THE EGS5 CODE SYSTEM

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ekenp=e(np)-RM call randomset(rnnolp) if (rnnolp.lt.ekenp/eks) then ! Follow np e(np-1)=e(np) iq(np-1)=iq(np) u(np-1)=u(np) v(np-1)=v(np) w(np-1)=w(np) end if ekenp=e(np-1)-RM wt(np-1)=wt(np-1)*eks/ekenp np=np-1 end if These statements to apply leading particle biasing for bremsstrahlung and pair are included in a version of UCCYL (called UC LP) at the proper locations within subroutine AUSGAB. If IAUSFL(8) or IAUSFL(17) is set as 1, AUSGAB is called for IARG of 7 and 16 respectively, then Leading Particle Biasing is applied after bremsstrahlung and pair production, respectively. The COMMON/EPCONT/ is now needed in MAIN in order to pass the IAUSFL(8) and IAUSFL(17) flags (1=on, 0=off). The subroutine RANDOMSET is explained in the EGS5 User Manual (see Appendix B). The other quantities are best understood with the help of the EGS5 Flow Diagrams for ELECTR and PHOTON (see Appendix A). Either statement can be explained as follows. An interaction of the proper type occurs and the flag has been turned “on”. A random number, uniformly distributed between 0 and 1, is drawn and compared with the fraction of the kinetic energy that was assigned to the current particle—i.e., the lower energy particle of the two produced in the interaction. If the random number is less than this fraction, the lower energy (NP) particle is kept and the one below it on the stack (NP-1) is thrown away. Otherwise the higher energy particle (NP-1) is selected and the current particle (NP) is tossed out. Obviously the particles in the shower with the highest energy will preferentially be selected by such a scheme and, to assure that the Monte Carlo game is “played fairly”, we have imposed two necessary requirements: • The lowest energy particles must be selected some of the time (which we have done by sampling). • The proper weight must be assigned to whichever particle chosen. To complete the process, one should make use of the particle weight when scoring information in subroutine AUSGAB. Namely, • Sum particle weights (WT(NP)) when “counting” particles. 192
• Sum the weighted energy deposition (WT(NP)*EDEP). The easiest way to see that the weights have been properly assigned in the statements above is by example. Assume that the incident particle has a kinetic energy of 1000 MeV and that one of the progeny has energy 100 MeV and the other has 900 MeV. Then clearly the 100 MeV particle will be chosen 10% of the time and will have a weight of 1000 100 , whereas the 900 MeV particle will be chosen 90% of the time and will have a weight of 1000 900 . But the total particle count will average out to two (ı.e. 0.1 × 1000 1000 100 + 0.9 × 900 = 2). This scheme has been found to increase the speed of shower calculations by a factor of 300 at 33 GeV. However, because the biasing can be somewhat severe at times during the calculation, the weights that are assigned tend to become rather large, and the net result is that the overall 1 efficiency ( variance×time ) is not usually 300 times better. Nevertheless, factors of 20 or more are generally obtained for many problems[75]and this technique can be invaluable. As an example, at one time it took about one minute of CPU time on the IBM-3081 to completely generate one 50 GeV shower in a large absorber. When simulating “real” beams of particles having spatial and/or angular distributions, analog EGS calculations gave only 60 incident events in one hour runs, which was inadequate. The use of leading particle biasing with a factor of 300 increase in speed, on the other hand, produced 18,000 events/hour, which was sufficient. As a final note, it should be understood that leading particle biasing, or any importance sampling scheme for that matter, should not be attempted in an arbitrary manner. For example, one should not use leading particle biasing for the “O-ring” problem above since, even though many more incident shower events will certainly be generated, the weights that are assigned to the low energy particles heading in the direction of the “O-ring” region will tend to be quite high, and no significant reduction in the variance will result. Quite the contrary, biasing of this sort can lead to very erroneous results, and one should really have a full grasp (ı.e. pre-knowledge) of the important aspects of the radiation transport before attempting to apply any of these variance reduction methods with EGS5 (or any Monte Carlo program for that matter). 4.2 UCBEND - Charged Particle Transport in a Magnetic Field Charged particle motion in a magnetic field is governed by the Lorentz force equation ⃗F = q⃗v × ⃗ B = d⃗p dt where ⃗ B is the magnetic field strength vector, ⃗v is the velocity vector, and q is the electric charge of the particle. This equation can be expanded into its Cartesian components to give mẍ = q(ẏB z − żB y ) (4.1) mÿ = q(żB x − ẋB z ) (4.2) m¨z = q(ẋB y − ẏB x ) 193
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THE EGS5 CODE SYSTEM 1 Hideo Hiraya
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Contents 1 INTRODUCTION 1 1.1 Inten
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2.15.6 Electron Step-Size Selection
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B.4.9 Output of Results (Step 9) .
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List of Figures 2.1 Program flow an
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C.4 Subprogram relationships in PEG
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B.5 Variable descriptions for COMMO
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PREFACE In the nineteen years since
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Chapter 1 INTRODUCTION 1.1 Intent o
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“shower book”. For various reas
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1.2.2 EGS1 About this time Nelson b
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MSCAT. These versions of EGS, PEGS,
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ten for energies less than 100 MeV
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- Molière multiple scattering (i.e
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EGS5. The primary advantages of thi
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ICRU37-compliant using the NIST dat
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high Z materials. Del Guerra et al.
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One of these six cross sections is
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at low energies. The latter, couple
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If E 1 and E 2 are expressions invo
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The result of this algorithm is tha
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2.4 Particle Transport Simulation T
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from appropriate distribution funct
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parameters which may be needed. The
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arrived at their values in a very m
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Math FORTRAN Program Table 2.1 (con
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Figure 2.2: Feynman diagrams for br
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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
Page 157 and 158: In order to use EGS5 to answer the
Page 159 and 160: write(6,100) 100 FORMAT(’ PEGS5-c
Page 161 and 162: ! plate is 1 mm thick !------------
Page 163 and 164: implicit none include ’include/eg
Page 165 and 166: 0.989 MeV kinetic energy Brem photo
Page 167 and 168: ! locally (in fact EDEP = particles
Page 169 and 170: inmax=max(binmax,ebin(j)) end do wr
Page 171 and 172: 0.40 0.0058 * 0.60 0.0054 * 0.80 0.
Page 173 and 174: !----------------------------------
Page 175 and 176: endif if(loop.lt.3) then write(6,12
Page 177 and 178: 180 FORMAT(/’ Knock-on electrons
Page 179 and 180: common/score/escore(3), iscore(3) r
Page 181 and 182: Brem photons can be created and any
Page 183 and 184: in any combination of 31 well speci
Page 185 and 186: end do end do ! nmed and dunit defa
Page 187 and 188: ! ------------------------------ cl
Page 189 and 190: if (iarg.eq.17) then ! A Compton sc
Page 191 and 192: ! the general purpose geometry subr
Page 193 and 194: eturn end !------------------------
Page 195 and 196: open(UNIT= 6,FILE=’egs5job.out’
Page 197 and 198: write(6,130) 130 format(/’ Start
Page 199 and 200: icol= * int(dlog10(ebin(j)*10000.0/
Page 201 and 202: 0.0300 0.0000* 0.0320 0.0001* 0.034
Page 203 and 204: 0.0780 0.0014 * 0.0800 0.0012 * 0.0
Page 205 and 206: The main purpose of this section, h
Page 207: 4.1.3 Leading Particle Biasing The
Page 211 and 212: 4 z 6 Vac 11 5 Pb 6 5 Air 7 4 9 10
Page 213 and 214: Figure 4.3: UCBEND simulation at 3.
Page 215 and 216: necessary geometry input. The follo
Page 217 and 218: Appendix A EGS5 FLOW DIAGRAMS Hideo
Page 219 and 220: subroutine annih Version 051219-143
Page 221 and 222: ¡ eq 1 anormr = 1./sqrt(anorm2) si
Page 223 and 224: 1 br = max(br,0.D0) ekse2 = br*ekin
Page 225 and 226: 1 2 3 br = br*p esg = eie*br yes es
Page 227 and 228: ¤ ne ¤ ne subroutine collis (lele
Page 229 and 230: ¦ ne ¦ ne call ausgab(iarg) 6 iq(
Page 231 and 232: subroutine compt Version 051219-143
Page 233 and 234: 3 4 5 6 icprof(medium) .eq. 3 no ye
Page 235 and 236: subroutine counters_out Version 051
Page 237 and 238: 1 2 3 4 5 6 7 no ii .ne. jj yes no
Page 239 and 240: © ne 1 2 3 neispl = (2*neispl + 1)
Page 241 and 242: subroutine electr(ircode) ielectr =
Page 243 and 244: 7 8 9 10 11 12 13 detot = e(np)-ecu
Page 245 and 246: 2324 25 26 27 28 29 30 ustep .gt. d
Page 247 and 248: 4142 43 44 45 46 47 48 49 ecut(irne
Page 249 and 250: 5859 60 61 62 63 64 tmscat .eq. 0.0
Page 251 and 252: 73 74 75 76 no edep .lt. e(np) yes
Page 253 and 254: subroutine hardx (charge,kEnergy,ke
Page 255 and 256: 1 2 3 4 5 iz = izz iz .eq. 0 no xsi
Page 257 and 258: 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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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
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[28] A. F. Bielajew. HOWFAR and HOW
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[59] K. Flöttmann. Investigations
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[92] H. Kolbenstvedt. Simple theory
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[123] Y. Namito, H. Hirayama, A. Ta
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[156] Y. A. Shreider, editor. The M
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Index “shower book”, 37 AE, 28,
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Klein-Nishina formula, 62 Landau di
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