Graduate lectures HT '08 T. Weidberg1 Calorimeters Purpose of calorimeters EM Calorimeters Hadron...

Graduate lectures HT '08

T. Weidberg 1

Calorimeters

• Purpose of calorimeters

• EM Calorimeters

• Hadron Calorimeters


T. Weidberg 2

EM Calorimeters

• Measure energy (direction) of electrons and photons.

• Identify electrons and photons.• Reconstruct masses eg

– Z e+ e- 0 – H

• Resolution important: • Improve S/N• Improve precision of mass measurement.


T. Weidberg 3

EM Calorimeters

• Electron and photon interactions in matter

• Resolution

• Detection techniques

• Sampling calorimeters vs all active

• Examples


T. Weidberg 4

12.2 Charged particles in matter(Ionisation and the Bethe-Bloch Formula, variation with )

+ can capture e-

Ec = critical energydefined via:dE/dxion.=dE/dxBrem.


T. Weidberg 5

Charged particles in matter(Bremsstrahlung = Brakeing Radiation)

• Due to acceleration of incident charged particle in nuclear Coulomb field

• Radiative correction to Rutherford Scattering. • Continuum part of x-ray emission spectra. • Emission often confined to incident electrons because

– radiation ~ (acceleration)2 ~ mass-2. • Lorentz transformation of dipole radiation from incident

particle centre-of-mass to laboratory gives narrow (not sharp) cone of blue-shifted radiation centred around cone angle of =1/.

• Radiation spectrum very uniform in energy. • Photon energy limits:

– low energy (large impact parameter) limited through shielding of nuclear charge by atomic electrons.

– high energy limited by maximum incident particle energy.

Ze

e- e-


T. Weidberg 6

12.2 Charged particles in matter(Bremsstrahlung EM-showers, Radiation length)

• dT/dx|Brem~T (see Williams p.247) dominates over dT/dx|ionise ~ln(T) at high T.

• For electrons Bremsstrahlung dominates in nearly all materials above few 10 MeV. Ecrit(e-) ≈ 600 MeV/Z

• If dT/dx|Brem~T dT/dx|Brem=T0exp(-x/X0)

• Radiation Length X0 of a medium is defined as:– distance over which electron energy reduced to 1/e.

– X0~Z2 approximately.

• Bremsstrahlung photon can undergo pair production (see later) and start an em-shower (or cascade)

• Length scale of pair production and multiple scattering are determined by X0 because they also depend on nuclear coulomb scattering.

The development of em-showers, whether started by primary e or is measured in X0.


T. Weidberg 7

Very Naïve EM Shower Model

• Simple shower model assumes:– E0 >> Ecrit

– only single Brem- or pair production per X0

• The model predicts:– after 1 X0, ½ of E0 lost by

primary via Bremsstrahlung– after next X0 both primary and

photon loose ½ E again – until E of generation drops

below Ecrit

– At this stage remaining Energy lost via ionisation (for e+-) or compton scattering, photo-effect (for ) etc.

– Abrupt end of shower happens at t=tmax = ln(E0/Ecrit)/ln2– Indeed observe logarithmic depth dependence


T. Weidberg 8

13.1 Photons in matter(Overview)• Rayleigh scattering

– Coherent, elastic scattering of the entire atom (the blue sky) + atom + atom– dominant at >size of atoms

• Compton scattering– Incoherent scattering of electron from atom + e-

bound + e-free

– possible at all E > min(Ebind)– to properly call it Compton requires E>>Ebind(e-) to approximate free e-

• Photoelectric effect– absorption of photon and ejection of single atomic electron + atom + e-

free + ion– possible for E < max(Ebind) + E(Eatomic-recoil, line width) (just above k-edge)

• Pair production– absorption of in atom and emission of e+e- pair– Two varieties:

+ nucleus e+ + e- + nucleus (more momentum transfer to nucleusdominates) + Z atomic electrons e+ + e- + Z atomic electrons• both summarised via: g + g(virtual) e+ + e-

– Needs E>2mec2

– Nucleus has to recoils to conserve momentum coupling to nucleus needed strongly Z-dependent crossection


T. Weidberg 9

13.1 Photons in matter(Note on Pair Production)

• Compare pair production with Bremsstrahlung

• Very similar Feynman Diagram• Just two arms swapped

Typical Lenth =Radiation LengthX0

Typical Lenth =Pair Production Length L0

L0=9/7 X0

Ze

e-

e-*

Bremsstrahlung

e-

Ze

e-*

e-

Pair production

e-


T. Weidberg 10

13.1 Photons in matter(Crossections)

• R Rayleigh

• PE Photoeffect

• C Compton

• PP Pair Production• PPE Pair Production on atomic electrons• PN Giant Photo-Nuclear dipole resonance

Carbon

Lead


T. Weidberg 11

Transverse Shower Size• Moliere radius = 21 MeV X0/Ec

Electrons Photons


T. Weidberg 12

Sampling vs All Active

• Sampling: sandwich of passive and active material. eg Pb/Scintillator.

• All active: eg Lead Glass.

• Pros/cons– Resolution– Compactness costs.


T. Weidberg 13

Detection Techniques

• Scintillators

• Ionisation chambers

• Cherenkov radiation

• (Wire chambers)

• (Silicon)


T. Weidberg 14

Organic Scintillators (1)

• Organic molecules (eg Naphtalene) in plastic (eg polysterene).

• excitation non-radiating de-excitation to first excited state scintillating transition to one of many vibrational sub-states of the ground state.


T. Weidberg 15

Organic Scintillators (2)

• gives fast scintillation light, de-excitation time O(10-8 s)

• Problem is short attenuation length.– Use secondary fluorescent material to shift

to longer wavelength (more transparent).– Light guides to transport light to PMT or– Wavelength shifter plates at sides of

calorimeter cell. Shift blue green (K27) longer attenuation length.


T. Weidberg 16

Inorganic Scintillators (1)

• eg NaI activated (doped) with Thallium, semi-conductor, high density: (NaI=3.6), high stopping power

• Dopant atom creates energy level (luminescence centre) in band-gap

• Excited electron in conduction band can fall into luminescence level (non radiative, phonon emission)

• From luminescence level falls back into valence band under photon emission

• this photon can only be re-absorbed by another dopant atom crystal remains transparent


T. Weidberg 17

Inorganic Scintillators (2)

• High density of inorganic crystals good for totally absorbing calorimetry even at very high particle energies (many 100 GeV)

• de-excitation time O(10-6 s) slower then organic scintillators.

• More photons/MeV Better resolution.

• PbWO4. fewer photons/MeV but faster and rad-hard (CMS ECAL).


T. Weidberg 18

PMT

Detectors (1)

• Photomultiplier:– primary electrons liberated by photon from photo-cathode (low

work function, high photo-effect crossection, metal, conversion≈¼ )– visible photons have sufficiently large photo-effect cross-section– acceleration of electron in electric field 100 – 200 eV per stage– create secondary electrons upon impact onto dynode surface

(low work function metal) multiplication factor 3 to 5– 6 to 14 such stages give total gain of 104 to 107

– fast amplification times (few ns) good for triggers or veto’s– signal on last dynode proportional to #photons impacting


T. Weidberg 19

Detectors (2)

• APD (Avalanche Photo Diode)– solid state alternative to PMT– strongly forward biased diode gives

“limited” avalanche when hit by photon


T. Weidberg 20

13.2 Detectors

• Ionisation Chambers– Used for single particle and flux measurements– Can be used to measure particle energy up to few

MeV with accuracy of 0.5% (mediocre)– Electrons more mobile then ions medium fast

electron collection pulse O(s)– Slow recovery from ion drift


T. Weidberg 21

Resolution• Sampling fluctuations for sandwich calorimeters.• Statistical fluctuations eg number of photo-electrons or number

of e-ion pairs.• Electronic noise.• Others

– Non-uniform response– Calibration precision– Dead material (cracks).– Material upstream of the calorimeter.– Lateral and longitudinal shower leakage

• Parameterise resolution as– a Statistical– b noise– c constant

cE

b

E

a

E

E


T. Weidberg 22

Classical Pb/Scintillator


T. Weidberg 23

Lead Glass

• All active• Pb Glass


T. Weidberg 24

BGO

• Higher resolution

)1(%1~)(

GeVEE

E


T. Weidberg 25

Liqiuid Argon

• Good resolution eg NA31.

EE

E%8~

)(


T. Weidberg 26

Fast Liquid Argon

• Problem is long drift time of electrons (holes even slower).

• Trick to create fast signals is fast pulse shaping. – Throw away some of the signal and

remaining signal is fast (bipolar pulse shaping).

– Can you maintain good resolution and have high speed (LHC)?


T. Weidberg 27

Accordion Structure

Lead plates

Cu/kapton electrodes for HV and signal

Liquid Argon in gaps.

Low C and low L cf cables in conventional LAr calorimeter.


T. Weidberg 28

Bipolar Pulse Shaping


T. Weidberg 29


T. Weidberg 30

ATLAS Liquid Argon

• Resolution– Stochastic term

~ 1/E1/2. – Noise ~ 1/E– Constant (non-

uniformity over cell, calibration errors).


T. Weidberg 31

Calibration

• Electronics calibration– ADC counts to charge in pC. How?

• For scintillators– Correct for gain in PMT or photodiode. How?– Correct for emission and absorption in scintillator

and light guides. How ?

• Absolute energy scale.– Need to convert charge seen pC E (GeV). How?


T. Weidberg 32

Hadron Calorimeters

• Why you need hadron calorimeters.

• The resolution problem.

• e/pi ratio and compensation.

• Some examples of hadron calorimeters.


T. Weidberg 33

Why Hadron Calorimeters

• Measure energy/direction of jets– Reconstruct masses (eg tbW or h bbar)– Jet spectra: deviations from QCD quark

compositeness)

• Measure missing Et (discovery of Ws, SUSY etc).

• Electron identification (Had/EM)• Muon identification (MIPs in calorimeter).• Taus (narrow jets).


T. Weidberg 34

Hadron Interactions• Hadron interactions on nuclei produce

– More charged hadrons further hadronic interactions hadronic cascade.

0 EM shower– Nuclear excitation, spallation, fission.– Heavy nuclear fragments have short range

tend to stop in absorber plates.– n can produce signals by elastic scattering

of H atoms (eg in scintillator)

• Scale set by int (eg = 17 cm for Fe, cf X0=1.76 cm) next transparency


T. Weidberg 35


T. Weidberg 36

Resolution for Hadron Calorimeters

• e/pi ≠ 1 fluctuations in 0 fraction in shower will produce fluctuations in response (typically e/pi >1).

• Energy resolution degraded and no longer scales as 1/E1/2 and response will tend be non-linear because 0 fraction changes with E.


T. Weidberg 37

e/h Response vs Energy


T. Weidberg 38

Resolution Plots E)/E vs 1/E1/2.

Fe/Scint (poor).

ZEUS U/scint and SPACAL (good).


T. Weidberg 39

Compensation (1)

• Tune e/pi ~= 1 to get good hadronic resolution.

• U/Scintillator (ZEUS)– Neutrons from fission of U238 elastic

scatter off protons in scintillator large signals compensate for nuclear losses.

– Trade off here is poorer EM resolution.


T. Weidberg 40

Compensation (2)

• Fe/Scintillator (SPACAL)– Neutrons from spallation in any heavy absorber

can scatter of protons in scintillator large signals.

– If the thickness of the absorber is increased greater fraction of EM energy is lost in the passive absorber.

– tune ratio of passive/active layer thickness to achieve compensation.

– Needs ratio 4/1 to achieve compensation. No use for classical calorimeter with scintillator plates (why).

– SPACAL: scintillating fibres in Fe absorber.


T. Weidberg 41

Scintillator Readout


T. Weidberg 42

SPACAL

1 mm scintillating fibres in Fe


T. Weidberg 43


T. Weidberg 44


T. Weidberg 45

Compensation (3)

• Software weighting (eg H1)• EM component localized de-weight large

local energies• Very simplified:

' (1 )

'K K K

TOTAL Kk

E E CE

E E


T. Weidberg 46

Fine grain Fe/Scintillator Calorimeter (WA1)

• With weighting resolution improved. EE

E %58)(


T. Weidberg 47

H1 Hadronic resolution with weighting

Standard H1 weighting

Improved (Cigdem Issever)

Graduate lectures HT '08 T. Weidberg1 Calorimeters Purpose of calorimeters EM Calorimeters Hadron...

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