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.