Cherenkov Radiation (and other shocking waves). Perhaps also the ones of the fish? Shock Waves May Confuse Birds’ Internal Compass

The density effect in the energy loss is intimately connected to the coherent response of a medium to the passage of a relativistic particle that causes the emission of Cherenkov radiation. Calculate the electromagnetic energy flow in a cylinder of radius a around the track of the particle. Define If a is in the order of atomic dimension and | a|<<1 we will then get the Fermi relation for dE/dX with the density effect. If | a|>>1, we get ( after some steps ): If has a positive real part  the integrand will vanish rapidly at large distances  all energy is deposited near the track If  is purely imaginary  the integrand is independent of a  some energy escapes at infinite as radiation  Cherenkov radiation and or and a subscript 1 : along particle velocity 2, 3 : perpendicular to we assume  real as from now on

Let us consider a particle that interacts with the medium The behavior of a photon in a medium is described by the dispersion relation Conservation of energy and momentum W.W.M. Allison and P.R.S. Wright RD/ January 1984 Argon at normal density

2 eV345 A particle with velocity  v/c in a medium with refractive index nn=n( ) may emit light along a conical wave front. The angle of emission is given by and the number of photons by

cos(  ) = 1/  n m = p/   m/m = [(  p/p) 2 + (  2  tg  ) 2 ] ½ set : n1.28 (C 6 F 14 )  p/p 2 5   15 mrad L 1 cm 1/ 1 -1/ 2 = 1/ /1800 ( in A) with Q=20% p K   max = 38.6 o  min =.78

Threshold Cherenkov Counter Flat mirror Photon detector Particle with charge q velocity  Spherical mirror Cherenkov gas To get a better particle identification, use more than one radiator. A radiator : n= B radiator : n= Positive particle identification :

Directional Isochronous Selfcollimating Cherenkov (DISC) Cherenkov radiator n=f(photon energy) r=f(  n)  (r)=f(resolution) More general for an Imaging Detector Transformation Function 200nm 150  N photons N=f(  ) (n-1)*10 6

The Cherenkov radiator Q  The particle The light cone

Cherenkov media Focusing Mirror Detector e-e+ E Proportional Chamber Quartz Plate Photon to Electron conversion gap e e e    Hey! Did I mention TMAE to you?! Did I?!?

Particle Identification in DELPHI at LEP I and LEP II 2 radiators + 1 photodetector n = 1.28 C 6 F 14 liquid n = C 5 F 12 gas  /K  /K/p K/p  /h  /K/p K/p  0.7  p  45 GeV/c  15°    165°

Particle Identification with the DELPHI RICHes Liquid RICH Gas RICH p (GeV) Cherenkov angle (mrad) From data p from  K from  D *  from K o DELPHI, NIM A: 378(1996)57

Yoko Ono  1994 FRANKLIN SUMMER SERIES, ID#27 I forbindelse med utstillingen i BERGEN KUNSTMUSEUM, 1999 ABB.com More beautiful pictures (which has next to nothing to do with) Cherenkov radiation

An exact calculation of Transition Radiation is complicated J. D. Jackson ( bless him ) and he continues: A charged particle in uniform motion in a straight line in free space does not radiate A charged particle moving with constant velocity can radiate if it is in a material medium and is moving with a velocity greater than the phase velocity of light in that medium (Cherenkov radiation) There is another type of radiation, transition radiation, that is emitted when a charged particle passes suddenly from one medium to another. If  <1 no real photon can be emitted for an infinite long radiator. Due to diffraction broadening, sub-threshold emission of real photons in thin radiators.  0 2 =plasma frequency 2  (electron density) If  

If  p2 >  p1 then  max   -1 Total radiated power S   (eV)  which is a small number All this for a small number?

Coherent addition in point P (-1) k : The field amplitude for successive interfaces alternate in sign A(  k ) : Amplitude  k =  (R/c-t) : phase factor  = l 1 = 25  m l 2 = 0.2 mm polypropylene - air Egorytchev, V ; Saveliev, V V ;Monte Carlo simulation of transition radiation and electron identification for HERA-B ITEP Moscow : ITEP, 17 May Periodic radiator for Transition Radiation.

Production with multi foils Absorption in foils Conversion t=0t=T Pulse Height  -electron MIP X radiation Threshold   10 keV M.L. Cerry et al., Phys. Rev. 10(1974) saturation effect due to multi layer