Transcript ｽﾗｲﾄﾞ ﾀｲﾄﾙなし - KEK 放射線科学

Japan-Korea Joint Summer School on Radiation Science and Engineering
Kitakyusyu International Conference Center (15 Jul 2009)
EGS code and reaction between
electrons and photons
Y. Namito (KEK)
Last modified on 2009.7.9
History of EGS system
Period
Program
Languag
e
Authors
1963～1965 SHOWER1
Fortran
Nagel
SHOWER2
Fortran
Nicoli
1967～1972 SHOWER3/PREPRO
Fortran
Ryder, Talwar, Nelson
1970～1972 SHOWER4/SHINP
Fortran
Ford
1966
1974
EGS1/PEGS1
Fortran
Ford, Nelson
1975
EGS2/PEGS2
Mortran 2
Ford, Nelson
1976～1977 EGS3/PEGS3(SLAC-210) Mortran 2 Ford, Nelson
1982～1985 EGS4/PEGS4(SLAC-265) Mortran 3 Nelson, Hirayama, Rogers
2006
EGS5(SLAC-R-730 and
KEK Report 2005-8)
Fortran
Hirayama, Namito, Bielajew,
Wilderman and Nelson
About EGS
•
•
•
•
Monte Carlo particle transport simulation code.
Interaction of electron and photon with matter.
Energy range: 103eV - 1012eV.
EGS5: Released in 2006. Authors: Hirayama,
Namito, Bielajew, Wilderman, and Nelson.
• Runs on Linux, Cygwin and Windows-PC.
• Combinatorial geometry is available.
– Geometry check program (CGVIEW) is available.
– Separation of geometry and other preparation.
• Transport in EM field.
Combinatorial Geometry CG
1. Specify BODY using parameters.
2. Specify ZONE by operation (AND,
OR, OUTSIDE) of bodies.
3. Specify material for ZONE
User
Control data
USER CODE
MAIN
PEGS5
HATCH
HOWFAR
SHOWER
BLOCK
SET
EGS CODE
BLOCK
DATA
BLOCK
DATA
ATOM
Information
Extracted
from Shower
AUSGAB
ELECTR
PHOTON
MSCAT
COMPT
ANNIH
PAIR
BHABHA
PHOTO
MOLLER
BREMS
UPHI
g
Electron
What is interact with photon and electron ?
Whole One Atom? Electron? Nucleus?
Photon Monte Carlo Simulation
Photon Interaction with Matter
positron
e+
photon g
θ
photon g
nucleus e electron
e
e
e
Atom
j
e
photoelectron
scattered
photon
photon g
e
L
nucleus
e
e K
e
e
electron
Compton scattering
Pair Production
photon g
scattered
photon
L
e
e
nucleus
e K e e
e
e
e
Photoelectric effect
Atom
Rayleigh scattering
Pair Production
Future
Time
e-,E-
e+, E+
N
Place
Past
N
γ,k0
Positron
g
e+
nucleus
Electron
k0=E+ +E-
sketch
Feynman diagram
• Interact in the field of a nucleus
e-
• PHOTX CS
•Annihilate and produce e+ - e- pair • default q=m0c2/k0
• Realistic angle. dist.: optional
• triplet distribution ignored,
incl. in total σpair
Pair Production (Cont’)
Electron-positron pair production
cross section
Electron energy dist of Pair
Production for 5.11 MeV g
2
10
log k @ k→∞
82-Pb
0
101
Electron production DCS (arb)
1.5
Threshold Energy @ 2m c2
Electron Pair Production CS (b)
103
0
10
10-1
-2
10
10-3
10-1
8-O
1
0.5
Scale as Z(Z+1)
0
0
1
10
10
Photon energy (MeV)
2
10
0
0.5 1 1.5 2 2.5 3 3.5
Electron kinetic energy (MeV)
4
Compton scattering
k0+ me = k’ + Ee-, Eγ, k’
Klein- Nishina dσ
Time
1
0.01 MeV
0.8
0.6
0.1 MeV
γ, k0
e-, me
DCS (r
2
0
-1
sr )
Place
0.4
Feynman diagram
photon, k0
scattered
 photon, k
j
e
electron, Ee, v
sketch
0.2
1 MeV
10 MeV
0
0
45
90
135
Scattering angle (o)
180
Compton scattering (Cont’)
3
Compton scattering CS (b)
10
Optional treatment in egs5
const@k→0
(e- is “free”)
102
1
82-Pb
0
8-O
10
10
• Binding effect (0 @ k→0)
• Doppler Broadening
•e- pre-collision motion
• Linearly polarized photon
scattering
1/k @
k→∞
Scale like Z
-1
10
-2
10
-2
10
-1
0
1
10
10
10
Photon energy (MeV)
2
10
Double Differential Compton Cross Section
100
Cu
10-1
Total
K
L
M
N
Binding
effect
-2
10
2
d /d/dk (barn/keV/sr.)
o
k0=40keV q=90
-3
10
30
32
34
36
38
Scattered Photon Energy, k (keV)
40
Z
Set up of
Experiment
Y
Target
40 keV g
Cu,40 keV(EGS4+LP+DB=EGS5)
-2
Cu 40 keV
Compton
Rayleigh
Measurement
EGS4(DB)
EGS4(w/o DB)
-3
10
L-Edge
-1
Photons sr. keV per source
10
-4
-1
10
K-Edge
-5
10
-6
10
30
k00928a
32
34
36
38
Photon Energy, k (keV)
40
Effect of Doppler to Ge detector response
-2
10
Doppler Broadening
100 keV
Doppler Broadening
-3
10
No Doppler Broadening
Pulse Height Distrib. /source particle
Pulse Height Distrib. /source particle
No Doppler Broadening
10-3
Compton
edge
-4
10
500 keV
Back
scat.
Peak
10-5
-6
10
Back scat.
Peak
-4
10
Compton
edge
10-5
-6
10
-7
-7
10
10
0
20
file: k30321d
40
60
Energy /keV
80
100
0
100
file: k30321b
200
300
Energy /keV
400
500
Auger
Number of Electron (arb.)
Example of
Compton and
Auger electron
spectrum
2500
k00906c
2000
Exp
EGS4
1500
Compton Recoil
1000
500
0
0
5
10
Electron Kinetic Energy (keV)
15
700
Al 48.1 nm, 57.0 keV
600
Number of Electron (arb.)
eγ
Θ<10°
ΔE=3%
Guadala,Land&Price’s exp
Ti 68 nm, 57.25 keV
Compton Recoil
Auger
500
k00906b
Exp
EGS4
400
300
200
100
0
0
5
10
Electron Kinetic Energy (keV)
15
Photoelectric effect
105
Place
γ, k0
g
Atom, EN
②
①
e
e
e
nucleus
e
e
e
e
4
10
Photoelectric CS (b)
Time
k0+ EN = E- + EN*
e-, E- Atom*, En*
82-Pb
Absorption Edge
103
σ∝Z4/E3
102
1
10
8-O
100
10-1
10-2
e
10-3
10-2
Scale like Z4 →Z4.6
10-1
100
101
Photon energy (MeV)
102
Photoelectric effect (Cont’)
q=0! (Realistic dist. optional)
Photoelectron emission DCS d/d (arb)
70
60
50
40
30
20
10
0
0
45
90
135
Photo electron angle (o)
180
Relaxation of atom (option in egs5)
- Fluorescent X ray and Auger electron from K and L shell
1
Fluorescent Yield
0.8
K
L1
L2
L3

0.6
0.4
0.2
Data from TOI-8th(96)
00
20
40
60
Z
80
100
Photon spectrum from Pb target
EGS4 (General Treatment of PE) = EGS5
-2
10
Counts (/keV/sr/source)
L L
Pb 40 keV
Ge K-X
Escape
-3
10
Lg
Ll
-4
10
Rayleigh
COUNT
COUNT
EGS4 H =EGS5 H
EGS4 V =EGS5 V
Compton
Ge K-X
Escape
-5
10
Pile Up
-6
10
0
5
10
15
20
25
30
Energy Deposition (keV)
35
40
Rayleigh Scattering
k0+ EN = k0+ EN
γ, k0
Atom, E
Time
N
• elastic process
• independent atom approx.
5
10
γ, k0
g
Atom, EN
②
①
e
e
e
nucleus
e
e
e
e
e
Rayleigh Scattering CS (b)
4
Place
10
3
10
82-Pb
Scale as Z2
102
101 8-O
0
10
-1
10
10-2
10-3
10-2
10-1
100
101
Photon energy (MeV)
102
Rayleigh Scattering (Cont’)
Optional treatment in egs5
• Interference effect between nearby atoms
2
10
F (x)
Form Factor
2
Liquid Water
Sampled
Atomic Water
Sampled
1
10
0
sin2f
30 keV,q=5o
10
o
30 keV,q=45
-1
10
10-3
x=E(keV)/12.4 sin(q/2)
10-2
10-1
100
• Linearly polarized photon scattering
2
x
101
Components of g in C
Diag.
Radiation Therapy
HEP
100
Compton
Compton plateau
fraction of total 
Photoelectric
10-1
Pair
Rayleigh
10-2
free
bound
10-3
-3
10
10
-2
-1
0
10
10
Incident Photon Energy (MeV)
1
10
2
10
100
Components of g in Pb
fraction of total 
Photoelectric
10-1
Pair
Compton
Rayleigh
10-2
free
10-3
-3
10
10
-2
bound
-1
0
10
10
Incident Photon Energy (MeV)
1
10
2
10
Total photon S vs g-energy
photoelectric
region
2
10
Water
1
Ek
2
 (cm /g)
10
0
10
-1
10
-2
10
10-3
Lead
Hydrogen
Compton plateau
free
bound
30% diff @ 3 keV
Z independent
pair
region
H2 is the best g attenuator
for this energy region
10-2
10-1
100
Incident Photon Energy (MeV)
101
102
End of Photon Monte Carlo
Simulation
Electron Monte Carlo Simulation
- interaction
- approximations
- transport methods
5mm
Electron interaction with matter
electron
electron
electron
e
e
e
nucleus
e
1. Electron scattering by nucleus
(Rutherford scattering): Change direction
electron
e
2. Inelastic scattering of electron
and electron: Loose energy
electron
e
nucleus
Brems. X-ray
electron
e
Brems. X-ray
3. Generation of bremsstrahlung x ray
Condensed Random Walk
d
e-
d g
d
d
g d
g d
g
d
In Reality, mean free path
is in nm or mm unit.
g
Continuous slowing down
ed
g
dray, brems: Treated only if,
2nd particle energy > threshold
Multiple scattering
ed
g
M.S. Angle qms(E,Z,t)
Moliere theory
GS theory
How do we treat both hard interaction and
continuous approximation consistently?
Use Threshold energy (AE, AP) by User’s choice
• “Hard” interaction: Discrete sampling
–large ΔE Moller/Bhabha (2nd particle energy>AE)
–large ΔE bremsstrahlung (photon energy>AP)
–annihilation “in flight” & at rest
• “Soft” interaction
–small DE Moller/Bhabha
–atomic excitation
–soft bremsstrahlung
–multiple e ± Coulomb scattering
Energy
Absorption
Hard Interaction
Bremsstrahlung
electron
electron
e
Brems. X-ray
nucleus
•Z2 scaling
e
•3 body angular dist’n ignored
e
Brems. X-ray
•Z2 →Z(Z+x(Z))
•<50 MeV Normalize to ICRU-37
E0=E + k
Time
Future
•>50 MeV ERL
e±,Eγ,k
N
Place
Past
e±,E0
Feynman diagram
N
•Migdal ignored >10 GeV
•TF screening
•e- , e+ treated as same
•e± not deflected
Example of brems photon spectrum
1000
d/dk (b MeV-1 per atom)
1/k divergence
Electron energy E0=5 MeV
100
qg＝me/E0
Z=47
10
Z2 scaling
1
Z=6
0.1
Data from Selter&Berger (1986)
0.01
0
1
2
3
k (MeV)
4
5
Bhabha
e-, E1’
e+, E2’ e-, E1’ e+, E2’
Time
Moller
-, E ’
e
e , E1’
2
+
e-, E1
e-, E2
identical particles
- threshold 2(AE-RM)
• goes like 1/v2
• scale like Z
• Target e- is “free”
e-, E1
e+, E2
Place
e-, E1 e+, E2
different particles
- threshold AE-RM
Optional treatment in EGS5
- K-X ray production in Moller
(Electron Impact Ionization)
Annihilation
γ,E２’
Time
γ,E1’
Place
• in flight and at rest
• e+ e- → nγ(n>2) ignored
• e+ e- →γN* ignored
• at ECUT e+ annihilates
Residual drift is ignored
• no binding
annihilation g-ray
e+,E
2
e-,E1
e+
positron
e
electron
annihilation g-ray
Statistically grouped interactions
(Soft Interaction)
• Continuous energy loss
• Multiple scattering
”Continuous” energy loss
1. collisional energy loss （e± different)
1. Bethe-Bloch theory density effect
2. well-above K shell energy
3. many electron atoms ∝Zav
2. radiative energy loss （e± treated same)
1. integration of bremsstrahlung cross
sections
2. same approximations
3. e+, e- treated as identical
Density effect
Reduction of the collision stopping power due to the
polarization of the medium by the incident electron.
e
- -e - e
nucleus
e
e e e - e
e
e
e
e - e ee
ee
nucleus
ee- - e- - e
e e eenucleus
ee
e
e
e
e
e
e
e
e-nucleuseLarge polarization
in Conductor (ex. Carbon)
Small polarization in Rare Gas (ex. Ar)
Density effect (2)
30
15
1 MeV
10 MeV
100 MeV
D/(dE/dx)coll in %
25
20
Electron energy
D/(dE/dx)total in %
Electron energy
1 MeV
10 MeV
100 MeV
10
15
10
Pages,AD 4,1(1972)
5
5
0
H
O Ne Ar C Al Cu Pb
Material
0
H
O Ne Ar C Al Cu Pb
Material
Density effect in egs5
• Berger, Seltzer, and Sternheimer
– Parameters for 278 materials
• Sternheimer and Peierls
– general treatment
• Less precise, Needs only Z and r
Electron stopping power (unrestricted)
Collision
C
2
Stopping power (MeV cm / g)
1
10
small density effect for Ar
Z scaling
Ar
Pb
Sn
Z/A differences
and I differences
0
10
1 / v2 saturation
Radiative
Z2 scaling
-1
10
Pb
-2
10
-1
10
Sn
Ar
0
C
10
10
Electron kinetic energy (MeV)
Data from estar of NIST
1
10
2
Energy absorption
energy absorption for e± transport of t
  (dE

 (dE

restricted
stopping
power
/ dx)
restricted
stopping
power
/ dx)
t
  (dE

Radiative
sub
cutoff
/ dx)
Collision
sub
cutoff
(dE / dx)
Mean energy loss from Gaussian distribution
Needs Landau’s distribution for thin geometry
Absorption Dose (Gy) = Energy absorption (J) / mass(kg)
t
s
ρ
Θ
Multiple Scattering
Z
e-
Z
Z
Z
Z
t
Z
q
Z
f(q)=? : after path length t
• Fermi-Eyges theory
• Goudsmit-Saunderson theory: EGS5
• Moliere’s small angle large pathlength theory:EGS5
Moliere theory
（Middle precision, Middle restriction, Simple）
• Convert scattering angle
Q (E,Z,t) to reduced angle q
• Use single set of f(n)(q) → Simple
• Good for small angle (<20o)
• Needs long t (>100 elastic mfp)
Goudsmit-Saunderson (GS) theory
（High precision, Little restriction, Cumbersome）
• Expand scattering CS by Legendre function
• Coefficient f (E, Z, t, q) → Need large Data Base
• Good for all scattering angle without restriction
Concept figure for single scattering and
multiple scattering
Multiple scattering model
Moliere theory
GS theory
Single scattering Cross section
Rutherford scattering
Mott scattering
e
Electron transport in EGS5
• Elastic scattering cross section
– Rutherford CS（Default)(=EGS4)
• Coulomb interaction between nucleus and electron.
Nucleus is treated as a point.
– Mott CS
• Consider spin relativistic effect
• Multiple scattering
– Moliere theory (Default)(=EGS4)
– Goudsmit-Saunderson theory (GS)
• Transport mechanics inside m.s. step
– Dual Hinge
Transport Mechanics inside step
EGS4
Transport mechanics
inside m.s. step of
EGS5 (1)
Developed at U.Mich and U.Barcelona
1．Sampling m.s. step s
（straight step size)
2．Evaluate curved length (t),
scattering angle (t )
and lateral displacement
(Dx2+Dy2)
EGS5
Multiple scattering random hinge
1. Sampling multiple scattering
hinge point inside curved
length t
2．Change electron direction at
that point based on m.s. model
< t/s > and <Δx2+Δy2> are
adequately calculated in this hinge
model as long as energy loss is ignored.
Transport mechanis inside m.s. hinge
in EGS5 (2)
• Instead of hinge model of zt and (1-z)t, hinge
model based on scattering strength is used. zK1(t)
and (1-z)K1(t).
– To account for energy loss.
• Introduce “Energy loss hinge ” to simplify
integral of G1 to evaluate K1.
– Energy is constant between energy loss hinge.
• Introduce “Characteristic dimension” to make
setting of adequate step length easy.
Simple
Accurate
Class I (ITS,MCNP)
Energy loss without correlation
E0
t
E
Eδ
E=E0-DE(t)
Edep=DE(t) - Ed
Class II (EGS,Penelope)
Energy loss with correlation
E0
t
E
Eδ
E=E0 - t LcolAE - Ed
Edep=t LcolAE
• DE(t) : energy loss sampled from energy loss distribution
(Straggling considered)
• LcolAE : restricted stopping power for 2nd particle (<AE)
t : Fixed length (Function of Max energy) @ITS,
Variable @ EGS, Penelope
Comparison of Electron transport model
Code
EGS5
Spin
M.S. model Class Transport mechanism in step
×
Moliere
○
GS
EGSnrc ○
GS
2
Dual Hinge
Characteristic dimension
2
Separate single scatt.
Dual Hinge
Separate large q scatt.
Penelope ○
GS
2
ITS 3.0 # ○
GS
1
#
Adopted as electron transport of MCNP
g
Electron
Photon and electron interact with
Whole One Atom, Electron, and Nucleus
Exception
- Density effect
- Interference in Rayleigh scattering
Complement
• Electron impact ionzation
• Shielding of ,,g ray
Electron Impact Ionization (EII)
eeN
K-X
K-X
Brem.γ
N
N
Brems. → Photoelectric
EII
10 keV–3 MeV
eProp, NaI
Dick et al (1973)’s
exp set up
Al,Ti,Cu,Ag,Au
K X-ray yield for Cu
-2
10
C/M=0.82
K-X ray yield (photons/sr/e-)
(c) Cu
o
180
-3
10
o
120
o
180
-4
10
o
C/M=0.053
-5
10
120
o
Exp(Dick et al)180
o
Exp(Dick et al)120
EGS5(GR)
EGS4+EII(GR)
EGS4
-6
10
-7
10
-2
10
file:k40622c
-1
0
10
10
Incident electron kinetic energy (MeV)
1
10
CSDA range of  and  ray
(Almost) independent of Z
2
2
10
10

1
10
C
Al
Pb
0
0
10
CSDA Range (g/cm2)
10
CSDA Range (g/cm2)

1
10
-1
10
Large Iav
-2
10
-3
10
-4
10
-5
C
Al
Pb
-1
10
-2
10
-3
10
-4
10
-5
10
10
Small Iav
-6
10
-3
10
10
-2
-1
10
Data from astar of NIST
Data from estar of NIST
-6
10
0
1
10
10
Energy (MeV)
2
10
3
10
-3
10
10
-2
-1
10
0
1
10
10
Energy (MeV)
2
10
3
10
Total photon S vs g-energy
photoelectric
region
2
10
Water
1
Ek
2
 (cm /g)
10
0
10
-1
10
-2
10
10-3
Lead
Hydrogen
Compton plateau
free
bound
30% diff @ 3 keV
Z independent
pair
region
H2 is the best g attenuator
for this energy region
10-2
10-1
100
Incident Photon Energy (MeV)
101
102
In reality,  ray and  ray range (g/cm2) or
g ray MFP is (almost) independent of Z!
End of Electron Monte Carlo
Simulation