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Cherenkov Radiation

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Cherenkov Radiation TheThe CherenkovCherenkov effecteffect A charged particle traveling in a dielectric medium with n>1 radiates Cherenkov radiation B Wave front if its velocity is larger than the C phase velocity of light v>c/n or > 1/n (threshold) A β Charged particle The emission is due to an asymmetric polarization of the medium in front and at the rear of the particle, giving rise to a varying electric dipole momentum. dN Some of the particle energy is convertedγ = 491into light. A coherent wave front is dx generated moving at velocity v at an angle Θc If the media is transparent the Cherenkov light can be detected. If the particle is ultra-relativistic β~1 Θc = const and has max value c t AB n 1 cosθc = = = In water Θc = 43˚, in ice 41AC˚ βct βn 37 TheThe CherenkovCherenkov effecteffect The intensity of the Cherenkov radiation (number of photons per unit length of particle path and per unit of wave length) 2 2 2 2 2 Number of photons/L and radiation d N 4π z e 1 2πz 2 = 2 1 − 2 2 = 2 α sin ΘC Wavelength depends on charge dxdλ hcλ n β λ and velocity of particle 2πe2 α = Since the intensity is proportional to hc 1/λ2 short wavelengths dominate dN Using light detectors (photomultipliers)γ = sensitive491 in 400-700 nm for an ideally 100% efficient detector in the visibledx € 2 dNγ λ2 d Nγ 2 2 λ2 dλ 2 2 11 1 22 2 d 2 z sin 2 z sin 490393 zz sinsinΘc photons / cm = ∫ λ = π α ΘC ∫ 2 = π α ΘC 2 −− 2 = α ΘC λ1 λ1 dx dxdλ λ λλ1 λ2 d 2 N d 2 N dλ λ2 d 2 N = = dxdE dxdλ dE 2πhc dxdλ Energy loss is about 104 less hc 2πhc than 2 MeV/cm in water from € E = hν = = € λ λ ionization but directional effect 38 TransitionTransition RadiationRadiation Theory: Ginzburg, Frank 1946 Radiation is emitted when a fast charged particle crosses the boundary between two media with different indices of refraction (even below Cherenkov threshold) Radiation is due to a coherent superposition of radiation fields generated by polarization of the medium (given a charge moving towards the 2 media interface it can be considered together with its mirror charge an electric dipole whose field strength varies with time. The time dependent dipole field causes the emission of electromagnetic radiation). Coherence is assured in a small region whose extension is called coherent length or formation zone. An observable amount of X-rays can be emitted when a particle with γ >>1 crosses the boundary of a macroscopically thick medium. The number of emitted photons can be enhanced by radiators consisting of several boundaries. 39 TransitionTransition radiationradiation When a particle with charge ze crosses the boundary between vacuum and a medium with plasma frequency ωp the energy radiated is Where the plasma frequency of the gas of electrons of the material is 2 ω p Nee ν p = = 2π πme And the emitted photon energy is ZρN e2 Zρ Zρ € hν = h A = 4πN r h2c 2 ≈ 28.8eV p m A A e A A π e Photons are emitted in a cone of half-aperture θ ∼ 1/γ and the emission is peaked in the forward direction The radiation yield drops fast for ω>γω and diverges logaritmically at low € p energies. For a particle with γ = 1000 the radiated photons are in soft X-ray range between 2-20 keV. The number of emitted photons above an energy is 2 Nγ ∝ z α. The radiation probability is of order of α = 1/137 hence the necessity to have many boundaries 40 TransitionTransition RadiationRadiation When the interface is between 2 media of plasma frequencies ωp1,2 the energy radiated by the particle of charge ze at the boundary per unit solid angle and unit frequency is 2 2 2 d W z hα 2 1 1 ≈ θ −2 2 2 − −2 2 2 dνdΩ π γ + θ + Υ1 γ + θ + Υ2 ω Υ = p,1,2 1,2 ω Where θ is the angle between the particle and the emitted photon. Three regions can be identified as a function of γ: € 2 2 d W z α 4 << 1/Y low yield ≈ (γY1) 1) γ 1 ⇒ d(hν)dΩ 6π 2) 1/Y1 << γ << 1/Y2 ⇒ log increase with γ (used for PID) d 2W 2z2α ≈ [ln(γY1) −1] € d(hν)dΩ π 3) γ >> 1/Y2 ⇒ saturation (yield is constant) The total emitted energy in the forward direction is proportional to z2γ 2 ∞ dW 2 αh (ν p,1 −ν p,2) W = ∫ d(hν) ≈ z γ € 0 d(hν) 3 ν p,1 + ν p,2 41 € EmissionEmission inin radiatorsradiators andand TRTR detectorsdetectors 2 2 For a foil of thickness l : d W 2 ϕ d W 1 = 4sin 1 Interference produces d(hν)dΩ foil 2 d(hν)dΩ a threshold effect in γ Interference term −2 2 (γ + Y1 )ωl1 ϕ1 ≈ € 2c Formation zone 2c For foil thickness << Z 1 ( ω ) = − 2 2 the yield is strongly suppressed (γ +€Y1 )ω 2cγ 2 For large ω in order to have radiation emission l ≥ Z (ω) ≈ 1 1 ω € When many thin layers of material are joined together the number of photons can be increased and the limiting factor is reabsorption€ in the radiator itself. In a TR detector, to minimize the photoelectric cross section (∝Z5) materials with small Z (eg Li) must be chosen while the γ detectors can be gas detectors with large Z (eg Xe). TR detectors are characterized by a threshold 42 AnAn example:example: calibrationcalibration ofof MACROMACRO TRDTRD TRD exposed to a pion/electron beam with various crossing angles. Number of hits in proportional counters vs γ of incident particles. Below the threshold only ionization contributes, for 103 < γ < 104 TR is the main contribution and the number of hits increases logaritmically with γ. For larger values it saturates 43 SuggestedSuggested readingsreadings Textbooks: Konrad Kleinknecht, Detectors for Particle Radiation (2nd edition) Cap 1 C. Leroy and PG Rancoita, Principles of Radiation Interaction in Matter and detection, World Scientific, 2004 (Cap 2) M.S. Longair, High Energy Astrophysics, Third ed., Vol 1, Particles, photons and their interactions (Cap 2-4) Online: http://pdg.lbl.gov/2002/passagerpp.pdf R.K. Bock & A. Vasilescu - The Particle Detector BriefBook, Springer 1998 http://physics.web.cern.ch/Physics/ParticleDetector/BriefBook/ http://www.shef.ac.uk/physics/teaching/phy311/#books http://www-physics.lbl.gov/%7Espieler/physics_198_notes_1999/index.html http://besch2.physik.uni- siegen.de/%7Edepac/DePAC/DePAC_tutorial_database/grupen_istanbul/gr upen_istanbul.html 44.
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