sensitivities of monte carlo simulations to ......27 novembre 2018 | slide 10 cea | 10 avril 2012...

SENSITIVITIES OF MONTE

CARLO SIMULATIONS TO

NUCLEAR RESONANCE

PARAMETERS

E. Vandermeersch

P. Tamagno

C. De Saint Jean

NOVEMBER 27, 2018 | SLIDE 1CEA | 10 AVRIL 2012WPEC - SG44 AND 46

CROSS SECTIONS EVALUATION

CONTEXT

27 NOVEMBRE 2018

| SLIDE 2

CEA | 10 AVRIL 2012

+

Covariances

,... ,, FissionOMPRRRx

Neutron/Gamma

Transport

,...),,,,( ji fissionOMURRRRRn xxxxE

Integral Data

Assimilation

on Parameters

CROSS SECTIONS EVALUATION CONTEXT NOW

Processing

Real Life Application

IntegralExperiments

A long way between nuclear physics and reactor physicsFormat/processing issues Uncertainty a side product

– Expérience

– Model

+

Covariances

,... ,, FissionOMPRRRx

Neutron/Gamma

Transport

,...),,,,( ji fissionOMURRRRRn xxxxE

Integral Data

Assimilation

on Parameters

CROSS SECTIONS EVALUATION IN THE FUTURE ?

Real Life Application

IntegralExperiments

Direct connection between Nuclear Physicists and Reactor PhysicistsImpact of simplified nuclear data representation (format/processing)Neutronic parameters sensitivities (keff …) to basic nuclear data ((E),x)Better uncertaitny propagation covariances replaced by pdfs

– Expérience

– Model

CROSS SECTIONS EVALUATION

Various nuclear reaction models are used to describe the cross section

Nuclear reaction parameters are the initial information (x).

This work was limited to the R-Matrix formalism in the Resolved Resonance Range (RRR).

Future Works on RRR/URR and Continuum

27 NOVEMBRE 2018 | SLIDE 5CEA | 15 MAY 2018

Resonances, Coumpound nucleus et al. !

239Pu total cross section

Optical Models

Statistical Model

Transmission Models

R Matrix

',,, RaEx ca

aca SDRax ,,,, 0

,...,,,,2 WVdax cc

CONRAD COde for Nuclear Reaction Analysis and Data assimilation

Can work with various formalisms in Resolved Resonances Range (RRR) (R-Matrix

approximation, Reich-Moore, Multi-Level Breit-Wigner), Unresolved Resonances

Range (URR) (Average R-Matrix) and continuum (Optical model)

Used to compute cross sections 𝜎𝑖 ,𝑟 and their sensitivities 𝑆𝜎𝑖,𝑟, Γi to resonance

parameters Γi∶

𝑆𝜎𝑖,𝑟, Γi = න

𝐸,Ω

𝜕𝜎𝑖 ,𝑟 𝐸, Ω

𝜕Γi⋅ Γi𝑑𝐸𝑑Ω

NUCLEAR PHYSIC TOOL

AND NEUTRONIC CALCULATION TOOLS


TRIPOLI-4 neutron/gamma and electron transport in materials

Used to compute neutronic observables and their sensitivities𝑆𝜌,𝜎𝑛,𝑐 to cross sections 𝜎𝑖 ,𝑟 :

𝑆𝜌,𝜎𝑛,𝑐 = න

𝑟, 𝐸,Ω

𝜎𝑛,𝑐 𝑟, 𝐸 ⋅𝜕𝜌 𝑟, 𝐸, Ω

𝜕𝜎𝑛,𝑐 𝑟, 𝐸𝑑𝐸𝑑²𝛺𝑑3𝑟

PERTURBATIONS AND SENSITIVITIES

IN MONTE CARLO SIMULATIONS

Exact Perturbations & IFP method

Exact perturbation for two states of the reactor, with 𝓟 the production operator, 𝓚 the

disappearance operator, 𝜙 the direct flux and 𝜙† the adjoint flux:

𝛿𝜌 =𝜙2†, (𝜆2Δ𝓟 − Δ𝓚)𝜙1

𝜙2†, 𝓟1𝜙1


Notice that the adjoint flux can

be estimated with the Iterated

Fission Probability IL:

𝜙† ∝ 𝐼𝐿 =ෑ

𝑔=1

𝐿𝑘𝑔

𝑘𝑔→∞

F

A

C

F C A

C

A

Generation 1 Generation 2

N

IFP cycle principle

CONRAD AND TRIPOLI-4 JUNCTION

IFP algorithm + Link to CONRAD calculation

The IFP method uses the following algorithm:

This algorithm can be modified to compute sensitivities to resonance parameters with

CONRAD:


For each simulationFor each collision {

Retrieve reactionsFor each reaction

For each nucleus{Retrieve & compute parameters (cross section, local flux)Compute sensitivity or perturbationAdd score to required integrated value

}}

𝑆𝜌 ,Γi = න

𝐸,Ω

Γi ⋅𝜕𝜌 𝐸, Ω

𝜕Γi𝑑𝐸𝑑Ω = න

𝐸,Ω

𝑟

𝜕𝜌 𝐸, Ω

𝜕𝜎𝑖 ,𝑟 𝐸, Ω⋅𝜕𝜎𝑖 ,𝑟 𝐸, Ω

𝜕Γi⋅ Γi 𝑑𝐸𝑑Ω

SENSITIVITIES COMPUTATION

Extended IFP method


RESULTS

27 NOVEMBRE 2018

| SLIDE 10

CEA | 10 AVRIL 2012

RESULTS


System studied

Plutonium-Solution-Thermal (ICSBEP):

- 239Pu/240Pu: 20

PST scheme

RESULTS


239Pu 𝐸𝜆 sensitivities

27 NOVEMBRE 2018 | SLIDE 13CEA | 10 AVRIL 2012

RESULTS

239Pu 𝜆 sensitivities


RESULTS


RESULTS


Details of the cross sections sensitivities for the first 240Pu resonance. So-called "Sensitivity (E) to GN1/Eλ1" are in

fact σr𝜕ρ

𝜕σr E

𝜕σr E

𝜕ΓE , with r all the reactions possible for 240Pu

CONCLUSION

27 NOVEMBRE 2018

| SLIDE 17

CEA | 10 AVRIL 2012

CONCLUSION

A functional new method has been implemented, tested, compared withthe other methods.

Add and test new formalisms : RRR/URR/Continuum nuclear reactionsmodels

Improvements:o Short term Improve TRIPOLI-4/JIMMY/CONRAD coupling.o Mid-term Remove as much as possible format/processing


APPENDIX

Resizing of the energy grid

Each resonance influences only a few number of neighbours:


Neighboursresonances

Targeted parameters

Energy Grid

239Pu Fission cross section, with the 31st resonance 𝐸𝜆 modified by 5%

APPENDIX

Results


Impact of the direct batches number.

APPENDIX

Cross sections


239Pu radiative capture (MT=102), fission (MT=18) and elastic (MT=2) cross section

240Pu radiative capture (MT=102), fission (MT=18) and elastic (MT=2) cross section

APPENDIX

Cross sections


235U radiative capture (MT=102), fission (MT=18) and elastic (MT=2) cross section

Figure B.4 - 238U radiative capture (MT=102), fission (MT=18) and elastic (MT=2) cross section

sensitivities of monte carlo simulations to ......27 novembre 2018 | slide 10 cea | 10 avril 2012...

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