Детектори - II 4-ти курс УФЕЧ 1

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Спирачно лъчение (bremsstrahlung) Z 2 electrons, q=-e 0 M, q=Z 1 e 0 A charged particle of mass M and charge q=Z 1 e 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. 4

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/b 2 Characteristic frequency  c  1/  t  v/2b We now have an additional photon. 5

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Electron Momentum MeV/c Critical Energy: If dE/dx (Ionization) = dE/dx (Bremsstrahlung) Muon in Copper: p  400GeV Electron in Copper: p  20MeV W. Riegler/CERN7 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 7

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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. 9

For E  >>m e c 2 =0.5MeV : = 9/7X 0 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 E 0 to E 0 *Exp(-1) by photon radiation. Раждане на двойка е+е- 10

Rossi B. Approximation to Shower Development. 1) Electrons loses a constant amount of energy (  ) for each radiation length, X 0 2) Radiation and Pair production at all energies are described by the asymptotic formulae. Electromagnetic Calorimeter e±e±  11

How a shower looks like F.E. Taylor et al., IEEE NS 27(1980)30 BB Electron shower in lead. Cloud chamber. W.B. Fretter, UCLA Electron shower in lead gauss in cloud chamber. CALTECH 12

t max = 1.4 ln(E 0 /E c ) N tot  E 0 /E c Longitudinal containment: t 95% = t max Z Shower profile for electrons of energy: 10, 100, 200, 300… GeV X0X0 EM showers: longitudinal profile E c  1/Z shower max shower tail Shower parametrization From M. Diemoz, Torino

The shower maximum Shower maximum t=t(E,  ) and there must be a difference between e and  for e for  U. Amaldi, Physica Scripta 23(1981)409 14

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 the average lateral deflection of critical energy electrons after traversing 1X 0 75% E 0 within 1R M, 95% within 2R M, 99% within 3.5R M EM showers: transverse profile From M. Diemoz, Torino

Why isSpace Resolution an issue in calorimeters ? For a calorimeter with limited granularity, this would give: Set R=2 m Consider a   - decay 16

20 GeV  in copper (simulation) charged particles onlyall particles J.P. Wellisch 17

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Nuclear Interaction Length i 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 z 20

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Hadronic Showers 20 GeV  in copper (simulation) Hadronic Showers ( , n, p,...) Propagation : inelastic hadron interactions  multi particle production Nuclear disintegration J.P. Wellisch 22

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Монте Карло симулация на адронен каскад 38

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