Post on 01-Apr-2015
Precision validation of Precision validation of Geant4 electromagnetic Geant4 electromagnetic
physicsphysicsKatsuya Amako, Susanna Guatelli, Vladimir
Ivanchenko, Michel Maire, Barbara Mascialino, Koichi Murakami, Petteri Nieminen, Luciano
Pandola, Sandra Parlati, Andreas Pfeiffer, Maria Grazia Pia, Michela Piergentili, Takashi Sasaki,
Lazslo Urban
Monte Carlo 2005Topical Meeting
Chattanooga, April 2005
IntroductionIntroduction
The validation of Geant4 physics models with respect to authoritative reference dataauthoritative reference data is a critical issuecritical issue,
fundamentalfundamental to establish the reliabilityreliability of Geant4-based simulations.
is an object-oriented toolkit for the simulation of the passage of particles through matter
It offers an ample set of complementary and alternative physics models for both electromagnetic and hadronic interactions, based on:
theoryexperimental
data parameterisations
Aim of the projectAim of the project
• Validation of Geant4 electromagnetic models against established references (ICRU - NIST), with the purpose of to evaluate their accuracy and to document their respective strengths
• Simulation of physics quantities in the same experimental set-up as reference data
• Rigorous quantitative statistical comparison
PHYSICAL TESTGOODNESS-OF-FIT
TESTINGQuantitative statistical analysis
- Evaluation of Geant4 physics models goodness- How the various Geant4 models behave in the same experimental condition - Systematic data analysis allows to improve the physics models and guarantees the reliability
Scope
Alternative and complementary models are provided in the various packages for Alternative and complementary models are provided in the various packages for the same physics processthe same physics process
High energy modelsHigh energy models– fundamental for LHC experiments, cosmic ray experiments etc.
Low energy modelsLow energy models– fundamental for space and medical applications, neutrino experiments, antimatter
spectroscopy etc.– two “flavours” of models:
• model based on Livermore libraries • à la Penelope
Geant4 includes a number of packages to handle the e.m. interactions of electrons and positrons, gamma, X-ray and
optical photons, muons, charged hadrons, ions
• multiple scattering • bremsstrahlung• ionisation• annihilation• photoelectric effect • Compton scattering • Rayleigh effect• gamma conversion• e+e- pair production• synchrotron radiation• transition radiation• Cherenkov• refraction• reflection• absorption• scintillation• fluorescence• Auger
Geant4 Electromagnetic
Package
Standard Package
LowEnergy Package
Muon Package
Optical photon Packagespecialised according to - the particle type managed, - the energy range of processes covered.
Geant4 Geant4 Electromagnetic Electromagnetic Physics modelsPhysics models
• PhotonPhoton Mass Attenuation Coefficient
• PhotonPhoton Partial Interaction Coefficient (mass attenuation coefficients with only one process
activated)
• ElectronElectron CSDA range and Stopping Power (no multiple scattering, no energy fluctuations)
• ProtonProton CSDA range and Stopping Power (no multiple scattering, no energy fluctuations)
• AlphaAlpha CSDA range and Stopping Power (no multiple scattering, no energy fluctuations)
Physics quantities under studyPhysics quantities under study
Elements: Be, Al, Si, Fe, Ge, Ag, Cs, Au, Pb, U+ water
Energy range: 1 keV – 100 GeV photon10 keV – 1 GeV electron1 keV – 10 GeV proton1 keV – 1 GeV alpha
Testing activity has been automatised (INFN Gran Sasso Laboratory and KEK)
Ionisation potentials of the selected materials were modified w.r.t. the default values in Geant4, and were set as in the
NIST database.
- The simulation results were produced with Geant4 version 6.2.
- The Geant4 test process verifies that the accuracy of the physics models will not deteriorate in future versions of the toolkit with respect to the results presented here.
- Results obtained can be considered as an objective guidance to select the Geant4 electromagnetic models most appropriate to any specific simulation application.
Simulation resultsSimulation results
Statistical analysisStatistical analysis• The statistical analysis has been performed by means of a Goodness-of-Fit Statistical Toolkit, specialised in the comparison of data distributions
• The two alternative hypothesis under test are the following:
H0: Geant4 simulations = NIST data H1: Geant4 simulations ≠ NIST data
GoF test(χ2 test)
Distance between Geant4 simulations
and NIST reference data
Test result(p-value)
GoF Toolkit
The p-value represents the probability that the
test statistics has a value at leastat least as extreme as
that observed, assuming the null hypothesis is true
0 0 ≤ p ≤ 1≤ p ≤ 1
p < 0.05: Geant4 simulations and NIST data differ significantly
p > 0.05: Geant4 simulations and NIST data do not differ significantly
Test of Geant4 photon Test of Geant4 photon processesprocesses
Photon mass attenuation Photon mass attenuation coefficientcoefficientPhysics models under test:
• Geant4 Standard• Geant4 Low Energy – EPDL• Geant4 Low Energy – Penelope
Reference data:• NIST - XCOM
Mass attenuation coefficient in Fe
Geant4 LowE Penelope Geant4 StandardGeant4 LowE EPDLNIST - XCOM
• The three Geant4 models reproduce total attenuation coefficients with high accuracy
• The two Geant4 LowE models exhibit the best agreement with reference data
p-value stability study
H0 REJECTION AREA
Experimental set-up
Monochromaticphoton beam (Io)
Transmitted photons (I)
0
ln1
I
I
d
1 keV – 100 GeV
Compton interaction coefficientCompton interaction coefficientPhysics models under test:
• Geant4 Standard• Geant4 Low Energy – EPDL• Geant4 Low Energy – Penelope
Reference data:• NIST - XCOM
• The three Geant4 models reproduce Compton scattering cross sections with high
accuracy
• The Geant4 LowE – EPDL model exhibits the best overall agreement with reference data
Geant4 LowE Penelope Geant4 StandardGeant4 LowE EPDLNIST - XCOM
Compton interaction coefficient in Ag
cc )(
AVN
A
p-value stability study
H0 REJECTION AREA
1 keV – 100 GeV
Photoelectric interaction Photoelectric interaction coefficientcoefficientPhysics models under test:
• Geant4 Standard• Geant4 Low Energy – EPDL• Geant4 Low Energy – Penelope
Reference data:• NIST - XCOM
• The three Geant4 models reproduce photoelectric cross sections with high accuracy
• The two Geant4 LowE models exhibit the best agreement
Geant4 LowE PenelopeGeant4 LowE Penelope Geant4 StandardGeant4 StandardGeant4 LowE EPDLGeant4 LowE EPDLNIST - XCOMNIST - XCOM
Geant4 LowE Penelope Geant4 StandardGeant4 LowE EPDLNIST - XCOM
Photoelectric interaction coefficient in Ge
phph )(
AVN
A
H0 REJECTION AREA
p-value stability study
1 keV – 100 GeV
Pair production interaction Pair production interaction coefficientcoefficientPhysics models under test:
• Geant4 Standard• Geant4 Low Energy – EPDL• Geant4 Low Energy – Penelope
Reference data:• NIST - XCOM
• The three Geant4 models reproduce pair production cross sections with high accuracy
Geant4 LowE Penelope Geant4 StandardGeant4 LowE EPDLNIST - XCOM
Pair production interaction coefficient in Au
pppp )(
AVN
A
p-value stability study
H0 REJECTION AREA
p-va
lue
(pai
r pr
oduc
tion
inte
ract
ion
coef
fici
ent t
est)
1 keV – 100 GeV
Rayleigh interaction coefficientRayleigh interaction coefficientPhysics models under test:
• Geant4 Low Energy – EPDL• Geant4 Low Energy – Penelope
Reference data:• NIST - XCOM
The Geant4 Low Energy models seem to be in disagreement with the reference data for some materials
Geant4 LowE Penelope Geant4 LowE EPDLNIST - XCOM
Rayleigh interaction coefficient in Be
rr )(
AVN
A
Be 0.99 1
Al 0.32 <0.05
Si 0.77 <0.05
Fe 1 <0.05
Ge <0.05 0.39
Ag 0.36 0.08
Cs <0.05 <0.05
Au <0.05 <0.05
Pb <0.05 <0.05
U <0.05 <0.05
EPDLXCOM
PenelopeXCOM
1 keV – 100 GeV
Rayleigh interaction coefficientRayleigh interaction coefficient
Zaidi H., 2000, Comparative evaluation of photon cross section libraries for materials of interest in PET Monte Carlo simulation IEEE Transaction on Nuclear Science 47 2722-35
The disagreement is evident between 1 keV and 1 MeV photon energies.
For what concerns the Geant4 Low Energy EPDL model, the effect observed derives from an intrinsic inconsistency between Rayleigh
cross section data in NIST-XCOM and the cross sections of EPDL97, on which the model
is based.
Differences between EPDL97 and NIST-XCOM have already been highlighted in a
paper by Zaidi, which recommends the Livermore photon and electron data libraries
as the most up-to-date and accurate databases available for Monte Carlo
modeling.
EPDL 97
NIST
Rayleigh interaction coefficient in Au
rr )(
AVN
A
Test of Geant4 electron Test of Geant4 electron processesprocesses
Electron Stopping PowerElectron Stopping Power
centre
Experimental set-up
Physics models under test:• Geant4 Standard• Geant4 Low Energy – Livermore• Geant4 Low Energy – Penelope
Reference data:• NIST ESTAR - ICRU 37
The comparison test exhibited that all the Geant4 physics models are in
excellent agreement with the NIST-ESTAR reference data.
The test has not pointed out any particular difference among the three
sets of models.
p-value stability study
H0 REJECTION AREA
)(1
SP dx
dE
Geant4 LowE Penelope Geant4 StandardGeant4 LowE LivermoreNIST - ESTAR
Electrons are generated with random direction at the center of the box and stop inside the box
10 keV – 1 GeV
CSDA: particle range without energyloss fluctuations and multiple scattering
Maximum step allowed in tracking particles was set about1/10 of the expected range value, to ensure the accuracy of the calculation
Electron CSDA RangeElectron CSDA RangeCSDA: particle range without energyloss fluctuations and multiple scattering
Physics models under test:• Geant4 Standard• Geant4 Low Energy – Livermore• Geant4 Low Energy – Penelope
Reference data:• NIST ESTAR - ICRU 37
The three Geant4 models are equivalent
Geant4 LowE Penelope Geant4 StandardGeant4 LowE LivermoreNIST - ESTAR
CSDA range in U p-value stability study
H0 REJECTION AREA
10 keV – 1 GeV
Test of Geant4 proton and Test of Geant4 proton and alpha processesalpha processes
Protons and alpha particlesProtons and alpha particles• Comparison of Geant4 models with respect to ICRU 49 protocol
• Geant4 LowE Package has ICRU 49 parameterisations as one of its modelsverification, not validation
• The Ziegler parameterisations are as authoritative as the ICRU 49 referencecomparison rather than
validation
NIST PSTAR – ICRU 49
• StandardStandard• Low Energy – ICRU 49Low Energy – ICRU 49• Low Energy – Ziegler 85Low Energy – Ziegler 85• Low Energy – Ziegler 2000Low Energy – Ziegler 2000
Geant4 models under test:
Reference data:
ProtonsProtons Alpha particlesAlpha particles
• StandardStandard• Low Energy – ICRU 49Low Energy – ICRU 49• Low Energy – Ziegler 77Low Energy – Ziegler 77
Geant4 models under test:
NIST ASTAR – ICRU 49
Reference data:
Proton Proton processesprocesses
Stopping power in Al
Geant4 LowE Ziegler 1985Geant4 LowE Ziegler 2000Geant4 StandardGeant4 LowE ICRU 49NIST - PSTAR
+
H0 REJECTION AREA
Stopping power: p-value stability study
H0 REJECTION AREA
CSDA range: p-value stability study
1 keV – 10 GeV
Alpha particles processesAlpha particles processes
H0 REJECTION AREA
Stopping power: p-value stability studyCSDA range in Si
Geant4 LowE Ziegler 1977 Geant4 StandardGeant4 LowE ICRU 49NIST - ASTAR
The complex physics modeling of ion interactions in the low energy range is addressed by the Geant4 Low Energy package and it represented one of the main motivations for the developing of this package.
1 keV – 1 GeV
ConclusionsConclusions
• Systematic validationSystematic validation of Geant4 electromagnetic models against ICRU protocols and NIST reference data
• Validation based on a rigorousrigorous, quantitativequantitative statistical analysis of test results
• All Geant4 electromagnetic models are found in good agreement with the reference data
• Quantitative statistical analysis documents the respective strengths of
the Geant4 models in detail, for each of the physics distributions considered in the NIST reference.
The quantitative documentation presented provides an objective guidance to select the Geant4 electromagnetic models most appropriate to any specific
simulation application.
This work is a part of a wider project for the systematic validationsystematic validation of Geant4 Geant4 electromagnetic physics modelselectromagnetic physics models,
covering also other particles types, physics processes and energy ranges outside the
scope of the NIST reference data.