Monte Carlo methods in Monte Carlo methods in ADS experimentsADS experiments

Study for state exam 2008Study for state exam 2008

Mitja MajerleMitja Majerle

“Phasotron”

and

“Energy Plus Transmutation”

setups

(schematic drawings)

What are Accelerator Driven What are Accelerator Driven Systems ?Systems ?

Accelerator Driven SystemsAccelerator Driven Systems

Subcritical reactorSubcritical reactor Wider choice for reactor fuel (Wider choice for reactor fuel (238238U, U, 232232Th)Th) Transmutation of nuclear wasteTransmutation of nuclear waste Increased safetyIncreased safety

AcceleratorAccelerator Protons or light ions of energy around 1 GeVProtons or light ions of energy around 1 GeV Very high powers (hundreds of MW)Very high powers (hundreds of MW) Stable beamStable beam

Spallation reactionSpallation reaction

SpallationSpallation(process in which hadrons or light ions are ejected (process in which hadrons or light ions are ejected

from the nucleus due to impact of relativistic particle)from the nucleus due to impact of relativistic particle)

In textbooks divided In textbooks divided to two phases:to two phases: Intra Nuclear CascadeIntra Nuclear Cascade De-excitation De-excitation

(evaporation, fission)(evaporation, fission) INC phase has to be INC phase has to be

corrected at lower corrected at lower energies to fit the energies to fit the experiments – experiments – preequilibrium phasepreequilibrium phase

CalculationsCalculations

Monte Carlo method:Monte Carlo method: Event by event simulation on nuclear scale Event by event simulation on nuclear scale Accuracy Accuracy sqrt(N) sqrt(N) sqrt(calculation time), sqrt(calculation time), Parallelization is possible (MPI, PBS)Parallelization is possible (MPI, PBS)

Used codes: MCNPX, FLUKAUsed codes: MCNPX, FLUKA Resources:Resources:

CESNET Meta CentrumCESNET Meta Centrum 56 processors on OJS (MPI and PBS)56 processors on OJS (MPI and PBS)

How MC code worksHow MC code works Pseudorandom numbers - Pseudorandom numbers - Example - photon source in matter:Example - photon source in matter:

Determine track (Determine track (for direction)for direction) Determine where the reaction will happen - l=1/Determine where the reaction will happen - l=1/ ln( ln( Determine which interaction will happen (photoeffect, Determine which interaction will happen (photoeffect,

Compton, pair production …) - Compton, pair production …) - Determine angles – Determine angles – , energies of generated particles , energies of generated particles

(physics)(physics) Loop until particles escape from the phase space of interestLoop until particles escape from the phase space of interest

Tallying:Tallying: Count the particles that passed through selected phase Count the particles that passed through selected phase

space (surfaces, volumes, deposited energy …)space (surfaces, volumes, deposited energy …) Precision and accuracy:Precision and accuracy:

Wrong physics => wrong results Wrong physics => wrong results Central limit theorem – for large N, Central limit theorem – for large N,

results distribution approach results distribution approach normal distributionnormal distribution

Phasotron experimentPhasotron experiment Simple, lead target (diameter 10 cm, Simple, lead target (diameter 10 cm,

length 0.5 m)length 0.5 m) Intensive protons 660 MeV, 10 minIntensive protons 660 MeV, 10 min Activation detectors, iodine samples (Activation detectors, iodine samples (129129I)I)

Simulated neutron spectrumSimulated neutron spectrum

NAA experimental dataNAA experimental data

1E-8

1E-7

1E-6

1E-5

1E-4

0 10 20 30 40 50

Position along the target [cm]

B [g

-1 p

roto

n-1

] Au-198

Au-196

Au-194

Au-193

Au-192

Au-191

proton range

Exp/sim comparisonsExp/sim comparisons

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

0 10 20 30 40 50

Position along the target [cm]

Exp

erim

ent/

calc

ula

tio

n

Na-24Au-196Au-194Au-192Au-191

MCNPX - INCL4/ABLA

MCNPX – CEM03

FLUKA

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

0 10 20 30 40 50

Position along the target [cm]

Exp

erim

ent/

calc

ula

tio

n

Na-24Au-196Au-194Au-192Au-191

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

0 10 20 30 40 50

Position along the target [cm]

Exp

erim

ent/

calc

ula

tio

n

Na-24Au-196Au-194Au-192Au-191

Proton influenceProton influence

Proton fluence in the target central plane – around 30th cm protons are scattered out of the target

Contribution of proton reactions to total reaction rate

0

1

2

3

4

5

6

0 10 20 30 40

Position along the target [cm]

Prod

uctio

n ra

te [1

0-7

g-1

pro

ton

-1]

sum(n,7n)(p,6np)

Iodine samplesIodine samples

0

0.5

1

1.5

2

I-130 I-128 I-126 I-124 I-123 I-121 I-120 I-119 I-118

Produced isotope

expe

rim

ent/s

imul

atio

n

I-127

I-129

0

0.5

1

1.5

2

I-130 I-128 I-126 I-124 I-123 I-121 I-120 I-119 I-118

Produced isotope

expe

rim

ent/s

imul

atio

n

I-127

I-129

Sample 1 – 9th cm Sample 2 – 21st cm

Systematic uncertaintiesSystematic uncertainties

Simulations with changed Simulations with changed parameters are comparedparameters are compared Beam parameters (3 mm ~ 15% Beam parameters (3 mm ~ 15%

uncertainty)uncertainty) Detector displacement (1 mm ~ <5%)Detector displacement (1 mm ~ <5%)

Worse situation:Worse situation: Around 30Around 30thth cm, protons exit the target, cm, protons exit the target,

beam parameters have bigger influencebeam parameters have bigger influence Iodine samples – not precise placementIodine samples – not precise placement

Energy Plus TransmutationEnergy Plus Transmutation

SABRINA plot from MCNPX input file, provided by J. Šolc.

MC analysisMC analysis

Influence of setup parts Influence of setup parts polyethylene boxpolyethylene box iron and detectors have negligible influenceiron and detectors have negligible influence

Systematic uncertainties – Systematic uncertainties – displacements:displacements: incident beam : 3mm = 15-20% uncertaintyincident beam : 3mm = 15-20% uncertainty detectors displacement: 5mm = 20%detectors displacement: 5mm = 20% The calculations apply only to threshold The calculations apply only to threshold

activation detectors.activation detectors.

PolPolyethylene box –yethylene box –biological shieldingbiological shielding

1E-8

1E-7

1E-6

1E-5

1E-4

1E-3

1E-2

1E-1

1E-9 1E-6 1E-3 1E+0 1E+3Energy [MeV]

Nn

eu

tro

ns [

cm

-2 p

roto

n-1]

target-blankettb+boxtb+box+Cd

10-9 10-6 10-3 1 103

10-2

10-3

10-4

10-5

10-6

10-7

10-8

10-1

1E-5

1E-4

1E-3

1E-2

1E-1

1E+0

1E+1

1E-9 1E-6 1E-3 1E+0 1E+3Energy [MeV]

Nn

eu

tro

ns [

pro

ton-1

]

without shielding

with shielding

10-9 10-6 10-3 1 103

10-1

10-2

10-3

10-4

10-5

1

10

Neutron spectra inside box

Neutron spectra emitted to environment

0.8

0.9

1.0

1.1

1.2

1.3

0.1 1 10 100 1000

Energy [MeV]

Rat

io

tg+box/tgtg+box+Cd/tg

10-1 1 10 102 103

Neutron production, kNeutron production, keffeff

At 1.5 GeV At 1.5 GeV experiment, 50 experiment, 50 neutrons were neutrons were produced per protonproduced per proton

Maximum production Maximum production (proton(proton-1-1 GeV GeV-1-1) in 1-) in 1-1.5 GeV range1.5 GeV range

kkeffeff=0.202=0.202 flooded with water kflooded with water keffeff

rises to 0.41 (and rises to 0.41 (and heavy water 0.26)heavy water 0.26)

Total neutron production with the EPT setup.

0

5

10

15

20

25

30

35

0 1 2 3

Beam energy [GeV]

Nn

eutr

on

s[p

roto

n-1

GeV

-1]

MC vs. experimentMC vs. experiment

Good agreement Good agreement below 1.25 AGeVbelow 1.25 AGeV

Wrong predictions Wrong predictions at 1.5 and 2 GeVat 1.5 and 2 GeV

Similar behavior Similar behavior reported for thin reported for thin target experiments target experiments – could there be – could there be any connection ?any connection ?

0

1

2

3

4

0 5 10 15

Radial distance [cm]

Bex

p/B

sim

Au-196Au-194Au-193Au-192Au-191

FLUKA calculations of reaction rates in Au detectors placed in the first gap

ConclusionConclusion Phasotron experimentPhasotron experiment

Completely analyzedCompletely analyzed Good agreement with MC codesGood agreement with MC codes Uncertainties ca. 15%Uncertainties ca. 15%

EPTEPT All performed experiments (4x protons, 2x deuterons) were All performed experiments (4x protons, 2x deuterons) were

simulatedsimulated Significant disagreement with MC codes at higher energiesSignificant disagreement with MC codes at higher energies Uncertainties 30%Uncertainties 30%

OutlooksOutlooks MC in spectrometry – revision of spectrometry methods MC in spectrometry – revision of spectrometry methods

used at our work (precision of different corrections: used at our work (precision of different corrections: geometrical, COI …)geometrical, COI …)

Is EPT disagreement connected with thin target experiments Is EPT disagreement connected with thin target experiments ??

Acknowledgments to META Centrum, where most of presented calculations were performed.