THE EGS5 CODE SYSTEM

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where ẋ and ẍ (for example) are the x-components of velocity and acceleration, respectively. Noattempt is made to solve these coupled differential equations. Instead, in the example user codecalled UCBEND, we use a simple vector expression for the change in the direction of motion aftera very small translation, ∆l, in a constant magnetic field strength, B, in which the particle energyis assumed to remain constant. Namely,whereˆv = ˆB(ˆv 0 · ˆB) + [ˆv 0 − ˆB(ˆv 0 · ˆB)] cos α − ˆv 0 × ˆB sin α (4.3)α = ∆l/R,R = radius of curvature = qp/B,p = particle momentum,ˆB = magnetic field unit vector,ˆv 0 = particle direction unit vector (before)= U 0 î + V 0 ĵ + W 0ˆk,ˆv = particle direction unit vector (after)= Uî + V ĵ + W ˆk.The problem that we attempt to solve with UCBEND relates to a series of spectral measurementsperformed at SLAC [100]. An RF cavity was tested and found to emit high levels of radiation.Because the cavity was subjected to very high power levels, surface electrons were found to beproduced from two locations within the structure and were accelerated to kinetic energies of 8.5and 3.5 MeV, respectively, depending on their point of origin. Upon exiting the cavity they passedthrough a 0.015 inch copper window, where they lost energy primarily by ionization and weremultiply scattered. The experimentalists attempted to measure the spectrum of the electronsusing a magnet, a lead slit, and a Faraday cup. A strong peak corresponding to the 8.5 MeV groupwas observed, but the 3.5 MeV peak was not observed. The object of the <strong>EGS5</strong> simulation wasto try to understand these observations, particularly with the help of graphics showing particletrajectories.Subroutine HOWFAR of UCBEND was designed using the diagram shown in Figure 4.1. Electronsstart from the origin (at plane 1), transport through the copper window (Region 2), emanate outinto the air (Region 3), and pass through the magnetic field, which is constant and along the positivey-direction (in Region 4 only). They are then bent in the direction of the lead wall (Regions 6 and8) where some of them pass through the slit (Region 7) and get scored (at Plane 10). By varyingthe field strength of the magnet one should be able to re-create the observations for both 3.5 MeVand 8.5 MeV.In order to gain a more complete understanding of the geometry, it is suggested that the readerstudy the listing for UCBEND, which is included with the <strong>EGS5</strong> distribution. What is of interesthere is the method that we employ in order to transport the electrons through the magnetic fieldregion. Using Equation 4.3 with ∆l/R
4z6Vac115Pb65Air749 1012AirAir8Vac Vac Vac73113Air8Pb91022Cu11e -VacxFigure 4.1: Diagram used with UCBEND (not to scale).V = V 0 , (4.4)W = (W 0 − αU 0 )F ,whereF = unit vector renormalization factor= (1 + α 2 ) −1/2 . (4.5)The following code listing, which pertains only to that HOWFAR section relating to Region 4, shouldbe fairly self-explanatory (Note that USTEP has been limited to 0.1 cm in this example, but thiscan be changed by the user).else if (irl.eq.4) thenif (ifield.ne.0.and.iq(np).ne.0) thenpsq=e(np)*e(np)-RMSQif (psq.lt.0.0) psq=1.0E-9p=sqrt(psq)195
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THE EGS5 CODE SYSTEM 1Hideo Hirayam
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4.1 UCCYL - Cylinder-Slab Geometry
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E CONTENTS OF THE EGS5 DISTRIBUTION
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2.17 Convergence of energy depositi
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List of Tables2.1 Symbols used in E
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C.2 Goudsmit-Saunderson-related sub
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With the release of the EGS4 versio
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“shower book”.For various reaso
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1.2.2 EGS1About this time Nelson be
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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 SimulationTh
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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 ProgramTable 2.1 (cont
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Figure 2.2: Feynman diagrams for br
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defined byδ ij = 1 if i = j,0 othe
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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 haveNow defineδ ′ = ∆ 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−timedE=[23 − 1
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Angular distribution formulasThe fo
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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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whereX 0 = radiation length (cm),n
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whereα ′ 1 =α ′ 2 =k 0′k 0
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+ 1 E 2′ − 1 E 1′− C 2 ln E
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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 De
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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 thatln [1.13 + 3.76(αZ i
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g 3 (θ) =θ4 ()λf (0) (θ) + f (1
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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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xFinalDirectionφΘ∆xtInitialDire
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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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FinalDirectionxEnergy HingesφΘt(
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Transport Steps,∆ E = E x ESTEPEt
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tranport step 1DEINITIAL1 DERESID1t
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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 slowstep
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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 Electrons0.010.001LiCLWAlST
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actions involving photons with ener
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Cu 40 keVCounts (/keV/sr/source)10
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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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ZθkYOφe0Xk0Figure 2.23: Photon sc
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Note the similarities and differenc
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XZωk0Oe0YFigure 2.25: Direction of
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W = Atomic, molecular and mixture w
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In order to use EGS5 to answer the
Page 159 and 160: write(6,100)100 FORMAT(’ PEGS5-ca
Page 161 and 162: ! plate is 1 mm thick!-------------
Page 163 and 164: implicit noneinclude ’include/egs
Page 165 and 166: 0.989 MeV kinetic energyBrem photon
Page 167 and 168: ! locally (in fact EDEP = particles
Page 169 and 170: inmax=max(binmax,ebin(j))end dowrit
Page 171 and 172: 0.40 0.0058 *0.60 0.0054 *0.80 0.00
Page 173 and 174: !----------------------------------
Page 175 and 176: endifif(loop.lt.3) thenwrite(6,120)
Page 177 and 178: 180 FORMAT(/’ Knock-on electrons
Page 179 and 180: common/score/escore(3), iscore(3)re
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 doend do! nmed and dunit defaul
Page 187 and 188: ! ------------------------------clo
Page 189 and 190: if (iarg.eq.17) then! A Compton sca
Page 191 and 192: ! the general purpose geometry subr
Page 193 and 194: eturnend!--------------------------
Page 195 and 196: open(UNIT= 6,FILE=’egs5job.out’
Page 197 and 198: write(6,130)130 format(/’ Start t
Page 199 and 200: icol=* int(dlog10(ebin(j)*10000.0/f
Page 201 and 202: 0.0300 0.0000*0.0320 0.0001*0.0340
Page 203 and 204: 0.0780 0.0014 *0.0800 0.0012 *0.082
Page 205 and 206: The main purpose of this section, h
Page 207 and 208: 4.1.3 Leading Particle BiasingThe s
Page 209: • Sum the weighted energy deposit
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 AEGS5 FLOW DIAGRAMSHideo H
Page 219 and 220: subroutineannihVersion051219-1435ia
Page 221 and 222: ¡eq1anormr = 1./sqrt(anorm2)sineta
Page 223 and 224: 1br = max(br,0.D0)ekse2 = br*ekines
Page 225 and 226: 12 3br = br*pesg = eie*bryesesg.lt.
Page 227 and 228: ¤ne¤nesubroutinecollis(lelec,irl,
Page 229 and 230: ¦ne¦necallausgab(iarg)6iq(np).eq.
Page 231 and 232: subroutinecomptVersion051219-1435ic
Page 233 and 234: 3456icprof(medium).eq.3noyescallran
Page 235 and 236: subroutinecounters_outVersion051227
Page 237 and 238: 1234567noii.ne.jjyesnoledgb(ii,medi
Page 239 and 240: ©ne1 2 3neispl = (2*neispl + 1)/3f
Page 241 and 242: subroutineelectr(ircode)ielectr = i
Page 243 and 244: 7 8 9 10 11 12 13detot = e(np)-ecut
Page 245 and 246: 2324 25 26 27 282930ustep.gt.dnear(
Page 247 and 248: 4142 43 44 45 4647 48 49ecut(irnew)
Page 249 and 250: 5859 60 61 6263 64tmscat.eq.0.0noye
Page 251 and 252: 73 7475 76noedep.lt.e(np)yescallran
Page 253 and 254: subroutinehardx(charge,kEnergy,keIn
Page 255 and 256: 1 2 3 4 5iz = izziz.eq.0noxsi = zer
Page 257 and 258: 13 14 15 16 17sint.ne.0.yesrdev = m
Page 259 and 260: 19im=1im=im+1im >nmednoyesnoiprofm(
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2223write(kmpo,1610)read(kmpi,1260)
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26 27 28iprofm(im).ne.1noyeswrite(6
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30 31 32 33 34esig0(i,im) = esig0(i
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36 37 38noiedgfl(ii).ne.0.or.iauger
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nokaug.eq.6calllshell(3)kaug.eq.7ka
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subroutinekxrayVersion051219-1435ik
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123dfl3aug(5,iz).eq.0.nonauger = na
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12 3 4rnnow.le.omegal2(iz) + f23(iz
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1 2dflx3(6,iz).eq.0.nonxray=nxray+1
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1impacr(ir(np)).eq.1.and.iedgfl(ir(
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12fject = (ktot - k1grd(iprt,ik1))
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56789thr = 1./eta"Central correctio
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1 2 3delta = delcm(medium)*del"Reje
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89101112galpha.ge.0.0yesnoximid = 0
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subroutinephotoVersion051219-1435"C
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4 5 6 7 8rnnow.le.pbran(i)noyesiz =
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121314beta = sqrt((eelec - RM)*(eel
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subroutinephotonVersion051219-1435i
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678910idisc.gt.0yesnoedep = 0.iarg
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1718192021iausfl(iarg+1)ne0nocallpa
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2728iausfl(iarg+1)ne0noircode = 2np
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subroutinerk1Version060313-0945open
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4 5 6j=1j=j+1j>neke-1noyesj.eq.1noj
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18 19 20 21 22 23elkeold = elkek1ol
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1 2"end of file; go to 13"read(17,*
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4 5"go to 30"noabs(k1mine-k1grd(1,1
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7 8read(17,'(72a1)') bufferread(17,
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subroutine shower(iqi,ei,xi,yi,zi,u
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subroutineuphi(ientry,lvl)Version05
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subroutinerandomset(rndum)Version05
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subroutinerluxinitVersion051219-143
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1i=1i=i+1i>24noyesseeds(i) = real(i
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subroutinerluxinVersion051219-1435w
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Appendix BEGS5 USER MANUALHideo Hir
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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 modificationsThe
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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 rluxinitafter specifying LUXLE
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END OF FILE ON UNIT 12PROGRAM STOPP
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do i=1,ncasesuf(1)=ufivf(1)=vfiwf(1
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crossed, then USTEP should be set t
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subroutine howfarimplicit noneinclu
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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=3do i=2,nregecut(i)=100.0pcut(
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nlines=0nwrite=15!-----------------
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if (nlines.lt.nwrite) thenwrite(6,1
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Appendix CPEGS USER MANUALHideo Hir
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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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NameDCSLOADDCSSTORDCSTABELASTINOELI
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NameAFFACTAINTPALKEALKEIALINALINIAD
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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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ColumnLine 123456789112345678921234
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interiors of the intervals. If FEXA
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C.3.6The TEST OptionThe TEST option
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C.3.9The HPLT OptionThe Histogram P
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Appendix DEGS5 INSTALLATION GUIDEHi
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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 ECONTENTS OF THE EGS5DISTR
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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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ismuth krypton silverboron lanthanu
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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”, 37AE, 28, 3
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Klein-Nishina formula, 62Landau dis
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