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EM for Particle Detectors

VIEWS: 13 PAGES: 44

  • pg 1
									  Interaction of Particles
        with Matter

         Alfons Weber
CCLRC & University of Oxford
    Graduate Lecture 2004
Nov 2004                                                          2




               Table of Contents
              Bethe-Bloch Formula
                  Energy loss of heavy particles by Ionisation
              Multiple Scattering
                  Change of particle direction in Matter
              Cerenkov Radiation
                  Light emitted by particles travelling in
                   dielectric materials
              Transition radiation
                  Light emitted on traversing matter boundary
Nov 2004                                                3




               Bethe-Bloch Formula
              Describes how heavy particles (m>>me)
               loose energy when travelling through
               material
              Exact theoretical treatment difficult
                  Atomic excitations
                  Screening
                  Bulk effects
              Simplified derivation ala MPhys course
              Phenomenological description
Nov 2004                                                       4




               Bethe-Bloch (1)
              Consider particle of charge ze, passing a
               stationary charge Ze                  ze


                                         b              y
                       r
                                   θ
                                                    x
              Assume               Ze

                  Target is non-relativistic
                  Target does not move
              Calculate
                  Energy transferred to target   (separate)
Nov 2004                                             5




             Bethe-Bloch (2)
          Force on projectile
                 Zze2             Zze2
           Fx            cos          cos3 
                4 0 r 2        4 0b2

          Change of momentum of target/projectile
                          Zze2 1
            p   dtFx 
                        2 0  c b

          Energy transferred
                 p 2   Z 2 z 2e4         1
            E       
                 2M 2M (2 0 )2 (  c) 2 b2
Nov 2004                                                 6




               Bethe-Bloch (3)
              Consider α-particle scattering off Atom
                  Mass of nucleus:    M=A*mp
                  Mass of electron:   M=me
              But energy transfer is
                    p 2   Z 2 z 2e4       1 Z2
               E                           
                    2M 2M (2 0 ) (  c) b
                                  2      2  2
                                                M
              Energy transfer to single electron is
                                   2 z 2 e4      1
               Ee (b)  E 
                             mec 2 (4 0 )2  2 b2
Nov 2004                                                         7




               Bethe-Bloch (4)
              Energy transfer is determined by impact
               parameter b
              Integration over all impact parameters

                      b
                                 db
                      ze


                dn
                    2 b  (number of electrons / unit area )
                db
                              NA
                   =2 b  Z     x
                               A
Nov 2004                                                                    8




               Bethe-Bloch (5)
              Calculate average energy loss
                          bmax
                               dn            me c 2 Zz 2
                    E   d b    Ee (b)  2C 2          x  ln b b
                                                                     bmax

                        bmin
                               db                   A                min



                          me c 2 Zz 2
                        C 2          x  ln E E
                                                  Emax

                                 A                min



                                   e2       
               with C  2 N A            2 
                                4 0 me c 
              There must be limit for Emin and Emax
                   All the physics and material dependence is in
                    the calculation of this quantities
Nov 2004                                                                9




               Bethe-Bloch (6)
              Simple approximations for
                  From relativistic kinematics
                              2 2  2 me c 2
                   Emax                      2
                                                 2 2  2 me c 2
                                 me  me 
                          1  2       
                                  M       M 
                  Inelastic collision
                    Emin  I 0  average ionisation energy
              Results in the following expression

               E     me c Zz       2  me c 
                                      2     2               2   2   2
                   2C 2       ln            
               x          A           I0    
Nov 2004                                                                       10




                Bethe-Bloch (7)
              This was just a simplified derivation
                   Incomplete
                   Just to get an idea how it is done
              The (approximated) true answer is
               E     me c 2 Zz 2  1  2 2  2 me c 2 Emax       ( ) 
                   2C 2           ln                       
                                                                2
                                                                           
               x            A 2               2
                                                 I0              2   2 

               with
                   ε screening correction of inner electrons
                   δ density correction, because of polarisation
                    in medium
Nov 2004                          11




           Energy Loss Function
Nov 2004                               12




           Average Ionisation Energy
Nov 2004                                                    13




               Density Correction

              Density Correction does depend on
               material



               with
                  x = log10(p/M)
                  C, δ0, x0 material dependant constants
Nov 2004                             14




           Different Materials (1)
Nov 2004                             15




           Different Materials (2)
Nov 2004                                   16




           Particle Range/Stopping Power
Nov 2004                                             17




               Application in Particle ID
              Energy loss as measured in tracking
               chamber
              Who is Who!
Nov 2004                                                             18




               Straggling (1)
              So far we have only discussed the mean
               energy loss
              Actual energy loss will scatter around the
               mean value
              Difficult to calculate
                  parameterization exist in GEANT and some
                   standalone software libraries
                  From of distribution is important as energy
                   loss distribution is often used for calibrating
                   the detector
Nov 2004                                                19




               Straggling (2)
              Simple parameterisation
                  Landau function
                             1       1        
                    f ( )     exp   (  e ) 
                             2      2          


                              E  E
                   with  
                             me c 2 Zz
                            C 2        x
                               A

                  Better to use Vavilov distribution
Nov 2004                    20




           Straggling (3)
Nov 2004                                                      21




               δ-Rays
              Energy loss distribution is not Gaussian
               around mean.
              In rare cases a lot of energy is transferred
               to a single electron
                               δ-Ray
              If one excludes δ-rays, the average
               energy loss changes
              Equivalent of changing Emax
Nov 2004                                                                    22




               Restricted dE/dx
              Some detector only measure energy loss
               up to a certain upper limit Ecut
                  Truncated mean measurement
                  δ-rays leaving the detector
            E               me c 2 Zz 2  1  2 2  2 me c 2 Ecut 
                          2C 2           ln                     
            x  E  E               A 2             I 02         
                       cut


                                                      Ecut    (  ) 
                                                1 
                                                  2
                                                                     
                                                   Emax  2      2 
Nov 2004                                        23




               Electrons
              Electrons are different light
                  Bremsstrahlung
                  Pair production
Nov 2004                                             24




               Multiple Scattering
              Particles don’t only loose energy …




               … they also change direction
Nov 2004                                                                25




               MS Theory
              Average scattering angle is roughly
               Gaussian for small deflection angles
              With    13.6 MeV   x           x 
                       0              z       1  0.038ln      
                                 cp        X0               X 0 
                               X 0  radiation length
              Angular distributions are given by
                   dN    1         space 
                                     2

                            exp  
                   d  2 0
                           2      2 2   
                                       0 


                  dN          1          plane 
                                           2

                                  exp  
                d plane     2 0      2 2   
                                             0 
Nov 2004                                                        26




               Correlations
              Multiple scattering and dE/dx are normally
               treated to be independent from each
              Not true
                  large scatter  large energy transfer
                  small scatter  small energy transfer
              Detailed calculation is difficult but possible
                  Wade Allison & John Cobb are the experts
Nov 2004                                                                                                             27




               Correlations (W. Allison)
   nuclear small angle                                                                              nuclear backward
  scattering (suppressed                                                                            scattering in CM
       by screening)                                               electrons                     (suppressed by nuclear
                                                                    at high                           form factor)
                                                                       Q2




                                                      whole
                                                    atoms at                                           17
      Log cross                                      low Q2
       section                                       (dipole
         (30                                         region)
      decades)
                           2

                                                                            electrons
                               log
                       Log pL or kL                                                         log kT
                                                                          backwards in
                    energy transfer
                                                                               CM
                     (16 decades)

                                                                                         Log pT transfer
Example: Calculated cross section for 500MeV/c  in Argon gas.              18 7          (10 decades)
Note that this is a Log-log-log plot - the cross section varies over 20
and more decades!
Nov 2004                                                       28




               Signals from Particles in Matter
              Signals in particle detectors are mainly
               due to ionisation
                  Gas chambers
                  Silicon detectors
                  Scintillators
              Direct light emission by particles travelling
               faster than the speed of light in a medium
                  Cherenkov radiation
              Similar, but not identical
                  Transition radiation
Nov 2004                                        29




               Cherenkov Radiation (1)
              Moving charge in matter




               at rest          slow     fast
Nov 2004                                                 30




               Cherenkov Radiation (2)
              Wave front comes out at certain angle




                                                    1
                                        cos  c 
                                                    n

              That’s the trivial result!
Nov 2004                                                                  31




               Cherenkov Radiation (3)
              How many Cherenkov photons are
               detected? 2
                                 z
                       N  L
                                re me c 2     ( E ) sin 2  c ( E )dE

                                  z2                    1 
                                        2 
                            L               ( E )  1  2 2  dE
                                re me c               n 
                                              1 
                             LN 0 1  2 2 
                                      n 
                                                     
               with  ( E )  Efficiency to detect photons of energy E
                        L  radiator length
                        re  electron radius
Nov 2004                                                  32




               Different Cherenkov Detectors
              Threshold Detectors
                  Yes/No on whether the speed is β>1/n
              Differential Detectors
                  βmax > β > βmin
              Ring-Imaging Detectors
                  Measure β
Nov 2004                                          33




               Threshold Counter




              Particle travel through radiator
              Cherenkov radiation
Nov 2004                                                 34




               Differential Detectors




              Will reflect light onto PMT for certain
               angles only  β Selecton
Nov 2004                                35




           Ring Imaging Detectors (1)
Nov 2004                                36




           Ring Imaging Detectors (2)
Nov 2004                                                 37




               Ring Imaging Detectors (3)
              More clever geometries are possible
                  Two radiators  One photon detector
Nov 2004                                                       38




               Transition Radiation
              Transition radiation is produced when a
               relativistic particle traverses an
               inhomogeneous medium
                  Boundary between different materials with
                   different n.
              Strange effect
                  What is generating the radiation?
                  Accelerated charges
Nov 2004                                            39




           Transition Radiation (2)
                             Initially observer sees
                              nothing
                             Later he seems to
                              see two charges
                              moving apart
                               electrical dipole
                             Accelerated charge is
                              creating radiation
Nov 2004                                                            40




            Transition Radiation (3)
          Consider relativistic particle traversing a
           boundary from material (1) to material (2)
                                                                2
             2
            d N   z 2 
                       2
                                 1                  1       
                  2   2 2                 
           d d        /    2  1/  2  2  1/  2 
                                                            
                          p                                
                  p  plasma frequency
          Total energy radiated




          Can be used to measure γ
Nov 2004                                   41




           Transition Radiation Detector
Nov 2004                                                          42




               Table of Contents
              Bethe-Bloch Formula
                  Energy loss of heavy particles by Ionisation
              Multiple Scattering
                  Change of particle direction in Matter
              Cerenkov Radiation
                  Light emitted by particles travelling in
                   dielectric materials
              Transition radiation
                  Light emitted on traversing matter boundary
Nov 2004                                                           43




               Bibliography
              PDG 2004 (chapter 27 & 28) and
               references therein
                  Especially Rossi
              Lecture notes of Chris Booth, Sheffield
                  http://www.shef.ac.uk/physics/teaching/phy311
              R. Bock, Particle Detector Brief Book
                  http://rkb.home.cern.ch/rkb/PH14pp/node1.html


              Or just             it!
Nov 2004                                        44




               Plea
              I need feedback!
              Questions
                  What was good?
                  What was bad?
                  What was missing?
                  More detailed derivations?
                  More detectors?
                  More…
                  Less…
              A.Weber@rl.ac.uk

								
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