THE EGS5 CODE SYSTEM

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2.2 Probability Theory and Sampling Methods—A Short Tutorial . . . . . . . . . . . . 21 2.3 Simulating the Physical Processes—An Overview . . . . . . . . . . . . . . . . . . . 26 2.4 Particle Transport Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 2.5 Particle Interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 2.6 General Implementation Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 2.7 Bremsstrahlung and Electron-Positron Pair Production . . . . . . . . . . . . . . . . 37 2.7.1 Bremsstrahlung Photon Angular Distribution . . . . . . . . . . . . . . . . . . 54 2.7.2 Pair Angle Sampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 2.8 Interactions With Atomic Electrons – General Discussion . . . . . . . . . . . . . . . 61 2.9 Compton Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 2.10 Møller Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 2.11 Bhabha Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 2.12 Two Photon Positron-Electron Annihilation . . . . . . . . . . . . . . . . . . . . . . . 69 2.13 Continuous Electron Energy Loss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 2.14 Multiple Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 2.14.1 The Molière Multiple Scattering Distribution . . . . . . . . . . . . . . . . . . 82 2.14.2 The Goudsmit-Saunderson Multiple Scattering Distribution . . . . . . . . . . 91 2.15 Transport Mechanics in EGS5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 2.15.1 Random Hinge Transport Mechanics . . . . . . . . . . . . . . . . . . . . . . . 98 2.15.2 Modified Random Hinge Transport Mechanics . . . . . . . . . . . . . . . . . 99 2.15.3 Dual Random Hinge Approach . . . . . . . . . . . . . . . . . . . . . . . . . . 101 2.15.4 Boundary Crossing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 2.15.5 EGS5 Transport Mechanics Algorithm . . . . . . . . . . . . . . . . . . . . . . 104 iii
2.15.6 Electron Step-Size Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 2.15.7 Energy Hinge Step-Size Determination in PEGS . . . . . . . . . . . . . . . . 108 2.15.8 Multiple Scattering Step-size Specification Using Fractional Energy Loss Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 2.15.9 Multiple Scattering Step-Size Optimization Using Media “Characteristic Dimensions” . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 2.15.10 Treatment of Initial Steps of Primary Electrons . . . . . . . . . . . . . . . . . 118 2.16 Photoelectric Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 2.16.1 General Treatment of Photoelectric-Related Phenomena . . . . . . . . . . . . 121 2.16.2 Photoelectron Angular Distribution . . . . . . . . . . . . . . . . . . . . . . . 127 2.17 Coherent (Rayleigh) Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128 2.18 Binding Effects and Doppler Broadening in Compton Scattering . . . . . . . . . . . 129 2.19 Scattering of Linearly Polarized Photons . . . . . . . . . . . . . . . . . . . . . . . . . 132 2.20 Electron Impact Ionization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 3 A SERIES OF SHORT EGS5 TUTORIALS 140 3.1 Tutorial 1 (Program tutor1.f) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140 3.2 Tutorial 2 (Program tutor2.f) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150 3.3 Tutorial 3 (Program tutor3.f) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152 3.4 Tutorial 4 (Program tutor4.f) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155 3.5 Tutorial 5 (Program tutor5.f) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166 3.6 Tutorial 6 (Program tutor6.f) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174 3.7 Tutorial 7 (Program tutor7.f) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177 4 ADVANCED EGS5 USER CODES 188 iv
Page 1 and 2: THE EGS5 CODE SYSTEM 1 Hideo Hiraya
Page 3: Contents 1 INTRODUCTION 1 1.1 Inten
Page 7 and 8: B.4.9 Output of Results (Step 9) .
Page 9 and 10: List of Figures 2.1 Program flow an
Page 11 and 12: C.4 Subprogram relationships in PEG
Page 13 and 14: B.5 Variable descriptions for COMMO
Page 15 and 16: PREFACE In the nineteen years since
Page 17 and 18: Chapter 1 INTRODUCTION 1.1 Intent o
Page 19 and 20: “shower book”. For various reas
Page 21 and 22: 1.2.2 EGS1 About this time Nelson b
Page 23 and 24: MSCAT. These versions of EGS, PEGS,
Page 25 and 26: ten for energies less than 100 MeV
Page 27 and 28: - Molière multiple scattering (i.e
Page 29 and 30: EGS5. The primary advantages of thi
Page 31 and 32: ICRU37-compliant using the NIST dat
Page 33 and 34: high Z materials. Del Guerra et al.
Page 35 and 36: One of these six cross sections is
Page 37 and 38: at low energies. The latter, couple
Page 39 and 40: If E 1 and E 2 are expressions invo
Page 41 and 42: The result of this algorithm is tha
Page 43 and 44: 2.4 Particle Transport Simulation T
Page 45 and 46: from appropriate distribution funct
Page 47 and 48: parameters which may be needed. The
Page 49 and 50: arrived at their values in a very m
Page 51 and 52: Math FORTRAN Program Table 2.1 (con
Page 53 and 54: Figure 2.2: Feynman diagrams for br
Page 55 and 56:
defined by δ ij = 1 if i = j, 0 ot
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Davies, Bethe and Maximon[49] (e.g.
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cross section given in Equation 2.4
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and use this as the variable to be
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we have Now define δ ′ = ∆ C
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This agrees with formula (10) of Bu
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That is, using Equations 2.122 and
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d˘Σ P air, Run−time dE = [ 2 3
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Angular distribution formulas The f
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at either x = 0, x = (πE 0 ) 2 (i.
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The following table, derived from t
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Figure 2.3: Feynman diagrams for tw
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where X 0 = radiation length (cm),
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where α ′ 1 = α ′ 2 = k 0 ′
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+ 1 E 2 ′ − 1 E 1 ′ − C 2 l
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PEGS functions BHABDM, BHABRM, and
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To find the limits of E, we first c
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Figure 2.5: Feynman diagram for sin
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Ī adj = average adjusted mean ioni
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Table 2.2 (cont.) Z Symbol Atomic D
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Table 2.3 (cont.) LABEL a m s x 0 x
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(c) If 10.5 ≤ −C < 11.0 then x
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obtain the real scattering angle. E
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ρ = material mass density (g/cm 3
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Hence, so that ln [1.13 + 3.76(αZ
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g 3 (θ) = θ4 ( ) λf (0) (θ) + f
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Actually, b = 0 does not correspond
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Assume that an electron starts off
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At small path lengths t, a very lar
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x Final Direction φ Θ ∆x t Init
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shown that this version of the rand
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and as we noted earlier, they are d
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Final Direction x Energy Hinges φ
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Transport Steps, ∆ E = E x ESTEPE
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tranport step 1 DEINITIAL1 DERESID1
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= ∆E ( ∣ ∣∣∣ dE −1 ∣
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Since the CSDA range is uniquely de
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short steps accurate, but slow step
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Table 2.4: Materials used in refere
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Average Lateral Displacement (cm) 0
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100 MeV Electrons 0.01 0.001 Li C L
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actions involving photons with ener
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Cu 40 keV Counts (/keV/sr/source) 1
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Table 2.6: Data sources for general
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2.16.2 Photoelectron Angular Distri
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where r 0 is the classical electron
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second term on the right-hand side
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Z θ k Y O φ e 0 X k 0 Figure 2.23
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Note the similarities and differenc
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X Z ω k 0 O e 0 Y Figure 2.25: Dir
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W = Atomic, molecular and mixture w
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In order to use EGS5 to answer the
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write(6,100) 100 FORMAT(’ PEGS5-c
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! plate is 1 mm thick !------------
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implicit none include ’include/eg
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0.989 MeV kinetic energy Brem photo
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! locally (in fact EDEP = particles
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inmax=max(binmax,ebin(j)) end do wr
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0.40 0.0058 * 0.60 0.0054 * 0.80 0.
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!----------------------------------
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endif if(loop.lt.3) then write(6,12
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180 FORMAT(/’ Knock-on electrons
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common/score/escore(3), iscore(3) r
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Brem photons can be created and any
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in any combination of 31 well speci
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end do end do ! nmed and dunit defa
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! ------------------------------ cl
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if (iarg.eq.17) then ! A Compton sc
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! the general purpose geometry subr
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eturn end !------------------------
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open(UNIT= 6,FILE=’egs5job.out’
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write(6,130) 130 format(/’ Start
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icol= * int(dlog10(ebin(j)*10000.0/
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0.0300 0.0000* 0.0320 0.0001* 0.034
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0.0780 0.0014 * 0.0800 0.0012 * 0.0
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The main purpose of this section, h
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4.1.3 Leading Particle Biasing The
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• Sum the weighted energy deposit
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4 z 6 Vac 11 5 Pb 6 5 Air 7 4 9 10
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Figure 4.3: UCBEND simulation at 3.
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necessary geometry input. The follo
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Appendix A EGS5 FLOW DIAGRAMS Hideo
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subroutine annih Version 051219-143
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¡ eq 1 anormr = 1./sqrt(anorm2) si
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1 br = max(br,0.D0) ekse2 = br*ekin
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1 2 3 br = br*p esg = eie*br yes es
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¤ ne ¤ ne subroutine collis (lele
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¦ ne ¦ ne call ausgab(iarg) 6 iq(
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subroutine compt Version 051219-143
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3 4 5 6 icprof(medium) .eq. 3 no ye
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subroutine counters_out Version 051
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1 2 3 4 5 6 7 no ii .ne. jj yes no
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© ne 1 2 3 neispl = (2*neispl + 1)
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subroutine electr(ircode) ielectr =
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7 8 9 10 11 12 13 detot = e(np)-ecu
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2324 25 26 27 28 29 30 ustep .gt. d
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4142 43 44 45 46 47 48 49 ecut(irne
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5859 60 61 62 63 64 tmscat .eq. 0.0
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73 74 75 76 no edep .lt. e(np) yes
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subroutine hardx (charge,kEnergy,ke
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1 2 3 4 5 iz = izz iz .eq. 0 no xsi
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13 14 15 16 17 sint .ne. 0. yes rde
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19 im=1 im=im+1 im >nmed no yes no
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22 23 write(kmpo,1610) read(kmpi,12
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26 27 28 iprofm(im) .ne. 1 no yes w
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30 31 32 33 34 esig0(i,im) = esig0(
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36 37 38 no iedgfl(ii).ne.0 .or. ia
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no kaug .eq. 6 call lshell(3) kaug.
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subroutine kxray Version 051219-143
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1 2 3 dfl3aug(5,iz) .eq. 0. no naug
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1 2 3 4 rnnow .le. omegal2(iz) + f2
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1 2 dflx3(6,iz) .eq. 0. no nxray=nx
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1 impacr(ir(np)).eq.1 .and. iedgfl(
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1 2 fject = (ktot - k1grd(iprt,ik1)
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5 6 7 8 9 thr = 1./eta "Central cor
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1 2 3 delta = delcm(medium)*del "Re
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8 9 10 11 12 galpha .ge. 0.0 yes no
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subroutine photo Version 051219-143
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4 5 6 7 8 rnnow .le. pbran(i) no ye
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12 13 14 beta = sqrt((eelec - RM)*(
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subroutine photon Version 051219-14
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6 7 8 9 10 idisc .gt. 0 yes no edep
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17 18 19 20 21 iausfl(iarg+1) ne 0
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27 28 iausfl(iarg+1) ne 0 no ircod
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subroutine rk1 Version 060313-0945
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4 5 6 j=1 j=j+1 j>neke-1 no yes j .
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18 19 20 21 22 23 elkeold = elke k1
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1 2 "end of file; go to 13" read(17
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4 5 "go to 30" no abs(k1mine-k1grd(
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7 8 read(17,'(72a1)') buffer read(1
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subroutine shower (iqi,ei,xi,yi,zi,
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subroutine uphi(ientry,lvl) Version
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subroutine randomset(rndum) Version
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subroutine rluxinit Version 051219-
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1 i=1 i=i+1 i>24 no yes seeds(i) =
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subroutine rluxin Version 051219-14
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Appendix B EGS5 USER MANUAL Hideo H
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Table B.1: Variable descriptions fo
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Page 333 and 334:
Page 335 and 336:
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Table B.12: Variable descriptions f
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Optional parameter modifications Th
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the call to PEGS5 may be skipped if
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egions. Execution of EGS5 is termin
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of the transport in the walls of el
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call rluxinit after specifying LUXL
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END OF FILE ON UNIT 12 PROGRAM STOP
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do i=1,ncases uf(1)=ufi vf(1)=vfi w
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crossed, then USTEP should be set t
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subroutine howfar implicit none inc
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Table B.18: IARG values program sta
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As an example of how to write an AU
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!**********************************
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nreg=3 do i=2,nreg ecut(i)=100.0 pc
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nlines=0 nwrite=15 !---------------
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if (nlines.lt.nwrite) then write(6,
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Appendix C PEGS USER MANUAL Hideo H
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is entered. On each pass through th
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(from previous figure) (to previous
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(from previous figure) | | + ------
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+------+ |BREMTR| +------+ | V +---
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+------+ |PAIRTR| +------+ | V +---
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Name DCSLOAD DCSSTOR DCSTAB ELASTIN
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Name AFFACT AINTP ALKE ALKEI ALIN A
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Table C.5: Functions in PEGS, part
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+------+ +------+ +------+ +------+
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Table C.8: ELEM option input data l
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Table C.10: MIXT option input data
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Table C.12: PWLF option input data
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Table C.17: PLTN option input data
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ICPROF is set to 3, the user must c
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Column Line 12345678911234567892123
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interiors of the intervals. If FEXA
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C.3.6 The TEST Option The TEST opti
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C.3.9 The HPLT Option The Histogram
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Appendix D EGS5 INSTALLATION GUIDE
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egs5 directory (preferably using th
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6. The user is then asked to key-in
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* User code tutor1.f has been compi
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Appendix E CONTENTS OF THE EGS5 DIS
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All of the actual FORTRAN source co
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aprime.data Data for empirical brem
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eryllium iron silicon bismuth krypt
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The tutorial problems and advanced
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Bibliography [1] R. G. Alsmiller Jr
Page 427 and 428:
[28] A. F. Bielajew. HOWFAR and HOW
Page 429 and 430:
[59] K. Flöttmann. Investigations
Page 431 and 432:
[92] H. Kolbenstvedt. Simple theory
Page 433 and 434:
[123] Y. Namito, H. Hirayama, A. Ta
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[156] Y. A. Shreider, editor. The M
Page 437 and 438:
Index “shower book”, 37 AE, 28,
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Klein-Nishina formula, 62 Landau di
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