The application of sensitivity theory to cross section adjustment and integral experiment analysis

Mulley, Shaun Lloyd (1985). The application of sensitivity theory to cross section adjustment and integral experiment analysis. University of Birmingham. Ph.D.

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Abstract

Sensitivity theory has been used to computationally design and analyse two integral experiments, associated with a non fissile and a fissile fusion reactor. The sensitivities of certain performance parameters have been obtained for the reactors and their associated integral experiments and these have been used in conjunction with some assumed covariance matrices to perform a standard uncertainty analysis. In addition, the two integral experiments have been remodelled using three dimensional methods to correctly account for neutron leakage. Ultimately the purpose of the above is to adjust cross sections so that we can determine the behaviour of the fusion reactors more accurately. The work presented here represents the first (computational) half that is needed for such a cross section adjustment. With this information, most of the partials in the 100 neutron energy group structure of the ENDF/B-4 cross section set of the LI6, LI7, F19, PB, FE, U238 and U235 isotopes can be adjusted.

In chapter 1 the principles of fusion are given and the benefits of ion beams are discussed. In addition, the benefits of using a coupled fission fusion reactor are outlined.

In chapter 2 the theory and ideas behind sensitivity analysis is discussed. The chapter starts with an outline and history of sensitivity theory and next a derivation of the sensitivity function is presented. Finally, a general sensitivity theory section is given, which discusses the meaning of the adjoint flux, the meaning of the sensitivity equation, and the sensitivity methodology and sensitivity definitions.

In chapter 3 the calculational tools are discussed with an outline of the physics and mathematics behind each computer code. In addition, the cross section data sources and the codes used to extract the cross section information are outlined.

Chapter 4 gives the theory and ideas behind the cross section adjustment procedure. The relevant equation is derived from first principles and discussed. Also included here is an outline of integral experiments and their uses.

Chapter 5 gives a summary of the physical and mathematical model designs of the two fusion reactors, whilst chapter 6 gives a detailed breakdown of the responses and sensitivities for the two reactors. These results give information as to the behaviour of the two reactors and forms the basis for the designing of the integral experiments.

Chapters 7 and 8 give the methods behind the design and construction of the non fissile and fissile integral experiments, respectively. The neutronic changes recorded in passing from the reactor design to the integral experiment are given and each integral experiment is compared to its fusion reactor using some important sensitivity profiles to see how and why the radiation environments differ.

Chapter 9 details the uncertainty analysis of the reactors and experiments. It discusses uncertainty analysis in general and derives the necessary equation. The analysis presented here deals with the standard cross section uncertainties only and does not deal with the energy or angular distributions of second neutrons or the uncertainties introduced by modelling ar. computational methods. The covariance matrices were constructed from information contained in the ENDF files and by choosing a range of suitable correlation values. The total uncertainty in a certain performance parameter is shown for the different strengths of chosen correlation. The uncertainty analysis shows that most of the errors are below 10%.

In chapter 10 the results from a 3-dimensional modelling on the two integral experiments is presented as well as the sensitivities of Ni(n,p) and \(^{232}\)Th(n,f) foils placed at various spatial positions in the assemblies. Comparisons are made between the sensitivities obtained by the 3-dimensional and 1-dimensional computational codes and it is seen that the similarity between the profiles is quite good. This leads to the important result that the 1-dimensional radiation environment is roughly the same as that calculated by the 3-dimensional code. Thus foil measurements made by an experimentalist at the central positions of the integral experiments can be used with confidence with the sensitivities obtained from the 1-dimensional code (which is very cheap and easy to run) for the cross section adjustment scheme.

Chapter 11 lists the main conclusions and recommendations and briefly summarises all the work performed in this thesis.

Type of Work:

Thesis (Doctorates > Ph.D.)

Award Type:

Doctorates > Ph.D.

Supervisor(s):