Fischer, Ulrich

Nunnenmann, Elena

Stieglitz, Robert

English

KITopen

EPJ Web of Conferences 146, 09025 (2017) DOI: 10.1051/epjconf/201714609025ND2016Sensitivity and uncertainty analysis for the tritiumbreeding ratio of a DEMO fusion reactor with a heliumcooled pebble bed blanketElena Nunnenmanna, Ulrich Fischer, and Robert StieglitzInstitute for Neutron Physics and Reactor Technology, Karlsruhe Institute of Technology, Hermann-von-Helmholtz-Platz 1, 76344Eggenstein-Leopoldshafen, GermanyAbstract. An uncertainty analysis was performed for the tritium breeding ratio (TBR) of a fusion powerplant of the European DEMO type using the MCSEN patch to the MCNP Monte Carlo code. The breedingblanket was of the type Helium Cooled Pebble Bed (HCPB), currently under development in the EuropeanPower Plant Physics and Technology (PPPT) programme for a fusion power demonstration reactor (DEMO).A suitable 3D model of the DEMO reactor with HCPB blanket modules, as routinely used for blanket designcalculations, was employed. The nuclear cross-section data were taken from the JEFF-3.2 data library. Forthe uncertainty analysis, the isotopes H-1, Li-6, Li-7, Be-9, O-16, Si-28, Si-29, Si-30, Cr-52, Fe-54, Fe-56,Ni-58, W-182, W-183, W-184 and W-186 were considered. The covariance data were taken from JEFF-3.2where available. Otherwise a combination of FENDL-2.1 for Li-7, EFF-3 for Be-9 and JENDL-3.2 for O-16were compared with data from TENDL-2014. Another comparison was performed with covariance data fromJEFF-3.3T1. The analyses show an overall uncertainty of ±3.2% for the TBR when using JEFF-3.2 covariancedata with the mentioned additions. When using TENDL-2014 covariance data as replacement, the uncertaintyincreases to ±8.6%. For JEFF-3.3T1 the uncertainty result is ±5.6%. The uncertainty is dominated by O-16,Li-6 and Li-7 cross-sections.1. IntroductionThe Helium Cooled Pebble Bed (HCPB) blanket is oneof several types of breeding blanket currently underdevelopment in the European Power Plant Physics andTechnology (PPPT) programme for a fusion powerdemonstration reactor (DEMO). An important function ofthe blanket of DEMO is the capability to breed sufficienttritium. This is described by the tritium breeding ratio(TBR) which is the ratio of the tritium produced in theblanket divided by the tritium consumed in the fusionreactions in the plasma. To calculate the TBR, neutronicscodes such as MCNP [1] are employed. As they rely onnuclear cross-section data with finite accuracy, uncertaintyanalyses need to be performed to estimate the uncertaintymargin of the TBR result.Sensitivity and uncertainty analyses of the TBR of theHCPB blanket module have already been undertaken fora mock-up of a single breeding blanket [2] and for thisbreeding blanket integrated into the ITER port for blankettesting [3]. TBR calculations without uncertainty analysiswere routinely performed for the HCPB blanket integratedinto a DEMO sector model [4].The objective of this work was to calculate the nucleardata uncertainty of the TBR for the DEMO reactor witha full HCPB blanket, using the track length estimatorapproach of MCNP patched with the MCSEN code [6].The Sandwich code [7] is used to create sensitivity profiles,a e-mail: elena.nunnenmann@kit.educalculate integrated sensitivities, and use covariance datafrom JEFF-3.2 and other sources to assess uncertainties.2. The DEMO geometry with integratedHCPB blanketA slightly revised version of the model used in [4]was made available for the present work. It was createdfrom a generic 11.25◦ sector CAD DEMO model withoutblankets, into which the blanket modules where placed onthe CAD platform. This model was converted into MCNPgeometry using the McCAD [5] automated conversiontool. Into the converted model, the manually createdinterior structure of the blanket modules was insertedutilising the repeated structure technique available withMCNP.The CAD DEMO model can be seen in Fig. 1. Intoroidal direction there is one full inboard blanket moduleon the inboard side and 1.5 outboard blanket modules onthe outboard side. Their dimensions in radial × toroidal ×poloidal are approximately 0.6 m × 1.2 m × 1.7 m for theinboard modules and approximately 0.9 m × 1.5 m × 2 mfor the outboard modules.A schematic of the HCPB blanket modules can be seenin Fig. 2. The structure is stiffened with an internal gridof helium cooled steel plates, which accommodates thebreeder units. Every breeder unit consists of two breederbeds filled with Li4SiO4 pebbles with Li-6 enriched to60 at% contained between u-shaped cooling plates withinternal helium cooling channels. The remaining space is© The Authors, published by EDP Sciences. This is an Open Access article distributed under the terms of the Creative Commons Attribution License 4.0(http://creativecommons.org/licenses/by/4.0/).EPJ Web of Conferences 146, 09025 (2017) DOI: 10.1051/epjconf/201714609025ND2016Figure 1. The CAD DEMO 11.25◦ sector model.Figure 2. The HCPB blanket module (upper) with the u-shapedbreeder unit (lower).filled with beryllium pebbles for neutron moderation andmultiplication.The resulting neutron spectrum seen by the breederblankets is displayed in Fig. 3. It has the characteristic peakat 14.1 MeV caused by neutrons coming directly from theplasma. In the range between 10−5 MeV till 10 MeV thereis a strong, fluctuating neutron flux, caused by neutronswhich have undergone interactions with the breeder andother reactor materials.3. The sensitivity evaluationThe TBR was calculated with the track length estimatortally of MCNP with nuclear cross-section data from theFigure 3. The normalised neutron flux spectrum calculated in theVitamin-J energy structure averaged over the breeder volume.JEFF-3.2 library. The sensitivity calculations were per-formed for 109 particle histories with the MCSEN code [6],which is a local update to MCNP and can be installed asa patch. The newest version MCSEN5 was used which isbased on MCNP5 1.3. The sensitivities were calculated forevery occurence of an isotope in the reactor not only in thebreeder materials.The investigated isotopes were chosen from the breed-ing material (Li-6, Li-7), the neutron multiplier (Be-9),the breeder ceramic material (O-16, Si-28, Si-29, andSi-30), and the most abundant structural materials(Fe-54, Fe-56, Cr-52, Ni-58, W-182, W-183, W-184,W-186, and H-1).The MCSEN code assumes the TBR does not explicitlydepend on the nuclear cross-section, which is true for allcross-sections except the tritium breeding cross-sections ofLi-6 and Li-7. In these cases a correction of the MCSENresult needs to be performed with the Add Response Termcode [7].Relative sensitivities are calculated by normalising thesensitivity results to the respective Li-6 and Li-7 TBRcontribution. Integrating over the whole energy range andadding up the contributions of the different reactions ofan isotope yields the total integrated relative sensitivities,which can be seen in Table 1. The results of H-1 and Ni-58were not included because they were below 0.001 %/%.The strongest sensitivity impact comes from O-16,Li-6, Si-28, Li-7, and Be-9. It is noted that these areall breeding, breeder ceramic and multiplier constituents,while the impact of structural materials is less strong. Onlythe less abundant breeder ceramic isotopes Si-29 and Si-30have a smaller absolute value than the most abundant andhighest scoring structural material isotope Fe-56.For the isotopes with the highest sensitivity results, thestrongest individual reactions are displayed as well and itcan be seen that for most cases elastic scattering has thestrongest impact, followed by inelastic scattering. Only forBe-9 the elastic scattering reaction is in third place afterthe (n,2n) and the (n,α) reaction.Most sensitivities are negative, which means that anincrease of the cross-section would cause a decrease oftritium breeding. Only the sensitivity to the elastic and(n,2n) reaction of Be-9 and the tritium breeding reaction ofLi-6 is positive. For Li-6 the negative impact of the elastic2EPJ Web of Conferences 146, 09025 (2017) DOI: 10.1051/epjconf/201714609025ND2016Table 1. The total integrated relative sensitivity of the TBR to theconsidered isotopes. For the strongest isotopes the results of thestrongest individual reactions are displayed as well.isotope MT Sensitivity [%/%] Error [%/%]Li-6 −0.630 5.7E-04elastic −0.600 2.8E-05(n,n′) −0.035 4.5E-06(n,t) 0.009 5.7E-04Li-7 −0.435 1.9E-05elastic −0.421 1.8E-05(n,2n) −0.001 1.5E-07(n,n′) −0.012 2.3E-06Be-9 0.196 4.5E-04elastic 0.017 4.4E-04(n,2n) 0.215 8.2E-05(n,α) −0.029 3.1E-06O-16 −2.830 1.1E-04elastic −2.777 1.1E-04(n,n′) −0.028 4.3E-06(n,α) −0.015 2.2E-06Si-28 −0.497 2.2E-05elastic −0.471 2.2E-05(n,n′) −0.015 2.2E-06(n,p) −0.005 8.1E-07Si-29 −0.024 1.7E-06Si-30 −0.016 9.9E-07Fe-56 −0.105 3.4E-04Fe-54 −0.020 1.1E-04Cr-52 −0.010 8.6E-05W-182 −0.018 6.1E-05W-183 −0.020 4.4E-05W-184 −0.020 6.8E-05W-186 −0.015 6.4E-05and inelastic scattering overlays the small positive tritiumbreeding result, causing an overall negative sensitivity.3.1. Sensitivity profilesSensitivity profiles were calculated in the Vitamin-J energygroup structure. The profile of the sensitivity to theelastic scattering reaction of O-16, which has the highestintegrated sensitivity impact, can be seen in Fig. 4.There is a negative peak at 14.1 MeV, the energy theneutrons have when they come directly from the plasma,both for the Li-6 and the Li-7 contribution to the TBR.The sensitivity of the Li-7 contribution is less strong andonly present above the threshold for the tritium producingreaction at ≈ 3 MeV. In contrast, the sensitivity of theLi-6 contribution is strongly negative throughout theenergy range down to below 10−4 MeV where the neutronflux (see Fig. 3) also vanishes.An increase in the elastic scattering cross-section ofO-16 would cause a decrease of tritium breeding bothat 14.1 MeV and throughout the lower energy range.Elastic scattering slows down neutrons and the Li-6 tritiumbreeding cross-section increases towards lower energies.Therefore, the tritium breeding should benefit from elasticscattering. However, when considering Table 1, it can beFigure 4. The relative sensitivity profile of the elastic scatteringreaction of O-16 for the total TBR, and the Li-6, and Li-7contribution.seen that the sensitivity to elastic scattering can both benegative (for Li-6, Li-7, O-16 and Si-28) and positive (forBe-9). This indicates that it depends on the energy rangeinto which the neutrons are being slowed down. In thecase of Li-6, Li-7, O-16, and Si-28 it is probable that theneutrons are being slowed down into the energy range of astrong absorbing reaction and for Be-9, this doesn’t happenand the tritium breeding can benefit from the slowed downneutrons.4. The uncertainty evaluationWith the sensitivity profiles available from the MCSENcalculations for all the reactions of all the consideredisotopes, and, if necessary, the response term correctionperformed, the Sandwich code [7] can be applied tocalculate the resulting relative standard deviations (StDs).To this end, covariance data are required. To achieveconsistency with the nuclear cross-section data, thecovariance data were taken from JEFF-3.2 for all isotopesfor which they are available. For the other isotopes acombination of FENDL-2.1 for Li-7, EFF-3 for Be-9 andJENDL-3.2 for O-16 was used. In addition, covariancedata from TENDL-2014 and JEFF-3.3T1 were used forcomparison.The results can be seen in Table 2. H-1 and Ni-58 arenot shown as their results were below 0.01%. The totalstatistical error was 0.0001% which is significantly smallerthan the results for the nuclear data uncertainty.The different library combinations yield significantlydifferent results: JEFF-3.2 + TENDL-14 yields a resultbigger by a factor of almost 3 than JEFF-3.2 + FENDL-2.1+ EFF-3 + JENDL-3.2, and for JEFF-3.3T1 it’s a factor ofalmost 2. This is caused by the O-16 result being biggerby a factor of 2 for both other libraries and the Li-7 resultbeing bigger by a factor of almost 8 for TENDL-14. TheLi-7 result of TENDL-14 is judged as questionable sinceTENDL data are not very reliable for low mass nuclei.Especially the result for the Li-7 contribution to the TBRhas an unrealistically high value of 39.45%.For all library combinations, O-16 and Li-6 provide thebiggest contribution to the total standard deviation (exceptfor the questionable Li-7 value from TENDL-14). Like3EPJ Web of Conferences 146, 09025 (2017) DOI: 10.1051/epjconf/201714609025ND2016Table 2. Relative StDs of the total TBR calculated withcovariance data from JEFF-3.2 + FENDL-2.1 + EFF-3 + JENDL-3.2, JEFF-3.2 + TENDL-14 and JEFF-3.3T1.JEFF-3.2 JEFF-3.2 JEFF3.3T1+ other∗ + TENDL-14∗rel. StD [%] rel. StD [%] rel. StD [%]Li-6 1.25 1.25 1.25Li-7 0.85∗ 6.57∗ 0.85Be-9 0.59∗ 0.42∗ 0.59O-16 2.64∗ 5.29∗ 5.29Si-28 0.48 0.48 0.48Si-29 0.11 0.11 0.11Si-30 0.10 0.10 0.10Fe-56 0.29 0.29 0.29Fe-54 0.07 0.07 0.07Cr-52 0.06 0.06 0.06W-182 0.08 0.08 0.08W-183 0.12 0.12 0.12W-184 0.27 0.27 0.27W-186 0.14 0.14 0.14total 3.17 8.57 5.58Table 3. Absolute standard deviations of the TBR calculated withcovariance data from JEFF-3.2 + FENDL-2.1 + EFF-3 + JENDL-3.2, JEFF-3.2 + TENDL-14 and JEFF-3.3T1.Li-6 Li-7 totalTBR 1.071 0.012 1.083±JEFF-3.2+other 0.034 0.0003 0.034JEFF-3.2+TENDL-14 0.093 0.005 0.093JEFF-3.3T1 0.060 0.0003 0.060for the sensitivities, structural materials have less impacton the uncertainty than breeder materials. Only the leastabundant breeder ceramic isotopes Si-29 and Si-30 yieldsmaller results than some structural materials.The result for the TBR was calculated with thetrack length estimator tally of MCNP. Multiplicating theTBR results with the relative standard deviations yieldsthe absolute standard deviations displayed in Table 3.It can be seen that the standard deviation of the Li-7contribution does not have an effect on the total standarddeviation.TBR results were also calculated with JEFF-3.2 +TENDL-14 and JEFF-3.3T2 (updated version of JEFF-3.3T1). This yielded TBR results of 1.065 and 1.084respectively, which are well within the range of all of theestimated absolute standard deviations.5. ConclusionsThe MCSEN Monte Carlo sensitivity code was success-fully applied to the TBR uncertainty calculation of aDEMO reactor model. An 11.25◦ torus sector model witha full, integrated HCPB breeding blanket was used.With the codes Add Response Term and Sandwich,the sensitivity data were further processed and combinedwith covariance data to yield standard deviation results.These results were found to strongly vary depending onthe libraries used for the covariance data. The cross-sectioninduced uncertainties vary between 3.2% for covariancesby JEFF-3.2, FENDL-2.1, EFF-3 and JENDL-3.2, 5.6%for JEFF-3.3T1 and 8.6% for JEFF-3.2 and TENDL-14.The breeder ceramic material O-16 and particularly itselastic scattering reaction were found to have the highestimpact on the uncertainty of the TBR. Next in line wasthe main tritium breeding material constituent Li-6 andalso the elastic scattering reaction. The sensitivity of theLi-7 contribution to the TBR was found to have no impacton the final standard deviation of the total TBR. Structuralmaterials were found to have less uncertainty impact thanbreeder materials.This work was supported by Fusion for Energy (F4E), Barcelona,through the Specific Grant Agreement F4E-GRT-168.02 on“Nuclear Data Improvements and Development of Tools –Nuclear Data”. The views and opinions expressed herein reflectonly the authors’ views.The authors would like to acknowledge the support of OscarCabellos for processing covariance data and Reuven Perel forhandling the MCSEN, Add Response Term and Sandwich code.References[1] Brown, Forrest B and others, Los Alamos NationalLab Report: LA-UR-03-1987 (2003)[2] D. Leichtle, U. Fischer, I. Kodeli, R.L. Perel,M. Angelone, P. Batistoni, P. Carconi, M. Pillon,I. Scha¨fer, K. Seidel, R. Villari, and G. Zappa, FusionEngineering and Design 82(15), 2406–2412 (2007)[3] U. Fischer, D. Leichtle, and R.L. Perel, FusionEngineering and Design 83(7), 1222–1226 (2008)[4] P. Pereslavstev, P. Lu, and U. Fischer, Report for TAWP13-SYS-022 (2014)[5] L. Lu, U. Fischer, and P. Pereslavtsev, FusionEngineering and Design 89(9), 1885–1888 (2014)[6] R.L. Perel, J.J. Wagschal, and Y. Yeivin, NuclearScience and Engineering 124(1), 197–209 (1996)[7] R. Perel, Task 3.3 of the F4E Grant F4E-FPA-168.01(2014)4

Sensitivity and uncertainty analysis for the tritium breeding ratio of a DEMO fusion reactor with a helium cooled pebble bed blanket

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Sensitivity and uncertainty analysis for the tritium breeding ratio of a DEMO fusion reactor with a helium cooled pebble bed blanket

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