Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Nuclear Engineering, 1980. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND SCIENCE. / Vita. / Includes bibliographical references. / by Kord Sterling Smith. / Ph.D.

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Nuclear Engineering, 1981. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND SCIENCE. / Vita. / Includes bibliographical references. / by Alexander Y.C. Cheng. / Ph.D.

Thesis. 1976. Sc.D.--Massachusetts Institute of Technology. Dept. of Nuclear Engineering. / Microfiche copy available in Archives and Science. / Bibliography: leaves 221-224. / Sc.D.

Thesis. 1977. Ph.D.--Massachusetts Institute of Technology. Dept. of Nuclear Engineering. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND SCIENCE. / Vita. / Includes bibliographical references. / Ph.D.

Thesis (Nucl.E.)--Massachusetts Institute of Technology, Dept. of Nuclear Engineering, 1979. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND SCIENCE. / Includes bibliographical references. / by John A. Bernard, Jr. / Nucl.E.

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This thesis presents a detailed analysis of the bRAPID (burnup for RAPID – Real Time Analysis for Particle transport and In-situ Detection) code system, and the implementation and validation of two new algorithms for improved burnup simulation. bRAPID is a fuel burnup algorithm capable of performing full core 3D assembly-wise burnup calculations in real time, through its use of the RAPID Fission Matrix methodology. A study into the effect of time step resolution on isotopic composition in Monte Carlo burnup calculations is presented to provide recommendations for time step scheme development in bRAPID. Two novel algorithms are implemented into bRAPID, which address: i) the generation of time-dependent correction factors for the fission density distribution in boundary nuclear fuel assemblies within a reactor core; ii) the calculation of pin-wise burnup distributions and isotopic concentrations. Time step resolution analysis shows that a variable time step scheme, developed to accurately characterize important isotope evolution, can be used to optimize burnup calculations and minimize computation time. The two new algorithms have been benchmarked against the Monte Carlo code system Serpent. Results indicate that the time-dependent boundary correction algorithm improves fission density distribution calculations by including a more detailed representation of boundary physics. The pin-wise burnup algorithm expands bRAPID capabilities to provide material composition data at the pin level, with accuracy comparable to the reference calculation. In addition, wall-clock time analyses show that burnup calculations performed using bRAPID with these novel algorithms require a fraction of the time of Serpent. / Master of Science / Fuel burnup modeling is an important aspect of nuclear reactor design that provides information about the energy extracted (called burnup) and isotopes created or used in the fuel of a reactor over time. A reactor core is a collection of fuel assemblies, and assemblies are simply a bundle of fuel pins, which contain nuclear fuel such as Uranium. The desire for accurate and fast computer codes to calculate fuel burnup rises each year as engineers working in reactor core design seek to arrange fuel assemblies in an optimal pattern to extract the most energy. State of the art burnup codes exist, however they have certain limitations due to their underlying methodologies. To satisfy this need, the bRAPID algorithm was developed by the Virginia Tech Transport Theory Group (VT³G). bRAPID is a new methodology capable of performing full core fuel burnup calculations in real time. bRAPID is able to calculate the criticality and burnup distribution of a reactor orders of magnitude faster than comparable algorithms, while addressing many of the shortcomings seen in other burnup codes. In this thesis, studies of standard burnup codes are conducted in order to aid in bRAPID analysis: first in the form of a detailed study of the reference Monte Carlo model used in this thesis, and secondly in an investigation of the effect of time step selection – or the time intervals used in burnup calculations – on isotope concentration. Both of these studies are conducted using the benchmark code system, Serpent, with the latter study providing useful insight that can be used for bRAPID database development. This thesis then presents two new algorithms for bRAPID that expand its capability and improve performance. First, an algorithm to more accurately simulate the boundary regions of the core – called the time dependent boundary correction algorithm – is presented and benchmarked. Next, an algorithm to expand bRAPID capability from assembly-wise to pin-wise burnup calculations is implemented and tested. These two algorithms are benchmarked against the Serpent Monte Carlo based burnup code.

It is shown that multigroup transport equations with nondiagonal cross section matrices arise when the modal approximation is applied to energy dependent transport equations. This work is a study of such equations for the case that the cross section matrix is nondiagonalizable. For the special case of a two-group problem with a noninvertible scattering matrix, the problem is solved completely via the Wiener-Hopf method. For more general problems, generalized Chandrasekhar H equations are derived. A numerical method for their solution is proposed. Also, the exit distribution is written in terms of the H functions. / Ph. D. / incomplete_metadata

This thesis is a blend of neutron transport theory and numerical analysis. We start with the study of the problem of the Mika/Case eigenexpansion used in the solution process of the homogeneous one-speed Boltzmann neutron transport equation with anisotropic scattering for plane symmetry. The anisotropic scattering is expressed as a finite Legendre series in which the coefficients are the ``scattering coefficients'. This eigenexpansion consists of a discrete spectrum of eigenvalues with its corresponding eigenfunctions and the continuous spectrum [-1,+1] with its corresponding eigendistributions. In the general case where the anisotropic scattering can be of any (finite) order, multiple discrete eigenvalues exist and these have to be located to have the complete spectrum. We have devised a stable and robust method that locates all these discrete eigenvalues. The method is a two-step process: first the number of discrete eigenvalues is calculated and this is followed by the calculation of the discrete eigenvalues themselves, now being able to count them down and make sure none are forgotten. <p><p>During our numerical experiments, we came across what we called near-singular eigenvalues: discrete eigenvalues that are located extremely close to the continuum and hence lead to near-singular behaviour in the eigenfunction. Our solution method has been adapted and allows for the automatic detection of such a near-singular eigenvalue. <p><p>For the elements of the continuous spectrum [-1,+1], there is no non-zero function satisfying the associated eigenequation but there is a non-zero distribution that does satisfy it. It is not feasible to compute a distribution as such but one can evaluate integrals in which this distribution appears. The continuum part of the eigenexpansion can hence only be characterised by its (angular) moments. Accurate and fast numerical quadrature is needed to evaluate these integrals. Several quadrature methods have been evaluated on a representative test function. <p><p><p>The eigenexpansion was proved to be orthogonal and complete and hence can be used to represent the infinite medium Green's function. The latter is the building block of the Boundary Sources Method, an integral solution method for the neutron transport equation. Using angular and angular/spatial moments of the Green's function, it is possible to solve with high accuracy slab problems. We have written a one-dimensional slab code implementing this Boundary Sources Method allowing for media with arbitrary order anisotropic scattering. Our results are very good and the code can be considered as a benchmark code for others. <p><p><p>As a final application, we have used our code to study the discrete spectrum of a well-known scattering kernel in radiative transfer, the Henyey-Greenstein kernel. This kernel has one free parameter which is used to fit the kernel to experimental data. Since the kernel is a continuous function, a finite Legendre approximation needs to be adopted. Depending on the free parameter, the approximation order and the number of secondaries per collision, the number of discrete eigenvalues ranges from two to thirty and even more. Bounds for the minimum approximation order are derived for different requirements on the approximation: non-negativity, an absolute and relative error tolerance. <p> / Doctorat en sciences appliquées / info:eu-repo/semantics/nonPublished

Thesis (PhD)--Stellenbosch University, 2012. / ENGLISH ABSTRACT: The objective of this research was to develop a neutron detection system that incorporates a mass spectrometer to measure high neutron flux in a nuclear reactor environment. This system consists of slow and fast neutron detector elements for measuring fluxes in those energy regions respectively. The detector should further be capable of withstanding the harsh conditions associated with a high temperature reactor. This novel detector which was initially intended for use in the PBMR reactor has possible applications as an in-core neutron and indirect temperature-monitoring device in any of the HTGR. Simulations of a generic HTGR core model were performed in order to obtain the neutron energy spectrum with emphasis on the behavior of three energy regions, slow, intermediate and fast neutrons within the core at different temperatures. The slow neutron flux which has the characteristic of a Maxwell- Boltzmann distribution were found to shift to larger values of neutron flux at higher energies as the fuel temperature increased, while fast neutron flux spectra remained relatively constant. In addition, the results of the fit of the slow neutron flux with a modified Maxwell-Boltzmann equation confirmed that in the presence of the neutron source, leakage and absorption, the effective neutron temperatures is above the medium temperatures. From these results, it was clear that the detection system will need to monitor both slow and fast neutron flux. Placing neutron detectors inside the reactor core, that are sensitive to a particular energy range of slow and fast neutrons, would thus provide information about the change of temperature in the fuel and hence act as an in-core temperature monitor. A detection mechanism was developed that employs the neutron-induced break-up reaction of 6Li and 12C into α-particles. These materials make excellent neutron converters without interference due to γ-rays, as the contributions from 6Li(γ,np)4He and 12C(γ,3α) reactions are negligible. The mass spectrometer measures the 4He partial pressure as a function of time under high vacuum with the help of pressure gradient provided by a high-vacuum turbomolecular pump and a positive-displacement fore-vacuum pump connected in series. A cryogenic trap, which contains a molecular sieve made of pellets 1.6 mm in diameter, was also designed and manufactured to remove impurities which cause a background in the lighter mass region of the spectrum. The development and testing of the high flux neutron detection system were performed at the iThemba Laboratory for Accelerator Based Sciences (LABS), South Africa. These tests were carried out with a high energy proton beam at the D-line neutron facility, and with a fast neutron beam at the neutron radiation therapy facility. To test the principle and capability of the detection system in measuring high fluxes, a high intensity 66 MeV proton beam was used to produce a large yield of α-particles. This was done because the proton inelastic scattering cross-section with 12C nuclei is similar to that of neutrons, with a threshold energy of about 8 MeV for both reactions. Secondly, the secondary fast neutrons produced from the 9Be(p,n)9B reaction were also measured with the fast neutron detector. The response of this detection system during irradiation was found to be relatively fast, with a rise time of a few seconds. This is seen as a sharp increase in the partial pressure of 4He gas as the proton or neutron beam bombards the 12C material. It was found that the production of 4He with the proton beam was directly proportional to the beam intensity. The number of 4He atoms produced per second was deduced from the partial pressure observed during the irradiation period. With a neutron beam of 1010 s−1 irradiating the detector, the deduced number of 4He atoms was 109 s−1. When irradiation stops, the partial pressure drops exponentially. This response is attributed to a small quantity of 4He trapped in the present design. Overall, the measurements of 4He partial pressure produced during the tests with proton and fast neutron beams were successful and demonstrated proof of principle of the new detection technique. It was also found that this system has no upper neutron flux detection limit; it can be even higher than 1014 n·cm−2·s−1. The lifetime of this detection system in nuclear reactor environment is practically unlimited, as determined by the known ability of stainless steel to keeps its integrity under the high radiation levels. Hence, it is concluded that this high flux neutron detection system is excellent for neutron detection in the presence of high γ-radiation level and provides real-time flux measurements. / AFRIKAANSE OPSOMMING: Die doel van hierdie navorsing was om ’n neutrondetektorstelsel te ontwikkel wat hoë neutronvloed binne in ’n kernreaktor kan meet. Die stelsel bevat twee aparte detektorelemente sodat die termiese sowel as snelneutronvloed gemeet kan word. Die detektor moet verder in staat wees om die strawwe toestande, kenmerkend aan ’n hoë temperatuur reaktor, te kan weerstaan. Die innoverende detektorstelsel, oorspronklik geoormerk vir gebruik in die PBMR reaktor, het toepassingsmoontlikhede as in-kern neutron- sowel as indirekte temperatuurmonitor. Simulasies van ’n generiese model van ’n HTGR reaktorkern is uitgevoer ten einde die neutronenergiespektrum in die kern by verskillende temperature te bekom met klem op die gedrag van neutrone in drie energiegroepe: stadig (termies), intermediêr en snel (vinnig). Daar is bevind dat die stadige neutrone, wat ’n Maxwell-Boltzman verdeling toon, in intensiteit toeneem en dat die piek na hoër energie verskuif met toename in temperatuur, terwyl die vinnige neutronspektrum relatief onveranderd bly. ’n Passing van die stadige spektrum op ’n gemodifiseerde Maxwell-Boltzmann verdeling het bevestig dat die effektiewe neutrontemperatuur weens die teenwoordigheid van bronterme, verliese en absorpsie, hoër as die temperatuur van die medium is. Hierdie resultate maak dit duidelik dat die detektorstelsel beide die stadige sowel as die vinnige neutronvloed moet kan waarneem. Deur detektorelemente wat sensitief is vir die onderskeie spekrale gebiede in die reaktorhart te plaas, kan informasie bekom word wat tot in-kern temperatuur herleibaar is sodat die stelsel inderdaad as indirekte temperatuurmonitor kan dien. Die feit dat alfa-deeltjies geproduseer word in neutron-geïnduseerde opbreekreaksies van 6Li en 12C is as die basis van die nuwe opsporingsmeganisme aangewend. Hierdie materiale funksioneer uitstekend as neutron-selektiewe omsetters in die teenwoordigheid van gamma-strale aangesien laasgenoemde se bydraes tot helium produksie via die 6Li(γ,np)4He en 12C(γ,3α) reaksies, weglaatbaar is. Die massaspektrometer meet die tydgedrag van die 4He parsiële druk binne ’n hoogvakuum wat met behulp van ’n seriegeskakelde kombinasie van ’n turbomolekulêre en positiewe-verplasingsvoorpomp verkry word. ’n Koueval met ’n molekulêre sif, bestaande uit 1.6 mm diameter korrels, is ontwerp en vervaardig om onsuiwerhede te verwyder wat andersins as agtergrond by die ligter gedeelte van die massaspektrum sou wys. Die ontwikkeling en toetsing van die hoëvloed detektorstelsel is te iThembaLABS (iThemba Laboratories for Accelerator Based Sciences) gedoen. Dit is uitgevoer deur gebruik te maak van die hoë energie protonbundel van die D-lyn neutronfasiliteit asook van die bundel vinnige neutrone by die neutronterapiefasiliteit. Om die beginsel en vermoë te toets om by ’n hoë neutronvloed te kan meet, is van die intense 66 MeV protonbudel gebruik gemaak om ’n hoë opbrengs alfa-deeltjies te verkry. Dit is gedoen omdat die reaksiedeursnit vir onelastiese verstrooiing van protone vanaf 12C kerne soortgelyk is aan die van neutrone, met ’n drumpelenergie van 8 MeV vir beide reaksies. Tweedens is die sekondêre vinnige neutrone afkomstig van die 9Be(p,n)9B reaksie ook met die neutrondetektor gemeet. Daar is bevind dat die reaksietyd van die deteksiestelsel tydens bestraling relatief vinnig is, soos gekenmerk deur ’n stygtyd van etlike sekondes. Laasgenoemde manifesteer as ’n toename in die parsiële druk van die 4He sodra die proton- of neutronbundel op die 12C teiken inval. Daar is verder bevind dat die 4He produksie direk eweredig aan die bundelintensiteit is. Vir ’n neutronbundel van nagenoeg 1010 s−1, invallend op die neutrondetektor, is vanaf die gemete parsiële druk afgelei dat die produksie van 4He atome sowat 109 s−1 beloop. In die geheel beoordeel, was die meting van die 4He parsiële druk tydens die toetse met vinnige protone en neutrone suksesvol en het dit die nuwe meetbeginsel bevestig. Dit is verder bevind dat die meetstelsel nie ’n beperking op die boonste neutronvloed plaas nie, maar dat dit vloede van selfs hoër as 1014 s−1 kan hanteer. Die leeftyd van die detektorstelsel in die reaktor is prakties onbeperk en onderhewig aan die bevestigde integriteit van vlekvrystaal onder hoë bestraling. Die gevolgtrekking is dus dat die nuwe detektorstelsel uitstekend geskik is vir die in-tyd meting van ’n baie hoë vloed van neutrone ook in die teenwoordigheid van intense gammabestraling.