ACTAUNIVERSITATIS

UPSALIENSISUPPSALA

2017

Digital Comprehensive Summaries of Uppsala Dissertationsfrom the Faculty of Science and Technology 1508

Development of a Neutron FluxMonitoring System for Sodium-cooled Fast Reactors

VASUDHA VERMA

ISSN 1651-6214ISBN 978-91-554-9897-9urn:nbn:se:uu:diva-319945

Dissertation presented at Uppsala University to be publicly examined in Polhemsalen,Ångströmlaboratoriet, Lågerhyddsvägen 1, Uppsala, Thursday, 1 June 2017 at 09:15 for thedegree of Doctor of Philosophy. The examination will be conducted in English.

AbstractVerma, V. 2017. Development of a Neutron Flux Monitoring System for Sodium-cooledFast Reactors. Digital Comprehensive Summaries of Uppsala Dissertations from theFaculty of Science and Technology 1508. 70 pp. Uppsala: Acta Universitatis Upsaliensis.ISBN 978-91-554-9897-9.

Safety and reliability are one of the key objectives for future Generation IV nuclear energysystems. The neutron flux monitoring system forms an integral part of the safety design of anuclear reactor and must be able to detect any irregularities during all states of reactor operation.The work in this thesis mainly concerns the detection of in-core perturbations arising fromunwanted movements of control rods with in-vessel neutron detectors in a sodium-cooled fastreactor. Feasibility study of self-powered neutron detectors (SPNDs) with platinum emittersas in-core power profile monitors for SFRs at full power is performed. The study shows thatan SPND with a platinum emitter generates a prompt current signal induced by neutrons andgammas of the order of 600 nA/m, which is large enough to be measurable. Therefore, it ispossible for the SPND to follow local power fluctuations at full power operation. Ex-core andin-core detector locations are investigated with two types of detectors, fission chambers andself-powered neutron detectors (SPNDs) respectively, to study the possibility of detection of thespatial changes in the power profile during two different transient conditions, i.e. inadvertentwithdrawal of control rods (IRW) and one stuck rod during reactor shutdown (OSR). It is shownthat it is possible to detect the two simulated transients with this set of ex-core and in-coredetectors before any melting of the fuel takes place. The detector signal can tolerate a noise levelup to 5% during an IRW and up to 1% during an OSR.

Keywords: Protection systems, safety, accidents, sodium-cooled fast reactor, instrumentation,fission chamber, self powered neutron detector

Vasudha Verma, Department of Physics and Astronomy, Applied Nuclear Physics, Box 516,Uppsala University, SE-751 20 Uppsala, Sweden.

© Vasudha Verma 2017

ISSN 1651-6214ISBN 978-91-554-9897-9urn:nbn:se:uu:diva-319945 (http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-319945)

To my parents

Cover Page:

A form of Indian architectural decoration, ’Jali’ (lattice) work at the Taj Mahalbuilt by carving into stone, modeled with the neutronics code SERPENT.

List of papers

This thesis is based on the following papers, which are referred to in the textby their Roman numerals.

I V.Verma, P. Filliatre, C. Hellesen, S. Jacobsson Svärd, C. Jammes,Neutron flux monitoring with in-vessel fission chambers to detectinadvertent control rod withdrawal in Sodium-cooled fast reactor.Annals of Nuclear Energy, 94 (2016) pp. 487-493My contribution: Performed the simulations, analysed the results andwrote the paper.

II V. Verma, C. Hellesen, C. Jammes, P. Filliatre, CalculationMethodology assessment to detect localised perturbation insodium-cooled fast reactor with ex-core instrumentation. Proceedingsfrom PHYSOR - International Conference on the Physics of Reactors,(Peer-reviewed). Idaho Falls, USA: American Nuclear Society, May2016My contribution: Performed the simulations, analysed the results andwrote the paper.

III C. Jammes, P. Filliatre, Zs. Elter, V. Verma, G. de Izarra, H. Hamrita,M. Bakkali, N. Chapoutier, A-C. Scholer, D. Verrier, C. Hellesen, S.Jacobsson Svärd, B. Cantonnet, J-C. Nappé, P. Molinié, P. Dessante, R.Hanna, M. Kirkpatrick, E. Odic, F. Jadot, Progress in the developmentof the neutron flux monitoring system of the French GEN-IV SFR:Simulations and experimental validations. Proceedings from the 4thInternational Conference on Advancements in Nuclear InstrumentationMeasurement Methods and their Applications (ANIMMA). 2015, pp.1-8My contribution: Performed the neutron transport simulations,analysed the results and wrote the related part in the paper.

IV V. Verma, L. Barbot, P. Filliatre, C. Hellesen, C. Jammes, S. JacobssonSvärd, Self Powered Neutron Detectors as in-core detectors forSodium-cooled Fast Reactors. In Press, Accepted in NuclearInstruments and Methods in Physics Research, Section A:Accelerators, Spectrometers, Detectors, and Associated Equipment(2017), �������������� � ��������� �� � ��My contribution: Performed most of the simulations, analysed theresults and wrote the major part of the paper.

V V.Verma, P. Filliatre, C. Hellesen, S. Jacobsson Svärd, C. Jammes,Neutron flux monitoring during slow transient conditions in aSodium-cooled fast reactor. Manuscript (2017)My contribution: Performed most of the simulations, analysed theresults and wrote the major part of the paper.

Reprints were made with permission from the publishers.

Contents

Part I: Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131.1 Motivation for the thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141.2 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2 Future nuclear energy systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162.1 Generation-IV systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162.2 Fast reactors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172.3 Reactivity control in fast reactors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

3 The neutron flux monitoring system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223.1 Detection of neutrons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3.1.1 Fission chambers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243.1.2 Self powered neutron detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253.1.3 Proportional counters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283.1.4 Ionisation chambers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283.1.5 Other detector types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

Part II: Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

4 Neutronic codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334.1 Monte Carlo codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

4.1.1 SERPENT2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 344.1.2 TRIPOLI−4 R©

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 344.1.3 MCNP6/X . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

4.2 Deterministic codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

5 Reactor Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 375.1 Description of the reactor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 375.2 Detector locations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

Part III: Results & discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

6 In-vessel, ex-core fission chambers to detect IRW in an SFR . . . . . . . . . . . . . . . . 436.1 Detection of inadvertent control rod withdrawal, IRW . . . . . . . . . . . . . . . 436.2 Calculation methodology assessment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

7 Self Powered Neutron Detectors as in-core detectors for SFRs . . . . . . . . . . . . . 487.1 Calculation route . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

7.2 Detector response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

8 Neutron flux monitoring during transient conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 538.1 Transient conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 538.2 Calculation route . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 538.3 Detector response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

Part IV: Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

9 Conclusions and outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

Summary in Swedish . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

Abbreviations

ACS . . . . . . .Above-core structureBOC . . . . . . .Beginning-of-cycleBOL . . . . . . .Beginning-of-lifeCEA . . . . . . .Commissariat à l’energie atomique et aux energies alternativesCFV . . . . . . .Cœer à faible effet de vide sodiumCSD . . . . . . .Control and shutdown rodDSD . . . . . . .Diverse shutdown rodEFPD . . . . . .Equivalent full power daysFC . . . . . . . . .Fission chamberGIF . . . . . . . .Generation-IV international forumHTFC . . . . . .High temperature fission chamberIFR . . . . . . . .Integral fast reactorIRW . . . . . . .Inadvertent withdrawal of control rodLWR . . . . . . .Light water reactorMI . . . . . . . . .Monitoring indicationMOX . . . . . .Mixed-oxide fuelMTR . . . . . . .Material testing reactorNFMS. . . . . .Neutron flux monitoring systemOSR . . . . . . .One stuck rodSFR . . . . . . . .Sodium-cooled fast reactorSPND . . . . . .Self-powered neutron detector

Part I:Background

"’Begin at the beginning,’ the King said gravely, ’and go on till you come tothe end: then stop.’"- Lewis Carroll, Alice in wonderland

1. Introduction

Energy is one of the most crucial commodities of the 21st century. The globaldemand for energy is expected to continue to increase in the next few decadeswith rapid economic development and increasing population in developingcountries. This is in addition to the large per capita energy consumption indeveloped nations. For instance, during 2015, per capita electricity productionin Sweden was 17 MWh compared to 1 MWh in India [1]. It is important tomeet the world’s energy demand with the current resources in a sustainablemanner keeping in mind the commitments following the Paris agreement [2].

Nuclear power has a share of 11% in the world electricity production andthe remainder comes from fossil fuels, hydro-power and renewable resourcessuch as wind and solar power, where fossil fuels constitute 68% [1]. Today,the status of nuclear power across the world is in transition. Technologicalchallenges and social ramifications are entangled with political volatility. Thecurrent nuclear power plants operating around the world are predominantlythermal reactors commonly using natural or low-enriched uranium as fuel.Natural uranium contains 0.72% U-235, which is a fissile isotope, and the restis the fertile isotope U-238. Thermal reactors have poor efficiency regard-ing the use of uranium since mainly the fissile isotope U-235 is used as fuelwhile the potentially useful fertile isotope remains largely untapped. Further,long-lived actinides, such as plutonium, are accumulated in thermal reactorsfollowing repeated neutron captures. Therefore, thermal reactors have severallimitations regarding efficient fuel utilisation and waste management.

In contrast, a fast reactor has the potential to address both these shortcom-ings of a thermal reactor. The operational experience of fast reactors extendsback as early as the mid-1940s. The first fast reactors were motivated by pluto-nium production and obtaining the data needed for weapons design [3]. Later,the civilian fast reactor programs were driven by pessimistic early projectionsof uranium reserves. Since fast reactors offer the possibility of tapping thefertile isotopes, uranium resources can be utilized more efficiently. Fast reac-tors also have the ability to recycle and fission minor-actinides and plutonium.The Integral fast reactor (IFR) is one such fast reactor concept developed atArgonne National Laboratory in the 1980s [4]. Perceived as a complete pro-gram, the IFR project aimed to demonstrate an improved waste managementplan with a closed fuel cycle and efficient uranium use. In addition, a pas-sive inherently safe reactor design was also an important objective in the IFRproject. In the last two decades, nuclear research on fast reactors has typicallycome under the aegis of Generation-IV systems. Several reactor types with

13

different designs, but with common Generation-IV goals, have been proposed,and are explained in more detail in Section 2.1.

Generation-I systems refer to the early prototype reactors that were the firstcommercialised power plants, of which none are operational today. Generation-II mainly consists of standard light-water reactors (LWRs), both pressurizedand boiling water type, of which the majority are still in operation today.Generation-III nuclear systems consist of evolved LWR technologies with ex-tended lifetimes and advanced safety features.

Safety is one key aspect that must be addressed satisfactorily, more so in thelight of recent events, namely the Fukushima-Daiichi accident. The conceptof defense-in-depth is fundamental to the safety of nuclear installations [5].There are three cornerstones of this concept. A nuclear reactor must have aconservative design that provides margins between operating conditions andfailure of systems. It must offer control of operation via protection/monitoringsystems during normal or abnormal operation and prevent evolution of suchevents into postulated accidental scenarios. Lastly, it must have engineeredsafety features to control and prevent any postulated incidents and accidentsand mitigate their consequences [5]. The definition was further refined toinclude feedback gained through experience and investigation regarding severeaccidents.

1.1 Motivation for the thesisAs part of the defense-in-depth concept, incident prevention is first priority.There is a need to reliably detect incidents in their earliest possible stages.The monitoring instrumentation must monitor relevant reactor parameters inorder to assist with the execution of standard guidelines for management andmitigation. In a nuclear reactor, this instrumentation includes thermocouplesand resistance temperature detectors for temperature measurements, coolantflow meters, radiation monitors, and neutron flux monitors [6]. This thesisfocuses on the neutron flux monitoring system, NFMS.

The NFMS forms an integral part of the safety design of any nuclear reac-tor. It is essential for the prevention of incidents and accidents as well as inthe regulation of the overall reactor power and the reactivity in the core overseveral reactor cycles [7]. It must be able to provide detection of any driftsand irregularities during all states of reactor operation. A detailed overview ofa NFMS is presented in Chapter 3. The work presented in this thesis is partof, but not limited to, an ongoing effort towards the development of a neutronflux monitoring system for the foreseen French sodium-cooled fast reactor,ASTRID. This is one of the key R&D areas identified within the research pro-gram run by the French Atomic Energy and Alternative Energies Commission(CEA), EDF and AREVA French partners on Generation-IV sodium-cooledfast reactors (SFRs).

14

1.2 OutlineIn this thesis, the detection of in-core perturbations in a fast reactor due tounwanted movements of control rods is studied. The reactor type and designgoverns the choice of the detectors and their location to a major extent. Asodium-cooled fast reactor core, which is described in Chapter 2 & 5, has atighly-packed hexagonal lattice and placing neutron instrumentation as closeas possible to the neutron source, i.e., in-core, is challenging due to the highneutron fluxes (up to 1015 cm−2s−1) and high temperatures (around 550◦C).The work in the thesis consists of three main parts, which are listed below.

• The first part of the work includes the detection of an inadvertent con-trol rod withdrawal (IRW) using ex-core fission chambers in an SFR.Two different calculational approaches are pursued. The results showthat it is possible to detect changes in the neutron flux distribution initi-ated by an IRW of an outer control rod with in-vessel fission chamberslocated azimuthally around the core. It is, however, difficult to followan inner control rod withdrawal and precisely know the location of theperturbation in the core. The results from this part are included in PaperI, II and III.

• In the second part of the work, a feasibility study of self-powered neu-tron detectors (SPNDs) with platinum emitters as in-core power profilemonitors at full power for SFRs, is performed. It is shown that such anSPND generates a sufficiently measurable prompt current from neutronsand gammas, and this signal provides dynamic information on the lo-cal power fluctuations. The results from the second part are included inPaper IV.

• The third part of the work is a study of the possibility of using a set of pe-ripheral ex-core fission chambers and in-core SPNDs to detect the spatialchanges in the power profile during two different transient conditions. Acoupled neutron transport and thermal-hydraulics/point-kinetics code isused for the study. The use of complimentary in-core detectors coupledwith the peripheral fission chambers is proposed to enable robust coremonitoring across the radial direction. The results show that it is possi-ble to reliably detect the two simulated transients with the two detectorsets before any melting of the fuel occurs. The results are summarizedin Paper V.

The neutronic codes used during the thesis are described in Chapter 4. Thereactor model is described in Chapter 5. The results are discussed in Chapter6, 7 and 8. Finally, conclusions and future outlook are given in Chapter 9.

15

2. Future nuclear energy systems

2.1 Generation-IV systemsThe Generation-IV international forum (GIF) is an international cooperationthat was set up in 2001 to carry out joint development of the next generationof nuclear energy systems. Charter members include USA, Argentina, Brazil,Canada, China, France, Japan, Russia, South Korea, South Africa, Switzer-land, UK, and Australia, along with EU (Euratom) [8]. Most of the membersare signatory to the framework agreement that commits them to undertakeresearch and development of one or more Generation-IV nuclear systems se-lected by GIF. The GIF outlined several technological challenges and goals,which include sustainability, economic competitiveness, safety and reliability,as well as proliferation resistance and physical protection [8]. The six nuclearreactor concepts identified by this forum are:

• Sodium-Cooled Fast Reactor (SFR)

• Gas-Cooled Fast Reactor (GFR)

• Lead-Cooled Fast Reactor (LFR)

• Supercritical-Water-Cooled Reactor (SCWR)

• Molten Salt Reactor (MSR)

• Very-High-Temperature Reactor (VHTR)

The first three reactor types (SFR, GFR and LFR) operate with a fast neu-tron spectrum. The two following types (SCWR and MSR) can operate withboth thermal as well as fast spectra while the VHTR is a thermal only design.The sodium-cooled fast reactor design is one of the most matured reactor sys-tems in place today, having a vast operational experience of over 70 years.In view of the objectives of the Generation-IV international forum, modernSFRs are designed with superior safety features, better economy and prolifer-ation resistance. Lead-cooled fast reactor technology is at an advanced stageof research and development and is backed by committed investment. The op-erational experience of fast reactors using liquid-metals as coolants stretchesas far back as 1946 and is summarized in Table 2.1.

16

Table 2.1. Civilian operational experience of liquid-metal cooled fast reactors.

Reactors Country First Coolant Power StatusCriticality [MWth]

Clementine USA 1946 Hg 0.023 ShutdownEBR-I USA 1951 Na/K 1.4 ShutdownBN2 Russia 1956 Hg 1-0.1 ShutdownBR-5/BR-10 Russia 1958 Na 5/8 ShutdownDFR UK 1959 Na/K 60 ShutdownFermi USA 1963 Na 200 ShutdownEBR-II USA 1963 Na 62.5 ShutdownRapsodie France 1967 Na 40 ShutdownBOR-60 Russia 1968 Na 55 ShutdownSEFOR USA 1969 Na 20 ShutdownKNK-II Germany 1972 Na 58 ShutdownBN-350 Kazakhstan 1972 Na 750 ShutdownPhénix France 1973 Na 563 ShutdownPFR UK 1974 Na 650 ShutdownFFTF USA 1980 Na 400 ShutdownBN-600 Russia 1980 Na 1470 OperationalJOYO Japan 1982 Na 140 Operational1

FBTR India 1985 Na 40 OperationalSuper-Phénix France 1985 Na 3000 ShutdownMONJU Japan 1995 Na 714 Operational1

CEFR China 2010 Na 65 OperationalBN-800 Russia 2014 Na 2100 OperationalPFBR India 2017 Na 1253 Construction completedASTRID France - Na 1500 Active developmentBREST-OD-300 Russia - Pb 700 Active developmentSEALER Sweden - Pb 3-10 MWe Active developmentALFRED Europe - Pb 300 Active development

The Advanced High-Temperature Reactor, AHTR, which is an MSR con-cept with graphite and solid-fuel core structures and molten salt as coolant isunder construction at Shanghai Institute of Nuclear Applied Physics, China.An HTR-PM demonstration unit based on VHTR technology is under con-struction at Shidaowan, China.

2.2 Fast reactorsA typical fast reactor neutron spectrum is plotted in Figure 2.1 and comparedto a typical LWR neutron spectrum. The fast reactor has an unmoderated spec-trum with neutrons mainly between 100 keV and 1 MeV, while the LWR hasboth fast and thermal (0.1 eV) spectral components. A comparison of the fis-sion cross-section of the isotopes U-235 and Pu-239 is shown in Figure 2.2.The fission cross-section is significantly lower for fast neutrons than for ther-mal neutrons. Therefore, in the absence of a moderator, the fuel is typically

1Following the Fukushima accident, the status of the Japanese nuclear reactors is uncertain.

17

enriched to about 20% or higher in a fast reactor. In contrast, thermal reactorsuse low-enriched or natural uranium, depending on the moderator type.

Figure 2.1. Comparison of a typical LWR and SFR spectra.

Figure 2.2. Microscopic fission cross-sections of U-235 and Pu-239. Data are takenfrom the JEFF-3.1 library [9].

All operational fast reactors to date have used liquid-metals, such as sodiumand lead as coolants. Since these metals are heavier than hydrogen and oxygentypically found in an LWR, the energy loss is small in each scattering event.Therefore, it takes many collisions to thermalise, and nearly all neutrons areabsorbed during the slowing down.

Fertile isotopes such as U-238 and Th-232 can capture neutrons and con-vert to fissile isotopes like Pu-239 and U-233. This process is also known asbreeding. The two reaction chains are

18

238U +n→239 U +β− →239 N p+β− →239 Pu

and

232T h+n→233 T h+β− →233 Pa+β− →233 U .

From this, a conversion ratio can be defined as

CR =nproduced

nconsumed, (2.1)

where nproduced and nconsumed are the number of fissile nuclei produced bybreeding, and consumed by absorption respectively. Thermal reactors withUranium fuel have a CR ranging from about 0.5 to 0.7, which means that theyare net consumers of fissile material and therefore, have a poor utilisationof the natural resource. In contrast, a fast reactor can be designed with aCR ≥ 1. This means that they can be operated with no net consumption offissile material, therefore, potentially utilising close to 100% of the naturalresource. Thorium-fueled reactors can achieve a CR = 1 with a thermal neutronspectrum. This is the route followed in many MSR designs.

Besides being used as a breeder, a fast reactor can also operate as a burner.A burner can consume minor actinides that are accumulated in a reactor fol-lowing repeated neutron captures. Spent LWR fuel, containing around 95%U-238, 1% non-fissioned U-235, 1% plutonium and 3% fission products hasplenty of unextracted energy [10]. The fission products are highly radioac-tive, short-lived wastes (few hundred years), while the minor actinides arehighly radioactive, long-lived wastes, which dominate for a few hundred thou-sand years. It is possible to employ a closed fuel cycle in which the spentnuclear fuel is reprocessed to recycle/extract unused plutonium and uranium,which is later used as a fresh fuel to feed current and future nuclear reactors.Furthermore, the long-lived minor actinides can be recycled and burned infast reactors as the fission probability is higher for fast neutrons. Recyclingspent nuclear fuel helps reduce long-term radioactivity in high-level wastes,and minimize the volume of waste, which needs to be disposed. Therefore,a fast reactor with a fuel cycle closed on plutonium, or even better on all ac-tinides i.e. U, Np, Pu, Am, Cm minimizes uranium usage and shortens thetime needed to bring the radiotoxicity of nuclear waste down to the level ofnatural uranium. Spent fuel is a resource here rather than a waste.

2.3 Reactivity control in fast reactorsMore than 99% of the neutrons that are released from a fission reaction areprompt. The rest are released with a delay following the half-lives of their

19

precursors, which are normally treated as distinct groups. 6 or 8 group struc-tures are common. The half-lives range from 0.25s to 1 minute. The core2

of the reactor control lies with these delayed neutrons. Even though they arepresent in small numbers, they provide a long time-constant needed for con-trolling the reactor.

The power of the reactor is proportional to the neutron density. The timeevolution of the neutron density can be described with the point-kinetics ap-proximation given by

dN(t)dt

=ρ(t)−β

ΛN(t)+

n

∑i=1

λiCi(t), (2.2)

dCi(t)dt

=βi

ΛN(t)−λiCi(t), (2.3)

where Ni(t) is the neutron density, n is the number of delayed neutron groups,Ci(t) is the delayed neutron precursor of the ith group, βi is the effective de-layed neutron fraction of the ith group, β = ∑βi, Λ is the prompt neutrongeneration time, λi is the decay constant of the ith group and ρ(t) is the reac-tivity at time t. The reactivity in the core is given by the sum of all contributingcomponents, some of which are given below.

ρ(t) = ρD +ρcoolant +ρexp +ρCR, (2.4)

where ρD is the Doppler reactivity, ρcoolant is the coolant density reactivity,ρexp is the core expansion reactivity and ρCR is the reactivity from the move-ments of control rods. ρD, ρcoolant and ρexp are reactivity feedbacks governedby temperatures in the core, while ρCR is an external reactivity. The Dopplerreactivity at temperature T is given by

ρD = KDlnTT0

, (2.5)

where KD is the Doppler constant and T0 is a reference temperature.Although there is no moderation in an SFR, the sodium coolant still causes

a softening of the neutron spectrum. An increase in the coolant temperatureresults in a decrease in the coolant density, which leads to a hardened neutronspectrum and increased reactivity. Therefore, most metal-cooled fast reactorshave a positive coolant temperature feedback that needs to be compensated forby other negative feedbacks. The coolant density feedback is normally treatedas linear given by

2pun intended

20

ρcoolant = Kcoolant(T −T0), (2.6)

where Kcoolant is a constant.The expansion feedback originates from the increasing neutron leakage fol-

lowing a structural expansion of the core. An increase in the fuel temperatureduring normal operation and transients leads to an axial expansion of the fuel,and an increase in the coolant inlet temperature results in a radial expansionof the structure that supports the core. Such changes in the core dimensionscontribute with a negative reactivity due to enhanced leakage. The expansionfeedbacks are normally treated in a linear way. Control rod movements con-tribute with a reactivity following an S-curve, which is illustrated in Figure2.3.

0 20 40 60 80 100Withdrawal (%)

0

20

40

60

80

100

Rea

ctiv

ity i

nse

rtio

n (

%)

Figure 2.3. Typical S-curve for control rod reactivity insertion in an SFR core

21

3. The neutron flux monitoring system

The neutron flux monitoring system, NFMS forms an integral part of the in-strumentation needed to provide continued monitoring of a nuclear reactor.The NFMS must provide an overlapping monitoring range during all states ofnormal reactor operation, i.e., from shutdown to full power as well as duringaccidental situations. The detectors must enable continuity of service and beable to operate for several operating cycles in the given reactor environment[11]. The signals from the detectors are proportional to the reactor power andhence, are used for plant control. The NFMS must reliably detect incidents intheir earliest possible stages by processing signals from the detectors.

A sodium-cooled fast reactor core is a tightly-packed hexagonal latticewith the presence of liquid sodium. This poses a few instrumentation chal-lenges. The environment in the core is very harsh, with neutron fluxes up to1015 cm−2s−1 and temperatures up to 550 ◦C. Note that this is a fast neu-tron flux environment, which is prone to introducing material damage. Sinceclosely packed sub-assemblies do not offer ample space to insert neutron in-strumentation, in-core placement of neutron detectors is a challenge in suchan environment. Typically, SFRs have a set of ex-vessel neutron detectors foroverall neutron flux monitoring during full power. In addition, in-vessel orin-core detectors are also used during initial startup and refueling. This is away to ensure continuous flux monitoring during low power, mid-range andfull power operations.

As an example, the 590 MWth French fast breeder reactor Phénix had in-vessel fission chambers to monitor the chain reaction during off-power opera-tion [12]. Boron proportional counters were used as starting detectors duringlow power operation. The in-vessel fission chambers were unavailable duringmid-range power, and therefore ex-vessel fission chambers were used insteadto monitor the status of the reactor. Boron ionization chambers with gammacorrection were used during full power operation. Figure 3.1 shows the neu-tron instrumentation-range coverage in Phénix. The objective is to develop asimplified neutron flux monitoring system with fewer, but diverse neutron in-strumentation that provides continuous flux monitoring over all power levels.

Choosing the right detector type and corresponding location is limited byvarious performance criteria [7]. The challenges associated with detectorchoices for SFRs constitute the basis of the following sections in this chap-ter. A brief discussion on the principles of neutron detection is followed by adescription of some possible detector candidates.

22

Figure 3.1. Neutron instrumentation over range of reactor operation in the Phénix.

3.1 Detection of neutronsNeutrons are uncharged particles and do not interact electro-magnetically.This makes direct detection of neutrons difficult. In order to detect a neu-tron, it must first undergo a nuclear reaction that creates secondary particles,which can then be detected via conventional radiation detectors. There areseveral possible processes as explained below.

1. Neutrons can scatter elastically and transfer energy to the recoil nucleus,which can be used for detection. The total kinetic energy is conservedin an elastic scattering. It can be visualised as a billiard ball collisionbetween a neutron and an atomic nucleus.

2. Neutrons can scatter inelastically as well. During an inelastic scattering,the recoil nucleus is left in an excited state. When the nucleus de-excites,it emits a beta particle or a gamma. These can also be detected.

3. In neutron capture reactions, a gamma is released through radiative cap-ture (n, γ). In addition, a beta particle is emitted as well if the daughternucleus is unstable. Both the gamma and the beta can be detected.

4. Neutrons can induce fission (n, f). During induced fission, the emittedcharged fission fragments can be detected.

23

Figure 3.2. Schematic diagram of a simple fission chamber.

5. Neutrons can be detected via direct charged particle production (n,α),(n,p), (n,d) or through break-up reactions.

In the following subsections, various neutron detector types are discussed.

3.1.1 Fission chambersA fission chamber is a type of ionization chamber that contains a fissile de-posit. A typical design consists of a set of concentric electrodes called anodeand cathode with a few hundred volts applied across them [13]. A thin layerof fissile material is deposited on the anode, which has a thickness that variesfrom a few μg to g. Depending on the detector type, the inter-electrode spac-ing can vary from a few hundred μm to few mm. The chamber is sealed andfilled with a pressurized gas. The insulator between the electrodes must beradiation-resistant. Typically Al2O3 is used. The external shell is made ofaluminium, stainless steel or inconel. The schematic diagram of a simple fis-sion chamber is shown in Figure 3.2. The following processes occur when aneutron enters a fission chamber and initiates a fission reaction.

• Two heavy charged particles called fission fragments are generated andemitted in two nearly opposite directions.

• The fission fragments ionize the gas along their trajectory and createelectron-ion pairs.

• The electric field that is generated by the DC voltage applied across theelectrodes makes the electrons and ions drift across the gas.

• The electrons and ions move towards anode and cathode, respectively.This generates a current signal, which is later amplified and recorded.

The applied DC voltage is selected such that the fission chamber operates inthe saturation regime. The neutron-induced saturation current is proportionalto the neutron flux. The large amount of energy (200 MeV) dissipated perfission reaction makes it possible to discriminate against any other competing

24

reaction or background interference. The background signal might result fromthe direct ionisation of the gas by alpha and gamma particles. The fission rateis given by

R(t) = A∑i

ni(t)∫

Eσ f ,i(E)φ(E, t)dE, (3.1)

where i is the fissile isotope, ni(t) is the number density of the fissile iso-tope per unit area at time t, A is the surface area of the deposit, σ f ,i(E) isthe microscopic fission cross-section of the isotope and φ(E, t) is the neutronspectrum at the detector at time t. Note that ni(t) is a function of time and willchange as the deposit undergoes depletion, as described later in this section.The preferred fissile material depends on the fission reaction cross-section inthe desired energy range. Most common fissile deposits are natural or en-riched uranium. Note that Pu-242 has also been suggested as a fissile coatingfor monitoring the fast component of the neutron flux [14].

The fissile coating on the electrode will undergo depletion and isotopic evo-lution over time. It is important to consider burn-up of the fissile deposit dur-ing long term operation of in-core detectors. However, for the applicationconsidered in this thesis, the timescale for the evolution of the signal, i.e., thechange of fission rate due to depletion is negligible compared to the phenom-ena studied (movements of control rods). In principle, it is possible to correctfor the evolution of the signal by coupling depletion codes with the data ac-quisition system. Regenerative fission chambers where the neutron-sensitivecoating is a mix of fertile and fissile material are another option [13].

Previous studies made at CEA from the early 1980s to the late 1990s haveshown that high temperature fission chambers (HTFCs) are promising detec-tor candidates in the NFMS since they can provide reliable in-vessel measure-ments in SFRs for about 10 years of operation [15], [16]. The wide rangecapability of HTFCs results from the fact that a fission chamber can operate inpulse mode at low count rates and Campbelling mode at high count rates [17].In HTFCs, there is a sufficient overlap of the signals in pulse and Campbellingmodes in order to ensure the linearity of the neutron flux measurement [18].For the purpose of this thesis, the sensitivity of fission chambers to the spectralchanges in the flux is not relevant. U-235 fission chambers were chosen forthis study. Note that it is difficult to use fission chambers as in-core detectorsdue to the high neutron flux inside the core. It would quickly deplete theirfissile coating and render them inefficient for long term use [11].

3.1.2 Self powered neutron detectorsAn SPND is generally constructed in a co-axial configuration. A schematic di-agram is shown in Figure 3.3. The inner electrode, called the emitter is madefrom a material (eg. Co, V, Rh, Pt) that is chosen for its ability to interact with

25

neutrons through radiative capture. This is followed by emission of promptgammas and/or a delayed electron in the case where a β emitting daughter nu-cleus is formed. The instantaneous and delayed responses together constitutethe signal of an SPND. The outer electrode, typically made of stainless steel,is called the collector. Sandwiched between the two electrodes is an insulator,often made of Al2O3 or MgO. These non-emitter components are made of ma-terials which are almost transparent to neutrons and can withstand the harshenvironment inside a reactor. SPNDs operate without any externally appliedvoltage and are therefore called self-powered. The corresponding current ismeasured between the emitter and the collector. Some possible interactionscontributing to the current are illustrated in Figure 3.4.

Figure 3.3. Schematic of a self-powered neutron detector.

Figure 3.4. Examples of possible interactions in an SPND that contribute to the detec-tor current are (I), (II) (n,β−), (III) (n,γ)(γ,e−) and (IV) (γ,e−).

Instantaneous Response

An SPND can generate a signal due to the electrons produced by gammasreleased following the capture of neutrons in the detector and directly from the

26

external gammas coming from the activated surrounding materials. In Figure3.4, this interaction is represented by sequence (III) and (IV), respectively.This is an instantaneous response of the SPND. The gammas must interactwith the detector material to generate electrons via the photoelectric effect,Compton scattering or pair production. There is a finite possibility that theelectrons might stop in the insulator or the emitter material. The electrons thatstop in the emitter after multiple collisions yield no signal. Others that cometo rest in the insulator create a negative charge build-up in the region, resultingin an electric field. The field pushes the electrons out of the insulator, either tothe emitter or the collector [19].

Delayed Response

A neutron capture (n,γ) in the emitter results in the formation of a radioactivenucleus that beta decays into another state, which may or may not be stable.The emitted betas can reach the collector if they have sufficiently high en-ergy. These recoil electrons undergo multiple secondary interactions beforecontributing to the current. Two such interactions are represented by sequence(I) and (II) in Figure 3.4. The charge transfer process described above holdstrue here as well. The transfer of betas from the emitter to the insulator leadsto a build-up of negative charge resulting in an electric field. The net currentmeasured by the collector is affected because of the resulting field, depend-ing on whether the betas are pushed towards the collector or returned to theemitter. The response time of the detector is determined by the half-life ofthe beta-emitting nucleus, which could range from a few seconds to severalminutes. Common examples are Rh and V SPNDs where betas create chargetransfers with response times of several minutes [20], [21], [22].

The SPND is qualified as a delayed or prompt-response detector dependingon which signal contribution (delayed or instantaneous) that is dominant. Theprompt signal is generated via a two-step process, each with a limited probabil-ity. Thus, the resulting sensitivity of a prompt-response SPND is lower com-pared to that of a delayed-response SPND. However, the response is promptand the current is proportional to the prompt neutron flux, which enables thedetector to follow the change in the power profile of the reactor.

Self-powered neutron detectors can withstand long term operation underharsh working conditions. An apparent limitation of SPNDs is their sensitivityto both neutrons and gammas [23], [24], [25]. For local power distributionmeasurement, the prompt gamma flux is proportional to the fission rate in thefuel. In addition, there is delayed gamma flux that comes from the activationof the structural materials as well as the decay gammas from fission products.However, there is no discrimination between the prompt and delayed gammaflux. SPNDs are a common choice for in-core neutron detectors in thermalreactors [13]. The structural activation is high in such reactors. The sensitivityto gammas can be neglected in LWRs as the emitter material of the detector

27

is chosen such that its neutron capture cross-section is high enough [23]. Inthe case of SFRs, it is not possible to neglect the sensitivity to gammas as theneutron capture cross-section is low compared to that of thermal neutrons forall available emitter materials. In order to follow variations in the local powerdistribution, there should be a small sensitivity to delayed gammas. Thus,the magnitudes of the signal contributions of neutrons, prompt gammas anddelayed gammas to the detector response must be analysed. Regarding the useof self-powered neutron detectors in a fast neutron environment, a feasibilitystudy of using SPND in the test blanket modules in ITER was done recently[26]. In the past, online measurement of the intense neutron flux in the materialtesting reactor (MTR), OSIRIS was performed using SPNDs [27]. The totalneutron flux in an MTR is similar to what is expected in an SFR. SPNDs area suitable choice for in-core monitoring in SFRs at full power, complimentaryto ex-core fission chambers. This is discussed in more detail in Chapter 7.

3.1.3 Proportional countersThe detector contains a metal cylinder with a coaxial electrode. The cylindercould be either filled with BF3 or the electrodes could be coated with boron,and enclosed in an inert gas environment [13], [28]. The neutrons are detectedthrough a neutron-induced reaction, B10(n,α)Li7, which produces ionised par-ticles. The electrons are accelerated by the electric field towards the collectingelectrode where they contribute to the current. During acceleration, these elec-trons gain sufficient energy and ionize other molecules. The detector currentis a sum of these contributions. The rate of detection is a linear function ofthe incident neutron flux. It can provide gamma ray discrimination as the out-put pulses have different heights. The secondary electrons produced by thegammas cause less ionisation than the charged particles released during theneutron-induced reaction. BF3 or boron-lined proportional counters are usu-ally used in pulse mode in the reactor to monitor the core during start-up afterlong-term shutdown or during the initial fuel loading operation.

3.1.4 Ionisation chambersNeutron-sensitive ionisation chambers are used during mid-range and full poweroperation range in the reactor [13], [28]. The chamber contains surfaces coatedwith B10. The recoil alpha particle produced by an incoming neutron throughB10(n,α)Li7 ionises the gas, like in proportional counters. At high flux levels,the ionisation chamber cannot be operated in pulse mode. Switching to cur-rent mode removes any chance of inherent gamma-ray discrimination as allpulses add some contribution to the measured current [13]. Thus, neutron fluxdetection range is limited by gamma-ray background in which the chambermust operate. There are two methods to solve this. One method is to operate

28

the chamber in Campbelling mode. The other method is to use gamma-raycompensated ion-chamber. It employs two ion-chambers, one (Boron-lined)which is sensitive to both neutron and gamma rays and the other (no lining)sensitive to gamma rays only. The final signal current is derived by subtract-ing the two independent currents. The response to gamma-rays is often notidentical and hence, the compensation must be adjusted according to varyinggamma flux.

3.1.5 Other detector typesIn addition, there are other types of detectors, such as plastic organic scintil-lators based on elastic scattering and diamond semiconductor detectors basedon the C12(n,α)Be9 nuclear reaction. Plastic scintillators cannot be used inan SFR environment but diamond detectors have been considered as possibledetector choice.

The neutron instrumentation presently in use in SFRs includes fission cham-ber, proportional counter and ionisation chamber. Self-powered neutron detec-tors are possible candidates for future such reactors. Proportional counters andionisation chambers have not been studied as potential detectors for SFRs inthis thesis.

29

Part II:Modeling

"All we have to decide is what to do with the time that is given to us."- J.R.R. Tolkien

4. Neutronic codes

The work in this thesis is performed using several Monte-Carlo and determin-istic transport codes, which are all frequently used to perform particle trans-port calculations for nuclear reactors [29], [30]. To enhance the efficiency ofa simulation process, it is also possible to combine the two types of codes in acalculation route. There are advantages and disadvantages with each approachand the choice is made based on the nature of the problem under consideration.

Asymmetrical movements of control rods result in changes of the neutronsource profiles. The problem addressed in this thesis is partly a shieldingproblem due to long distances between the source and the detectors and partly,a 3-D criticality problem due to the asymmetrically distorted neutron sourceprofile during in-core perturbations.

A description of the calculation tools used during the study is given in thefollowing sections. The calculation route for each part of the work employingthese codes is described further ahead in Chapters 6, 7 & 8. During mostpart of the thesis, calculations are performed with the Monte-Carlo methodbased codes. For a comparative study of calculation routes, a coupled systemwith deterministic and Monte-Carlo method based codes is used, described inSection 6.

4.1 Monte Carlo codesA Monte-Carlo method employs a probabilistic approach to calculate an ap-proximate solution of a physical quantity of interest. A large number of ran-dom histories of individual particles are simulated and averaged to find an esti-mate of the measured quantity. The random walk of a particle only depends onits present state, thus making the neutron interactions as independent events.It is called an analog Monte-Carlo mode because the history of each particleis simulated exactly. A Monte-Carlo method relies on the detailed physics ofthe interaction between the particles and the nuclei and use point-wise cross-sections. Point-wise refers to continuous non-binned cross-sections. Suchcodes allow for a detailed geometry description. The error in a Monte-Carlocode is normally dominated by the statistical uncertainty of the sampled ran-dom histories, which scales as 1/

√N, with N being the sampled random his-

tories. For a geometrically-complex source-detector response problem in alarge power reactor, it is not possible to obtain flux estimates with classicaldeterministic codes avoiding certain approximations, such as discretization.

33

Monte-Carlo codes are a natural choice for such problems where the detectoris located in a far-away region of the system. Although, it is computationallyexpensive. Non-analog mode involving variance-reduction techniques can beused to provide appropriate bias to source particles and steer them to the de-sired detector location(s). The choice of optimized bias parameters is based ona prior knowledge of the magnitudes of the various physical effects that comeinto play, and could be costly for a multiple-detector system. These codesoffer both external-source and criticality simulation modes.

4.1.1 SERPENT2SERPENT2 is a 3D continuous-energy reactor physics burn-up calculationcode developed at VTT Technical Research Centre in Finland. It is a newlyimproved version of the previous code with emphasis on memory managementand parallelization [31]. It uses a universe-based logic which nests indepen-dent structures inside one another to build geometry. Neutron transport isbased on a combination of conventional surface-to-surface ray-tracing and theWoodcock delta-tracking method [32], which is proven well suited for geome-tries where the neutron mean-free-path is long compared to the dimensions.SERPENT2 reads the continuous-energy cross-sections from the JEFF-3.1 li-brary. For this work, the standard collision estimators are used with the un-resolved resonance probability table sampling switched off. Typically, SER-PENT2 runs faster than several other Monte Carlo codes like MCNP5 [33],[34], which is an advantage. Note that the on-going development work withSERPENT2 includes weight-window based variance reduction techniques andcoupled neutron-photon transport mode among other topics [31], [35] andhence, the choice of other Monte-Carlo based codes was made for these cal-culations.

4.1.2 TRIPOLI−4 R©

TRIPOLI− 4 R© is the fourth generation of the 3D continuous-energy MonteCarlo code developed by the Service d’Études des Réacteurs et de Mathé-matiques Appliquées (SERMA) at CEA Saclay. TRIPOLI− 4 R© belongs tothe family of radiation transport codes dedicated to shielding, reactor physicswith depletion, criticality safety and nuclear instrumentation [36]. Besideshaving its own native geometry package which can use a pure surface-basedrepresentation and a combinatorial representation with predefined shapes andBoolean operators, this code has been made compatible with any geometrydeveloped in the format of the ROOT software. ROOT is an object orientedsoftware package used for processing and analyzing data, developed by theCERN [37]. Such an arrangement allows the user to directly use a pre-builtROOT geometry without recompiling. For this study, classes of templates

34

written in the PYTHON language were used. This is a modular approach,which uses iterative structures for building complex geometry. The code usesfull point-wise representation of cross-sections produced by NJOY processingcode system. The associated CEA-V5.1.1 nuclear data library is mainly basedon the JEFF-3.1.1 evaluations. In external source mode, a built-in variancereduction module called INIPOND can be used, which is based on the expo-nential transform method, with an automatic pre-calculation of the importancemap [36], [38]. TRIPOLI−4 R© was chosen for the external source mode cal-culation as it is a validated and benchmarked code for shielding calculations,which extensively employs variance reduction techniques.

4.1.3 MCNP6/XMCNP6/MCNPX is a general purpose Monte Carlo radiation transport codethat tracks nearly all particles at nearly all energies, developed at Los AlamosNational Laboratory, USA [39]. It belongs to the family of radiation transportcodes dedicated to shielding, reactor physics, criticality safety, nuclear instru-mentation & medical physics etc. This code was used during part of the workinvolving gamma transport calculations using ENDF/B-VII.1 nuclear data li-brary. The computational model of the SFR was verified and validated forneutron transport calculations with SERPENT2.

4.2 Deterministic codesDeterministic methods consider that particle transport is governed by the Boltz-mann transport equation predicting neutron production and loss rates. Theyare based on mostly solving the integro-differential form of the equation, dis-cretized in phase space: energy, angle and space.

Nodal methods or finite elements/difference methods treat spatial discretiza-tion. This discretization results in a large algebraic system of equations whichare solved numerically. Spherical harmonics method, PN, Simplified PN, alsocalled SPN or Discrete ordinate method, SN treat angular discretization. Ex-ceptions include Method of characteristics and collisional probabilities method,which instead solve the integral form of transport equation [40].

These methods provide detailed computationally-efficient solution. But forshielding applications, they have limitations regarding uncertainties associatedwith the discretization of the independent variables of the transport equation.For the source-detector problem addressed in this thesis, the deterministic codeERANOS [41] is used to obtain a power map of the core representing thefission sources, which are further fed into TRIPOLI−4 R© to perform neutrontransport in external-source mode.

35

The ERANOS neutronic system consists of data libraries, codes and calcu-lation procedures, which have been developed within the European Collabo-ration on Fast Reactors. It contains all the functions required for the referenceand the design calculations of an SFR (core as well as blankets, reflectors andshields), with extended capabilities for Generation-IV type advanced fast re-actors. As part of the ERANOS code package, ECCO [42] and VARIANT[43] codes were used during this work. The ECCO code performs cell fluxand cross-sections calculations based on European JEFF3.1 library. The 3Dfinite-difference nodal code, VARIANT is used to perform core calculationsof the SFR core. PARIS-GUI is a user-friendly interface (part of the PARIScode [44]), which enables to prepare input deck for the ERANOS code using areference database of routines, procedures, properties. ECCO cell calculationsare performed with PARIS-GUI using standard schemes for cross-section cal-culations.

36

5. Reactor Model

5.1 Description of the reactorA generic core design of a Generation IV, 1500 MWth pool-type sodium-cooled fast reactor designed at CEA [45] is used for the study. The reactordesign is MOX fueled and has an evolutionary axially heterogeneous low voideffect core (CFV) [46]. CFV is a French acronym of Cœur á Faible effet deVide sodium, which stands for low sodium void effect core. The radial cross-section of the SFR core modeled with SERPENT2 is shown in Figure 5.1(A).The main design parameters of the reactor core are given in Table 5.1.

Figure 5.1. (A) Top view of the SFR core modeled with SERPENT2. (B) A part ofthe axial cross-section of the SFR core.

The core is focused on optimizing the reactivity coefficients in order toobtain an improved behavior during accidental conditions such as the Loss of

37

Flow. The aim is to minimize sodium void effect, i.e. loss of sodium in thehottest zones of the core. The fissile zone is radially divided into two parts withdifferent heights, and is further surrounded by a reflector and a radial neutronshield. The outer fissile zone is made higher and lesser enriched than the innerone. This is done to increase the radial neutron leakage. Axially from bottomto top, the active CFV core is composed of a lower fertile blanket, a lowerinner fissile zone, an inner fertile zone, an upper inner fissile zone followed bya sodium plenum and an upper neutron shield, as illustrated in Figure 5.1(B).

During normal operation, liquid sodium in the plenum acts as a reflectiveshield. During void conditions, the sodium density reduces and the neutronsare able to escape until they are absorbed by the upper neutron shield. Inaddition, the internal fertile blanket pushes the peaking flux upwards towardsthe upper fissile zone. This increases the leakage effect in case of sodiumvoiding. One counter effect to the overall negative void effect due to leakageis the neutron spectral hardening in the fuel as a result of decrease in sodiumdensity. Therefore, this core, which has a negative void coefficient, maximizesneutron leakage from the core in the event of an accident and reduces the corereactivity in case of a coolant temperature increase. It is an improvement onthe previous Superphénix core [47], where sodium void resulted in higher corereactivity. Another design objective is to achieve easy natural convection andcirculation of sodium for passive and diversified decay heat removal.

The active core contains 291 fuel subassemblies. Each fuel subassembly inthe hexagonal lattice contains 217 pins, made up of axially stacked cylindricalMOX fuel pellets encased in stainless steel. The CFV core is an iso-breedercore with no radial fertile blankets. The fertile blanket/zone is made up ofnatural or depleted uranium oxide. The control and safety system contains 18control rods, out of which 12 are Control and Shutdown Devices (CSD) and 6are Diverse Shutdown Devices (DSD) made with B4C absorber pins. The ab-sorber pins are contained in a stainless steel cylindrical tube that moves insidea hexagonal wrapper tube with the same dimensions of a core subassembly.In a control rod, the active absorber region is sandwiched between the drivemechanism (upper part) and the follower (lower part). CSDs are inserted intothe core during normal operation for flux flattening and reactivity control whileDSDs are inserted only in the event of an accidental scram. During normal op-eration conditions, DSDs stay in parking position, just above the upper fissilezone in the sodium plenum.

5.2 Detector locationsThe active core is modeled accurately with a heterogeneous description. Thereflector and the neutron shields have homogeneous compositions. A previousstudy [7] evaluated diverse detector locations on the basis of several perfor-mance criteria such as operational conditions, neutron detection rate, rate-to-

38

Table 5.1. Main design parameters of the reactor core.

Reactor Power (MWth) 1500Fuel residence time 1440 EFPD∗Fuel cycle length 360 EFPDAverage breeding gain per cycle -0.02Delayed neutron fraction, βeff 364 pcmVoid at End-of-cycle (EOC) - 0.5 $∗Equivalent Full Power days

power proportionality etc., and chose two ex-core detector locations. The twolocations are beyond the radial neutron shield and lower part of the above-core structure (ACS). The ACS consists of two rotatable plugs that handle thecontrol rod drive mechanisms. The ACS is located at a distance of approx-imately 15 cm above the core sub-assemblies, i.e., above the upper neutronshield. The detectors are proposed to be placed at the foot of the ACS. Onemajor drawback associated with this location is that the detector signal is cutoff during fuel handling operations as the ACS moves along with the rotatableplugs. Outer part of radial neutron shield ensures continuity of service, evenduring fuel handling and this location is chosen for the studies performed aspart of this thesis.

Figure 5.2. Illustration of the neutron channel.

In the neutron flux monitoring system described in this thesis, the ex-corefission chambers are located symmetrically around the radial neutron shield.Neutron channels are introduced in the radial neutron shield to enhance thetransport of neutrons from the core to the detectors. The channels are taperedto reduce unnecessary leakage and activation outside the core. The tapered de-sign is formed by leaving out an intermediate space filled with sodium in threeradially consecutive neutron shield subassemblies. The sodium filled channeldecreases in height as we move outwards from the core. A detailed view ofthe neutron channel is shown in Figure 5.2. The azimuthal fission chambersare located beyond the neutron channel at a radial distance of about 285 cmfrom the core center. This CFV core is axially strongly in-homogeneous dueto the presence of the internal fertile zone and it is not obvious where the op-timal neutron channel location is. Based on an optimization study described

39

in Chapter 6, the axial plane of the neutron channel is chosen such that itcoincides with the upper fissile zone of the core.

The in-core self-powered neutron detectors are placed in the four centrally-located empty subassemblies, highlighted in light blue in Figure 5.1. TheSPNDs are located at an axial plane coinciding with the upper fissile zone.Thus, there are six ex-core azimuthal fission chambers and four in-core self-powered neutron detectors in the core.

40

Part III:Results & discussion

"I almost wish I hadn’t gone down that rabbit-hole - and yet - and yet - it’srather curious, you know, this sort of life."- Lewis Carroll, Alice in wonderland

6. In-vessel, ex-core fission chambers to detectIRW in an SFR

The core that is used in this work is axially heterogeneous due to the presenceof an internal fertile zone, and is described in more detail in Chapter 5. Anoptimization calculation is performed to determine the axial plane for the de-tectors, using SERPENT2 in criticality mode. Two sets of six equally-spacedU-235 fission chambers each are placed at the end of each neutron channel giv-ing six azimuthal detectors around the core at two axial locations. Throughoutthe current chapter, the two detector sets are referred to as the lower and upperdetectors, respectively.

6.1 Detection of inadvertent control rod withdrawal,IRW

In an SFR, the control rods are inserted in the core at the beginning-of-cycle(BOC) to compensate for the reactivity swing. Of the many postulated reac-tivity insertion accidents, an inadvertent control rod withdrawal is consideredto be one of the most penalising [7]. During an IRW, the control rod movesat a rate of 4mm/s and gradually results in a spatially distorted neutron fluxand power level around the withdrawn rod. An IRW may lead to a local core-melting accident. The likelihood of such an event is reduced by design asmuch as possible; however, the NFMS has to be able to reliably detect itspossible occurrence as early as possible.

During an IRW, the detector responses are calculated in a series of with-drawal steps from the bottom of the core up to the parking position of thecontrol rods, situated just above the upper fissile zone. An IRW is a transientslow enough to be considered quasi-static. Hence, it is treated here as a seriesof static problems, one for each control rod position. The reaction rates seenby the detector at location i is given by

Ri = nU235

∫σ f ,U235(E).φi(E).dE, (6.1)

where nU235 is the nuclear density of the isotope U235 that constitutes theactive material in the fission chamber, φi(E) is the neutron flux at the detectorlocation, and σ f ,U235(E) is the fission cross-section of the detector material.The vector of all detector responses at the same axial location is referred to as

43

R without the subscript i. A normalized detector response (R̃i) for the detectorat location i is then defined according to

R̃i =Ri

〈R〉 −Ri,0

〈R0〉 , (6.2)

where 〈R〉 is the mean value of the 6 detectors in each ring (same plane) andthe extra subscript 0 refers to the reaction rates with the control rod at thereference position. This provides a detector signal that is independent of thereactor power level (and flux normalization in the simulation as well), but in-stead monitors the angular profile changes in the core’s neutron flux. Specif-ically, R̃ measures the azimuthal distortion from the chosen reference powerprofile of the core, R0. Finally, a monitoring indication (MI), which quantifiesthe impact of the control rod withdrawal is defined as the value of AMI thatminimizes χ2 in the least chi-squared fit

χ2(AMI) = ∑i

(R̃i−AMI .R̃i,1

)2

σ2i

, (6.3)

where σi is the uncertainty of Ri, and R̃i,1 is the normalized response at fullcontrol rod withdrawal. An assumption is made here that R̃ only changesin amplitude as the control rod is withdrawn, and the shape stays constant.The confidence interval of MI is then obtained from the interval of AMI thatencloses the region χ2 < χ2

min+1. The fitting procedure to obtain MI is furtherillustrated in the results in the Figure 6.1 which shows the normalised detectorresponse for the upper and lower detectors. The points with error bars showthe normalized reaction rates (R̃i) for each individual fission chamber, and thelines show the results of the best fits of AMI according to equation 6.3. The fitto the data for half withdrawal validates the assumption that R̃ only changes inamplitude.

The monitoring indication (MI) derived from the fits is shown as a functionof control rod withdrawal in Figure 6.2. There is a close to quadratic rela-tionship between MI and the control rod position for both the detector sets.However, the upper detector set gives an earlier response in MI during a con-trol rod withdrawal than the lower detector set. The statistical uncertainty inMI for both sets is about ±0.03. It is seen from the Figure 6.2 that the up-per detector location is more suitable for the azimuthal detectors as it gives aslightly earlier response during an IRW. Also, the use of multiple detector setsdoes not provide any extra information regarding detector response.

6.2 Calculation methodology assessmentThe series of static calculations are performed in two modes: a) critical-ity mode with SERPENT2 and b) external source mode with ERANOS and

44

Figure 6.1. Relative response in the case of full (100%) and partial (50%) withdrawalfor outer IRW; (A) and (B) corresponds to the upper and lower detectors respectively.

TRIPOLI−4 R©. The criticality mode calculations are made for Beginning-of-life (BOL) condition of the core, namely a fresh core, as a starting point. Thecalculation route for external source mode is illustrated in Figure 6.3.

PARIS-GUI builds an ERANOS input for 2/3rd core. The concentrations atthe last cycle of BOC state are updated for the whole core to obtain a full corepower map for an equilibrium core. Individual rod withdrawal is performedusing an ERANOS procedure which gives the distorted power map for the fullcore corresponding to each control rod withdrawn configuration. The powermap represents the fission source distribution for the fissile zone in the core.The fission source distribution, corresponding to each fissile subassembly, isformatted and input as source definition for performing neutron transport withTRIPOLI− 4 R©. Variance reduction technique is used to provide appropriatebiasing to the source neutrons to be transported to the peripheral fission cham-bers. Finer cells are defined in the areas of importance around the detectori.e. the contributing path between the source and the detector compared to the

45

Figure 6.2. Monitoring Indication for the outer and inner IRW; (A) and (B) corre-sponds to the outer and inner IRW respectively.

rest of the geometry using a variable mesh in the variance reduction moduleof TRIPOLI−4 R©, INIPOND.

The monitoring indications, obtained with SERPENT2 and TRIPOLI−4 R©

as a function of control rod withdrawal, are compared in Figure 6.4. A sta-tistically significant increase in the monitoring indication is seen during thewithdrawal of control rods from the reference state.

The difference in the magnitudes arises because of the different calcula-tional methodologies employed to perform the simulations. The error sourcein the criticality mode is primarily due to statistical uncertainty, which canbe reduced by making better use of the neutron histories. This approach iscomputationally intensive. In the external source mode, the simulation time isconsiderably reduced per calculation; however, the number of calculations isincreased. It is suggested to use an optimised biasing mesh for each detectorlocation in order to reduce the statistical uncertainty up to 1%, and match theresults obtained with SERPENT2 in criticality mode.

46

Figure 6.3. Flowchart for external source mode calculation

Figure 6.4. Monitoring Indication obtained with SERPENT2 and TRIPOLI−4 R©.

47

7. Self Powered Neutron Detectors as in-coredetectors for SFRs

As discussed in Section 3.1.2, it is proposed to use SPNDs as in-core detec-tors in a Generation IV sodium-cooled fast reactor core. In order to track thechanges in the reactor power, a major prompt response is needed with a negli-gible delayed contribution to achieve a linear response w.r.t the reactor power.Emitter materials with stable activation products or very long half-lives wouldhave a negligible delayed contribution. Platinum is the chosen emitter ma-terial for this study as it has a high atomic number to facilitate the gammainteraction in the emitter via the dominant photoelectric effect [48]. The cap-ture cross-section of platinum is high compared with many other materials andonly changes by 1 order of magnitude across 1 keV and 1 MeV neutron en-ergy, thereby making it relatively insensitive to small changes in the neutronspectrum.

A smaller model containing a first ring of subassemblies with homogenisedfuel as the source is used, which is shown in Figure 7.1. The detector is locatedin the cylinder in the central subassembly. In addition to the prompt neutronand gamma fluxes at the SPND location, the activated gamma component inthe structural materials and gammas arising from fission products decay is alsomodeled.

Figure 7.1. SFR model used for this study. The central sub-assembly (blue) housingthe SPND is surrounded by homogenised fuel sub-assemblies, modelled here as auniform cylinder (green).

48

7.1 Calculation routeFigure 7.2 shows the calculation scheme used to perform the simulations. Thecalculations are done in three main steps denoted by the dotted lines.

Figure 7.2. Calculation scheme for this study. Convention for the nodes is as follows:Cyan (Input parameters), Indigo (Codes), Green (Output), Yellow (Final Current out-put), Red Dotted box (Step I), Green dotted box (Step II) & Orange dotted box (StepIII).

In step I, a criticality mode MCNPX neutron and photon transport calcula-tion is performed to obtain prompt neutron and gamma fluxes at the detectorand source locations. The prompt gamma flux includes both fission gammasand those arising from neutron captures in the fuel. A separate MCNPX pho-ton transport calculation is done using an approximate fission product decaygamma spectrum with an average energy of 0.52 MeV as a source to obtainthe decay gamma flux at the detector location. Furthermore, a decay heatpower model with 23 precursors [49] is used to obtain the time dependent re-sponse of the decay heat. The model is explained in more detail in Paper IV.In step II, FISPACT is used to generate the activation gamma sources fromstructural materials after a prescribed period of irradiation (2.5 years in thiscase) and at various cooling times. It should be noted that the prompt and de-layed fluxes mentioned here are source terms. In Step III, the total neutron andgamma spectra obtained in the previous steps are used to define the sources in

49

the MATiSSe tool box. The calculation steps as part of the MATiSSe toolbox are described in Paper IV. The MATiSSe output is a direct electrical cur-rent, derived from the outward net electron currents at both emitter/insulatorand insulator/collector boundaries for all contributions. The final detector re-sponse obtained in terms of current has contributions of prompt neutron re-sponse (n,γ)(γ,e−), prompt gamma response (γ,e−) and a delayed signal as-sociated with the neutron response due to (n,β−). This delay is governed bythe half-life of emitter material, Pt-197 (T1/2=19.9 hrs), which beta-decaysinto Au-197.

7.2 Detector responseDuring the calculations, it is assumed that the gamma produced due to ac-tivation of sodium is negligible for the purpose of this study as the coolantsodium circulates throughout the vessel continuously. For activation of struc-tural materials, the gamma spectrum does not change significantly during thefirst few minutes of cooling time. This means that the activation gammas canbe considered as constant for the time frames of this study, i.e., few minutes.The results show that the delayed gamma flux due to activation in the clad,and from the fission products in the fuel is 19.7% of the total gamma fluxseen by the detector. Thus, it can be concluded that the time evolution of thelocal prompt gamma flux at the detector location follows the time evolutionof the local neutron flux. Various contributions to the platinum SPND and itsconnecting cable, calculated at equilibrium power are presented in Table 7.1.

Table 7.1. Current sensitivities per detector length for the platinum SPND.

Total Current Contribution (%)(A/m) Delayed Prompt Prompt

(n,β−) (n,γ)(γ,e−) (γ,e−)

Pt Emitter 6.53 ·10−7 1.9 27.1 70.9Cable 1.28 ·10−8 9.7 −19.7 109.9

The step change in reactor power is simulated in such a way that it goesdown from full power to 50% level after 500 s, maintained at that level until1500 s, after which it is brought back to full power again. The total currentseen by the platinum SPND is 653nA/m, which is sufficiently measurable. Theprompt neutron and gamma-induced contribution to the total current, which isaround 98%, is dominating whereas the delayed neutron-induced contributionis about 2%, and thus can be neglected. The induced current in the connectingcable is about 2% of the platinum detector current, which can be neglected.Note that the prompt and delayed contributions to the total current mentioned

50

Figure 7.3. (A) Time response of various contributions to the detector current withstep change in power. (B) Total detector response (blue) following a step change inpower. The red dotted line is the ideal detector response.

here are detector responses. The contributions to the detector response duringthis change in power are plotted in Figure 7.3(A). The total detector responseis shown in Figure 7.3(B). The red dotted line represents the ideal detectorresponse. The prompt neutron response (n,γ)(γ,e−) and the prompt gammaresponse (γ,e−) follows the step change in power. There is a small delayedsignal associated with the neutron response due to (n,β−), which can be con-sidered constant at these time scales. The dominant beta emitter is Pt-197 witha half-life of 19.9 hours. Finally, the activation gammas and decay gammasfrom fission products contribute negligibly to the total detector response. Theslight delay in the response due to decay gammas is within the time scales ofinterest.

The prompt contribution dominates at high power levels only. In the condi-tion when the reactor power is reduced to 10%, following long term operation

51

at 100%, the delayed contribution of 2% will dominate due to the presenceof fission products in the reactor core, and thus cannot be neglected. This isdifferent from a fresh core operating at 10% power where the fission prod-ucts precursors have not yet built up. In such a case, the relative contributionswould be identical to the ones shown in Table 7.1.

Thus, it is shown that the platinum SPND placed in an SFR-like environ-ment would give a sufficiently measurable prompt neutron induced current ofthe order of 600 nA/m. It can operate as an in-core detector which followspower perturbations within the core.

52

8. Neutron flux monitoring during transientconditions

Previous studies described in Chapter 6 were performed at steady-state oper-ating conditions. The IRW transient was considered as quasi-static and treatedas a series of multiple steady-state simulations since the rate of control rodwithdrawal occurs at 4mm/s. In practice, the presence of negative feedbacks,such as Doppler reactivity could compensate for the increase in reactivity dur-ing in-core perturbations like IRW. This could modify the extent of changeof neutron flux profile in the core. The previous calculation route did nottake into account the negative feedback effects and examined their interactionwith reactor kinetics during a transient. This part of the work investigates thepossibility of using a set of in-vessel but ex-core fission chambers in combina-tion with a set of in-core self-powered neutron detectors to detect the spatialchanges in the power profile during two different transient scenarios.

8.1 Transient conditionsThe two different transients that are studied here are inadvertent control rodwithdrawal (IRW) and one stuck rod during shutdown (OSR). An IRW resultsin an increase in reactivity and consequently local power, during the with-drawal of one of the control rods. This is a reactivity insertion accident thatcould lead to local core-melting. The rod withdrawal is performed on an outeras well as an inner control rod.

An OSR leads to an overall decrease in the reactor power due to the inser-tion of all but one (stuck) control rods during shutdown. Since the reactor isbeing shutdown, the power decreases as expected. In principle, a reactor isdesigned such that there is sufficient shutdown margin even when the most re-active control rod is fully withdrawn. As expected, the reactor will shutdowneven with the stuck rod being undetected and this condition will not lead toa core-melting accident. However, when the reactor is restarted following ashutdown, the undetected stuck rod might pose a problem and thus, must bedetected at the earliest.

8.2 Calculation routeThe transient behaviour of the control rod movements is simulated using thethermal hydraulics and point kinetics code CHD coupled with the 3D Monte

53

Carlo based neutron transport code SERPENT2. A simplified CHD model[50] that only includes the core part of the primary loop is used for this work.The time scale of the transient considered here is too short for the other coolantloops, i.e., the secondary sodium loop and steam generators to have any effect.Thus, they are excluded from the CHD model. The fissile zone is divided intofive different channels as part of the CHD model used for the outer IRW andthe OSR, which are highlighted in Figure 8.1(A). The fissile zone is dividedinto four different channels for the inner IRW, as shown in Figure 8.1(B).

Figure 8.1. Top view of the SERPENT2 model used to calculate the power profileduring the transient. (A) Five channels used in the CHD model for the outer IRW andOSR transient (B) Four channels used in the CHD model for the inner IRW. The ’Sur-rounding’ channel refers to the immediate fissile zone around the faulty rod. ’Innernear’ and ’Outer near’ are the nearby inner and outer fissile zones, respectively. ’In-ner’ and ’Outer’ are the standard inner and outer fissile zones in the core. The faultyrod is shown in black.

The coupled SERPENT2/CHD model is illustrated in Figure 8.2. First, thesteady state temperature and power profiles are found with an iterative processuntil convergence is achieved. The iteration is initiated with a starting guessof temperature profiles for all the individual channels in the core model. Theaxial power profiles of the core calculated with SERPENT2 are then input tothe thermal hydraulics calculation to obtain the updated temperature profiles.The thermal hydraulics reactor model showing the components included inthe simulation, i.e., coolant channels, wrapper tubes as well as fuel rods withcladding, gas plenum and axial shields, is shown in Figure 8.3.

Transient behaviour is calculated by initiating the point kinetics calcula-tion in the CHD code. Temperature feedbacks of the fuel and the coolant areincluded in the point-kinetics model. The power profile of the core is dis-torted asymmetrically with the movements of control rods. The control rodsare moved over a distance of 80 cm from the bottom of the core to the park-ing position through 10 s to 35 s during the transient. During the simulation,

54

Power profile

Did the temperature profile change?

yes no yesTemperature profile

Time dependent reactivity from CR movement

eraturenge?

Reached tstop?

no yes no

Time dependent CR position

Temperature profile

Power profile

Figure 8.2. Illustration of the flow of the coupled SERPENT2 / CHD simulation.

time-dependent reactivities are added that correspond to the movement of con-trol rods in the core. Further, SERPENT2 is rerun each second with updatedtemperature profiles to obtain new power profiles. The calculations accountsfor the skewed control rod pattern as well as the feedback from the Dopplerreactivity and coolant density changes. Finally, high accuracy neutron trans-port calculations with SERPENT2 are performed at a time interval of 5 s toobtain fission reaction rates for all 10 detectors, i.e., 6 fission chambers and 4SPNDs. The power density (W/cm3), averages fuel temperatures and coolantoutlet temperatures for the different channels in the core are shown in PaperV.

8.3 Detector responseThe detector signal is loaded with additional noise levels. In the case of theIRWs, a 5% noise is added, and in the case of the stuck rod, 1% noise is added.The relative detector response (R̃rel(t, i)) for the detector at location i at time tis defined according to

R̃rel(t, i) =R(t, i)R(t0, i)

−1, (8.1)

where R(t, i) is the detector response at location i at time t and R(t0, i) is thedetector response at location i at t=0, obtained with SERPENT2. The relative

55

rod1

clad1

shield1

rodN

cladN

shieldN

wrap1 wrapN

Cor

e

wrap1

ch1 chN

coolant in

coolant out

Figure 8.3. Illustration of the thermal hydraulics reactor model showing the compo-nents included in the simulation, i.e., coolant channels, wrapper tubes as well as fuelrods with cladding, gas plenum and axial shields.

detector response is normalised with the average power in the core. As dis-cussed in the previous section, the SPND signal is sensitive to decay gammasfrom the fission products. The detector signals from the four SPNDs are cor-rected for the contribution of delayed gammas. A monitoring indication (MI)that tracks power profile changes in the core, is used to quantify the impact ofcontrol rod movement on the detector signal. It is defined as the value of thedeviation of the relative detector response from the averaged value at time t,summed over fission chambers and SPNDs separately. The final MI is givenby

MI(t) = MIFC +MISPND, (8.2)

where MIFC & MISPND are calculated according to the following equation.

MIk(t) =n

∑i=1

(R̃rel(t, i)−< R̃rel(t)>)2, (8.3)

k stands for the type of detector set, i.e., FC or SPND and n stands for thenumber of detectors in a set. < R̃rel(t) > is the averaged relative detectorresponse for a particular set of detectors at time t.

56

The relative detector responses at location i, R̃rel(t, i) for both outer con-trol rod withdrawal and OSR are shown in Figure 8.4(A) & (B), respectively.Note that the effect of fission products decay is visible at low power duringthe OSR transient (Figure 8.4(B)). The detector signals from fission chambersand SPND start to diverge around 20 s. Since the SPND signal is sensitiveto both neutrons and gammas, the prompt gamma contribution competes withthe delayed gamma contribution at low power. The delayed gamma contri-bution includes gammas from the decay of fission products and the activationof structural materials. This is not the case with the IRW transient. Paper IVshows that the prompt neutron and gamma-induced contribution dominates atfull power.

Figure 8.4. Relative detector response during (A) Outer IRW and (B) OSR.

57

The monitoring indications during IRW of an outer and inner control rod,and OSR transients are shown in Figure 8.5(A), (B) and (C), respectively. Inaddition, a smoothened MI is shown using a 10-point moving average filter,which is a low pass filter. It is seen that noise levels up to 5% are acceptablefor maintaining a statistically relevant monitoring indication for both outerand inner IRW. MI tends to increase monotonically after 20 s into the transientduring the outer and inner IRW. At 25 s, the fuel temperature is around 1500K for all channels, which is much lower than the melting-point of the fuel.

There is a visible increase in MI after 10 s during the OSR transient, whichis still statistically significant even with the added noise. The noise level tol-erance is around 1%. After about 20 s into the transient, the increase in MIfades away. At this time, the power in the reactor drops to around 20%. Cor-respondingly, the signal in the fission chambers and the SPNDs decrease, withonly the contribution of decay gammas from fission products present.

Thus, it is possible to reliably detect transients occurring due to movementsof control rods with the proposed set of ex-core and in-core detectors. Thechange in the detector response is prominent during IRW compared to OSR.This is due to the overall decrease of power in the core during the latter case.

58

Figure 8.5. Monitoring Indication during (A) Outer IRW, (B) Inner IRW and (C) OSR59

Part IV:Future work

"Each problem that I solved became a rule, which served afterwards to solveother problems."- René Descartes

9. Conclusions and outlook

The work presented in this thesis is focused on the neutron flux monitoringsystem, NFMS of a Generation-IV sodium-cooled fast reactor. Mainly, twodetector locations, ex-core, beyond the lateral neutron shield and in-core werestudied with regards to the detection of transients related to the movements ofcontrol rods in the core. Conventionally used in SFRs, fission chambers wereemployed as peripheral detectors. For in-core power profile detectors, a fea-sibility study of self-powered neutron detector, SPND with platinum emitterswas performed to measure the detector signal at full power. The importantconclusions and some future perspectives are summarized below.

• It was shown that in-core self-powered neutron detectors are capable ofoperating as local power monitors in an SFR being operated at nominalpower. The simulations show that the monitors provide a sufficientlymeasurable prompt neutron and gamma induced current of the order of600 nA/m. So far, SPNDs have only been used as in-core monitors inthermal reactors, but this work shows that they can also be used duringfull power operation in fast reactors.

• An SPND with a platinum emitter was modeled as part of this work.However, other emitter materials can be explored as well as possiblecandidates for an SNPD located in an SFR or other non-SFR nuclearfacilities with fast neutron environment, such as ITER [26]. On-goingefforts include a feasibility study of using SPNDs in the fast neutron en-vironment of test blanket modules in ITER.

• A standard geometrical design of an SPND was used in this work. A de-sign optimisation study of an SPND suited for SFRs can be performedwith regards to the width of the emitter, the insulator and the collector.

• Another possibility is to perform reference experiments in order to cal-culate SPND signals in a fast reactor environment for validation studies.As a suggestion, the Fast Breeder Test Reactor (FBTR) in India is onesuch facility, which was deployed as a test bed for fast reactor fuelsand structural materials [51]. Also, SPNDs with a platinum emitter isconsidered as a standard detector in material testing reactors because ofthe mixed prompt neutron and gamma response [52]. Therefore, JulesHorowitz Reactor (JHR), an MTR, which is about to finish construction

63

at CEA Cadarache, France [53], with a high fast neutron flux of the or-der of 1014n/cm2/s, can be used as well.

• The steady-state calculations, which step-by-step simulated an inadver-tent withdrawal of an outer control rod showed that it is possible to de-tect the resulting changes in the neutron source profile with in-vesselfission chambers located azimuthally around the core. However, it wasfound difficult to follow an inner control rod withdrawal and preciselyknow the location of the perturbation in the core. Therefore, based onthe results from the feasibility study of in-core SPNDs for SFRs, periph-eral fission chambers and in-core SPNDs were used to detect the spatialchanges in the power profile during two different transient conditionsinvolving asymmetrical movements of control rods, accounting for thedecay gammas from fission products at low power. The results showedthat it is possible to reliably detect the two simulated transients with thetwo detector sets before any melting of the fuel takes place. Similarstudies could be performed in future for other detector locations such asthe above core-structure or the core diagrid, which is below the activecore.

• Fission chambers offer wide-range capability because it is possible tooperate in pulse mode at low count rates and Campbelling mode at highcount rates. However, a reactor must be monitored during off-power op-eration state as well. Hence, other in-core detectors could be exploredfor use during off-power operations.

This thesis is an aim to contribute towards the development of a simpli-fied, yet reliable neutron flux monitoring system for a Generation-IV sodium-cooled fast reactor. There are, however, still many important aspects that needto be considered in order to ensure the reliability of the system, such as vali-dation and qualification tests that have been discussed in this chapter.

64

Acknowledgements

This thesis took around 4.5 years to shape up, spanning Uppsala and Cadarachein southern France, where I spent almost half of this time. There are manypeople who helped me along the way and I owe you all my earnest gratitude.

First of all, I would like to thank my supervisors at Uppsala, Carl, Staffan,Ane, Michael and Peter J for giving me an opportunity to pursue my PhDstudies at the division, and for your invaluable help over all these years. Ane,thank you for your productive feedback during our meetings, and sorry forbothering you with many visa-related problems. Staffan, thank you for sharingyour knowledge and some good advices. I miss being your neighbour. Carl,you have been a great supervisor. Thank you for sharing your ideas and foralways having the right answers. You have pushed me to continuously improvethe work and I have learnt a lot from all the discussions we have had. Yourenthusiasm and knowledge about reactors are both very inspiring. Also, I lovetalking about food, and I am glad that you enjoy Indian food!

I would like to thank my CEA supervisors, Christian and Philippe. Chris-tian, thank you for your incredible support and help. Philippe, thank you forsharing your vast knowledge and experience about neutron instrumentationand giving helpful feedback on my work and many a times, great advices onlife too! I would also like to mention Loic Barbot, who shared his invaluablework on SPNDs with me; Yannick Peneliau, Frederic Jasserand and LaurentBuiron for answering so many questions about TRIPOLI and ERANOS.

To all my former colleagues at LDCI, thank you for making the Cadaracheexperience fun and unforgettable. My former officemates Zsolti, Greg andVlad, and the other members of the Krfc-aix group, Micke and Augusto, thankyou for the insane laughs, the good times and the endless stories, both at workand outside. Victoria, thank you for the wonderful memories. I miss you and’Woohoo’! Jean-Michel, mon ami, merci beaucoup pour m’avoir sauvé dessangliers. Je n’oublierai jamais notre petite aventure.

My stay in France wouldn’t be half as good if it were not for my friendsfrom Masters. Li, you were one of the few familiar faces when I came toCadarache. Thank you for the friendly company and for passing on your lovelyapartment to me after you left! Sapti, Mir and Mithi, your presence made Aixhome away from home. Thank you for all the shared vacations and festivals.

At TK, I would like to thank all the colleagues, including former PhD stu-dents for the interesting conversations during fika and lunch. They made workmuch more enjoyable.

65

A special thanks to my friends back home, Prem and Sam, who have been ahuge support. Thank you for always being there. You never failed to ask whenwas I going to come back :) Prem, thanks for the cover tip!

Finally, I would like to thank my dearest family. Mummy and papa, thankyou for always believing in me. You have been a very patient and strongsupport throughout. Your encouragement has always kept me going. Chinmay,you are the best bhai. Thank you for everything!

66

Summary in Swedish

God säkerhet och tillförlitlighet är väsentligt för driften av nästa generationskärnkraftssystem (Generation-IV). Att förebygga olyckor och incidenter är avhögsta prioritet. Det finns behov av att upptäcka incidenter så tidigt sommöjligt i deras. Övervakningssystemet för neutroner utgör en viktig del avsäkerheten hos en kärnreaktor. Arbetet i denna avhandling gäller främst detek-teringen av störningar som uppkommer genom oönskade rörelser av styrstavari en natriumkyld snabbreaktor (SFR). Detektorer placerade inuti reaktortankenmen både inuti och utanför härden har studerats. En generisk Generation-IVdesign med en 1500 MWth natriumkyld reaktor av pool-typ utformad på CEAi Frankrike har använts till studierna. Den första delen av avhandlingen in-nefattar detektering av en oavsiktlig styrstavsutdragning med användning avfissionskamrar placerade utanför härden symmetriskt runt den radiella neu-tron skärmen. Neutronkanaler i den radiella skärmen användes för att för-bättra transporten av neutroner från härden till detektorerna. Kanalerna äravsmalnande för att minska onödigt läckage och aktivering utanför härden.Resultaten visar att det är möjligt att detektera förändringar i neutronflödetsfördelning från en oavsiktlig utdragning av en yttre styrstav. Det är dock svårtatt exakt följa en oavsiktlig utdragning av en inre styrstav. Resultaten fråndenna del ingår i papper I, II och III. I den andra delen av arbetet gjordes enprincipstudie för användningen av så kallade self powered neutron detectorsför att övervaka den lokala effekten i en natriumkyld reaktor. Till skillnadfrån fissionskamrar kan dessa placeras inuti härden och möjliggöra detekter-ing av oavsiktliga utdragningar även av inre styrstavar. Simuleringar visar atten SPND ger en tillräckligt hög ström (653 nA) för att kunna mätas. Dock ären SPND känslig för både gamma och neutron-flöden och den kommer därföratt ha en fördröjd signalkomponent från resteffekten i reaktorn. I arbetet togsen responsfunktion för detta fram. I denna avhandling har en SPND med enemitter i platina modelleras. Emellertid kan andra material också utforskassom möjliga kandidater för en SNPD belägen i en miljö dominerad av snabbaneutroner. Resultaten från den andra delen ingår i papper IV. Den tredje de-len av avhandlingen är en studie av ett neutron-detektionssystem bestående av6 stycken fissionskamrar och 4 stycken SPND:er. Undersökningar av effek-tiviteten att upptäcka två olika typer av incidenter gjordes. Dels oavsiktligautdragningar av styrstavar, men även fallet med en styrstav som fastnat. Simu-leringarna i den tredje delen av avhandlingen var dynamiska och tidsberoendetill skillnad från de simuleringar som gjordes i första delen. Resultaten visaratt båda typerna av incidenter kan upptäckas med det föreslagna detektorsys-temet, även i en brusig miljo, och presenteras i papper V.

67

References

[1] BP. Statistical review of world energy 2016. Technical report.[2] IPCC. Special report on renewable energy sources and climate change

mitigation. Technical report, IPCC, 2012.[3] M. E. Bunker. Early reactors. LOS ALAMOS SCIENCE, Winter/Spring 1983.[4] C. E. Till and Y. Il Chang. Plentiful Energy, The Story of the Integral Fast

Reactor: The complex history of a simple reactor technology, with emphasis onits scientific bases for non-specialists. 2011.

[5] IAEA. Accident monitoring systems for nuclear power plants. Technical report,IAEA NUCLEAR ENERGY SERIES No. NP-T-3.16, 2015.

[6] A.E. Waltar, A.B. Reynolds. Fast Breeder Reactors. 1981.[7] C. Jammes, et al. Neutron flux monitoring system of the french GEN-IV SFR:

Assessment of diverse solutions for in-vessel detector installation. NuclearEngineering and Design, 270(0):273–282, 2014.

[8] OECD/NEA. Technology Roadmap Update for Generation IV Nuclear EnergySystems. Technical report, OECD/NEA, 2014.

[9] ��������������� �����������. Accessed: 04.04.2017.[10] IAEA. Spent Fuel Reprocessing Options. Technical report, IAEA, 2008.[11] P. Filliatre, et al. In vessel neutron instrumentation for sodium-cooled fast

reactors: Type, lifetime and location. Annals of Nuclear Energy,37(11):1435–1442, 2010.

[12] IAEA. Benchmark Analyses on the Control Rod Withdrawal Tests Performedduring the PHENIX End-of-Life Experiments. Technical report, IAEA, 2014.

[13] G. F. Knoll. Radiation Detection and Measurement. 4th. John Wiley & Sons,2010.

[14] P. Filliatre, et al. Reasons why Plutonium 242 is the best fission chamberdeposit to monitor the fast component of a high neutron flux. NuclearInstruments and Methods in Physics Research Section A: Accelerators,Spectrometers, Detectors and Associated Equipment, 593(3):510 – 518, 2008.

[15] C. Jammes, et al. Research Activities in Fission Chamber Modeling in Supportof the Nuclear Energy Industry. IEEE Transactions on Nuclear Science,57(6):3678 –3682, 2010.

[16] C. Jammes, et al. Assessment of the high temperature fission chambertechnology for the French fast reactor program. IEEE Transactions on NuclearScience, 59(4):1351–1359, 2012.

[17] B. Lescop, et al. A new system for in-core wide range neutron monitoring. InNuclear Science Symposium Conference Record, 2004 IEEE, volume 3, pages1567–1570, 2004.

[18] Zs. Elter, et al. Performance investigation of the pulse and campbelling modesof a fission chamber using a poisson pulse train simulation code. NuclearInstruments and Methods in Physics Research Section A: Accelerators,Spectrometers, Detectors and Associated Equipment, 774:60 – 67, 2015.

68

[19] H. D. Warren. Calculational model for self-powered neutron detector. NuclearScience and Engineering, 48:331–342, 1972.

[20] P.S. Rao and S.C. Misra. Neutron sensitivity of vanadium self powered neutrondetectors. Nuclear Instruments and Methods in Physics Research Section A:Accelerators, Spectrometers, Detectors and Associated Equipment, 253(1):57 –60, 1986.

[21] O. Moreira, H. Lescano. Analysis of vanadium self powered neutron Detectorssignal. Annals of Nuclear Energy, 58:90 – 94, 2013.

[22] H. Böck, J. Rantanen. Temperature and radiation tests with Pt- andRh-self-powered neutron detectors. Nuclear Instruments and Methods,164(1):205 – 207, 1979.

[23] N. P. Goldstein, W. H. Todt. A survey of self-powered detectors - present andfuture. IEEE Transactions on Nuclear Science, 26, 1979.

[24] N. P. Goldstein, et al. Gamma-sensitive self powered detectors and their use forin-core flux mapping. IEEE Transactions on Nuclear Science, NS-28(1), 1981.

[25] L. Vermeeren. Neutron and gamma sensitivities of self-powered detectors:Monte Carlo modelling. 4th International Conference ANIMMA 2015, Lisbon,Portugal, 2015.

[26] M. Angelone, et al. Development of self-powered neutron detectors for neutronflux monitoring in HCLL and HCPB ITER-TBM. Fusion Engineering andDesign, 89(9 - 10):2194 – 2198, 2014.

[27] L. Barbot, et al. Final qualification of an industrial wide range neutroninstrumentation in the osiris mtr reactor. In 1st International ConferenceANIMMA 2009, Marseille, France, 2009.

[28] M.A. Schultz. Control of nuclear reactors and power plants. New York :McGraw-Hill, 1961.

[29] W. F. Miller, E. E. Lewis. Computational Methods of Neutron Transport.American Nuclear Society, LaGrange Park, Illinois, 1993.

[30] C. Demaziére. Modelling of Nuclear Reactors. Chalmers University ofTechnology, 2013.

[31] J. Leppänen, et al,. The Serpent Monte Carlo code: Status, development andapplications in 2013. Annals of Nuclear Energy, 82:142 – 150, 2015.

[32] E. R. Woodcock, et al. Techniques Used in the GEM Code for Monte CarloNeutronics Calculations in Reactors and Other Systems of Complex Geometry.In Proceedings of the Conference on Applications of Computing Methods toReactor Problems. Argonne National Laboratory, 1965.

[33] J. Leppänen. Standard comparison between SERPENT 1.1.13 and MCNP5.Technical report, VTT, 2010.

[34] X-5 Monte Carlo Team. MCNP - A General Monte Carlo N-Particle TransportCode, Version 5 (Los Alamos National Laboratory, Los Alamos, New Mexico,USA, April). Technical Report LA-UR-03-1987, Los Alamos NationalLaboratory (LANL), 2003.

[35] ������������� ����������� ��������� . Accessed: 03.04.2017.[36] E. Brun, et al. TRIPOLI-4 R©, CEA, EDF and AREVA reference Monte Carlo

code. Annals of Nuclear Energy, 82:151 – 160, 2015.[37] R. Brun, F. Rademakers. ROOT, an object-oriented data analysis framework.

Nuclear Instruments and Methods in Physics, Research Section A: Accelerators,

69

Spectrometers, Detectors and Associated Equipment, 389:81–86, 1997.[38] J.P. Both, J.C. Nimal, T. Vergnaud. Automated importance generation and

biasing techniques for Monte Carlo shielding techniques by the TRIPOLI-3code. Progress in Nuclear Energy, 24(1):273 – 281, 1990.

[39] X-5 Monte Carlo Team. MCNP - A General Monte Carlo N-Particle TransportCode, Version 5. Technical Report LA-UR-03-1987, Los Alamos NationalLaboratory (LANL), 2003.

[40] A. Hébert. Applied Reactor Physics. Presses inter Polytechnique, 2009.[41] J.M. Ruggieri, J. Tommasi, J.F. Lebrat. ERANOS 2.1: International Code

System for GEN IV Fast Reactor Analysis. In International Congress onAdvances in Nuclear Power Plants (ICAPP 2006), Reno, NV USA., 2006.

[42] G. Rimpault. Algorithmic features of the ECCO Cell Code for treatingheterogeneous fast reactor subassemblies. In Proc. Int. Topical Meeting onReactor Physics and Computations, Portland, USA, 1995.

[43] C. B. Carrico, E. E. Lewis, G. Palmiotti. Three-dimensional variational nodaltransport methods for cartesian, triangular, and hexagonal criticalitycalculations. Nuclear Science and Engineering, 111.2:168–179, 1992.

[44] R. Le Tellier, C. Suteau, D. Fournier, J.M. Ruggieri. High-order discreteordinate transport in hexagonal geometry: A new capability in ERANOS. In21st International Conference on Transport Theory; Torino (Italy), 2009.

[45] F. Varaine, et al. Pre-conceptual design study of ASTRID core. In Proceedingsof ICAPP’12 - Int. Congress on Advances in Nuclear Power Plants, number12173, Chicago, USA, 2012.

[46] B. Fontaine, et al. The French R&D on SFR core design and ASTRID project.In Proceedings of GLOBAL, Makuhari, Japan, 2011.

[47] J. Gourdon, et al. An overview of Superphénix commissioning tests. NuclearScience and Engineering, 106(1):1–10, 1990.

[48] R. B. Shields. A platinum in-core flux detector. IEEE Transactions on NuclearScience, NS-20(1), 1973.

[49] Decay heat power in light water reactors. ANSI/ANS, 5.1, 2014.[50] S. A. Qvist, et al. Tailoring the response of autonomous reactivity control

(ARC) systems. Annals of Nuclear Energy, 99:383 – 398, 2017.[51] P. Puthiyavinayagam, et al. Development of fast breeder reactor technology in

india. Progress in Nuclear Energy, 2017. In Press, Corrected Proof.[52] C. Reynard. et al. In core instrumentation for online nuclear heating

measurements of material testing reactor. In RRFM 2010 transactions, 2010.[53] D. Iracane, P. Chaix, A. Alamo. Jules horowitz reactor: a high performance

material testing reactor. Comptes Rendus Physique, 9(3):445 – 456, 2008.

70

Acta Universitatis UpsaliensisDigital Comprehensive Summaries of Uppsala Dissertationsfrom the Faculty of Science and Technology 1508

Editor: The Dean of the Faculty of Science and Technology

A doctoral dissertation from the Faculty of Science andTechnology, Uppsala University, is usually a summary of anumber of papers. A few copies of the complete dissertationare kept at major Swedish research libraries, while thesummary alone is distributed internationally throughthe series Digital Comprehensive Summaries of UppsalaDissertations from the Faculty of Science and Technology.(Prior to January, 2005, the series was published under thetitle “Comprehensive Summaries of Uppsala Dissertationsfrom the Faculty of Science and Technology”.)

Distribution: publications.uu.seurn:nbn:se:uu:diva-319945

ACTAUNIVERSITATIS

UPSALIENSISUPPSALA

2017