EGS code and reaction between electrons and photons

Y. Namito (KEK)

Last modified on 2009.7.9

Japan-Korea Joint Summer School on Radiation Science and Engineering Kitakyusyu International Conference Center (15 Jul 2009)

History of EGS system

Period Program Language

Authors

1963～1965

SHOWER1 Fortran Nagel

1966 SHOWER2 Fortran Nicoli

1967～1972

SHOWER3/PREPRO Fortran Ryder, Talwar, Nelson

1970～1972

SHOWER4/SHINP Fortran Ford

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, Nam

ito, 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

MAIN

Information Extracted from Shower

HOWFAR AUSGAB

BLOCK DATA

PEGS5 HATCH SHOWER ELECTR PHOTON

MSCAT

ANNIH

BHABHA

MOLLER

BREMS

UPHI

COMPT

PAIR

PHOTO

USER CODE

EGS CODE

BLOCK DATA ATOM

BLOCK SET

What is interact with photon and electron ?Whole One Atom? Electron? Nucleus?

Electron

Photon Monte Carlo Simulation

K

L

Photon Interaction with Matter

Photoelectric effect

enucleus

ee

e

e

e

e

photon ephoto-electron

Rayleigh scattering

Compton scattering

electrone

photon

scattered photon

θ

e+

Pair Production

nucleus e electron

photon

positron

Atom

K

L

nucleusee

ee

e

e

e

photon

e

scattered photon

Atom

Pair Production

• Interact in the field of a nucleus

•Annihilate and produce e+ - e- pair

• triplet distribution ignored,

incl. in total σpair

• PHOTX CS

• default =m0c2/k0

• Realistic angle. dist.: optional

e+, E+

N

Ne-,E-

γ,k0k0=E+ +E-

Feynman diagram

Place

Tim

e

Future

Past

sketch

Electronnucleus e-

e+

Positron

Pair Production (Cont’)

10-3

10-2

10-1

100

101

102

103

10-1 100 101 102

Ele

ctro

n P

air

Pro

duct

ion

CS

(b)

Photon energy (MeV)

82-Pb

8-O

Th

resh

old

En

ergy

@ 2

m0c2

0

0.5

1

1.5

0 0.5 1 1.5 2 2.5 3 3.5 4

Ele

ctro

n pr

odu

ctio

n D

CS

(ar

b)

Electron kinetic energy (MeV)

log k @ k→∞

Scale as Z(Z+1)

Electron energy dist of Pair

Production for 5.11 MeV

Electron-positron pair production

cross section

Compton scattering

Klein- Nishina dσ

γ, k’

e-, me

e-, E-

γ, k0

k0+ me = k’ + E-

Place

Tim

e

electron, Ee, vsketche

photon, k0

scattered photon, k 0

0.2

0.4

0.6

0.8

1

0 45 90 135 180

DC

S (

r 02 sr-1

)

Scattering angle (o)

0.01 MeV

0.1 MeV

10 MeV

1 MeV

Feynman diagram

10-2

10-1

100

101

102

103

10-2 10-1 100 101 102

Co

mp

ton

scat

terin

g C

S (

b)

Photon energy (MeV)

82-Pb

8-O

Scale like Z

1/k @

k→∞

const@k→0

(e- is “free”) • Binding effect (0 @ k→0)

• Doppler Broadening

•e- pre-collision motion

• Linearly polarized photon scattering

Optional treatment in egs5

Compton scattering (Cont’)

Double Differential Compton Cross Section

10-3

10-2

10-1

100

30 32 34 36 38 40

TotalKLMN

d2 /

d

/dk

(bar

n/k

eV/s

r.)

Scattered Photon Energy, k (keV)

Cu

k0=40keV =90o

Binding

effect

Set up of Experiment

40 keV

Target

Z

Y

Cu,40 keV(EGS4+LP+DB=EGS5)

10-6

10-5

10-4

10-3

10-2

30 32 34 36 38 40

MeasurementEGS4(DB)EGS4(w/o DB)

Ph

oto

ns

sr.-1

keV

-1 p

er s

ou

rce

Photon Energy, k (keV)

Cu 40 keV

k00928a

K-Edge

L-Edge

RayleighCompton

10-7

10-6

10-5

10-4

10-3

0 100 200 300 400 500

Doppler Broadening

No Doppler Broadening

Pul

se H

eig

ht D

istr

ib. /

sou

rce

par

ticle

Energy /keVfile: k30321b

10-7

10-6

10-5

10-4

10-3

10-2

0 20 40 60 80 100

Doppler Broadening

No Doppler Broadening

Pul

se H

eig

ht D

istr

ib. /

sou

rce

par

ticle

Energy /keVfile: k30321d

Comptonedge

Back scat.Peak

Back scat.Peak

500 keV100 keV

Comptonedge

Effect of Doppler to Ge detector response

Example of Compton and

Auger electron spectrum

0

500

1000

1500

2000

2500

0 5 10 15

Exp EGS4

Nu

mb

er

of

Ele

ctr

on

(ar

b.)

Electron Kinetic Energy (keV)

Auger

Compton Recoil

Ti 68 nm, 57.25 keVk00906c

0

100

200

300

400

500

600

700

0 5 10 15

Exp EGS4

Nu

mb

er

of

Ele

ctr

on

(ar

b.)

Electron Kinetic Energy (keV)

Auger Compton Recoil

Al 48.1 nm, 57.0 keVk00906b

e-Θ<10°ΔE=3%γ

Guadala,Land&Price’s exp

10-3

10-2

10-1

100

101

102

103

104

105

10-2 10-1 100 101 102

Pho

toel

ect

ric C

S (

b)

Photon energy (MeV)

82-Pb

8-O

Absorption Edge

Photoelectric effect

σ Z∝ 4/E3

k0+ EN = E- + EN*

γ, k0

Atom*, En*e-, E-

Atom, EN

Place

Tim

e

nucleusee

ee

e

e

e

e① ②

Scale like Z4 →Z4.6

Photoelectric effect (Cont’)

=0! (Realistic dist. optional)

0

10

20

30

40

50

60

70

0 45 90 135 180

Ph

otoe

lect

ron

emis

sion

DC

S d

/d

(ar

b)

Photo electron angle (o)

Relaxation of atom (option in egs5)- Fluorescent X ray and Auger electron from K and L shell

0

0.2

0.4

0.6

0.8

1

0 20 40 60 80 100

KL1L2L3

Z

Data from TOI-8th(96)

Fluorescent Yield

Photon spectrum from Pb target　EGS4 (General Treatment of PE) = EGS5

10-6

10-5

10-4

10-3

10-2

0 5 10 15 20 25 30 35 40

COUNTCOUNTEGS4 HEGS4 V

Co

un

ts (

/ke

V/s

r/so

urc

e)

Energy Deposition (keV)

Pb 40 keVRayleigh

ComptonGe K-XEscape

Ge K-XEscape

Pile Up

Ll

L L

L=EGS5 V=EGS5 H

Rayleigh Scattering

• elastic process

• independent atom approx.

γ, k0 Atom, EN

k0+ EN = k0+ EN γ, k0 Atom, EN

Place

Tim

e

10-3

10-2

10-1

100

101

102

103

104

105

10-2 10-1 100 101 102

Ra

ylei

gh

Sca

tter

ing

CS

(b

)

Photon energy (MeV)

8-O

82-PbScale as Z2

nucleusee

ee

e

e

e

e

①②

• Interference effect between nearby atoms

• Linearly polarized photon scattering

Optional treatment in egs5

Rayleigh Scattering (Cont’)

sin2

10-1

100

101

102

10-3 10-2 10-1 100 101

Liquid WaterSampledAtomic WaterSampled

F2(x

)

x2

30 keV,=5o

x=E(keV)/12.4 sin(/2)

30 keV,=45o

Form Factor

Compton plateau

Components of in CDiag. Radiation Therapy HEP

10-3

10-2

10-1

100

10-3 10-2 10-1 100 101 102

frac

tion

of t

ota

l

Incident Photon Energy (MeV)

PhotoelectricPhotoelectricPhotoelectricPhotoelectric

bound

Rayleigh

Pair

free

Compton

Components of in Pb

10-3

10-2

10-1

100

10-3 10-2 10-1 100 101 102

frac

tion

of t

ota

l

Incident Photon Energy (MeV)

Photoelectric

bound

Rayleigh

Pair

free

Compton

10-2

10-1

100

101

102

10-3 10-2 10-1 100 101 102

(c

m2 /g

)

Incident Photon Energy (MeV)

Lead

bound

Hydrogen

free

Water

Total photon vs -energy

H2 is the best attenuator

for this energy region

Compton plateau

Z independent pair

region

photoelectric

region

Ek

30% diff @ 3 keV

End of Photon Monte Carlo Simulation

Electron Monte Carlo Simulation

- interaction

- approximations

- transport methods

5mm

2. Inelastic scattering of electron and electron: Loose energy

eelectron

electron

e

e

electron

1. Electron scattering by nucleus(Rutherford scattering): Change direction

electron

e

nucleus

3. Generation of bremsstrahlung x ray

nucleus

e

electron

Brems. X-ray

e

electron

eBrems. X-ray

Electron interaction with matter

Condensed Random Walk

e-

In Reality, mean free path

is in nm or m unit.

ray, brems: Treated only if,

2nd particle energy > threshold

Continuous slowing down

Multiple scattering

e-

e-

M.S. Angle ms(E,Z,t)

Moliere theory

GS theory

How do we treat both hard interaction and continuous approximation consistently?

• “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 E Moller/Bhabha Energy

–atomic excitation Absorption

–soft bremsstrahlung

–multiple e ± Coulomb scattering

Use Threshold energy (AE, AP) by User’s choice

Hard Interaction

•Z2 scaling

•3 body angular dist’n ignored

•Z2 →Z(Z+(Z))

•<50 MeV Normalize to ICRU-37

•>50 MeV ERL

•Migdal ignored >10 GeV

•TF screening

Bremsstrahlung

e±,E0

N

N

e±,E γ,k

E0=E + k

Place

Tim

e

Future

Past

Feynman diagram

nucleus

eelectron

Brems. X-ray eelectron

eBrems. X-ray

•e- , e+ treated as same

•e± not deflected

Example of brems photon spectrum

0.01

0.1

1

10

100

1000

0 1 2 3 4 5

d/d

k (b

Me

V-1

pe

r at

om)

k (MeV)

Data from Selter&Berger (1986)

Z=6

Z=47

Z2 scaling

1/k divergence

＝ me/E0

Electron energy E0=5 MeV

+

e-, E1 e-, E2

e-, E1’ e-, E2’

e-, E1e+, E2

e-, E1’ e+, E2’

e-, E1e+, E2

e-, E1’ e+, E2’

Bhabha

• goes like 1/v2

• scale like Z

• Target e- is “free”

identical particles

- threshold 2(AE-RM)different particles

- threshold AE-RM

Moller

Optional treatment in EGS5

- K-X ray production in Moller (Electron Impact Ionization)

Place

Tim

e

Annihilation

e-,E1e+,E2

γ,E1’ γ,E ２’• 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 Place

Tim

e

eelectron

annihilation -ray

e+

positron

annihilation -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 effect2. well-above K shell energy3. many electron atoms 　∝ Zav

2. radiative energy loss （ e± treated same)1. integration of bremsstrahlung cross sect

ions2. same approximations3. e+, e- treated as identical

Reduction of the collision stopping power due to the

polarization of the medium by the incident electron.

Density effect

Large polarization

in Conductor (ex. Carbon)

e- e- e-e- e-e-

e- e- e-e-

e-e-

e-

e-e- e-e- e-

e-

e-

e-

e-

e- e-e-

e-

e-

nucleuse-

e-

nucleuse-

e-

e-

nucleuse-

e-

nucleuse-e-

Small polarization in Rare Gas (ex. Ar)

0

5

10

15

20

25

30

H O Ne Ar C Al Cu Pb

1 MeV10 MeV100 MeV

/(d

E/d

x)co

ll in %

Material

Electron energy

0

5

10

15

H O Ne Ar C Al Cu Pb

1 MeV10 MeV100 MeV

/(d

E/d

x)to

tal in

%

Material

Electron energy

Pages,AD 4,1(1972)

Density effect (2)

Density effect in egs5

• Berger, Seltzer, and Sternheimer– Parameters for 278 materials

• Sternheimer and Peierls– general treatment

• Less precise, Needs only Z and

10-1

100

101

10-2 10-1 100 101 102

Sto

ppin

g po

wer

(M

eV c

m2 /

g)

Electron kinetic energy (MeV)

Data from estar of NIST

Collision

Radiative

CAr

Sn

Pb

CArSnPb

Z scaling

Z2 scaling

1 / v2 saturation

small density effect for Ar

Z/A differences and I differences

Electron stopping power (unrestricted)

Energy absorption

t

sΘρ

energy absorption for e± transport of t

Mean energy loss from Gaussian distribution

Needs Landau’s distribution for thin geometry

Absorption Dose (Gy) = Energy absorption (J) / mass(kg)

)/()/()/( cutoffsubCollision

cutoffsubRadiative

powerstoppingrestricted

dxdEdxdEdxdE

tdxdE )/( powerstoppingrestricted

Multiple Scattering

Z

ZZ

Z

Z

Z

Ze -

t

f()=? : 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）

Goudsmit-Saunderson (GS) theory（ High precision, Little restriction, Cumbersome）

• Convert scattering angle (E,Z,t) to reduced angle • Use single set of f(n)() → Simple• Good for small angle (<20o)• Needs long t (>100 elastic mfp)

• Expand scattering CS by Legendre function • Coefficient f (E, Z, t, ) → Need large Data Base• Good for all scattering angle without restriction

Concept figure for single scattering and multiple scattering

Single scattering Cross section　　　　　 Rutherford scattering　　　　　Mott scattering

Multiple scattering model　　　　　Moliere theory　　　　　GS theory

e

• 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

Electron transport in EGS5

Transport Mechanics inside step

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 ()and lateral displacement (x2+y2)

EGS4

EGS5 1. Sampling multiple scattering hinge point inside curved length t

2 ． Change electron direction at that point based on m.s. model

Multiple scattering random hinge < 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 t and (1-)t, hinge model based on scattering strength is used. K1(t) and (1-)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.

E0 Et

Eδ

E=E0-E(t)

Edep=E(t) - E

Class II (EGS,Penelope)Energy loss with correlation

E0 tE

Eδ

E=E0 - t LcolAE - E

Edep=t LcolAE

• E(t) : energy loss sampled from energy loss distribution

(Straggling considered)

• LcolAE : restricted stopping power for 2nd particle (<AE)

Class I (ITS,MCNP)Energy loss without correlation

Simple Accurate

t : Fixed length (Function of Max energy) @ITS, Variable @ EGS, Penelope

Comparison of Electron transport model

Code Spin M.S. model Class Transport mechanism in step

EGS5× Moliere

2Dual Hinge

Characteristic dimension○ GS

EGSnrc ○ GS 2 Separate single scatt.

Penelope ○ GS 2Dual Hinge

Separate large scatt.

ITS 3.0 # ○ GS 1

# Adopted as electron transport of MCNP

Photon and electron interact with Whole One Atom, Electron, and

Nucleus

Electron

Exception - Density effect - Interference in Rayleigh scattering

Complement

• Electron impact ionzation

• Shielding of ray

Electron Impact Ionization (EII)e-

N

Brem.γ

N

N

K-X

Brems. → Photoelectric EII

e-

K-X

Dick et al (1973)’s exp set up

10 keV–3 MeVe-

Al,Ti,Cu,Ag,Au

Prop, NaI

K X-ray yield for Cu

10-7

10-6

10-5

10-4

10-3

10-2

10-2 10-1 100 101

Exp(Dick et al)180o

Exp(Dick et al)120o

EGS5(GR)EGS4+EII(GR)EGS4

K-X

ray

yie

ld (

ph

oto

ns/

sr/e

-)

Incident electron kinetic energy (MeV)

180o

120o

180o

120o

(c) Cu

file:k40622c

C/M=0.82

C/M=0.053

CSDA range of and ray

10-6

10-5

10-4

10-3

10-2

10-1

100

101

102

10-3 10-2 10-1 100 101 102 103

CAlPb

CS

DA

Ran

ge

(g/c

m2)

Energy (MeV)

Data from estar of NIST10-6

10-5

10-4

10-3

10-2

10-1

100

101

102

10-3 10-2 10-1 100 101 102 103

CAlPb

CS

DA

Ran

ge

(g/c

m2)

Energy (MeV)

Data from astar of NIST

(Almost) independent of Z

Large Iav

Small Iav

10-2

10-1

100

101

102

10-3 10-2 10-1 100 101 102

(c

m2 /g

)

Incident Photon Energy (MeV)

Lead

bound

Hydrogen

free

Water

Total photon vs -energy

H2 is the best attenuator

for this energy region

Compton plateau

Z independent pair

region

photoelectric

region

Ek

30% diff @ 3 keV

In reality, ray and ray range (g/cm2) or

ray MFP is (almost) independent of Z!

End of Electron Monte Carlo Simulation