 2.7%/E1/4 1983

Bi4Ge3O12 (BGO) (L3) 22X0 2%/!

E " 0.7% 1993

CsI (KTeV) 27X0 2%/!

E " 0.45% 1996

CsI(Tl) (BaBar) 16–18X0 2.3%/E1/4 " 1.4% 1999

CsI(Tl) (BELLE) 16X0 1.7% for E! > 3.5 GeV 1998

PbWO4 (PWO) (CMS) 25X0 3%/!

E " 0.5% " 0.2/E 1997

Lead glass (OPAL) 20.5X0 5%/!

E 1990

Liquid Kr (NA48) 27X0 3.2%/!

E" 0.42% " 0.09/E 1998

Scintillator/depleted U 20–30X0 18%/!

E 1988(ZEUS)

Scintillator/Pb (CDF) 18X0 13.5%/!

E 1988

Scintillator fiber/Pb 15X0 5.7%/!

E " 0.6% 1995spaghetti (KLOE)

Liquid Ar/Pb (NA31) 27X0 7.5%/!

E " 0.5% " 0.1/E 1988

Liquid Ar/Pb (SLD) 21X0 8%/!

E 1993

Liquid Ar/Pb (H1) 20–30X0 12%/!

E " 1% 1998

Liquid Ar/depl. U (DØ) 20.5X0 16%/!

E " 0.3% " 0.3/E 1993

Liquid Ar/Pb accordion 25X0 10%/!

E " 0.4% " 0.3/E 1996(ATLAS)

traditional sandwich structure is the LAr-tube design shown in Fig. 28.22(a).A relatively new variant is the use of Cerenkov light in hadron calorimetry. Such

a calorimeter is sensitive to e±’s in the EM showers plus a few relativistic pions. Anexample is the radiation-hard forward calorimeter in CMS, with iron absorber and quartzfiber readout by PMT’s.

Ideally, the calorimeter is segmented in ! and " (or # = # ln tan("/2)). Finesegmentation, while desirable, is limited by cost, readout complexity, practical geometry,and the transverse size of the cascades. An example, a wedge of the ATLAS central barrelcalorimeter, is shown in Fig. 28.22(b).

In an inelastic hadronic collision a significant fraction fem of the energy is removedfrom further hadronic interaction by the production of secondary $0’s and #’s, whosedecay photons generate high-energy electromagnetic (EM) cascades. Charged secondaries

January 29, 2010 16:23

Hom

ogeneousS

ampling

Resolution of typicalelectromagnetic calorimeter[E is in GeV]