# ASTM E1006-13

Designation: E1006 − 13Standard Practice forAnalysis and Interpretation of Physics Dosimetry Resultsfrom Test Reactor Experiments1This standard is issued under the fixed designation E1006; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon (´) indicates an editorial change since the last revision or reapproval.1. Scope1.1 This practice covers the methodology summarized inAnnex A1 to be used in the analysis and interpretation ofphysics-dosimetry results from test reactors.1.2 This practice relies on, and ties together, the applicationof several supporting ASTM standard practices, guides, andmethods.1.3 Support subject areas that are discussed include reactorphysics calculations, dosimeter selection and analysis, expo-sure units, and neutron spectrum adjustment methods.1.4 This practice is directed towards the development andapplication of physics-dosimetry-metallurgical data obtainedfrom test reactor irradiation experiments that are performed insupport of the operation, licensing, and regulation of LWRnuclear power plants. It specifically addresses the physics-dosimetry aspects of the problem. Procedures related to theanalysis, interpretation, and application of both test and powerreactor physics-dosimetry-metallurgy results are addressed inPractices E185, E853, and E1035, Guides E900, E2005, E2006and Test Method E646.1.5 This standard may involve hazardous materials,operations, and equipment. This standard does not purport toaddress all of the safety concerns, if any, associated with itsuse. It is the responsibility of the user of this standard toestablish appropriate safety and health practices and deter-mine the applicability of regulatory limitations prior to use.2. Referenced Documents2.1 ASTM Standards:2E185 Practice for Design of Surveillance Programs forLight-Water Moderated Nuclear Power Reactor VesselsE482 Guide for Application of Neutron Transport Methodsfor Reactor Vessel Surveillance, E706 (IID)E646 Test Method for Tensile Strain-Hardening Exponents(n -Values) of Metallic Sheet MaterialsE693 Practice for Characterizing Neutron Exposures in Ironand Low Alloy Steels in Terms of Displacements PerAtom (DPA), E 706(ID)E706 Master Matrix for Light-Water Reactor Pressure VesselSurveillance Standards, E 706(0) (Withdrawn 2011)3E844 Guide for Sensor Set Design and Irradiation forReactor Surveillance, E 706 (IIC)E853 Practice for Analysis and Interpretation of Light-WaterReactor Surveillance Results, E706(IA)E854 Test Method for Application and Analysis of SolidState Track Recorder (SSTR) Monitors for ReactorSurveillance, E706(IIIB)E900 Guide for Predicting Radiation-Induced TransitionTemperature Shift in Reactor Vessel Materials, E706 (IIF)E910 Test Method for Application and Analysis of HeliumAccumulation Fluence Monitors for Reactor VesselSurveillance, E706 (IIIC)E944 Guide for Application of Neutron Spectrum Adjust-ment Methods in Reactor Surveillance, E 706 (IIA)E1005 Test Method for Application and Analysis of Radio-metric Monitors for Reactor Vessel Surveillance, E 706(IIIA)E1018 Guide for Application of ASTM Evaluated CrossSection Data File, Matrix E706 (IIB)E1035 Practice for Determining Neutron Exposures forNuclear Reactor Vessel Support StructuresE2005 Guide for Benchmark Testing of Reactor Dosimetryin Standard and Reference Neutron FieldsE2006 Guide for Benchmark Testing of Light Water ReactorCalculations2.2 Nuclear Regulatory Documents:Code of Federal Regulations, “Fracture ToughnessRequirements,” Chapter 10, Part 50, Appendix G4Code of Federal Regulations, “Reactor Vessel MaterialsSurveillance Program Requirements,” Chapter 10, Part50, Appendix H41This practice is under the jurisdiction of ASTM Committee E10 on NuclearTechnology and Applications and is the direct responsibility of SubcommitteeE10.05 on Nuclear Radiation Metrology.Current edition approved June 1, 2013. Published July 2013. Originally approvedin 1984. Last previous edition approved in 2008 as E1006 – 08. DOI: 10.1520/E1006-13.2The reference in parentheses refers to Section 5 as well as to Figs. 1 and 2 ofMatrix E706.3The last approved version of this historical standard is referenced onwww.astm.org.4Available from Superintendent of Documents, U.S. Government PrintingOffice, Washington, DC 20402.Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States1Regulatory Guide 1.99, Rev 2, “Radiation Embrittlement ofReactor Vessel Materials,” U.S. Nuclear RegulatoryCommission, May 198843. Significance and Use3.1 The mechanical properties of steels and other metals arealtered by exposure to neutron radiation. These propertychanges are assumed to be a function of chemical composition,metallurgical condition, temperature, fluence (perhaps alsofluence rate), and neutron spectrum. The influence of thesevariables is not completely understood. The functional depen-dency between property changes and neutron radiation issummarized in the form of damage exposure parameters thatare weighted integrals over the neutron fluence spectrum.3.2 The evaluation of neutron radiation effects on pressurevessel steels and the determination of safety limits require theknowlege of uncertainties in the prediction of radiation expo-sure parameters (for example, dpa (Practice E693), neutronfluence greater than 1.0 MeV, neutron fluence greater than 0.1MeV, thermal neutron fluence, etc.). This practice describesrecommended procedures and data for determining theseexposure parameters (and the associated uncertainties) for testreactor experiments.3.3 The nuclear industry draws much of its informationfrom databases that come from test reactor experiments.Therefore, it is essential that reliable databases are obtainedfrom test reactors to assess safety issues in Light Water Reactor(LWR) nuclear power plants.4. Establishment of the Physics-Dosimetry Program4.1 Reactor Physics Computational Mode:4.1.1 Introduction—This section provides a reference set ofprocedures for performing reactor physics calculations inexperimental test reactors. Although it is recognized thatvariations in methods will occur at various facilities, thepresent benchmarked calculational sequence has been usedsuccessfully in several studies (1-4)5and provides proceduresfor performing physics calculations in test reactors. The MonteCarlo technique is used with about the same frequency asdiscrete ordinates techniques in test and research reactordosimetry. The method is used more frequently in test/researchreactors, as compared to power reactors, because of the veryheterogeneous geometry often encountered in test/researchreactors. Very complex geometries can be handled in 3D spaceusing the Monte Carlo approach.4.2 Determination of Core Fission Source Distribution—The total fission source distribution, in source neutrons per unitvolume per unit time, defined as:S~x, y, z! 5 *0`ν~E!(f~x, y, z, E!·φ~x, y, z, E!dE (1)where:ν(E) = number of neutrons per fission,∑f= macroscopic fission cross section, andφ = fluence rate.is determined from a k-eigenvalue calculation of the reactorcore, with the neutron fluence rate normalized to give thecorrect measured power output from the reactor, for example:P 5 *E*Vκ( f~x, y, z, E!φ~x, y, z, E!·dxdydzdE (2)where:κ = effective energy yield per fission, andP = experimentally determined thermal power with theintegral calculated over all energies E and the corevolume V.4.2.1 An accurate value for the reactor power, P, is impera-tive for absolute comparison with experimental data.4.2.2 If the axial core configuration is nonuniform, as mightresult from a partially inserted control rod, or from burnupeffects, then a three-dimensional k calculation is required.Multigroup discrete ordinates or Monte Carlo methods are usedalmost exclusively to model the core (that is, not few groupdiffusion theory). This is particularly important where there arespecial purpose loops in the core or at a reflector/core boundarywhere the fluence spectrum changes very rapidly. In thesecases, the few group diffusion models are typically not ad-equate.4.2.3 Whenever the axial shape of the neutron fluence rate isseparable from the shape in the other variables, then a fullthree-dimensional calculation is not required. In many experi-mental reactors, the axial dependence of the fluence rate is wellapproximated by a cosine shifted slightly from the midplane. Inthis case only a two-dimensional calculation (with a bucklingapproximation for axial leakage) is needed. In this case it ispossible to use two-dimensional transport theory.4.2.4 For reactor cores that generate a non-negligibleamount of thermal power, the shape of the fission source maychange with time due to burnup and changes in control rodpositions. In this case, the source should be averaged over thetime period during which the experiment was performed.4.2.5 If a few-group set is used to model the fission sourcedistribution, it is recommended that a fine-group cross-sectionlibrary of approximately 100 groups with at least 10 thermalgroups be used to generate the few-group set. Resonanceshielding of the fine-group cross sections can be done with anyof the methods acceptable for LWR analysis (5) (shieldingfactor, Nordheim, integral transport theory, etc.). The fine-group cross-section library shall be collapsed with weightingspectra obtained from cell calculations for each type of unit cellfound in the core. If experiments are located near control rodsor reflectors, then a separate calculation shall be performed foradjacent cells to account for the influence of these regions onthe thermal spectrum in the experiment.4.3 Transport Calculations-Discrete Ordinates Method:4.3.1 Transport calculations for test reactors may be per-formed by discrete ordinates or Monte Carlo methods, or by acombination of the two. The use of Monte Carlo codes isdescribed in 4.5. If discrete ordinates methods are used, it isrecommended that a multi-dimensional (2D or 3D) discreteordinates code such as DORT/TORT (6) or DANTSYS (7, 8),be used for the transport theory calculations of both in-core and5The boldface numbers in parentheses refer to the list of references appended tothis practice.E1006 − 132ex-core dosimeters. At least an S8order quadrature with a P3cross section expansion should be used. Because of significantspectrum changes that can occur over short distances in testreactor experiments, mesh spacing needs to be selected withcare to ensure converged solutions at experiment locations.Detailed 3D discrete ordinates calculations will benefit fromthe use of a code that runs in parallel on multiple processors(9,10,11). The space-dependent fission source from the corecalculation is input as a volumetric distributed source with afission spectrum energy distribution. It is recommended thatthe ENDF/B-VII representation (12) of the235U thermal fissionspectrum (MAT 9228, MF 5, MT 18), which is based on theMadland-Nix formalism (13) be used to represent the fissionneutron energy distribution. This assumes that the build-in ofother fissile isotopes with burnup is negligible. The latestapplicable ENDF/B cross section data files shall be used(12,14). If a three-dimensional discrete ordinates transportcode is not used, it is recommended that the three-dimensionalfluence rate distribution be synthesized from two two-dimensional calculations. A simple synthesis procedure thathas been found to produce accurate results in benchmarkdosimetry calculations is given in Refs (2,3).4.3.2 This synthesis procedure has been used successfully ina number of experiments in which the ex-core configuration isuniform axially along the full core height. For these types ofproblems, the three-dimensional synthesized fluence rates givedosimeter reactions that agree to within 10 % of the measuredvalues, even off the core midplane. However, for experimentsthat contain short (relative to the core height) attenuatingbodies, neutron streaming may occur around the edges of thebody, and this effect is not well-predicted with the synthesisprocedure. A “leakage iteration” procedure has been developedfor such problems (15), but since most experiments do notexperience this difficulty, it will not be discussed in thispractice.4.4 Calculation of Bias Factors:4.4.1 In order to reduce the number of mesh intervals in thetwo-dimensional discrete ordinates calculations, it is oftennecessary to smear some detailed structure into a homogeneousmixture or completely ignore it. The experimental data com-puted with the homogeneous two-dimensional model can becorrected for the effects of local heterogeneities with biasfactors. An example in which bias factors may be useful is incorrecting for fluence rate perturbations caused by the experi-ment itself. This factor has been observed to be as high as 1.3for a 1-in.2container in an ex-core location. For in-coreexperiments the effects of heterogeneities within the experi-mental assembly should be examined.4.4.2 Bias factors can be obtained with detailed one-dimensional (usually cylindrical) discrete ordinates calcula-tions (16) in the vicinity of the desired data. Two cellcalculations are usually done: one in which the experiment ismodeled with as much detail as possible, and the other inwhich it is smeared in the same manner as in the two-dimensional calculation. In both the heterogeneous and homo-geneous cases, the experiment zone should be surrounded by ahomogenized zone corresponding to the same material whichsurrounds the experiment in the two-dimensional model. Thisregion should be several mean free paths thick. It is recom-mended that the discrete ordinates calculations be performed asboundary source problems with an isotropic fluence rateboundary condition which is equal to the corresponding scalarfluence rate from the two-dimensional calculation. Group-dependent bias factors for the experiment zone are defined asthe ratio of the group fluence rates for the heterogeneous andhomogeneous geometries. These bias factors should multiplythe multigroup fluence rates for the experiment zone in thetwo-dimensional calculation.4.5 Transport Calculations—Monte Carlo Method:4.5.1 While this practice permits the use of a discrete-ordinates technique for test reactor analysis (4.3), the alterna-tive Monte Carlo technique may be preferred in many situa-tions. This approach has the inherent advantage, over thedeterministic method described in 4.3, of being able to treatthree-dimensional aspects as well as geometrical complexity inexplicit detail. Three Monte Carlo codes used for reactoranalysis are MCNP (17,18). MCBEND (19,20) and TRIPOLI(21,22).4.5.2 The Monte Carlo technique may be employed for theproduction of detailed core power distributions (for example,“eigenvalue” calculations).4.5.3 A relevant restriction of Monte Carlo lies in thedifficulty of calculating r