Детектори - II

4-ти курс УФЕЧ

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Спирачно лъчение (bremsstrahlung)

Z2 electrons, q=-e0

M, q=Z1 e0

A charged particle of mass M and charge q=Z1e is deflected by a nucleus of charge Ze which is partially ‘shielded’ by the electrons. During this deflection the charge is ‘accelerated’ and it therefore radiated Bremsstrahlung.

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Спирачно лъчение

Bremsstrahlung is the emission of photons by a charged particle accelerated in the Coulomb field of a nucleus.

The radiative process is characterised by:Impact parameter : b (non-relativistic!)Peak electric field prop. to e/b2 Characteristic frequency c 1/t v/2b

)(58.0 22

mbZZ

d

dB

B

We now have an additional photon.5

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Electron Momentum 5 50 500 MeV/c

Critical Energy: If dE/dx (Ionization) = dE/dx (Bremsstrahlung)

Muon in Copper: p 400GeVElectron in Copper: p 20MeV

W. Riegler/CERN 7

For the muon, the second lightest particle after the electron, the critical energy is at 400GeV.

The EM Bremsstrahlung is therefore relevant mainly for electrons at energies provided by present accelerators.(Caveat: muons at LHC!)

Critical Energy

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Раждане на двойка е+е- (Pair production)

Creation of an electron/positron pair in the field of an atom.

As the two diagrams are more or less identical, we would expect the cross sections to be similar.

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7ZmbBpair

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For E>>mec2=0.5MeV : = 9/7X0

Average distance a high energy photon has to travel before it converts into an e+ e- pair is equal to 9/7 of the distance that a high energy electron has to travel before reducing it’s energy from E0 to E0*Exp(-1) by photon radiation.

Раждане на двойка е+е-

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Rossi B. Approximation to Shower Development.

1) Electrons loses a constant amount of energy (e) for each radiation length, X0

2) Radiation and Pair production at all energies are described by the asymptotic formulae.

Electromagnetic Calorimeter

e±

g

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How a shower looks like

F.E. Taylor et al., IEEE NS 27(1980)30

BElectron shower in lead. Cloud chamber. W.B. Fretter, UCLA

Electron shower in lead. 7500 gauss in cloud chamber. CALTECH

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tetdt

dE

tmax = 1.4 ln(E0/Ec)

Ntot E0/Ec

Longitudinal containment:

t95% = tmax + 0.08Z + 9.6

Shower profile for electrons of energy:10, 100, 200, 300… GeV

X0

EM showers: longitudinal profile

Ec 1/Z • shower max• shower tail

Shower parametrization

From M. Diemoz, Torino 3-02-0513

The shower maximum

Shower maximum t=t(E,e)

and there must be a difference between e and g

3.0ln

1.1ln

0

0

E

Xt

EXt for e

for g

U. Amaldi, Physica Scripta 23(1981)409

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Transverse shower profile

• Multiple scattering make electrons move away from shower axis• Photons with energies in the region of minimal absorption can travel far away from shower axis

Molière radius sets transverse shower size, it gives theaverage lateral deflection of critical energy electronsafter traversing 1X0

75% E0 within 1RM, 95% within 2RM, 99% within 3.5RM

0C

M XE

MeV21R 1Z

Z

A

E

XR

C

0M

EM showers: transverse profile

From M. Diemoz, Torino 3-02-0515

Why is Space Resolution an issue in calorimeters ?

0

0

min 2

E

m

For a calorimeter with limited granularity, this would give:

M

M

R

mRE

R0

max0

min 2

Set R=2 m

Consider a p0 - decay

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20 GeV g in copper (simulation)

charged particles only all particles

J.P. Wellisch

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29.0Ai

Nuclear Interaction Length li

is the average distance a high-energy hadron has to travel inside a medium before a nuclear interaction occurs.

Probability not to have interacted after a path zi

z

eP

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Hadronic Showers

20 GeV p in copper (simulation)

Hadronic Showers (p, n, p, ...)Propagation : inelastic hadron interactions

multi particle productionNuclear disintegration

J.P. Wellisch

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Монте Карло симулация на адронен каскад

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