1. Cross Section Biasing & Path Length Biasing Jane Tinslay, SLAC March 2007

2. Jane Tinslay, SLAC2 Cross Section/Path Length Summary BiasingMultiple Context EGS4/EGS5/EGSn rc/BEAMnrc NN EGSnrc User codes (DOSRZnrc…) YY FlukaYY Geant4PartialN MCNP/MCNPXYY PenelopeNN

3. Jane Tinslay, SLAC3 EGS4/EGS4/EGSnrc Path length/cross section biasing don’t seem to be implemented by default Hooks allow them to be implemented by user Path length & cross section biasing implemented in EGSnrc user codes

4. Jane Tinslay, SLAC4 EGSnrc User Codes: Path Length Biasing Implemented in the RZ user codes Applied to photons Increase or decrease path length Use exponential transformation of photon path lengths Scale interaction probability as: = distance in mean free paths  = cosine of angle between photon and direction of interest C = scaling parameter Interaction probability distribution is

5. Jane Tinslay, SLAC5 For 0<C<1, average distance to interaction is stretched For C<0, average distance is shortened Sample from: Apply weighting

6. Jane Tinslay, SLAC6 MCNP Sample method as EGSnrc user codes Also makes sure weight is adjusted correctly when step is limited Recommed using with with weight window

7. Jane Tinslay, SLAC7 Fluka Need to look at in more detail Bias particle decay length Artificially shorten mean lifetime/average decay length Increase generation rate of decay products Bias direction of decay secondaries Similar to exponential transform Bias inelastic hadronic interaction length For hadrons or photons Artificially decrease mean free path for nuclear inelastic interactions Particle/material dependent Useful for think target problems

8. Jane Tinslay, SLAC8 DOSRZnrc: Photon cross section enhancement Applied to photons Similar techique implemented in CAVRZnrc Define a region dependent cross section enhancement factor C e Useful when calculating energy deposition in small sensitive regions Method: Apply cross section enhancement & split incoming photon into an interacting portion and a non-interacting portion

9. Jane Tinslay, SLAC9 Interacting portion Secondaries assigned a weight W 0 = incident photon weight All resulting electrons transported Use Russian Roulette to kill end photons with a probability Survivors assign weight W 0 Non-interacting portion with probability Use Russian Roulette to kill non-interacting photon with a probability Survivors assigned weight W 0 Net effect: Increase cross section while preserving features of non biased cross section

10. Jane Tinslay, SLAC10 Current Geant4 Cross section Biasing Built in G4HadronicProcess utility Applied to PhotonInelastic, ElectroNuclear, PositronNuclear processes Some information in: www.triumf.ca/geant4-03/talks/03- Wednesday-AM-1/03-J.Wellisch/biasing.hadronics.pdf To keep the game fair, splits particle into interacting portion and non interacting portion Increases cross section without disturbing non-interacting effects

11. Jane Tinslay, SLAC11 References BEAMnrc Users Manual, D.W.O. Rogers et al. NRCC Report PIRS-0509(A)revK (2007) The EGS4 Code System, W. R. Nelson and H. Hirayama and D.W.O. Rogers, SLAC-265, Stanford Linear Accelerator Center (1985) History, overview and recent improvements of EGS4, A.F. Bielajew et al., SLAC-PUB-6499 (1994) THE EGS5 CODE SYSTEM, Hirayama, Namito, Bielajew, Wilderman, Nelson SLAC-R-730 (2006) The EGSnrc Code System, I. Kawrakow et al., NRCC Report PIRS-701 (2000) Variance Reduction Techniques, D.W.O. Rogers and A.F. Bielajew (Monte Carlo Transport of Electrons and Photons. Editors Nelso, Jankins, Rindi, Nahum, Rogers. 1988) NRC User Codes for EGSnrc, D.W.O. Rogers, I. Kawrakow, J.P. Seuntjens, B.R.B. Walters and E. Mainegra-Hing, PIRS-702(revB) (2005) http://www.fluka.org/course/WebCourse/biasing/P001.html http://www.fluka.org/manual/Online.shtml http://geant4.web.cern.ch/geant4/UserDocumentation/UsersGuides/ForApplicationDeveloper/html/ Fundamentals/biasing.html MCNPX 2.3.0 Users Guide, 2002 (version 2.5.0 is restricted) PENELOPE-2006: A Code System for Monte Carlo Simulation of Electron and Photon Transport, Workshop Proceedings Barcelona, Spain 4-7 July 2006, Francesc Salvat, Jose M. Fernadez- Varea, Josep Sempau, Facultat de Fisica (ECM), Universitat de Barcelona