General Information

Today’s Agenda Schedule (papers, presentations etc) Calorimeter Project Presentation: Fermi/Glast

Calorimetry

Basic principles

Interaction of charged particles and photons (Review)

Electromagnetic cascades

Nuclear interactions

Hadronic cascades

Homogeneous calorimeters

Sampling calorimeters

Introduction Calorimetry:

Energy measurement by total absorption, combined with spatial reconstruction.

Calorimetry is a “destructive” method Detector response E Calorimetry works both for

charged (e and hadrons) and neutral particles (n,)

Basic mechanism: formation of electromagnetic or hadronic showers.

Finally, the energy is converted into ionization or excitation of the detector matter.

Interaction of Charged Particlesenergy loss (radiative + ionization) of electrons and protons in copperCritical energy Ec

For electrons one finds approximately:

density effect of dE/dx(ionisation) !

Ec(e-) in Fe(Z=26) = 22.4 MeV

For muons

Ec() in Fe(Z=26) 1 TeV

ion

cBrems

c EdxdEE

dxdE

24.1710

24.1610

ZMeVE

ZMeVE gas

cliqsolid

c

2

e

eleccc m

mEE

31

31

183ln4

183ln4

220

0

22

ZrZN

AX

XE

dxdE

ZEr

AZN

dxdE

eA

eA

Radiation Length

0/0

XxeEE

Interaction of Photons

(PDG)

1 M

eV

Rayleigh scattering(no energy loss !)

Compton scattering

pair production

photo effect

Photon Interactions•Photo Effect•Compton Scattering•Pair Production

Combined Effect:

...0

pairComptonphoto

xeII

: mass attenuation coefficient

gcmA

Ni

Ai /2

For pair production

ooPair XX 791

Electromagnetic Cascades

Electron shower in a cloud chamber with lead absorbers

Simple qualitative model:Consider only Bremsstrahlung and pair production; assume Xo = Pair

tt EparticletEtN 2/)(2)( 0

2lnln 0

maxcEEt

c

tt

t

tttotal

EEN 0

0

)1( 222122 maxmax

max

Process continues until E(t)<Ec

After t = tmax the dominating processes areionization, Compton effect and photo effect absorption.

EM Shower DevelopmentLongitudinal shower development:

Shower maximum at

95% containmentSize of a calorimeter grows only logarithmically with E0

Transverse shower development:

95% of the shower cone is located in a cylinder with radius 2 RM

tetdtdE

2ln1ln 0

maxcE

Et

6.908.0max%95 Ztt

]/[MeV21 20 cmgX

ER

cM Molière radius

6 GeV/c e-

Example:E0 = 100 GeV electrons in lead glass

Ec=11.8 MeV tmax 13, t95% 23X0 2 cm, RM = 1.8·X0 3.6 cm

46 cm

8 cm

Energy resolution of a calorimeter (intrinsic limit)

Energy Resolution

c

total

EE

N 0 total number of track segments

0

11)()(ENN

NE

E

Ecb

Ea

EE

)(

holds also for hadron calorimeters

Stochastic term

More general:

Constant term

InhomogenitiesBad cell inter-calibrationNon-linearities

Noise term

Electronic noiseradioactivitypile up

Also spatial and angular resolution scale like 1/E

Relative energy resolution of a calorimeter improves with E0

Nuclear InteractionsThe interaction of energetic hadrons (charged or neutral) is determined by inelastic nuclear processes.

Excitation and finally breakup up nucleus nucleus fragments + production of secondary particles.

For high energies (>1 GeV) the cross-sections depend only little on the energy and on the type of the incident particle (p, , K…).

In analogy to X0 a hadronic absorption length can be defined:

n

p

+

0

-

hadronZ,A

multiplicity ln(E)

pt 0.35 GeV/c

p,n,,K,…

inelAa N

A

mbAinel 3507.0

0

Hadronic Absorption LengthMaterial Z A [g/cm3] X0 [g/cm2] a [g/cm2]

Hydrogen (gas) 1 1.01 0.0899 (g/l) 63 50.8Helium (gas) 2 4.00 0.1786 (g/l) 94 65.1Beryllium 4 9.01 1.848 65.19 75.2Carbon 6 12.01 2.265 43 86.3Nitrogen (gas) 7 14.01 1.25 (g/l) 38 87.8Oxygen (gas) 8 16.00 1.428 (g/l) 34 91.0Aluminium 13 26.98 2.7 24 106.4Silicon 14 28.09 2.33 22 106.0Iron 26 55.85 7.87 13.9 131.9Copper 29 63.55 8.96 12.9 134.9Tungsten 74 183.85 19.3 6.8 185.0Lead 82 207.19 11.35 6.4 194.0Uranium 92 238.03 18.95 6.0 199.0

For Z > 6: a > X0

0.1

1

10

100

0 10 20 30 40 50 60 70 80 90 100

X 0,

a [c

m]

Z

a and X0 in cm

X0

a

Hadronic CascadesVarious processes involved. Much more complex than electromagnetic cascades.

Hadronic + electromagnetic component

Large energy fluctuations limited energy resolution

(Grupen)

neutral pions 2 electromagnetic cascade

charged pions, protons, kaons ….Breaking up of nuclei (binding energy), neutrons, neutrinos, soft ’smuons …. invisible energy

6.4)(lnn 0 GeVE

Example: 100 GeV: n(0)18

Hadronic Shower DevelopmentLongitudinal shower development:

Transverse (lateral) shower development:The shower consists of core + halo. 95% containment in a cylinder of radius I.

Hadronic showers are much longer and broader than electromagnetic ones !

bEacmtGeVEt I

ln)(7.0][ln2.0)(

%95

max For Iron: a = 9.4, b=39 a =16.7 cm

E =100 GeV t95% 80 cm

(C. F

abja

n, T

. Lud

lam

, C

ERN

-EP/

82-3

7)

Calorimeter Types Homogeneous calorimeters

Sampling calorimeters

Detector = absorber good energy resolution limited spatial resolution (particularly in longitudinal direction) only used for electromagnetic calorimetry

Detectors and absorber separated only part

of the energy is sampled.

limited energy resolution

good spatial resolution

used both for electromagnetic and hadron

calorimetry

Homogeneous Calorimeter

Liquid Nobel Gases(Nobel Liquids)

Scintillating Crystals, Plastic ScintillatorsCherenkov counters(Lead glas)

Ionization ChamberCollect the producedcharge

Collect the producedphotons

The total amount of charge (or photons) collected is proportional to the total track length is proportional to the energy of the incident particle

The incident electron or photon is completely absorbed

CMS@LHC, 25ns bunch crossing, high radiation dose

L3@LEP, 25us bunch crossing, Low radiation dose

Barbar@PEPII,10ms interaction rate, good light yield, good S/N

KTeV@Tevatron,High rate,Good resolution

Crystals for Homogeneous EM Calorimetry

Homogeneous Calorimeter Configurations

BaBar CsI Calorimeter duringconstruction

Noble Liquids for Homogeneous EM Calorimetry

When a charge particle traverses these materials, about half the lost energy is converted into ionization and half into scintillation.

The best energy resolution would obviously be obtained by collecting both the charge and light signal. This is however rarely done because of the technical difficulties to extract light and charge in the same instrument.

Krypton is preferred in homogeneous detectors due to small radiation length and therefore compact detectors. Liquid Argon is frequently used due to low cost and high purity in sampling calorimeters (see later).

Homogeneous EM Calorimeters, Examples

1%

0.8%

0.6%

1%

0.8%

0.6%

NA48 Experiment at CERN and KTeV Experiment at Fermilab, both built for measurement of direct CP violation. Homogenous calorimeters with Liquid Krypton (NA48) and CsI (KTeV). Excellent and very similar resolution.

NA48 Liquid Krypton2cmx2cm cellsX0 = 4.7cm125cm length (27X0)ρ = 5.5cm

KTeV CsI5cmx5cm andX0 = 1.85cm2.5cmx2.5cm crystals50cm length (27X0)ρ = 3.5cm

Sampling CalorimetersAbsorber + detector separated → additional sampling fluctuations!

d e te c to rs a b s o rb e rs

d

d

XEEF

dTN

c

10

det

Detectable track segments

0

1Xd

ENN

EE

Scintillators,Scintillation Fibers

Cryogenic noble gasesmainly LAr (LXe, LKr)

MWPCStreamer Tubes

ATLAS EM CalorimeterAccording geometry absorbers immersed in Liquid Argon.

Liquid Argon (90K)+ lead-steal absorbers (1-2 mm) + multilayer copper-polyimide

readout boards Ionization chamber.1 GeV E-deposit 5 x106 e-

• Accordion geometry minimizes dead zones.

• Liquid Ar is intrinsically radiation hard.• Readout board allows fine segmentation

(azimuth, pseudo-rapidity and longitudinal) acc. to physics needs cEbEaEE /)(

Stoachastic term: 10%

Spatial and angular uniformity 0.5%

Spatial resolution 5mm / E1/2

Test beam results, e- 300 GeV

CMS Hadronic CalorimeterCu absorber + scintillators

Scintillators fill slots and are read out via fibres by HPDs

2 x 18 wedges (barrel) + 2 x 18 wedges (endcap) 1500 T absorber

%5%65

EEETest beam

resolution for single hadrons

Today’s References

Material from the books by Leo and Grupen Physics 880.20 Lecture Notes, R. Kass Oxford Student Lecture Notes, M. Weber CERN Summer Student Lectures by Joram and Riegler PPE Lecture Notes, R. Bates