1. 조 성 구 ( 국립암센터 ) 2012. 9. 21 Geant4 Tutorial Monte Carlo 원리 및 활용

2. 연못 면적 ? ? !

3. 연못 면적 10 m 30 개 20 개

4. Monte Carlo 정의 난수 (random number) 사용  확률론적 (Stochastic) 계산기법  ‘Statistical sampling-based technique’ 역사 1940 년대 중반 제 2 차 세계대전 당시 Los Alamos 에서 개발  Manhattan Project (1942-1946) Stanislaw Ulam 최초 제안 John von Neumann 개발 주도 명칭 (Monte Carlo) Nicholas Metropolis 모나코 (city-state) 의 한 쿼터 이름 난수 이용 (casino 공통점 )  Roulette wheel

5. 난수 생성 Computer-generated numbers ‘Pseudo’ 난수 Linear congruent method rand() function in MATALB TM  Numbers between 0 and 1  Random, but also uniform RW3USB (speed: 1.5 Mbit/sec, Dimensions: 8 cm x 5.5 cm x 2.5 cm) 0.126810 0.390278 0.791098 0.139390

6. π 값 계산 r r

8. 컴퓨터 프로그래밍 1 1 x y d

9. Jumping Bug 점프 방향 : 0-360° ( 무작위, 균일분포 ) 점프 거리 : 0-20 mm ( 무작위, 균일 분포 ) start finish ? 900 번 점프한 후 벌레의 평균 위치는 ? ( 시작점부터의 거리 )

10. Jumping Bug 점프방향 결정 점프거리 결정 첫 번째 점프 두 번째 점프 16.7 mm 45° 10 mm 90° x y

11. Jumping Bug Max = 849 mm Min = 32 mm 평균 300mm

12. 방사선 수송 알고리즘 Use physics models and cross section data to sample direction, flight distance, etc. Source (determine position, direction, energy, time, and weight) Determine flight distance Determine new position (collision point) Determine type of interaction Absorption Store results as necessary Scattering, etc Determine direction and energy of the scattered particle 10 x y z x y z x y z

13. 방사선 수송 알고리즘 Source (determine position, direction, energy, time, and weight) Determine flight distance Determine new position (collision point) Determine type of interaction Absorption Store results as necessary Scattering, etc Determine direction and energy of the scattered particle Radioisotope (isotropic) x y z particle direction (cosine distribution) Beam polar, azimuthal angles fixed Use physics models and cross section data to sample direction, flight distance, etc.

14. 방사선 수송 알고리즘 Source (determine position, direction, energy, time, and weight) Determine flight distance Determine new position (collision point) Determine type of interaction Absorption Store results as necessary Scattering, etc Determine direction and energy of the scattered particle Use physics models and cross section data to sample direction, flight distance, etc. Single energy No sampling Multiple energies (e.g 60 Co) 1.17 MeV (50 %) 1.33 MeV (50 %) 0 0.5 1.0 1.17 MeV 1.33 MeV Polyenergetic (e.g. X-rays) Integration CDF Energy sampling

15. 방사선 수송 알고리즘 Use physics models and cross section data to sample direction, flight distance, etc. Source (determine position, direction, energy, time, and weight) Determine flight distance Determine new position (collision point) Determine type of interaction Absorption Store results as necessary Scattering, etc Determine direction and energy of the scattered particle d=? interaction p(d) d Distance Sampling

16. 방사선 수송 알고리즘 Use physics models and cross section data to sample direction, flight distance, etc. Source (determine position, direction, energy, time, and weight) Determine flight distance Determine new position (collision point) Determine type of interaction Absorption Store results as necessary Scattering, etc Determine direction and energy of the scattered particle Collision point coordinate

17. 방사선 수송 알고리즘 Use physics models and cross section data to sample direction, flight distance, etc. Source (determine position, direction, energy, time, and weight) Determine flight distance Determine new position (collision point) Determine type of interaction Absorption Store results as necessary Scattering, etc Determine direction and energy of the scattered particle Example Photoelectric effect : 30 % Compton scattering : 50 % Pair production : 20 % 0 0.3 1.0 Photoelectric effect (30 %) 0.8 Compton scattering (50 %) Pair production (20 %)

18. 방사선 수송 알고리즘 Use physics models and cross section data to sample direction, flight distance, etc. Source (determine position, direction, energy, time, and weight) Determine flight distance Determine new position (collision point) Determine type of interaction Absorption Store results as necessary Scattering, etc Determine direction and energy of the scattered particle

19. 방사선 수송 알고리즘 Use physics models and cross section data to sample direction, flight distance, etc. Source (determine position, direction, energy, time, and weight) Determine flight distance Determine new position (collision point) Determine type of interaction Absorption Store results as necessary Scattering, etc Determine direction and energy of the scattered particle “Acceptance-rejection” method Klein-Nishina cross section Photon energy

20. 실제 방사선수송 - More Complicated 이차입자 생성 광자  전자 전자  광자 ( 제동복사 X- 선 ) 양전자  소멸  광자 생성 (annihilation photons) Banking Heterogeneous 3-D geometry 입자 - 경계면 거리 계산 필요 복셀 (voxel) 모델 Non-analog simulation Russian roulette/particle splitting Forced collision Implicit capture Exponential transform

21. General-purpose Monte Carlo Codes

22. MCNPX (Monte Carlo N-Particle) History Features 34 particles (n,p,e, …) Continuous energy (roughly 0-1000 GeV) Data libraries below ~ 150 MeV (n,p,e,h) & models otherwise Interdependent source variables, 7 tally types, many modifiers Supported on virtually all computer platforms Developed at Los Alamos National Lab (LANL) Homepage: http://mcnpx.lanl.gov/http://mcnpx.lanl.gov/

23. Input File

24. Pros and Cons Source code is not open Pros Cons Wide range of particles and energies No programming knowledge required Automatic statistical checks on the results Highly accurate for neutron transport Criticality calculation Large and active user community

25. Application Examples Texas A&M University 1 MW MTR converted type TRIGA reactor Accelerator target Reactor core design Radiation shielding Space power reactor

26. Application Examples Proton therapy Radiation protection MOSFET detector for in vivo dosimetry Boron Neutron Capture Therapy Neutron detector for oil-well logging

27. Geant4 (GEometry ANd Tracking) History Dec 1994 - Project start Dec 1998 - First Geant4 public release Latest version – Geant4 version 9.1 (September 2008) Features Object-oriented technology based on C++ Particle: γ, e-/e+, n, p, muon, ion, neutrino, etc. Energy range  From thermal energy up to 1 PeV (hadronic)  From 250 eV to 1 PeV (EM interaction) Geant4 collaboration (RD44  MoU) Homepage: http://geant4.cern.ch/

28. Input File (Code Writing) Main.cc DetectorConstruction.cc PhysicsList.cc PrimaryGeneratorAction.cc

29. Pros and Cons The initial learning curve for Geant4 is steeper and higher than any other code A fairly detailed knowledge of the physics being modelled is required Pros Cons Versatility, flexibility and openness 4D simulation capability (moving object, decay) Visualization capability (geometry, track) Developed and maintained regularly through MoU between the many collaborating institutes

30. Application Examples Detector simulation in high energy physics Space application BaBar at SLAC ILC ATLAS at CERN XMM AMS

31. Application Examples Medical applications Etc. Geant4 DNA : analyzing the nano-scale effects of energetic particles at the cellular and DNA molecule level. Thyroi d Skul l Lung s Arm Bones Spine Esophagu s Spleen Stomach Kidneys Pelvis Ovaries Lower Large Intestine Leg Bones Urinary Bladder Uterus Upper Large Intestine Liver Breasts Heart Not visible: Brain (inside the skull) Pancreas LINACBrachyProton

32. EGSnrc (Electron Gamma Shower) History 1974 – 1977: EGS1 (Fortran) ~ EGS3 (Mortran) by Ford and Nelson at SLAC 1982- 1985: EGS4 (Mortran) by Nelson, Hirayama and Rogers at SLAC 1999: EGSnrc/BEAMnrc (Mortran) by Kawrakow and Rogers at CNRC 2005: EGSPP (C++) by Kawrakow and Rogers at CNRC 2006: EGS5 (Fortran) by Hirayama, Namito, Bielajew, Wilderman and Nelson at KEK Features Particles: photon (1 keV - ~100 GeV), electron (+/-, 10 keV - ~100 GeV) User codes: BEAMnrc, DOSRZnrc, FLURZnrc, CAVRZnrc, SPRRZnrc … Homepage: http://www.irs.inms.nrc.ca/EGSnrc/EGSnrc.html

33. Input File (Code Writing)

34. Pros and Cons Limited particles (photons, e + and e - ) Pros Cons Highly accurate for photons and electrons Large user community in medical physics Many user codes available

35. Application Examples Linear accelerator Medical radiation physics Ionization chamberBrachytherapy seed

36. FLUKA (FLUktuierende KAskade) History 1962-1978 : First generation (CERN SPS Project) 1978-1989 : Second generation (development of new hadron generators) 1988 to present: Third generation (the modern multiparticle/multipurpose code) Features Hadron-hadron and hadron-nucleus interactions up to10,000 TeV Electromagnetic and μ interactions 1 keV – 10,000 TeV Nucleus-nucleus interactions 100 MeV/n (with BME: ~10 MeV/n) to 10,000 TeV/n Neutron multi-group transport and interactions 0-19.6 MeV Transport in magnetic field Homepage: http://www.fluka.org/fluka.php

37. Input File

38. Pros and Cons Source code is not open Pros Cons Accurate high energy physics for 65 source particles Various visualization and debugging tools No programming knowledge is required

39. Application Examples ATIC test in CERN Radiation damage effects Irradiation test facility (Proton accelerator) CERN's LHCb detector Proton therapy

40. Comparison of Monte Carlo Codes MCNPXGEANT4EGSnrcFLUKA LanguageFortran 90/CC++MortranFortran 77 Particles3468 (unlimited)365 InputMacroCodingCoding (GUI)Macro Input Cards~120N/A ~85 Parallel ExecutionYes Cost$600-$1000Free CADSTEP NoFLUKACAD Major user group Nuclear engineering High energy physics Medical physics High energy physics Web Site http://mcnpx.lanl.g ov/ http://geant4.cern.c h/ http://www.irs.inms.nr c.ca/EGSnrc/EGSnrc. html http://www.fluka. org/fluka.php

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