THE EGS5 CODE SYSTEM

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where ẋ and ẍ (for example) are the x-components of velocity and acceleration, respectively. No attempt is made to solve these coupled differential equations. Instead, in the example user code called UCBEND, we use a simple vector expression for the change in the direction of motion after a very small translation, ∆l, in a constant magnetic field strength, B, in which the particle energy is assumed to remain constant. Namely, where ˆv = 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 measurements performed 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 be produced from two locations within the structure and were accelerated to kinetic energies of 8.5 and 3.5 MeV, respectively, depending on their point of origin. Upon exiting the cavity they passed through a 0.015 inch copper window, where they lost energy primarily by ionization and were multiply scattered. The experimentalists attempted to measure the spectrum of the electrons using a magnet, a lead slit, and a Faraday cup. A strong peak corresponding to the 8.5 MeV group was observed, but the 3.5 MeV peak was not observed. The object of the <strong>EGS5</strong> simulation was to try to understand these observations, particularly with the help of graphics showing particle trajectories. Subroutine HOWFAR of UCBEND was designed using the diagram shown in Figure 4.1. Electrons start from the origin (at plane 1), transport through the copper window (Region 2), emanate out into the air (Region 3), and pass through the magnetic field, which is constant and along the positive y-direction (in Region 4 only). They are then bent in the direction of the lead wall (Regions 6 and 8) where some of them pass through the slit (Region 7) and get scored (at Plane 10). By varying the field strength of the magnet one should be able to re-create the observations for both 3.5 MeV and 8.5 MeV. In order to gain a more complete understanding of the geometry, it is suggested that the reader study the listing for UCBEND, which is included with the <strong>EGS5</strong> distribution. What is of interest here is the method that we employ in order to transport the electrons through the magnetic field region. Using Equation 4.3 with ∆l/R
4 z 6 Vac 11 5 Pb 6 5 Air 7 4 9 10 12 Air Air 8 Vac Vac Vac 7 3 11 3 Air 8 Pb 9 10 2 2 Cu 1 1 e - Vac x Figure 4.1: Diagram used with UCBEND (not to scale). V = V 0 , (4.4) W = (W 0 − αU 0 )F , where F = 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, should be fairly self-explanatory (Note that USTEP has been limited to 0.1 cm in this example, but this can be changed by the user). else if (irl.eq.4) then if (ifield.ne.0.and.iq(np).ne.0) then psq=e(np)*e(np)-RMSQ if (psq.lt.0.0) psq=1.0E-9 p=sqrt(psq) 195
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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
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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 and 208: 4.1.3 Leading Particle Biasing The
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 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
Page 259 and 260: 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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THE EGS5 CODE SYSTEM

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