Variance Reduction of Fusion and Fission Neutron TransportProblems Using the ADVANTG Hybrid Code

Bor Kos, Ivan KodeliJozef Stefan Institute

Jamova cesta 391000 Ljubljana, Slovenia

bor.kos@ijs.si, ivan.kodeli@ijs.si

JET Contributors1

EUROfusion Consortium, JET, Culham Science CentreAbingdon, OX14 3DB, United Kingdom

ABSTRACT

The Automated Variance Reduction Generator (ADVANTG) [1] code is a hybrid transport codedeveloped by ORNL (Oak Ridge National Laboratory), utilizing the Denovo [2] deterministic neu-tron transport code and MCNP [3] a widely used Monte Carlo (MC) transport code.

ADVANTG’s reliability and consistent performance has to be tested on a variety of differentexample problems. The performance of ADVANTG on three different examples encompassing avariety of neutronics applications is presented in this paper.

1 INTRODUCTION

Hybrid methods in a good way combine the best attributes of Monte Carlo and deterministicmethods. Such hybrid computational radiation transport codes thus expand the potential for solvinglarge, complex real-world problems. The complementary use of both methods opens the way for thesimulation not achievable with “analog” MC simulations such as deep penetration or very large andcomplex streaming geometries.

Firstly the use of ADVANTG for accelerating MC simulations of deep penetration benchmarkexperiments such as the NESDIP-3 and JANUS-1 experiments is presented. In connection with thisthe importance of reducing statistical uncertainty of MC simulations when validating new nucleardata is shown.

Secondly ADVANTG coupled with MCNP is used to determine neutron flux and dose in a largestreaming geometry - the JET tokamak. More specifically the acceleration of the simulation in accor-dance with the NEXP benchmark experiment. The aim of this experiment is to measure the neutronstreaming through ducts and the dose rates outside of the JET Torus Hall.

Lastly, the use of ADVANTG for accelerating MC simulations on a newly developed detailedmodel of the Krsko nuclear power plant is presented. The aim of this simulations is to determinethe neutron dose fields in the steam generator and reactor coolant pump cubicles where “analog”simulations are difficult because of large attenuation of neutron flux between the reactor core andcubicle.

1See the Appendix of F. Romanelli et al., Proceedings of the 25th IAEA Fusion Energy Conference 2014, SaintPetersburg, Russia

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2 ADVANTG HYBRID CODE

The ADVANTG hybrid code generates space and energy dependent weight-window bounds using3D discrete ordinates solution of the adjoint transport equation (1):

〈Φ†,LΦ〉 = 〈Φ,L†Φ†〉 (1)

where L is the transport operator, and Φ is the angular flux.The fundamental concept is to generate an approximate importance function from a fast-running

deterministic adjoint calculation and use the importance map to construct variance reduction param-eters, more specifically weight window parameters, which can accelerate the tally convergence inthe MC simulation. ADVANTG’s approach is based on the Consistent Adjoint Driven ImportanceSampling (CADIS) where the statistical weight of particles is inversely proportional to the adjointflux:

w(P ) =R

Φ†(P )(2)

where w is the particle statistical weight, R is a response at some location and P is the phase spaceof (r, E, Ω). The Forward-Weighted CADIS (FW-CADIS) [4] method is used to determine globalweight window parameters.

3 EXAMPLE PROBLEMS

ADVANTG 3.0.1. was released in the summer of 2015. Since then we have thoroughly testedits reliability and consistent performance on several neutronic transport problems. The first problemconsists of two well known shielding benchmarks experiments from the Radiation shielding anddosimetry experiments database (SINBAD) [5] NESDIP-3 and JANUS Phase 1.

The second problem is a fusion relevant experiment, where neutron dose is measured far awayfrom the plasma source inside the personae entrance of the JET tokamak building. This is a largestreaming problem with complex geometry and high energy fusion neutrons. Analog Monte Carlosimulations of this problem are time consuming, so to achieve relevant statistical uncertainty in alimited time span, the calculations to support the experiment were accelerated using ADVANTG.

The last problem presented is a combination of streaming and high attenuation regions. Auto-mated weight-window parameter generation was successfully performed using ADVANTG to sup-port neutron dose calculations inside of the reactor coolant pump and steam generator cubicles of theKrsko NPP.

3.1 NESDIP-3 and JANUS Phase 1

The NESDIP-3 experiment was performed to study the neutron transport in a shielding config-uration simulating the radial shield of pressurized water reactor. The experimental setup consistsof alternating regions of water, steel, mild steel and cavities. The neutron source consists of 93 %enriched uranium plates driven by a thermal flux originating from the NESTOR reactor.

Similarly, the JANUS Phase 1 (Neutron Transport Through Mild and Stainless Steel) experimentutilizes a similar source but is intended to simulate fast reactor conditions. The fission plate is fol-lowed by a mild steel block, a block of stainless steel and another block of mild steel. Contrary tothe NESDIP-3 experiment this is a pure steel experiment and not a mixture of water and steel. Thisconfiguration has a significant impact on the results of statistical tests and will be investigated further.

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Both experiments were recently reviewed and were found to be of benchmark quality [6, 7]. Theywere chosen to test ADVANTG’s capabilities because of the shielding setup well documented uncer-tainties and other geometrical and physical relevant data to perform simulations. To test ADVANTGwe looked at two statistical tests, the Figure-Of-Merit (FOM) (3) and the convergence of the relativeMC error of the tally result (K) (4):

FOM =1

∆R2 · T(3)

K =√NPS ·∆R (4)

where ∆R is the relative statistical error, T time of simulations and NPS the number of particlehistories. On the left side of Figure 1 the normalized values of the FOM (3) to the analog simulation(FOM C/Canalog) are given against the NPS. On the right side of Figure 1 the convergence of therelative MC errors of the tally (4) results are given against the NPS. Significant increase of the FOMof the simulations is seen for both the NESDIP and Janus experiments. When using ADVANTG lessCPU time is needed to achieve the desired statistical uncertainty.

It should be noted that these benchmark experiments are ideal to test newly evaluated nuclear data,such as new cross sections for iron isotopes, which is of major significance for fusion applications.By using ADVANTG the statistical uncertainties of the MC simulations is significantly reduced andthe impact on the results is clearly seen in (2) because of the newly evaluated nuclear data. Figure2 shows the C/E (Calculation over Experiment) at different tally locations, which are increasinglydistant from the neutron source, for the newly evaluated data for iron (CIELO) and the ENDF/B-VII.1 libraries speed up with ADVANTG and an analog simulation with the ENDF/B-VII.1 library.

(a) FOM (b) MC relative error convergence

Figure 1: Statistical tests of the two benchmark experiments. Increase of the FOM and faster conver-gence of the relative error for the ADVANTG results is seen.

3.2 NEXP experiment

Due to the complexity of the geometry and the physical processes involved, thermoluminescencemeasurements of neutron streaming far from the plasma source of the ITER tokamak are challenging.It is therefore mandatory to experimentally verify nuclear data and transport codes which will beused for neutron transport simulations. One such experiment is the NEXP benchmark streaming

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(a) NESDIP-3 results (b) JANUS-1 results

Figure 2: Results of the Calculations over Experiment (C/E) for different nuclear data evaluations.Faster convergence of the ADVANTG results is seen.

experiment where neutron streaming was and will be measured in the personnel access labyrinth ofthe JET tokamak building.

The DT campaign with its 14 MeV neutrons is especially difficult to simulate because of largestreaming effects. The problem will be simulated using well-established MC techniques, determin-istic and newly developed hybrid codes, such as ADVANTG [8]. To test ADVANTG’s usability infusion applications we performed several variations of the ADVANTG input parameters [9]. The twomost important ones were found to be the mesh which is used to define the geometry of the deter-ministic DENOVO calculation and the multi-group nuclear data libraries used for the deterministiccalculations.

We tested 4 different mesh voxel sizes. The default size was found to sufficiently describe theproblem geometry shown in comparison with the original MCNP geometry in Figure 3. On the leftside of Figure 4 the absolute values of the flux and absolute error are given against the NPS for atally location inside the personnel labyrinth. On the right side of Figure 4 the normalized values ofthe FOM to the analog simulation (FOM C/Canalog) are given against the NPS. Smoother convergenceand FOM statistical test of the finer mesh and uneven convergence of the coarser meshes is observed.It should be noted that ADVANTG does not introduce any bias to the results.

Six different multi-group data libraries were tested. The 27n19g and the 200n47g are generalshielding libraries based on the ENDF/B-VII.0 data evaluation. The BPLUS and and DPLUS librariesare also based on the ENDF/B-VII.0 nuclear data evaluation and use the BUGLE-96 and DABL-69energy group structures respectfully. The 211n42g and 47n19g libraries are based on the FENDL-3nuclear data evaluation. On the left side of Figure 5 the absolute values of the flux and absoluteerror are given against the NPS for a tally location inside the personnel labyrinth. On the right sideof Figure 5 the normalized values of the FOM to the analog simulation (FOM C/Canalog) are givenagainst the NPS. Smoother convergence and FOM statistical test of the finer energy group librariesis observed. As expected the DPLUS and FENDL based bespoke fusion libraries perform best. Theperformance of the 27 group general shielding library (27n19g) is surprisingly good but welcomebecause of its low memory requirements.

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(a) MCNP geometry model. (b) DENOVO default mesh geome-try model.

Figure 3: Comparison of the original MCNP problem geometry and the DENOVO Cartesian ge-ometry. The tally locations of the NEXP streaming benchmark are located in the personel entrancelabyrinth in the top-left corner of the model.

(a) Calculation of the flux and the absolute statisti-cal uncertainty.

(b) Calculation over analog calculation of the FOMstatistical test.

Figure 4: Results of the flux and the Figure-Of-Merit statistical test for different deterministic calcu-lation mesh sizes.

(a) Calculation of the flux and the absolute sta-tistical uncertainty.

(b) Calculation over analog calculation of theFOM statistical test.

Figure 5: Results of the flux and the Figure-Of-Merit statistical test for different multi-group nucleardata libraries used for the deterministic calculation.

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3.3 Krsko NPP

A new detailed model based on the available data and CAD2 models of the Krsko NPP wasproduced in 2015 [10] using a newely developed method for CAD to MCNP geometry conversion[11]. The model was used to determine optimal shielding locations and shield configurations toreduce neutron dose rates in the steam generator and reactor coolant pump cubicles. Because this is astreaming and shielding problem variance reduction techniques are needed to get statistically relevantresults. In [10] a MC splicing technique was used but this introduces additional uncertainties. Theintegrated MCNP weight window generator was difficult to use. Several iterations were needed toimprove results.

Finally, ADVANTG was tested on this difficult streaming/shielding problem. The BPLUS shield-ing library was used in combination with a fine mesh. The mesh was defined in such a way to ac-curately describe all the major neutron pathways. A tally region was defined in the southern cubiclebetween the hot and cold leg penetrations. To check that optimal weight window parameters wereproduced a contributon field was plotted and is show in Figure 6. A contributon field is calculated bymultiplying the flux and the adjoint. It shows the most important regions that contribute to the tallyin question from the neutron source - the core.

Figure 6: Contributon field in the XY-cross section of the Krsko NPP for a tally located in thesouthern cubicle.

Resulting weight window parameters significantly speed up the simulations. No neutron historieswere tallied in the region of interest during the analog simulation of 107 neutrons. Using ADVANTGand simulating the same number of particle histories the tally uncertainty is below 1 %.

Absolute results of the neutron dose rate were compared to the calculations speed-up with the in-tegrated MCNP weight-window generator. The results were within the statistical uncertainty. Furtheroptimization of the source description is needed and will be presented in the future.

2Computer Assisted Design

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4 CONCLUSION

Newly developed transport codes have to be validated on several cases before they can be usedin everyday particle transport simulations. Three cases were chosen to encompass a large neutronicsfield of applications.

Simple setups, such as the JANUS Phase 1 and NESDIP-3 benchmark experiments were ideal fortesting ADVANTG’s capability in producing optimal weight-window variance reduction parameters.Results were compared to the experiment to ensure no bias was in introduced. A significant speed upof relative error convergence and Figure-Of-Merit statistical test was observed through the varyingmeasurement positions for the NESDIP-3 experiment and only slight increase of the relative errorconvergence and FOM for the JANUS Phase 1. These results will be investigated further as they areinteresting from a physics point of view.

Fusion neutronics problems include a whole new set of physical phenomena because of higherenergies of the DT neutrons. ADVANTG has to be tested at these energies. A challenging, butcurrent problem, was chosen to test the sensitivity of the final MC results on the input parametervariations. In this paper we have shown the sensitivity on the size of the deterministic mesh and onthe multi-group nuclear data libraries used for the determination of the variance reduction parameters.ADVANTG’s performance is satisfactory even with default input parameters but is improved oncethe user optimizes the input parameters based on the physical knowledge of the problem.

A practical application of the newly developed hybrid code ADVANTG on a difficult stream-ing/shielding fission problem was performed for the Krsko NPP. ADVANTG proved to be easy to use,significantly faster than ordinary variance reduction techniques such as the MCNP weight-windowgenerator and produces statistically significant results in a fraction of a time of analog simulations.

However there are some limitations of the code, for example large computer memory require-ments when dealing with large problems and multi-group data libraries, limited source specificationand a limitation to a Cartesian deterministic geometry. The program is at an early stage of use andhas room for improvement but nonetheless gives excellent results in return for little user effort.

ACKNOWLEDGMENTS

We would like to thank NEK for their support and for sharing the 3D CAD model of the reactorbuilding and all other blueprints of the RB and RV.

Part of this work has been carried out within the framework of the EUROfusion Consortium andhas received funding from the Euratom research and training programme 2014-2018 under grantagreement No 633053. The views and opinions expressed herein do not necessarily reflect those ofthe European Commission.

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REFERENCES

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