Packages for Monte Carlo
simulation of radiation
interaction with matter
Sergey Ananko
Saint-Petersburg State University
Department of Physics
Division of Computational Physics
JASS-06
Outline
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Actuality
Short description of physical model
Monte Carlo method
Geant4
Fluka
Comparison of packages
Conclusions
Future plans
JASS-06
Actuality
General
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Nuclear physics
High-energy physics
Cosmic rays
Neutrino physics
Medicine
Particular
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Necessity to have
several ways of the
solution of the same
problem
JASS-06
Physics review
Gamma-rays
Gamma-rays – high-frequency electromagnetic oscillations:
  10 20 s 1
and above
Gamma-particles characteristics:
velocity: c  3  1010 cm
s
energy: E  

momentum: p 
  1.054  10 27 erg  s
c
wave length:  
m0 c
E
Gamma photons energy range:E q  0.01;10 MeV
Effects: photoelectrical absorption, Compton effect and pair production
JASS-06
Physics review
Scattering cross-section
N 0 - number of photons
through unit square per unit of
time
N - number of scattered
photons
N
s 
N 0 - cross-section
N0
Z
N
O
Y
X
dN  N 0 s n0 d - number of
scattered gamma photons
dw   s n0 dl - probability
of photons scattering
JASS-06
Physics review
Photoelectrical effect
Photoelectrical effect is a process
of gamma photon absorption
by atom of substance
Ee  E q  Eb
E e - photoelectron energy
Eb - photon energy
E q - binding energy
JASS-06
Physics review
Compton effect
Compton effect is a process of gamma photon scattering on electron of atom
E' 
E
E- incident photon energy
m0 c
m0 c - electron rest-energy
 '    1  cos - wave length after interaction  - wave length before interaction
Ee  E  E ' - Compton electron energy
1 E
 1  cos  
- scattered photon energy
JASS-06
Physics review
Compton effect
E' 
E
1 2 E
- minimal value of scattered photon energy
m0c
E e     

1
E
m0 c
- maximum photoelectron energy
2E
- gamma-quantum
scattering angle

E'
- Compton electron
scattering angle

  0;  
  0;  2
E

Ee
JASS-06
Physics review
Pair production
Pair production is a process of generation electron-positron pair in
nucleus or atom field
JASS-06
Physics review
Total interaction coefficient
Number of photons lost by the beam:
dN  N 0 S  Cs   f   pp ndl where
 Cs  f  pp - cross-sections of Compton effect, photo effect,
pair production
n - atom number per unit of volume
N 0 - flux density
S - beam cross-section
   Cs   f   pp - total interaction cross-section per one
atom of matter
Quantum energy loss per unit of time:
dE  N 0 SE Cs f Cs ndl  N 0 SE f f f ndl  N 0 SE pp f pp ndl
JASS-06
Physics review
Total interaction coefficient
mass absorption coefficient for air
cm 2 g
  n
 
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 - mass absorption coefficient
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Cs 
- linear absorption coefficient
- matter density
f 
 pp 
E, meV
JASS-06
Physics review
Model
Air-filled
cubic volume:
Detecting plane
1  1  1m 3
Gamma energy range:
E  0.2;4MeV
Point-like source
Energy and angular distribution of
secondary particles
JASS-06
The Monte Carlo Method
Two approaches
Deterministic methods
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The Monte Carlo method
Finite difference method
Finite element method
JASS-06
The Monte Carlo Method
Model: probability estimation
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Source – anisotropic point-like
monoenergetic gamma
photon source
Shield – relatively thick
spherical shell,
only one sort of atom
Effects:
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Elastic scattering
Absorption
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Effects are characterized by:
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Cross-section
Probability density function for
path length
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e  x dx
JASS-06
The Monte Carlo Method
Simulation steps
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First step: free path length
xi  1   ln 1   i 
Second step: scattering or
absorption
0;1  0;0.1  0.1;1
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z
Third step: scattering angle
i  
Further steps: repeating
N - number of generated trajectories
n - number of escaped gamma
photons
s i - score
Estimated probability of escape:
s  1 N  si  n N
Variance of the : s i
1
Var si  
N
1
2
s

i i  N
Relative error
Var si  N
s

nN  n 

s


i i 
N2
2
N  n 
Nn
JASS-06
The Monte Carlo Method
Variance reduction
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Brute-force approach
Truncation
Population control:
Splitting
Russian roulette
Probability modification
Pseudodeterministic methods
JASS-06
The Monte Carlo Method
Geometry description
Combinatorial object
Surface-sense object
JASS-06
The Monte Carlo Method
Monte Carlo packages
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Main components:
Data base of cross-sections
and other parameters
Theoretical base
Random number generator
Tool for geometry description
 Main aspirations:
 Extended range of ability
 Flexibility
 Examples:
MNCP, Fluka, Geant, Geant4, Vulcanu, PYTHIA, ARIADNE
and so on
JASS-06
GEANT4
Geant4: status
Geant4 is a detector description and simulation
tool
Application areas:
High-energy physics, nuclear experiment, medical, accelerator and space
physics studies
Geant4 is a free software
It can be downloaded from
URL:
http://geant4.cern.ch
History:
1974 – GEANT first version
1982 – the appearance of GEANT3
1998 December – first release of GEANT4
Operating systems:
Unix, Linux, Windows
JASS-06
GEANT4
Main features
GEANT4 is written in C++
GEANT4 is based on an object-oriented technology
Experiment stages:
 Detector description
 Source description
 Physics description
 Detector reaction description
JASS-06
Fluka
Fluka: status
Fluka is a general purpose tool for calculations of particle transport and interactions with
matter, covering an extended range of applications spanning from proton and
electron accelerator shielding to target design, calorimetry, activation, dosimetry,
detector design, Accelerator Driven Systems, cosmic rays, neutrino physics,
radiotherapy etc.
Fluka is distributed under the licence as a tar file
It can be downloaded from its web-site:
www.fluka.org
Supported platforms:
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- Hewlett-Packard 9000 Series 700/800 running HP-UX
- Sun running SunOS
- Intel PCs running LINUX:
History:
- RedHat 7.3
First generation – the Fluka of the 70th
- RedHat 9.0
Second generation – the Fluka of the 80th
- Scientific Linux 4.1 `
Third generation – the Fluka of today
- Fedora Core
JASS-06
Fluka
Main features
Fluka is written in Fortran
Package consists of compiled libraries, user routing in source form,
INCLUDE files, various unformatted and formatted data and a
number of scripts for compiling, linking and running the program.
Structure of input file: particle source, geometry, transport options,
detectors
Example: source (kind of particle, energy, location in space, distribution)
BEAM 50.E+00
BEAMPOS
0.0
PROTON
0.0
-50.0
JASS-06
Comparison: main features
photoelectric effect:
Compton effect:
pair production:
multiple scattering:
Geant4
Fluka
10keV
10keV
1keV
1keV
1keV
1keV
1keV
1keV
threshold energy
5 10keV
- recommended
value for threshold
for Fluka
Conclusion
Both Fluka and Geant4 provide with ability
of simulation particles transport in a very
extended energy range.
JASS-06
Future plans
To receive results from Fluka
 To process them
 To compare them with Geant4
 To parallel both Fluka and Geant4
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JASS-06
Thank you for attention