# ASTM E944-13e1

Designation: E944 − 13´1Standard Guide forApplication of Neutron Spectrum Adjustment Methods inReactor Surveillance1This standard is issued under the fixed designation E944; 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.ε1NOTE—The title of this guide and the Referenced Documents were updated editorially in May 2017.1. Scope1.1 This guide covers the analysis and interpretation of thephysics dosimetry for Light Water Reactor (LWR) surveillanceprograms. The main purpose is the application of adjustmentmethods to determine best estimates of neutron damage expo-sure parameters and their uncertainties.1.2 This guide is also applicable to irradiation damagestudies in research reactors.1.3 This standard does not purport to address all of thesafety concerns, if any, associated with its use. It is theresponsibility of the user of this standard to establish appro-priate safety and health practices and determine the applica-bility of regulatory limitations prior to use.1.4 This international standard was developed in accor-dance with internationally recognized principles on standard-ization established in the Decision on Principles for theDevelopment of International Standards, Guides and Recom-mendations issued by the World Trade Organization TechnicalBarriers to Trade (TBT) Committee.2. Referenced Documents2.1 ASTM Standards:2E170 Terminology Relating to Radiation Measurements andDosimetryE262 Test Method for Determining Thermal Neutron Reac-tion Rates and Thermal Neutron Fluence Rates by Radio-activation TechniquesE263 Test Method for Measuring Fast-Neutron ReactionRates by Radioactivation of IronE264 Test Method for Measuring Fast-Neutron ReactionRates by Radioactivation of NickelE265 Test Method for Measuring Reaction Rates and Fast-Neutron Fluences by Radioactivation of Sulfur-32E266 Test Method for Measuring Fast-Neutron ReactionRates by Radioactivation of AluminumE393 Test Method for Measuring Reaction Rates by Analy-sis of Barium-140 From Fission DosimetersE481 Test Method for Measuring Neutron Fluence Rates byRadioactivation of Cobalt and SilverE482 Guide for Application of Neutron Transport Methodsfor Reactor Vessel SurveillanceE523 Test Method for Measuring Fast-Neutron ReactionRates by Radioactivation of CopperE526 Test Method for Measuring Fast-Neutron ReactionRates by Radioactivation of TitaniumE693 Practice for Characterizing Neutron Exposures in Ironand Low Alloy Steels in Terms of Displacements PerAtom (DPA)E704 Test Method for Measuring Reaction Rates by Radio-activation of Uranium-238E705 Test Method for Measuring Reaction Rates by Radio-activation of Neptunium-237E706 Master Matrix for Light-Water Reactor Pressure VesselSurveillance StandardsE844 Guide for Sensor Set Design and Irradiation forReactor SurveillanceE853 Practice forAnalysis and Interpretation of Light-WaterReactor Surveillance ResultsE854 Test Method for Application and Analysis of SolidState Track Recorder (SSTR) Monitors for Reactor Sur-veillanceE910 Test Method for Application and Analysis of HeliumAccumulation Fluence Monitors for Reactor Vessel Sur-veillanceE1005 Test Method for Application and Analysis of Radio-metric Monitors for Reactor Vessel SurveillanceE1018 Guide for Application of ASTM Evaluated CrossSection Data FileE2005 Guide for Benchmark Testing of Reactor Dosimetryin Standard and Reference Neutron Fields1This guide is under the jurisdiction of ASTM Committee E10 on NuclearTechnology and Applicationsand is the direct responsibility of SubcommitteeE10.05 on Nuclear Radiation Metrology. A brief overview of Guide E944 appearsin Master Matrix E706 in 5.4.1.Current edition approved Jan. 1, 2013. Published January 2013. Originallyapproved in 1983. Last previous edition approved in 2008 as E944 – 08. DOI:10.1520/E0944-13E01.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at service@astm.org. For Annual Book of ASTMStandards volume information, refer to the standard’s Document Summary page onthe ASTM website. DOI: 10.1520/E0944-08.Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United StatesThis international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for theDevelopment of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.1E2006 Guide for Benchmark Testing of Light Water ReactorCalculations2.2 Nuclear Regulatory Commission Documents:3NUREG/CR-1861 PCA Experiments and Blind TestNUREG/CR-2222 Theory and Practice of General Adjust-ment and Model Fitting ProceduresNUREG/CR-3318 LWR Pressure Vessel Surveillance Do-simetry Improvement Program: PCA Experiments, BlindTest, and Physics-Dosimetry Support for the PSF Experi-mentNUREG/CR-3319 LWR Power Reactor SurveillancePhysics-Dosimetry Data Base CompendiumNUREG/CR-5049 Pressure Vessel Fluence Analysis andNeutron Dosimetry2.3 Electric Power Research Institute:4EPRI NP-2188 Development and Demonstration of an Ad-vanced Methodology for LWR Dosimetry Applications2.4 Government Document:3NBSIR 85–3151 Compendium of Benchmark NeutronFields for Reactor Dosimetry3. Significance and Use3.1 Adjustment methods provide a means for combining theresults of neutron transport calculations with neutron dosimetrymeasurements (see Test Method E1005 and NUREG/CR-5049)in order to obtain optimal estimates for neutron damageexposure parameters with assigned uncertainties. The inclusionof measurements reduces the uncertainties for these parametervalues and provides a test for the consistency between mea-surements and calculations and between different measure-ments (see 3.3.3). This does not, however, imply that thestandards for measurements and calculations of the input datacan be lowered; the results of any adjustment procedure can beonly as reliable as are the input data.3.2 Input Data and Definitions:3.2.1 The symbols introduced in this section will be usedthroughout the guide.3.2.2 Dosimetry measurements are given as a set of reactionrates (or equivalent) denoted by the following symbols:ai, i 5 1,2,… (1)These data are, at present, obtained primarily from radio-metric dosimeters, but other types of sensors may be included(see 4.1).3.2.3 The neutron spectrum (see Terminology E170)atthedosimeter location, fluence or fluence rate Φ(E) as a function ofneutron energy E, is obtained by appropriate neutronics calcu-lations (neutron transport using the methods of discrete ordi-nates or Monte Carlo, see Guide E482). The results of thecalculation are customarily given in the form of multigroupfluences or fluence rates.Φj5 *EjEj11Φ ~E!dE, j 5 1,2, … k (2)where:Ejand Ej+1are the lower and upper bounds for the j-th energygroup, respectively, and k is the total number of groups.3.2.4 The reaction cross sections of the dosimetry sensorsare obtained from an evaluated cross section file. The crosssection for the i-th reaction as a function of energy E will bedenoted by the following:σi~E!, i 5 1,2, … (3)Used in connection with the group fluences, Eq 2, are thecalculated group-averaged cross sections σij. These values aredefined through the following equation:σij5 *EjEj11Φ~E!σi~E!dE/Φj(4)i 5 1,2,n;j 5 1,2, … k3.2.5 Uncertainty information in the form of variances andcovariances must be provided for all input data. Appropriatecorrections must be made if the uncertainties are due to biasproducing effects (for example, effects of photo reactions).3.3 Summary of the Procedures:3.3.1 An adjustment algorithm modifies the set of input dataas defined in 3.2 in the following manner (adjusted quantitiesare indicated by a tilde, for example, ãi):a˜i5 ai1∆ai(5)Φ˜~E! 5 Φ~E!1∆Φ~E! (6)or for group fluence ratesΦ˜j5 Φj1∆Φj(7)σ˜i~E! 5 σi~E!1∆σi~E!, (8)or for group-averaged cross sectionsσ˜ij5 σij1∆σij(9)The adjusted quantities must satisfy the following condi-tions:a˜i5 *0`Φ˜~E!σ˜i~E!dE, i 5 1,2,… n (10)or in the form of group fluence ratesa˜i5(j51kσ˜ijΦ˜j, i 5 1,2,… n (11)Since the number of equations in Eq 11 is much smaller thanthe number of adjustments, there exists no unique solution tothe problem unless it is further restricted. The mathematicalalgorithm in current adjustment codes are intended to make theadjustments as small as possible relative to the uncertainties ofthe corresponding input data. Codes like STAY’SL, FERRET,LEPRICON, and LSL-M2 (see Table 1) are based explicitly onthe statistical principles such as “Maximum Likelihood Prin-ciple” or “Bayes Theorem,” which are generalizations of thewell-known least squares principle. Using variances and cor-relations of the input fluence, dosimetry, and cross section data(see 4.1.1, 4.2.2, and 4.3.3), even the older codes, notablySAND-II and CRYSTAL BALL, can be interpreted as appli-cation of the least squares principle although the statistical3Available from Superintendents of Documents, U. S. Government PrintingOffice, Washington, DC 20402.4Available from the Electric Power Research Institute, P. O. Box 10412, PaloAlto, CA 94303.E944 − 13´12assumptions are not spelled out explicitly (see Table 1). Adetailed discussion of the mathematical derivations can befound in NUREG/CR-2222 and EPRI NP-2188.3.3.1.1 An important problem in reactor surveillance is thedetermination of neutron fluence inside the pressure vessel wallat locations which are not accessible to dosimetry. Estimatesfor exposure parameter values at these locations can beobtained from adjustment codes which adjust fluences simul-taneously at more than one location when the cross correlationsbetween fluences at different locations are given. LEPRICONhas provisions for the estimation of cross correlations forfluences and simultaneous adjustment. LSL-M2 also allowssimultaneous adjustment, but cross correlations must be given.3.3.2 The adjusted data ãi, etc., are, for any specificalgorithm, unique functions of the input variables. Thus,uncertainties (variances and covariances) for the adjustedparameters can, in principle, be calculated by propagation theuncertainties for the input data. Linearization may be usedbefore calculating the uncertainties of the output data if theadjusted data are nonlinear functions of the input data.3.3.2.1 The algorithms of the adjustment codes tend todecrease the variances of the adjusted data compared to thecorresponding input values. The linear least squares adjustmentcodes yield estimates for the output data with minimumvariances, that is, the “best” unbiased estimates. This is theprimary reason for using these adjustment procedures.3.3.3 Properly designed adjustment methods provide meansto detect inconsistencies in the input data which manifestthemselves through adjustments that are larger than the corre-sponding uncertainties or through large values of chi-square, orboth. (See NUREG/CR-3318 and NUREG/CR-3319.) Anydetection of inconsistencies should be documented, and outputdata obtained from inconsistent input should not be used. AllTABLE 1 Available Unfolding CodesProgram Solution MethodCode AvailableFromRefer-encesCommentsSAND-II semi-iterative RSICC Prog. No. CCC-112, CCC-619, PSR-3451Acontains trial spectra library. No output uncertainties in theoriginal code, but modified Monte Carlo code provides outputuncertainties (2, 3, 4)SPECTRA statistical, linear estimation RSICC Prog. No. CCC-1085, 6 minimizes deviation in magnitude, no output uncertainties.IUNFLD/UNFOLDstatistical, linear estimation 7 constrained weighted linear least squares code using B-splinebasic functions. No output uncertainties.WINDOWS statistical, linear estimation, linearprogrammingRSICC Prog. No. PSR-136, 1618 minimizes shape deviation, determines upper and lower boundsfor integral parameter and contribution of foils to bounds andestimates. No statistical output uncertainty.RADAK,SENSAKstatistical, linear estimation RSICC Prog. No. PSR-1229, 10,11,12 RADAK is a general adjustment code not restricted to spectrumadjustment.STAY’SL statistical linear estimation RSICC Prog. No. PSR-11313 permits use of full or partial correlation uncertainty data foractivation and cross section data.NEUPAC(J1) statistical, linear estimation RSICC Prog. No. PSR-17714, 15 permits use of full covariance data and includes routine ofsensitivity analysis.FERRET statistical, least squares with log normala priori distributionsRSICC Prog. No. PSR-1452, 3 flexible input options allow the inclusion of both differential andintegral measurements. Cross sections and multiple spectra maybe simultaneously adjusted. FERRET is a general adjustmentcode not restricted to spectrum adjustments.LEPRICON statistical, generalized linear leastsquares with normal a priori and aposteriori distributionsRSICC Prog. No. PSR-27716, 17, 18 simultaneous adjustment of absolute spectra at up to twodosimetry locations and one pressure vessel location. Combinesintegral and differential data with built-in uncertainties. Providesreduced adjusted pressure vessel group fluence covariancesusing built-in sensitivity database.LSL-M2 statistical, least squares, with log normala priori and a posteriori distributionsRSICC Prog. No.PSR-23319 simultaneous adjustment of several spectra. Providescovariances for adjusted integral parameters. Dosimetry cross-section file included.UMG Statistical, maximum entropy with outputuncertatintiesRSICC Prog. No.PSR-52920, 21 Two components. MAXED is a maximum entropy code. GRAVEL(22) is an iterative code.NMF-90 Statistical, least squares IAEA NDS 23, 24 Several components, STAY’NL, X333, and MIEKE. Distributed byIAEA as part of the REAL-84 interlaboratory exercise onspectrum adjustment (25).GMA Statistical, general least squares RSICC Prog. No.PSR-36726 Simultaneous evaluation with differential and integral data,primarily used for cross-section evaluation but extensible tospectrum adjustments.AThe boldface numbers in parentheses refer to the list of references appended to this guide.E944 − 13´13input data should be carefully reviewed whenever inconsisten-cies are found, and efforts should be made to resolve theinconsistencies as stated below.3.3.3.1 Input data should be carefully investigated for evi-dence of gross errors or biases if large adjustments arerequired. Note that the erroneous data may not be the ones thatrequired the largest adjustment; thus, it is necessary to reviewall input data. Data of dubious validity may be eliminated ifproper corrections cannot be determined. Any elimination ofdata must be documented and reasons stated which areindependent of the adjustment procedure. Inconsistent datamay also be omitted if they contribute little to the output underinvestigation.3.3.3.2 Inconsistencies may also be