Calorimetry I
Electromagnetic Calorimeters
6.1 Allgemeine Grundlagen
Funktionsprinzip – 1
! Introduction
In der Hochenergiephysik versteht man unter einem Kalorimeter einen
Detektor, welcher die zu analysierenden Teilchen vollständig absorbiert. Da
durch kann die Einfallsenergie des betreffenden Teilchens gemessen werde
Calorimeter:
! Die allermeisten Kalorimeter sind überdies positionssensitiv ausgeführt, um
Detector for energy measurement via total absorption of particles ...
die Energiedeposition ortsabhängig zu messen und sie beim gleichzeitigen
Also: most calorimeters
are position
sensitive
to measure
energy depositions
Durchgang
von mehreren
Teilchen
den
individuellen
Teilchen zuzuordnen.
depending on their location ...
! Ein einfallendes Teilchen initiiert innerhalb des Kalorimeters einen TeilchenPrinciple of(eine
operation:
schauer
Teilchenkaskade) aus Sekundärteilchen und gibt so sukzessi
seine
ganze
Energie
diesen
Schauer
ab.
Incoming
particle
initiatesand
particle
shower
...
Shower
Composition and shower dimensions
depend
on
Die
Zusammensetzung
und die
Ausdehnung
eines solchen Schauers
hänge
Schematic of
particle type and detector material ...
calorimeter principle
von
der Art des einfallenden Teilchens ab (e±, Photon oder
Hadron).
Energy deposited in form of: heat, ionization,
excitation of atoms, Cherenkov light ...
Different calorimeter types use different kinds of
Bild
rechts:
Grobes
Schema
these
signals
to measure
total energy
...
eines Teilchenschauers in
Important:
particle cascade (shower)
incident particle
einem (homogenen) Kalorimeter
Signal ~ total deposited energy
[Proportionality factor determined by calibration]
detector volume
Introduction
Energy vs. momentum measurement:
Calorimeter:
[see below]
σE
1
∼√
E
E
e.g. ATLAS:
σE
0.1
≈√
E
E
i.e. σE/E = 1% @ 100 GeV
Gas detector:
[see above]
σp
∼p
p
e.g. ATLAS:
σp
≈ 5 · 10−4 · pt
p
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]
E
L ∼ ln
Ec
[Ec: critical energy]
Shower depth nearly energy independent
i.e. calorimeters can be compact ...
Compare with magnetic spectrometer: σp/p ∼ p/L2
Detector size has to grow quadratically to maintain resolution
Introduction
Further calorimeter features:
Calorimeters can be built as 4π-detectors, i.e. they can detect
particles over almost the full solid angle
2
large
for small θ
2
Magnetic spectrometer: anisotropy due to magnetic field; remember: (σp/p) = (σpt/pt ) + (σθ/sin θ)
2
Calorimeters can provide fast timing signal (1 to 10 ns); can
be used for triggering [e.g. ATLAS L1 Calorimeter Trigger]
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) ...
...
Electromagnetic Showers
Reminder:
Dominant processes
at high energies ...
Photons : Pair production
Electrons: Bremsstrahlung
Pair production:
�
�
7
183
2 2
σpair ≈
4 αre Z ln 1
9
Z3
7 A
=
9 NA X0
Absorption
coefficient:
[X0: radiation length]
[in cm or g/cm2]
NA
7 ρ
µ = nσ = ρ
· σpair =
A
9 X0
X0
Bremsstrahlung:
dE
E
dE
Z2 2
183
= 4αNA
re · E ln 1 =
X0
dx
A
3
Zdx
➛ E = E0 e−x/X0
After passage of one X0 electron
has only (1/e)th of its primary energy ...
[i.e. 37%]
10 PeV
0
Electromagnetic Showers
0
0.25
0.5
0.75
y = k/E
1
Figure 27.11: The normalized bremsstrahlung cross section k dσLP M /dk
lead versus the fractional photon energy y = k/E. The vertical axis has un
of photons per radiation length.
200
�
�
�
�
dE
dE
(Ec )��
=
(Ec )��
dx
dx
Brems
Ion
�
dE
dx
710 MeV
=
Z + 0.92
�
Brems
��
dE
dx
EcSol/Liq
�
Ion
30
E
10
2
5
10
20
50
Electron energy (MeV)
[see also later]
100
200
Figure 27.12: Two definitions of the critical energy Ec .
with:
�
�
incomplete, dE
and� near y =
0, where
divergence is removed b
�the infrared
dE
E
Ec
�
�
=
≈
=
const.
& amplitudes
the interference
dx �of bremsstrahlung
X
dx �
X from nearby scattering cent
Brems
0
Ion
February 2, 2010
Transverse size of EM shower given by
radiation length via Molière radius
lu
ng
Ionization
Brems = ionization
610 MeV
=
Z + 1.24
Z ·E
≈
800 MeV
Rossi:
Ionization per X0
= electron energy
50
40
20
Approximations:
EcGas
l
ta
o
T
70
ss
tr
ah
Critical Energy [see above]:
Br
dE /dx × X0 (MeV)
100
em
Ex
s≈
ac
tb
re
m
Further basics:
Copper
X0 = 12.86 g cm−2
Ec = 19.63 MeV
RM
21 MeV
=
X0
Ec
0
15:55
RM : Moliere radius
Ec : Critical Energy [Rossi]
X0 : Radiation length
Electromagnetic Showers
Typical values for X0, Ec and RM of materials
used in calorimeter
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
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
Ar (liquid)
S
rlo
Ca
te
on
(M
rs
ue
ha
Sc
en
sch
−
eti
e
gn
+ +
ma
e
γ
tro
+
lek
K
e+
se
+
→
d
K
ine
ng
ge
K
→
hlu
+
lun
γ
K
tra
ick
s
+
tw
ms
e
e
En
Br
).
.2:
E0
rch
ern
se
g8
u
s
K
e
2
d
−
=
oz
=
o
Pr
1
se
K
E
(
a
ie
ev
d
i
igt
rd
rg
rt
t
e
ne
Nu
ich
rli
s
e
E
v
eE
ck
i
rü
,d
X0
=
be
X0
ke
en
E±
ch
rec
t
na
rd
we
f
Au
Analytic Shower Model
rS
de
Simple shower model:
[from Heitler]
Only two dominant interactions:
Pair production and Bremsstrahlung ...
γ + Nucleus ➛ Nucleus + e+ + e−
[Photons absorbed via pair production]
ert
isi
ial
e + Nucleus ➛ Nucleus + e + γ
Electromagnetic Shower
[Monte Carlo Simulation]
[Energy loss of electrons via Bremsstrahlung]
Shower development governed by X0 ...
Use
Simplification:
After a distance X0 electrons remain with
only (1/e)th of their primary energy ...
[Ee looses half the energy]
Photon produces e+e−-pair after 9/7X0 ≈ X0 ...
Ee ≈ E0/2
Assume:
E > Ec : no energy loss by ionization/excitation
du
E < Ec : energy loss only via ionization/excitation
Eγ = Ee ≈ E0/2
[Energy shared by e+/e–]
... with initial particle energy E0
rch
us assume that the energy is symmetrically shared between the part
Analytic Shower Model
Sketch of simple
shower development
E0
Simple shower model:
[continued]
Shower characterized by:
/
/
/
/
1
2
3
4
E 0 2 E 0 4 E 0 8 E 0 16
Number of particles in shower
Location of shower maximum
Longitudinal shower distribution
Transverse shower distribution
Number of shower particles
after depth t:
N (t) = 2
t
Energy per particle
after depth t:
E0
E=
= E0 · 2−t
N (t)
➛ t = log2 (E0/E)
0
5
6
7
8
t [X0]
Fig. 8.1. Sketch of a simple model for shower parametrisation.
Longitudinal components;
measured in radiation length ...
... use:
x
t=
X0
Total number of shower particles
with energy E1:
N (E0 , E1 ) = 2
t1
=2
Number of shower particles
at shower maximum:
N (E0 , Ec ) = Nmax
Shower maximum at:
tmax ∝ ln(E0/Ec )
log2 (E0/E1 )
E0
=
E1
E0
=2
=
Ec
N (E0 , E1 ) ∝ E0
tmax
Analytic Shower Model
Simple shower model:
[continued]
Longitudinal shower distribution increases only logarithmically with the
primary 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 ...
tmax−1
T = X0
�
2µ + t0 · Nmax · X0
µ=0
tmax
As only electrons
contribute ...
with t0: range of electron with energy Ec
[given in units of X0]
E0
= X0 · (2
− 1) + t0 ·
X0
Ec
E0
E0
log2 E0/Ec
X0 ∝ E0
= X0 · (2
− 1) + t0 ·
X0 ≈ (1 + t0 ) ·
Ec
Ec
E0
T =
· X0 · F
Ec
[ with
F < 1]
Energy proportional
to track length ...
27. Passage of particles through matter
16
Eq. (27.14) describes scattering from a single material, while the usual problem
involves the multiple scattering of a particle traversing many different layers and
mixtures. Since it is from a fit to a Molière distribution, it is incorrect to add the
individual θ0 contributions in quadrature; the result is systematically too small. I
is much more accurate to apply Eq. (27.14) once, after finding x and X0 for the
combined scatterer.
Lynch and Dahl have extended this phenomenological approach, fitting
Gaussian distributions to a variable fraction of the Molière distribution for
arbitrary scatterers [35], and achieve accuracies of 2% or better.
Analytic Shower Model
Transverse shower development ...
Multiple
coulomb scattering
Opening angle
for bremsstrahlung and pair production
2
�θ � ≈
2
(m/E )
=
x
1/γ 2
x /2
Small contribution as me/Ec = 0.05
Multiple scattering
splane
deflection angle in 2-dimensional plane ...
�θk2 � =
k
�
m=1
2
= k�θ2 �
θm
�
�
x
13.6 MeV/c
2
�θ � ≈
p
X0
In 3-dimensions extra factor √2:
�
19.2 MeV/c
2
�θ �3d ≈
p
Ψplane
yplane
θplane
Figure 27.9: Quantities used to describe multiple Coulomb scattering. The
particle is incident in the plane of the figure.
Assuming the approximate range of electrons
The[β
nonprojected
(space)
projected (plane) angular distributions
are given
⋅X0 ...
= 1]
to be Xand
0 yields lateral extension: R =〈θ〉
approximately by [33]
 2

21MeV
θ

1
space 




RM =2 �θ�
X0
(27.15
exp x=X
�
− 0 2· X
0dΩ≈,
2π
θ
2θ
EC
0
0
x
Molière Radius;
X0 [β = 1]
characterizes

 lateral shower spread ...
2
θplane 

1




√
exp −
(27.16
2  dθplane ,
Insertion – Multiple Scattering
M,v
Reminder:
τ = 2b/v
[Derivation of energy loss ...]
2Zze2
∆pt =
bv
∆pt
∆pt
2Zze2 1
θ≈
≈
=
p�
p
b pv
Atom
�θk2 � =
Proof:
θ�k2 =
m=1
�
m=1
�θm
�2
=
k
�
m=1
}b
Coulomb
scattering
θk
2
= k�θ2 �
θm
k
�
θ
Atomic number: Z
As θ ~ Z ➛ main influence from nucleus;
contribution due to electrons negligible ...
k
�
pt
Multiple
Coulomb scattering
θ�m2 + 2
�
i�=j
θ�i �θj =
k
�
θ�m2
m=1
Here, the term ∑θiθj vanishes as successive interactions
are statistically independent; to calculate ‹θk› one needs to average ...
Insertion – Multiple Scattering
n
:
dx, x : db, b:
N(b) :
N
:
Probability for a single collision
with impact parameter b:
N (b)
1
P (b) db =
=
· 2π b db dx · n
N
N
2
� = N · �θ2 � = N ·
�θN
N
≈
N
�
bmax
bmin
�
0
x
�
∞
with
N (b) = 2π
� b db dx · n
N=
2
P (b) [θ(b)] db
Estimation of bmin, bmax:
0
2π b · n
particle density
layer thickness
impact parameter
average number of collisions
total number of collisions
�
2Zze
bpv
2
�2
Atomic radius for bmax : bmax = aB ⋅Z–⅓
Nuclear size for bmin : bmin ~ A⅓ ~ Z⅓
db dx
�
4π �
2 2 1
2
=
me c
·
x
z
·
2
2
α
p v
Z
2
�
➛ bmax/bmin ~ Z–⅔
Also:
�
4π
m e c2
α
e2
1
X0 =
, re =
m e c2
4α n Z 2 re2 ln(183/Z 1/3 )
Es =
Z 2 z 2 e4 bmax
= 8π nx 2 2 ln
p v
bmin
�
N (b)db
2
e
m e c2
�2
ζ
nα ln 1/3
Z
�
=
Es2
�
1
pv
�2
x
z
X0
2
Analytic Shower Model
Transverse shower development ...
R
[continued]
θ
x
Deflection angle:
Lateral extension: R = x⋅tan θ ≈ x⋅ θ, if θ small ...
[Molière-Theory]
1
x
2
· 2 2 ·z ·
�θ � =
with Es =
p v
X0
�
x
21.2 MeV
➛ �θ� =
Ee
X0 [β = 1, c = 1, z = 1]
2
Es2
�
4π
(me c2 ) = 21.2 MeV
α
[Scale Energy]
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 ...
Molière Radius:
RM
21 MeV
=
X0
Ec
Lateral shower spread
characterized by RM !
On average 90% of the shower energy contained
in cylinder with radius RM around shower axis ...
Electromagnetic Shower Profile
8.1 Electromagnetic calorimeters
Longitudinal profile
600
5000 MeV
Parametrization:
dE / dt [MeV/X0]
[Longo 1975]
dE
= E0 tα e−βt
dt
α,β:free parameters
tα : at small depth number of
secondaries increases ...
e–βt : at larger depth absorption
dominates ...
400
2000 MeV
200
1000 MeV
500 MeV
Numbers for E = 2 GeV (approximate):
α = 2, β = 0.5, tmax = α/β
0
5
0
More exact
[Longo 1985]
[Γ: Gamma function]
➛ tmax =
α−1
= ln
β
�
�
E0
+ Ceγ
Ec 10
[MeV/X0]
(βt)α−1 e−βt
dE
= E0 · β ·
dt
Γ(α)
100
1
10
t [X0]
15
with:
Ceγ = −0.5
Ceγ = −1.0
[γ-induced]
lead
[e-induced]
iron
aluminium
20
Electromagnetic Shower Profile
Transverse profile
z/X0
Abbildung 8.4: Longitudinalverteilung der Energiedeposition in einem elektr
energy
deposit
Schauer für zwei Prim
ärenergien
der Elektronen
[arbitrary unites]
Parametrization:
dE
−r/RM
−r/λmin
= αe
+ βe
dr
α,β:free parameters
RM : Molière radius
λmin: range of low energetic
photons ...
Inner part: coulomb scattering ...
Electrons and positrons move away
from shower axis due to multiple scattering ...
Outer part: low energy photons ...
r/ R
r/RM
r/R
MM
Photons (and electrons) produced in isotropic
processes (Compton scattering,
photo-electric
move away from
Abbildung
8.5: effect)
Transversalverteilung
der Energie in einem elektromagnetisch
shower axis; predominant beyond shower maximum, particularly in high-Z absorber media...
unterschiedlichen Tiefen gemessen
Shower gets wider at larger depth ...
159
Elektromagnetische Schauer
Longitudinale und transversale Schauerentwicklung einer durch 6!GeV/c Elek
ausgelösten elektromagn
etischen Kas
kade in einem Absorber aus Blei.
Electromagnetic
Shower
Profile
2 s: lineare Skala.
– link
rprofil
Bild
– Bild rechts: hablogarithmische Skala
Longitudinal and transversal shower profile
6!GeV/c Elektronen
udinale und transversale Schauerentwicklung
for a einer
6 GeVdurch
electron in lead absorber ...
r aus Blei.
Absorbe
östen elektromagnetischen Kaskade in einem
[left: linear
scale; right: logarithmic scale]
energy deposit
unites]
Skala. – Bild rechts: hablogarithmische Skala
lineare
ks:[arbitrary
energy deposit
[arbitrary unites]
[X
pth
0]
e
d
gitu
n
lo
sh
l
a
n
rd
we
o
i
lateral shower width [X0]
ho
r
we
ls
ina
de
pth
]
[X 0
d
Quelle: C . Grup en, Teilchendetektoren, B.I. W issen
gitu schaftsverlag, 1993
M. Krammer: Detektoren, SS 05
lon
lateral shower width [X0]
Longitudinalshower
Showerprofiles
Shape (longitudinal)
ctromagnetic
Energy deposit per cm [%]
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
tmax ∝ ln(E0/Ec )
Depth [cm]
*EGS = Electron Gamma Shower
Longitudinal Shower Shape
Scaling is NOT perfect
Energy deposit per cm [%]
10 GeV electrons
Lead
Iron
Aluminum
Approximate scaling ....
Energy deposit of electrons as a function
of depth for different materials
[EGS4* calculation]
Depth [X0]
Pb Z = 8
Fe Z = 26
Al Z = 13
Longitudinal Shower Shape
Photons
Photons:
Photo-electric effect ...
σ ∝ Z 5 , E −3
Compton scattering ...
σ ∝ Z, E −1
Pair production ...
σ increases with E, Z
asymptotic at ∼ 1 GeV
Electrons:
Critical energy ...
1
Ec ∝
Z
In high Z materials
particle multiplication ...
... down to lower energies
➛ longer showers
[with respect to X0]
Electrons
Z
Lateral
profile
Transversal Shower Shape
Transverse profile
at different shower depths ....
Up to shower maximum broadening
mainly due to multiple scattering ...
Characterized by RM:
[90% shower energy within RM]
RM =
21 MeV
X0
Ec
Energy deposit [a.u.]
Molière Radii
Beyond shower maximum broadening
mainly due to low energy photons ...
Radial distributions of the energy deposited
by 10 GeV electron showers in Copper
[Results of EGS4 simulations]
Distance from shower axis [RM]
16
Lateral profile
Material dependence:
Scaling almost perfect at low radii ...
Most striking difference seen in
slope of 'tail' or 'halo' ...
Slope considerably steeper for high-Z
material due to smaller mean free path
for low-energy photons ...
Energy deposit [%]
Transversal Shower Shape
10
1
Halo
0.1
Radial energy deposit profiles for
10 GeV electrons showering in Al, Cu and Pb
[Results of EGS4 calculations]
Remark:
Even though calorimeters are intended
to measure GeV, TeV their performance
is determined by low energy particles ...
0.01
0
1
2
3
4
5
Distance from shower axis [RM]
15
Some Useful 'Rules of Thumbs'
Radiation length:
180A g
X0 =
Z 2 cm2
Critical energy:
550 MeV
Ec =
Z
[Attention: Definition of Rossi used]
Shower maximum:
Longitudinal
energy containment:
Transverse
Energy containment:
Problem:
Calculate how much Pb, Fe or Cu
is 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
− 1.0
E
tmax = ln
− 1.0
Ec
− 0.5
{
e– induced shower
γ induced shower
L(95%) = tmax + 0.08Z + 9.6 [X0 ]
R(90%) = RM
R(95%) = 2RM
Homogeneous Calorimeters
★
In a homogeneous calorimeter the whole detector volume is filled by a
high-density material which simultaneously serves as absorber as well
as as active medium ...
Signal
Material
Scintillation light
BGO, BaF2, CeF3, ...
Cherenkov light
Lead Glass
Ionization signal
Liquid nobel gases (Ar, Kr, Xe)
★
Advantage: homogenous calorimeters provide optimal energy resolution
★
Disadvantage: very expensive
★
Homogenous calorimeters are exclusively used for electromagnetic
calorimeter, i.e. energy measurement of electrons and photons
Example: CMS Crystal Calorimeter
Homogeneous Calorimeters
imeter (ECAL) are described. The section ends with a description of the preshower detec
which sits in front of the endcap crystals.
Two important
changes have
occurred to the
Example:
CMS Crystal
Calorimeter
ometry and configuration since the ECAL TDR [5]. In the endcap the basic mechanical u
the “supercrystal,” which was originally envisaged to hold 6×6 crystals, is now a 5×5 u
The lateral dimensions of the endcap crystals have been increased such that the supercry
remains little changed in size. This choice took advantage of the crystal producer’s a
ity to produce larger crystals, to reduce the channel count. Secondly, the option of a ba
preshower detector, envisaged for high-luminosity running only, has been dropped. T
simplification allows more space to the tracker, but requires that the longitudinal vertice
H → γγ events be found with the reconstructed charged particle tracks in the event.
Homogeneous Calorimeters
. Description of the ECAL
4.1.1
Scintillator : PBW04 [Lead Tungsten]
Photosensor: APDs [Avalanche Photodiodes]
The ECAL layout and geometry
147
The nominal geometry of the
ECAL (the
engineering
is simulated in detai
Number
of crystals:
~ specification)
70000
the
4/
model.Light
There output:
are 36 identical
supermodules, 18 in each half barrel, e
4.5 photons/MeV
covering 20 in φ. The barrel is closed at each end by an endcap. In front of most of
fiducial region of each endcap is a preshower device. Figure 4.1 shows a transverse sect
through ECAL.
e barrel part of the ECAL covers the pseudorapidity range |η| < 1.479. The barrel granuity is 360-fold in φ and (2×85)-fold in η, resulting in a total of 61 200GEANT
crystals.The truncatedOSCAR
ramid shaped crystals are mounted in a quasi-projective geometry so that their axes
◦ make
mall angle (3o ) with the respect to the vector from the nominal interaction vertex, in both
φ and η projections. The crystal cross-section corresponds to approximately 0.0174 ×
174◦ in η-φ or 22×22 mm2 at the front face of crystal, and 26×26 mm2 at the rear face. The
stal length is 230 mm corresponding to 25.8 X0 .
e centres of the front faces of the crystals in the supermodules are at a radius 1.29 m.
e crystals are contained in a thin-walled glass-fibre alveola structures (“submodules,” as
own in Fig. CP 5) with 5 pairs of crystals (left and right reflections of a single shape) per
bmodule. The η extent of the submodule corresponds to a trigger tower. To reduce the
mber of different type of crystals, the crystals in each submodule have the same shape.
ere are 17 pairs of shapes. The submodules are assembled into modules and there are
modules in each supermodule separated by aluminium webs. The arrangement of the 4
dules in a supermodule can be seen in the photograph shown in Fig. 4.2.
Barrel ECAL (EB)
y
=
9
7
1.4
Preshower (ES)
= 2.6
z
653
.
1
=
= 3.0
Endcap
ECAL (EE)
Figure 4.1: Transverse section through the ECAL, showing geometrical configuration.
Sampling Calorimeters
Scheme of a
sandwich calorimeter
Principle:
passive absorber
shower (cascade of secondaries)
Alternating layers of absorber and
active material [sandwich calorimeter]
Simple shower model
Absorber materials:
incoming particle
[high density]
Iron (Fe)
Lead
(Pb)Bremsstrahlung
Consider
only
Uranium (U)
production
and (symmetric) pair
active layers
[For compensation ...]
Active
Assume
X0materials:
! !pair
Plastic scintillator
After t XSilicon
0:
detectors
Liquid tionization chamber
!
N(t)
=
2
Gas detectors
!
E(t)/particle = E0/2t
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 and
thus cheaper than homogeneous calorimeters ...
★
Disadvantages:
Only part of the deposited particle energy is actually detected in the
active 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
Possible setups
Scintillators as active layer;
signal readout via photo multipliers
Absorber
Scintillator
Light guide
Photo detector
Scintillators as active
layer; wave length shifter
to convert light
Scintillator
(blue light)
Wavelength shifter
Charge amplifier
Absorber as
electrodes
HV
Ionization chambers
between absorber
plates
Argon
Active medium: LAr; absorber
embedded in liquid serve as electrods
Electrodes
Analogue
signal
Sampling Calorimeters
Example:
ATLAS Liquid Argon Calorimeter
Sampling Calorimeters
Example:
H1 SpaCal
Lead-Fibre Matrix
[Front view]
[Spaghetti Calorimeter]
4 SpaCal Supermodules
Lead matrix ...
[Technical drawing]
Example: CALICE Electromagnetic
Calorimeter
:;<=:9.642)1-
Sampling Calorimeters
‘Alveolar Structure’
Tungsten
frame
?4
Sensors
+ r/o electonics
>45?34232.53.
Detector
slabs
max.: 1.6 m
Tungsten
layer
/84.:;
Example: CALICE Electromagnetic
Calorimeter
Sampling Calorimeters
Aluminum protection
Heat shield
PCB with r/o-chips
Tungsten layer
Silicon matrices
Read-out chip
[embeddable?]
Detector
slab
PCB
!
~ 3 mm
!"#$%&' ()*+' ,-.&/01"-' 2"&3' 45' 0' 6477"89&' :&1&-14%' 7908;' <%&&=' "7' 1.&' >?@' "=' 3."-.' 1.&' A!B' 0%&'
"=-9$:&:C'1.&'7"9"-4='/01%"-&7'D4%0=#&E'0%&'#9$&:'4='>?@;'F.&'1$=#71&='7.&&1'D9"#.1'89$&E''"7'3%066&:'
"='-0%84='5"8%&'D8%43=E;'G='42&%099'6%41&-1"4='7.&&1'"='09$/"="$/'D#%&HE'7$%%4$=:7'&2&%H1."=#;'
!
4.3
Tungsten
1.4 mm
Current status of the project
Silicon Pads
! $%&!'(&)*'!+,!-%&!./+0&1-!1+)1&/)2!'32+!-%&!1+)2-/41-5+)!+,!'!2&1+)*!(&)&/'-5+)!+,!./+-+-6.&7!-%52!
[5 x 5 mm2]
-58&!'2!13+2&!'2!.+22593&!-+!-%&!,5)'3!*&-&1-+/:!$%52!2&1+)*!(&)&/'-5+)!52!.'/-5'336!,4)*&*!96!-%&!;<!./+(/'8!
;<=;$:!$%&!-&2-!>5-%!%'*/+)!9&'82!52!,+/&2&&)!-+!9&!*+)&!-+(&-%&/!>5-%!-%&!*5,,&/&)-!?@AB!+.-5+)2!+,!
@ABC@;:!!!
~ 3 mm
Example: CALICE Electromagnetic
Calorimeter
Sampling Calorimeters
Structure 2.8
Structure 1.4
Structure 4.2
Front End
Electronics
Event
Display
Energy Resolution
Ebeam = 1 GeV
[Pads: 10x10 mm2]
Active area
< 20%/√E
Ebeam = 45 GeV
!! !!!
!"#$%&' ()*+,' -"./%"0$/"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''
'
run 230243, Ebeam=1.5GeV
2.5
RMS
30
run 230252, E
9.518
=6GeV
mm)
GeV]
Entries
run 230248,
Ebeam=3GeV
Mean
17.78
40
!! !!!
center
ECAL ‘Physics’ Prototype
[CALICE]
Homogeneous vs. Sampling Calorimeters
28. Detectors at accelerators 57
Table 28.8:
Resolution of typical electromagnetic calorimeters. E is in GeV.
Energy resolution
Date
NaI(Tl) (Crystal Ball)
20X0
1983
Bi4 Ge3 O12 (BGO) (L3)
22X0
1993
[E is in GeV]
CsI (KTeV)
27X0
CsI(Tl) (BaBar)
2.7%/E1/4
√
2%/ E ⊕ 0.7%
√
2%/ E ⊕ 0.45%
Resolution of typical
electromagnetic calorimeter
16–18X0 2.3%/E 1/4 ⊕ 1.4%
1999
PbWO4 (PWO) (CMS)
25X0
1997
Lead glass (OPAL)
20.5X0
Liquid Kr (NA48)
27X0
Scintillator/depleted U
(ZEUS)
Scintillator/Pb (CDF)
20–30X0
CsI(Tl) (BELLE)
16X0
18X0
15X0
Liquid Ar/Pb (NA31)
27X0
Liquid Ar/Pb (SLD)
21X0
Liquid Ar/Pb (H1)
20–30X0
Liquid Ar/depl. U (DØ)
20.5X0
Liquid Ar/Pb accordion
(ATLAS)
25X0
√
13.5%/ E
√
5.7%/ E ⊕ 0.6%
√
7.5%/ E ⊕ 0.5% ⊕ 0.1/E
√
8%/ E
√
12%/ E ⊕ 1%
√
16%/ E ⊕ 0.3% ⊕ 0.3/E
√
10%/ E ⊕ 0.4% ⊕ 0.3/E
1998
1990
1998
1988
1988
1995
1988
1993
1998
1993
1996
Sampling
Scintillator fiber/Pb
spaghetti (KLOE)
1.7% for Eγ > 3.5 GeV
√
3%/ E ⊕ 0.5% ⊕ 0.2/E
√
5%/ E
√
3.2%/ E⊕ 0.42% ⊕ 0.09/E
√
18%/ E
1996
Homogeneous
Technology (Experiment) Depth