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Non-evaluation applications for covariance matrices

Description: The possibility for application of covariance matrix techniques to a variety of common research problems other than formal data evaluation are demonstrated by means of several examples. These examples deal with such matters as fitting spectral data, deriving uncertainty estimates for results calculated from experimental data, obtaining the best values for plurally-measured quantities, and methods for analysis of cross section errors based on properties of the experiment. The examples deal with realistic situations encountered in the laboratory, and they are treated in sufficient detail to enable a careful reader to extrapolate the methods to related problems.
Date: May 1, 1982
Creator: Smith, D.L.
Partner: UNT Libraries Government Documents Department

Nuclear data uncertainties: I, Basic concepts of probability

Description: Some basic concepts of probability theory are presented from a nuclear-data perspective, in order to provide a foundation for thorough understanding of the role of uncertainties in nuclear data research. Topics included in this report are: events, event spaces, calculus of events, randomness, random variables, random-variable distributions, intuitive and axiomatic probability, calculus of probability, conditional probability and independence, probability distributions, binomial and multinomial probability, Poisson and interval probability, normal probability, the relationships existing between these probability laws, and Bayes' theorem. This treatment emphasizes the practical application of basic mathematical concepts to nuclear data research, and it includes numerous simple examples. 34 refs.
Date: December 1, 1988
Creator: Smith, D.L.
Partner: UNT Libraries Government Documents Department

Investigation of the influence of the neutron spectrum in determinations of integral cross-section ratios

Description: Ratio measurements are routinely employed in studies of neutron interaction processes in order to generate new differential cross-section data or to test existing differential cross-section information through examination of the corresponding response in integral neutron spectra. Interpretation of such data requires that careful attention be given to details of the neutron spectra involved in these measurements. Two specific tasks are undertaken in the present investigation: (1) Using perturbation theory, a formula is derived which permits one to relate the ratio measured in a realistic quasimonoenergetic spectrum to the desired pure monoenergetic ratio. This expression involves only the lowest-order moments of the neutron energy distribution and corresponding parameters which serve to characterize the energy dependence of the differential cross sections, quantities which can generally be estimated with reasonable precision from the uncorrected data or from auxiliary information. (2) Using covariance methods, a general formalism is developed for calculating the uncertainty of a measured integral cross-section ratio which involves an arbitrary neutron spectrum. This formalism is employed to further examine the conditions which influence the sensitivity of such measured ratios to details of the neutron spectra and to their uncertainties. Several numerical examples are presented in this report in order to illustrate these principles, and some general conclusion are drawn concerning the development and testing of neutron cross-section data by means of ratio experiments. 16 refs., 1 fig., 4 tabs.
Date: November 1, 1987
Creator: Smith, D.L.
Partner: UNT Libraries Government Documents Department

Some comments on resolution and the analysis and interpretation of experimental results from differential neutron measurements

Description: Effects of finite resolution in differential neutron measurements are examined. General procedures for deriving the experimental resolution functions from a knowledge of the experimental parameters are presented. Problems encountered in the comparison of different data sets, when the measured cross section is known to fluctuate with energy, are discussed. The objective is to encourage closer attention to the matter of resolution by experimenters, evaluators and users of neutron nuclear data.
Date: November 1, 1979
Creator: Smith, D.L.
Partner: UNT Libraries Government Documents Department

Covariance matrices and applications to the field of nuclear data

Description: A student's introduction to covariance error analysis and least-squares evaluation of data is provided. It is shown that the basic formulas used in error propagation can be derived from a consideration of the geometry of curvilinear coordinates. Procedures for deriving covariances for scaler and vector functions of several variables are presented. Proper methods for reporting experimental errors and for deriving covariance matrices from these errors are indicated. The generalized least-squares method for evaluating experimental data is described. Finally, the use of least-squares techniques in data fitting applications is discussed. Specific examples of the various procedures are presented to clarify the concepts.
Date: November 1, 1981
Creator: Smith, D.L.
Partner: UNT Libraries Government Documents Department

Graphical representation of neutron differential cross section data for reactor dosimetry applications. [Fission neutrons]

Description: The need for improved understanding of the relationships between available differential and integral data for neutron reactions used in reactor dosimetry has prompted investigation of a method for graphically representing experimental differential data in a form which appears to be quite useful for dosimetry applications. The method involves weighting the differential cross sections by spectral functions and plotting these values. Graphs of this form clearly indicate which differential data are important for spectrum unfolding applications. Simultaneous plots of experimental and evaluated differential cross sections--weighted by spectral functions--provide a means for comparing evaluations from the point of view of their impact on specific dosimetry applications. 8 figures.
Date: June 1, 1977
Creator: Smith, D. L.
Partner: UNT Libraries Government Documents Department

Evaluation of the /sup 115/In(n,n)/sup 115m/In reaction for the ENDF/B-V dosimetry file

Description: An evaluation of the /sup 115/In(n,n')/sup 115m/In reaction for the ENDF/B-V Dosimetry File is presented. This evaluation is based entirely on reported experimental differential data. Several data sets were renormalized prior to the evaluation in order to take into account recent adjustments in corresponding standard cross sections and in other nuclear parameters used for derivation of cross sections. The present evaluation is compared with the corresponding ENDF/B-IV evaluation. The value of the spectrum-average cross section for the standard neutron field resulting from thermal-neutron fission of /sup 235/U has been computed for this reaction using cross section values from the present evaluation. This computed cross section compares favorably with the result of a recent evaluation of integral data.
Date: December 1, 1976
Creator: Smith, D. L.
Partner: UNT Libraries Government Documents Department

Analysis of the sensitivity of spectrum-average cross sections to individual characteristics of differential excitation functions

Description: A simple procedure for analyzing the sensitivity of computed spectrum-average cross sections to detailed properties of excitation functions for threshold nuclear reactions commonly used in reactor dosimetry is described. This procedure is shown to be useful in identifying specific needs for improved differential data and as a tool to be employed in performing evaluations. Several examples are presented to illustrate the subject matter.
Date: March 1, 1977
Creator: Smith, D. L.
Partner: UNT Libraries Government Documents Department

Remarks concerning the accurate measurement of differential cross sections for threshold reactions used in fast-neutron dosimetry for fission reactors

Description: Some remarks are submitted concerning the measurement of differential cross sections for threshold reactions which are used in fast-neutron dosimetry for fission reactors. The objective is to familiarize the reader with some of the problems associated with these measurements and, in the process, to explain why the existence of large discrepancies in the data sets for many of these reactions is not surprising. Limits to the accuracy which can be expected for these cross sections in the near future--using current technology and available resources--are examined in a general way and recommendations for improving the accuracy of the differential data base for dosimetry reactions are presented.
Date: December 1, 1976
Creator: Smith, D. L.
Partner: UNT Libraries Government Documents Department

Sample-size effects in fast-neutron gamma-ray production measurements: solid-cylinder samples

Description: The effects of geometry, absorption and multiple scattering in (n,X$gamma$) reaction measurements with solid-cylinder samples are investigated. Both analytical and Monte-Carlo methods are employed in the analysis. Geometric effects are shown to be relatively insignificant except in definition of the scattering angles. However, absorption and multiple-scattering effects are quite important; accurate microscopic differential cross sections can be extracted from experimental data only after a careful determination of corrections for these processes. The results of measurements performed using several natural iron samples (covering a wide range of sizes) confirm validity of the correction procedures described herein. It is concluded that these procedures are reliable whenever sufficiently accurate neutron and photon cross section and angular distribution information is available for the analysis. (13 figures, 5 tables) (auth)
Date: September 1, 1975
Creator: Smith, D.L.
Partner: UNT Libraries Government Documents Department

Nuclear data and measurements series: Some comments on the effects of long-range correlations in covariance matrices for nuclear data

Description: Attention is called to the considerable sensitivity of many uncertainty calculations to the magnitude of the long-ranged correlations which appear in covariance matrices. If such correlations do exist, they must be included in order to properly assess the impact of the uncertainties in the data. If, however, certain assumed long-range correlations are unrealistic, then analyses involving such correlation information are almost certain to produce misleading results. The issue is discussed in general terms, and its importance is illustrated by examples based in part on recent work from this laboratory. Some practical suggestions are offered for dealing with the matter of correlations in instances where the available information is incomplete. 23 refs., 2 figs., 1 tab.
Date: March 1, 1987
Creator: Smith, D.L.
Partner: UNT Libraries Government Documents Department

Least-squares method for deriving reaction differential-cross-section information from measurements performed in diverse neutron fields

Description: A generalized least-squares algorithm which refiens a prior multi-group energy-differential neutron-reaction cross-section evaluation by addition of new experimental data is described. Complete covariance information for the prior evaluation and for the new experimentla information is required in this procedure. The result is a revised best-estimate multi-group cross-section evaluation with complete covariance information. The algorithm tests the consistency of the ew and apriori information, and it readily indicates whether the new data significantly improve the knowledge of the differential cross section. These new data need not be specific differential cross sections. Therefore, the experimenter is not limited to measurements which involve only conventional monoenergetic techniques. This opportunity suggests exploration of diverse new experimental methods, e.g., ones which can exploit the high yield and favorable neutron-energy ranges offered by certain unconventional neutron sources which have received little past attention. This method is demonstratedby the detailed analysis of several hypothetical numerical examples. The understanding of the method's potential and limitations which has emerged from the present investigation is discussed.
Date: November 1, 1982
Creator: Smith, D.L.
Partner: UNT Libraries Government Documents Department

Monitoring and measurement of oxygen concentrations in liquid sodium

Description: The measurement of oxygen concentrations in sodium at levels of interest for LMFBR applications is reviewed. Additional data are presented to support the validity of the vanadium-equilibration method as a reference for determination of oxygen concentrations in sodium at levels equal to or less than 15 ppM. Operating experience with electrochemical oxygen meters that have a thoria-yttria electrolyte and a Na--Na/sub 2/O reference electrode is described. Meter lifetimes in excess of one year have generally been achieved for operating temperatures of 352 and 402/sup 0/C, and fairly stable emfs have been observed for periods of several months. 7 fig, 21 references. (auth)
Date: January 1, 1976
Creator: Smith, D. L.
Partner: UNT Libraries Government Documents Department

Examination of various roles for covariance matrices in the development, evaluation, and application of nuclear data

Description: The last decade has been a period of rapid development in the implementation of covariance-matrix methodology in nuclear data research. This paper offers some perspective on the progress which has been made, on some of the unresolved problems, and on the potential yet to be realized. These discussions address a variety of issues related to the development of nuclear data. Topics examined are: the importance of designing and conducting experiments so that error information is conveniently generated; the procedures for identifying error sources and quantifying their magnitudes and correlations; the combination of errors; the importance of consistent and well-characterized measurement standards; the role of covariances in data parameterization (fitting); the estimation of covariances for values calculated from mathematical models; the identification of abnormalities in covariance matrices and the analysis of their consequences; the problems encountered in representing covariance information in evaluated files; the role of covariances in the weighting of diverse data sets; the comparison of various evaluations; the influence of primary-data covariance in the analysis of covariances for derived quantities (sensitivity); and the role of covariances in the merging of the diverse nuclear data information. 226 refs., 2 tabs.
Date: January 1, 1988
Creator: Smith, D.L.
Partner: UNT Libraries Government Documents Department

Blanket materials for DT fusion reactors

Description: This paper presents an overview of the critical materials issues that must be considered in the development of a tritium breeding blanket for a tokamak fusion reactor that operates on the D-T-Li fuel cycle. The primary requirements of the blanket system are identified and the important criteria that must be considered in the development of blanket technology are summarized. The candidate materials are listed for the different blanket components, e.g., breeder, coolant, structure and neutron multiplier. Three blanket concepts that appear to offer the most potential are: (1) liquid-metal breeder/coolant, (2) liquid-metal breeder/separate coolant, and (3) solid breeder/separate coolant. The major uncertainties associated with each of the design concepts are discussed and the key materials R and D requirements for each concept are identified.
Date: January 1, 1981
Creator: Smith, D.L.
Partner: UNT Libraries Government Documents Department

Explosive demolition of activated concrete

Description: This paper describes the removal of a radiologically contaminated concrete pad. This pad was removed during 1979 by operating personnel under the direction of the Waste Management Program of EG and G Idaho, Inc. The concrete pad was the foundation for the Organic Moderated Reactor Experiment (OMRE) reactor vessel located at the Idaho National Engineering Laboratory (INEL). The pad consisted of a cylindrical concrete slab 15 ft in diameter, 2 ft thick, and reinforced with steel bar. It was poured directly onto basalt rocks approximately 20 ft below grade. The entire pad contained induced radioactivity and was therefore demolished, boxed, and buried rather than being decontaminated. The pad was demolished by explosive blasting.
Date: January 1, 1980
Creator: Smith, D.L.
Partner: UNT Libraries Government Documents Department

Thermal responses of tokamak reactor first walls during cyclic plasma burns

Description: The CINDA-3G computer code has been adapted to analyze the thermal responses and operating limitations of two fusion reactor first-wall concepts under normal cyclic operation. A component of an LMFBR computer has been modified and adapted to analyze the ablative behavior of first-walls after a plasma disruption. The first-wall design concepts considered are a forced-circulation water-cooled stainless steel panel with and without a monolithic graphite liner. The thermal gradients in the metal wall and liner have been determined for several burn-cycle scenarios and the extent of surface ablation that results from a plasma disruption has been determined for stainless steel and graphite first surfaces.
Date: January 1, 1977
Creator: Smith, D.L. & Charak, I.
Partner: UNT Libraries Government Documents Department

Modeling of liquid-metal corrosion/deposition in a fusion reactor blanket

Description: A model has been developed for the investigation of the liquid-metal corrosion and the corrosion product transport in a liquid-metal-cooled fusion reactor blanket. The model describes the two-dimensional transport of wall material in the liquid-metal flow and is based on the following assumptions: (1) parallel flow in a straight circular tube; (2) transport of wall material perpendicular to the flow direction by diffusion and turbulent exchange; in flow direction by the flow motion only; (3) magnetic field causes uniform velocity profile with thin boundary layer and suppresses turbulent mass exchange; and (4) liquid metal at the interface is saturated with wall material. A computer code based on this model has been used to analyze the corrosion of ferritic steel by lithium lead and the deposition of wall material in the cooler part of a loop. Three cases have been investigated: (1) ANL forced convection corrosion experiment (without magnetic field); (2) corrosion in the MARS liquid-metal-cooled blanket (with magnetic field); and (3) deposition of wall material in the corrosion product cleanup system of the MARS blanket loop.
Date: April 1, 1984
Creator: Malang, S. & Smith, D.L.
Partner: UNT Libraries Government Documents Department

Calculations on the compatibility of refractory metals in a tritium environment and cold trapping method for tritium removal from a lithium blanket

Description: From joint meeting of the American Nuclear Society and the Atomic Industrial Forum and Nuclear Energy Exhibition; San Francisco, California, USA (11 Nov 1973). Thermodynamic calculations were made on the distribution of hydrogen and tritium between various refractory metals and liquid lithium as a function of temperature. The limiting tritium pressures that can be attained by cold trapping of secondary liquid metals such as Na, K, and NaK were calculated. In the absence of tritium breeding, these pressures are 2.5 x 10/sup -5/, 2 x 10/ sup -7/ and 1.2 x 10/sup -10/o torr for Na, K, and NaK, respectively, and these correspond to tritium concentrations in lithium of 45, 4, and <1 ppM, respectively, at 700 deg C. For a thermonuclear reactor of 1000 MW(t) thermal power with a tritium breeding rate of 150 g/day, a tritium recovery system that incorporates a separate lithium purification loop with niobium as the permeable membrane, NaK as the secondary heat transport fluid and with tungsten cladding on the IHX tubes seems to yield tritium pressures of ~10/sup -9/ torr or less in the secondary system. This leads to tritium release rate of ~10/sup -6/g/ hr to the steam system for a steam generator clad with tungsten and operating at ~600 deg C. This corresponds to activity release rate of~300 Ci/yr. (17 figures, 61 references) (auth)
Date: January 1, 1973
Creator: Natesan, K. & Smith, D.L.
Partner: UNT Libraries Government Documents Department