Electromagnetic CalorimetersCalorimetry I
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
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
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) ...
...
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
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
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
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
E±
=
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
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
≈ (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 ]
�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 ...
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 ...
�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 =�
4π
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:
,
�θ� =21.2 MeV
Ee
�x
X0
�θ2� = E2s · 1
p2v2· z2 · x
X0
➛
⋅
RM =21 MeV
EcX0
Es =�
4π
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]
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
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 ...
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]
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)
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 ....
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
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]
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 ...
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]
★
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)
★
★
★
Homogeneous Calorimeters
Example: CMS Crystal Calorimeter
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
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
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 ...
★
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
Sampling Calorimeters
Example:ATLAS Liquid Argon Calorimeter
Sampling Calorimeters
Example:H1 SpaCal[Spaghetti Calorimeter]
Lead matrix ...[Technical drawing]
4 SpaCal Supermodules
Lead-Fibre Matrix[Front view]
Sampling Calorimeters
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!
4.2 The electromagnetic calorimeter concept
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Tungstenframe
Detectorslabs
max.: 1.6 m
Tungstenlayer
Sensors+ r/o electonics
‘Alveolar Structure’
Example: CALICE ElectromagneticCalorimeter
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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4.4.1 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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layers weighted by tungsten thickness0 10 20 30 40 50 60
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'
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12.3 The AHCAL data
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Sampling Calorimeters
! "#
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!
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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!
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!
$%&!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!!!
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
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Example: CALICE ElectromagneticCalorimeter
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]