Doses absorvidas e doses efetivas podem ser calculadas utilizando códigos computacionais de transporte de radiação. A qualidade desses cálculos depende dos dados nucleares, no entanto, são raras as informações sobre as diferenças nas doses causadas por diferentes bibliotecas. O objetivo desse estudo é comparar os valores de dose (absorvida e efetiva) obtidos utilizando diferentes bibliotecas de dados nucleares devido a uma fonte externa de nêutrons na faixa de 10-11 a 20 MeV. As bibliotecas de dados nucleares são: JENDL 4.0, JEFF 3.1.1 e ENDF/B-VII.0. Cálculos de doses foram realizados utilizando o código MCNPX considerando o modelo antropomórfico da ICRP-110. As diferenças nos valores das doses absorvidas utilizando as bibliotecas JEFF 3.1.1 e a ENDF/B.VII são pequenas, em torno de 1%, porém os resultados obtidos com a JENDL 4.0 apresentam diferenças de até 85 % compara aos resultados da ENDF/B-VII.0 e JEFF 3.1.1. Diferenças nas doses efetivas são em torno de 1,5% entre ENDF/B-VII.0 e JEFF 3.1.1, e 11 % entre ENDF/B-VII.0 e JENDL 4.0. / Absorbed dose and Effective dose are usually calculated using radiation transport computer codes. The quality of the calculations of absorbed dose depends on nuclear data utilized, however, there are rare information about the differences in dose caused by the use of different libraries. The objective of this study is to compare dose values obtained using different nuclear data libraries due to external source of neutrons in the energy range from 10-11 to 20 MeV. The nuclear data libraries used are: JENDL 4.0, JEFF 3.3.1 and ENDF/B.VII. Dose calculations were carried out with the MCNPX code considering the anthropomorphic ICRP 110 model. The differences in the absorbed dose values using JEFF 3.3.1 and ENDF/B.VII libraries are small, around 1%, but the results obtained with JENDL 4.0 presented differences up to 85% compared to ENDF and JEFF results. Differences in effective dose values are around 1.5% between ENDF and JEFF and 11% between ENDF/B.VII and JENDL 4.0.

In this thesis we study methods for solving the neutron transport equation (or linear Boltzmann equation). This is an integro-differential equation that describes the behaviour of neutrons during a nuclear fission reaction. Applications of this equation include modelling behaviour within nuclear reactors and the design of shielding around x-ray facilities in hospitals. Improvements in existing modelling techniques are an important way to address environmental and safety concerns of nuclear reactors, and also the safety of people working with or near radiation. The neutron transport equation typically has seven independent variables, however to facilitate rigorous mathematical analysis we consider the monoenergetic, steady-state equation without fission, and with isotropic interactions and isotropic source. Due to its high dimension, the equation is usually solved iteratively and we begin by considering a fundamental iterative method known as source iteration. We prove that the method converges assuming piecewise smooth material data, a result that is not present in the literature. We also improve upon known bounds on the rate of convergence assuming constant material data. We conclude by numerically verifying this new theory. We move on to consider the use of a specific, well-known diffusion equation to approximate the solution to the neutron transport equation. We provide a thorough presentation of its derivation (along with suitable boundary conditions) using an asymptotic expansion and matching procedure, a method originally presented by Habetler and Matkowsky in 1975. Next we state the method of diffusion synthetic acceleration (DSA) for which the diffusion approximation is instrumental. From there we move on to explore a new method of seeing the link between the diffusion and transport equations through the use of a block operator argument. Finally we consider domain decomposition algorithms for solving the neutron transport equation. Such methods have great potential for parallelisation and for the local application of different solution methods. A motivation for this work was to build an algorithm applying DSA only to regions of the domain where it is required. We give two very different domain decomposed source iteration algorithms, and we prove the convergence of both of these algorithms. This work provides a rigorous mathematical foundation for further development and exploration in this area. We conclude with numerical results to illustrate the new convergence theory, but also solve a physically-motivated problem using hybrid source iteration/ DSA algorithms and see significant reductions in the required computation time.

Neste trabalho o transporte de nêutrons é simulado em materiais presentes no núcleo de reatores. O espectro de nêutrons é decomposto como uma soma de três distribuições de probabilidade. Duas das distribuições preservam sua forma com o tempo, mas não necessariamente sua integral. Uma das duas distribuições é devido ao espectro de fissão, isto é, altas energias de nêutrons, a outra é uma distribuição de Maxwell-Boltzmann para nêutrons de baixas energias (térmicos). A terceira distribuição tem uma forma a priori desconhecida e que pode variar com o tempo, sendo determinada a partir de uma simulação Monte Carlo com acompanhamento dos nêutrons e suas interações com dependência contínua de energia. Isto é obtido pela parametrização das seções de choque dos materiais do reator com funções contínuas, incluindo as regiões de ressonâncias resolvidas e não resolvidas. O objetivo deste trabalho é implementar efeitos de up-scattering através do tratamento estat ístico da população de nêutrons na distribuição térmica. O programa de simulação calcula apenas down-scattering, pois o cálculo do up-scattering microscópico aumenta signi_cativamente tempo de processamento computacional. Além de contornar esse problema, pode-se reconhecer que up-scattering é dominante na região de energia mais baixa do espectro, onde assume-se que as condições de equilíbrio térmico para nêutrons imersos em seu ambiente são válidas. A otimização pode, assim, ser atingida pela manutenção do espectro de Maxwell- Boltzmann, isto é, up-scattering é simulado por um tratamento estatístico da população de nêutrons. Esta simulação é realizada utilizando-se dependência energética contínua, e, como um primeiro caso a ser estudado assume-se um regime recorrente. As três distribuições calculadas são então utilizadas no código Monte Carlo para calcular os passos Monte Carlo subsequentes. / In this work the neutron transport is simulated in reactor core materials. The neutron spectrum is decomposed as a sum of three probability distributions. Two of the distributions preserve shape with time but not necessarily the integral. One of the two distributions is due to prompt ssion, i.e. high neutron energies and the second a Maxwell-Boltzmann distribution for low (thermal) neutron energies. The third distribution has an a priori unknown and possibly variable shape with time and is determined from a Monte Carlo simulation with tracking and interaction with continuous energy dependence. This is done by the parametrization of the material cross sections with continuous functions, including the resolved and unresolved resonances region. The objective of this work is to implement up-scattering e ects through the treatment of the neutron population in the thermal distribution. The simulation program only computes down-scattering, for the calculation of microscopic upscattering increases signi cantly computational processing time. In order to circumvent this problem, one may recognize that up-scattering is dominant towards the lower energy end of the spectrum, where we assume that thermal equilibrium conditions for neutrons immersed in their environment holds. The optimization may thus be achieved by the maintenance of the Maxwell-Boltzmann spectrum, i.e. up-scattering is simulated by a statistical treatment of the neutron population. This simulation is performed using continuous energy dependence, and as a rst case to be studied we assume a recurrent regime. The three calculated distributions are then used in the Monte Carlo code to compute the Monte Carlo steps with subsequent updates.

This thesis comprises of essentially two parts. The first deals with materials in a fusion reactor and examines how neutron damage affects material in a fusion reactor, with focus on how this is important for plasma damage. The methods used are neutron transport, primary event analysis and molecular dynamics. It found that the neutron damage by 14 MeV neutrons is restricted to back scatter events within the surface (first 20 microns). Molecular dynamics analysis showed that the issue of cascades is heavily dependent on direction of primary event and the energy of such. Statistical analysis was done to provide a standard approach for modelling of damage through neutrons. The second deals with the relaxation of magnetic flux ropes with an emphasis on kink unstable flux ropes. A relaxation model was developed which shows good approximation to simulation results of merging magnetic flux ropes. Subsequently, work was done to establish the physical processes involved in relaxation. This was done by examining magnetohydrodynamic (MHD) simulations of two flux ropes, one unstable and one stable. It was found that there is is a clear distance at which merger does not occur any more. Furthermore, a critical current seems to be a requirement at the edge a stable flux rope.

Basierend auf dem Reaktordynamikcode DYN3D für LWR, wurde die Codeversion DYN3D-HTR für das Blockkonzept eines graphit-moderierten, helium-gekühlten Hochtemperaturreaktors entwickelt. Diese Entwicklung umfasst die: • methodische Weiterentwicklung der 3D stationären Neutronenflussberechnung für hexagonale Geometrie (HTR-Brennelement-Blöcke), • Generierung von Wirkungsquerschnittsdaten unter Berücksichtigung der doppelten Heterogenität, • Modellierung der Wärmeleitung und des Wärmetransports in der Graphitmatrix. Die nodale SP3-Neutronentransport-Methode in DYN3D wurde auf hexagonale Brennelementgeometrie erweitert. Es wird eine Unterteilung der Hexagone in Dreiecke vorgenommen, so dass die Verfeinerung hexagonaler Strukturen untersucht werden kann. Die Verifikation erfolgte durch Vergleiche mit Monte-Carlo-Referenzlösungen. Für die Behandlung der doppelten Heterogenität der Brennelementstruktur bei Homogenisierung der Wirkungsquerschnitte wurden neue Methoden entwickelt. Zum einen wurde ein zweistufiges Homogenisierungsverfahren basierend auf der Methode der sog. Reactivity Equivalent Transformation (RPT) weiterentwickelt. Zum anderen ermöglichte die Verfügbarkeit des neuen Monte-Carlo-Codes SERPENT die Anwendung eines einstufigen Verfahrens, wobei die 3D heterogenen Strukturen in einem Rechenschritt konsistent erfasst werden können. Weiterhin wur-de in DYN3D ein 3D Wärmeleitungsmodell implementiert, das den radialen und axialen Wärmetransport in der Graphitmatrix beschreiben kann. DYN3D-HTR wurde schließlich anhand der Testfälle für Reaktivitätstransienten erprobt. Die Verifikation erfolgte durch Vergleich zwischen 3D und 1D Berechnung der Wärmeleitung. Schließlich wurde DYN3D mit dem CFD-Code ANSYS-CFX gekoppelt, um auch dreidimensionale Strömungen in Reaktorkernen berechnen zu können. Der Kern wird als poröser Körper modelliert. Die Kopplung wurde an anhand von 2 Testbeispielen, dem Auswurf eines Steuerstabes und einer lokalen Strömungsblockade in einem Brennelement, erprobt.

A Variational Transport Theory Method for Two-Dimensional Reactor Core Calculations Scott W. Mosher 110 Pages Directed by Dr. Farzad Rahnema It seems very likely that the next generation of reactor analysis methods will be based largely on neutron transport theory, at both the assembly and core levels. Signifi-cant progress has been made in recent years toward the goal of developing a transport method that is applicable to large, heterogeneous coarse-meshes. Unfortunately, the ma-jor obstacle hindering a more widespread application of transport theory to large-scale calculations is still the computational cost. In this dissertation, a variational heterogeneous coarse-mesh transport method has been extended from one to two-dimensional Cartesian geometry in a practical fashion. A generalization of the angular flux expansion within a coarse-mesh was developed. This allows a far more efficient class of response functions (or basis functions) to be employed within the framework of the original variational principle. New finite element equations were derived that can be used to compute the expansion coefficients for an individual coarse-mesh given the incident fluxes on the boundary. In addition, the non-variational method previously used to converge the expansion coefficients was developed in a new and more thorough manner by considering the implications of the fission source treat-ment imposed by the response expansion. The new coarse-mesh method was implemented for both one and two-dimensional (2-D) problems in the finite-difference, multigroup, discrete ordinates approximation. An efficient set of response functions was generated using orthogonal boundary conditions constructed from the discrete Legendre polynomials. Several one and two-dimensional heterogeneous light water reactor benchmark problems were studied. Relatively low-order response expansions were used to generate highly accurate results using both the variational and non-variational methods. The expansion order was found to have a far more significant impact on the accuracy of the results than the type of method. The varia-tional techniques provide better accuracy, but at substantially higher computational costs. The non-variational method is extremely robust and was shown to achieve accurate re-sults in the 2-D problems, as long as the expansion order was not very low.

The Coarse-Mesh Transport Method (COMET) is a method developed by the Computational Reactor and Medical Physics Group at Georgia Tech. Its original application was neutron transport for nuclear reactor modeling. COMET has since been shown to be effective for coupled photon-electron transport calculations where the goal is to determine the energy deposition of a photon beam. So far COMET can simulate a mono-directional, mono-energetic, spatially-flat photon beam. The goal of this thesis will be to extend COMET by adding a generalized source treatment. The new source will be able to simulate beams that vary in intensity as a function of position, angle, and energy. EGSnrc will be used to verify the accuracy of the new method for 3D photon kerma calculations.

A new solution technique is derived for the time-dependent transport equation. This approach extends the steady-state coarse-mesh transport method that is based on global-local decompositions of large (i.e. full-core) neutron transport problems. The new method is based on polynomial expansions of the space, angle and time variables in a response-based formulation of the transport equation. The local problem (coarse mesh) solutions, which are entirely decoupled from each other, are characterized by space-, angle- and time-dependent response functions. These response functions are, in turn, used to couple an arbitrary sequence of local problems to form the solution of a much larger global problem. In the current work, the local problem (response function) computations are performed using the Monte Carlo method, while the global (coupling) problem is solved deterministically. The spatial coupling is performed by orthogonal polynomial expansions of the partial currents on the local problem surfaces, and similarly, the timedependent response of the system (i.e. the time-varying flux) is computed by convolving the time-dependent surface partial currents and time-dependent volumetric sources against pre-computed time-dependent response kernels.

Standardmäßig erfolgt die Datenaufbereitung der Neutronenwirkungsquerschnitte für Reaktorkernrechnungen mit 2D-Zellcodes. Ziel dieser Arbeit war es, einen 3D-Zellcode zu entwickeln, mit diesem Code 3D-Effekte zu untersuchen und die Notwendigkeit einer 3D-Datenaufbereitung der Neutronenwirkungsquerschnitte zu bewerten. Zur Berechnung des Neutronentransports wurde die Methode der Erststoßwahrscheinlichkeiten, die mit der Ray-Tracing-Methode berechnet werden, gewählt. Die mathematischen Algorithmen wurden in den 2D/3D-Zellcode TransRay umgesetzt. Für den Geometrieteil des Programms wurde das Geometriemodul eines Monte-Carlo-Codes genutzt. Das Ray-Tracing in 3D wurde auf Grund der hohen Rechenzeiten parallelisiert. Das Programm TransRay wurde an 2D-Testaufgaben verifiziert. Für einen Druckwasser-Referenzreaktor wurden folgende 3D-Probleme untersucht: Ein teilweise eingetauchter Regelstab und Void (Vakuum oder Dampf) um einen Brennstab als Modell einer Dampfblase. Alle Probleme wurden zum Vergleich auch mit den Programmen HELIOS (2D) und MCNP (3D) nachgerechnet. Die Abhängigkeit des Multiplikationsfaktors und der gemittelten Zweigruppenquerschnitte von der Eintauchtiefe des Regelstabes bzw. von der Höhe der Dampfblase wurden untersucht. Die 3D berechneten Zweigruppenquerschnitte wurden mit drei üblichen Näherungen verglichen: Lineare Interpolation, Interpolation mit Flusswichtung und Homogenisierung. Am 3D-Problem des Regelstabes zeigte sich, dass die Interpolation mit Flusswichtung eine gute Näherung ist. Demnach ist hier eine 3D-Datenaufbereitung nicht notwendig. Beim Testfall des einzelnen Brennstabs, der von Void umgeben ist, erwiesen sich die drei Näherungen für die Zweigruppenquerschnitte als unzureichend. Demnach ist eine 3D-Datenaufbereitung notwendig. Die einzelne Brennstabzelle mit Void kann als der Grenzfall eines Reaktors angesehen werden, in dem sich eine Phasengrenzfläche herausgebildet hat.

Standardmäßig erfolgt die Datenaufbereitung der Neutronenwirkungsquerschnitte für Reaktorkernrechnungen mit 2D-Zellcodes. Ziel dieser Arbeit war es, einen 3D-Zellcode zu entwickeln, mit diesem Code 3D-Effekte zu untersuchen und die Notwendigkeit einer 3D-Datenaufbereitung der Neutronenwirkungsquerschnitte zu bewerten. Zur Berechnung des Neutronentransports wurde die Methode der Erststoßwahrscheinlichkeiten, die mit der Ray-Tracing-Methode berechnet werden, gewählt. Die mathematischen Algorithmen wurden in den 2D/3D-Zellcode TransRay umgesetzt. Für den Geometrieteil des Programms wurde das Geometriemodul eines Monte-Carlo-Codes genutzt. Das Ray-Tracing wurde auf Grund der hohen Rechenzeiten parallelisiert. Das Programm TransRay wurde an 2D-Testaufgaben verifiziert. Für einen Druckwasser-Referenzreaktor wurden folgende 3D-Probleme untersucht: Ein teilweise eingetauchter Regelstab und Void (bzw. Moderator mit geringerer Dichte) um einen Brennstab als Modell einer Dampfblase. Alle Probleme wurden zum Vergleich auch mit den Programmen HELIOS (2D) und MCNP (3D) nachgerechnet. Die Abhängigkeit des Multiplikationsfaktors und der gemittelten Zweigruppenquerschnitte von der Eintauchtiefe des Regelstabes bzw. von der Höhe der Dampfblase wurden untersucht. Die 3D berechneten Zweigruppenquerschnitte wurden mit drei üblichen Näherungen verglichen: linearer Interpolation, Interpolation mit Flusswichtung und Homogenisierung. Am 3D-Problem des Regelstabes zeigte sich, dass die Interpolation mit Flusswichtung eine gute Näherung ist. Demnach ist hier eine 3D-Datenaufbereitung nicht notwendig. Beim Testfall des einzelnen Brennstabs, der von Void (bzw. Moderator geringerer Dichte) umgeben ist, erwiesen sich die drei Näherungen für die Zweigruppenquerschnitte als unzureichend. Demnach ist eine 3D-Datenaufbereitung notwendig. Die einzelne Brennstabzelle mit Void kann als der Grenzfall eines Reaktors angesehen werden, in dem sich eine Phasengrenzfläche herausgebildet hat.