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diff --git a/doc/IGE335/Section3.02.tex b/doc/IGE335/Section3.02.tex new file mode 100644 index 0000000..8d0d5e0 --- /dev/null +++ b/doc/IGE335/Section3.02.tex @@ -0,0 +1,955 @@ +\subsection{The {\tt LIB:} module}\label{sect:LIBData} + +The general format of the input data for the \moc{LIB:} module is the following: + +\vspace{-0.2cm} + +\begin{DataStructure}{Structure \dstr{LIB:}} +\dusa{MICLIB} \moc{:=} \moc{LIB:} $[$ \dusa{MICLIB} $]~[~\{$ \dusa{MICRHS} $|$ \dusa{MACRHS} $|$ \dusa{EVORHS} $\}~]$ +\moc{::} \dstr{desclib} +\end{DataStructure} + +\vspace{-0.6cm} + +\noindent +where + +\begin{ListeDeDescription}{mmmmmmmm} + +\item[\dusa{MICLIB}] {\tt character*12} name of the \dds{microlib} that will contain the internal +library. If \dusa{MICLIB} appears on both LHS and RHS, it is updated; otherwise, it is created. + +\item[\dusa{MICRHS}] {\tt character*12} name of a read-only \dds{microlib} data structure used by the +\moc{CATL} or \moc{MAXS} option of \Sect{desclib}. + +\item[\dusa{MACRHS}] {\tt character*12} name of a read-only \dds{macrolib} data structure to be included +directly in \dusa{MICLIB} before updating it. + +\item[\dusa{EVORHS}] {\tt character*12} name of a read-only \dds{burnup} data structure used by the +\moc{BURN} option of \Sect{desclib}. The number densities for the isotopes in file \dusa{MICLIB} +will be replaced selectively by those found in \dusa{EVORHS}. + +\item[\dstr{desclib}] input structure for this module (see \Sect{desclib}). + +\end{ListeDeDescription} + +\subsubsection{Data input for module {\tt LIB:}}\label{sect:desclib} + +In the case where \dusa{MICRHS} is absent or represents a \dds{macrolib}, \dstr{desclib} takes the form: + +\begin{DataStructure}{Structure \dstr{desclib}} +$[$ \moc{EDIT} \dusa{iprint} $]$ \\ +$[$ \moc{NGRO} \dusa{ngroup} $]$ \\ +$[$ \moc{MXIS} \dusa{nmisot} $]$ \\ +$[$ \moc{NMIX} \dusa{nmixt} $]$ \\ +$[$ \moc{CALENDF} \dusa{ipreci} $]$ \\ +$[$ \moc{CTRA} $\{$ \moc{NONE} $|$ \moc{APOL} $|$ \moc{WIMS} $|$ \moc{OLDW} $|$ \moc{LEAK} $\}$ $]$ +$[$ \moc{ANIS} \dusa{naniso} $]$ \\ +$[$ \moc{STERN} \dusa{nstern} $]$ \\ +$[$ \moc{ADJ} $]~[$ \moc{PROM} $]$ \\ +$[~\{$ \moc{CDEPCHN} $|$ \moc{RDEPCHN} $\}~]$ \\ +$[~\{$ \moc{SKIP} $|$ \moc{INTR} $|$ \moc{SUBG} $|$ \moc{PT} $|$ \moc{PTMC} $|$ \moc{PTSL} $|$ \moc{RSE} $[$ \dusa{svdeps} $]~|$ \moc{NEWL} $\}~]$ $[$ +\moc{MACR} $]$\\ +$[$ \moc{ADED} \dusa{nedit} ( \dusa{HEDIT}(i), i=1,\dusa{nedit} ) $]$ \\ +$[$ \moc{DEPL} $\{$ \moc{LIB:} $\{$ \moc{DRAGON} $|$ \moc{WIMSD4} $|$ \moc{WIMSE} $|$ \moc{WIMSAECL} $|$ \moc{NDAS} $|$ \moc{APLIB3} $\}$ \moc{FIL:} \dusa{NAMEFIL} \\ +\hskip 0.6cm $|$ \moc{LIB:} $\{$ \moc{APLIB2} $|$ \moc{APXSM} $\}$ \moc{FIL:} \dusa{NAMEFIL} \dstr{descdeplA2} \\ +\hskip 0.6cm $|$ \dusa{ndepl} \dstr{descdepl} $\}$ $]$ \\ +$[[$ \moc{MIXS} \moc{LIB:} \\ +\hskip 0.6cm $\{$ \moc{DRAGON} $|$ \moc{MATXS} $|$ \moc{MATXS2} $|$ + \moc{WIMSD4} $|$ \moc{WIMSE} $|$ \moc{WIMSAECL} $|$ \moc{NDAS} $|$ + \moc{APLIB1} $|$ \moc{APLIB2} \\ +\hskip 0.85cm $|$ \moc{APXSM} $|$ \moc{APLIB3} $|$ \moc{MICROLIB} $\}$ \\ +\hskip 0.6cm \moc{FIL:} \dusa{NAMEFIL} $[[$ \dstr{descmix1} $]]$ $]]$ \\ +{\tt ;} +\end{DataStructure} + +\noindent It is possible to reset an existing \dds{microlib} (i.e., \dusa{MICLIB} is present +in both the LHS and RHS) and to reprocess all the isotopes from the cross section libraries. +In this case, \dstr{desclib} takes the simplified form: + +\begin{DataStructure}{Structure \dstr{desclib}} +$[$ \moc{EDIT} \dusa{iprint} $]$ \\ +$\{$ \moc{INTR} $|$ \moc{SUBG} $|$ \moc{PT} $|$ \moc{PTMC} $|$ \moc{PTSL} $|$ \moc{RSE} $[$ \dusa{svdeps} $]~|$ \moc{NEWL} $\}~[$ \moc{MACR} $]$ \\ +\moc{MIXS} \\ +{\tt ;} +\end{DataStructure} + +\noindent +If keyword \moc{CATL} is given, \dusa{MICLIB} is catenated with the RHS \dusa{LIBRHS} \dds{microlib} . + +\begin{DataStructure}{Structure \dstr{desclib}} +$[$ \moc{EDIT} \dusa{iprint} $]$ \\ +$[$ \moc{MXIS} \dusa{nmisot} $]$ \\ +$[$ \moc{NMIX} \dusa{nmixt} $]$ \\ +$[~\{$ \moc{SKIP} $|$ \moc{MACR} $\}~]$ +$[~\{$ \moc{CDEPCHN} $|$ \moc{RDEPCHN} $\}~]$ \\ +$[$ \moc{DEPL} $\{$ \moc{LIB:} $\{$ \moc{DRAGON} $|$ \moc{WIMSD4} $|$ \moc{WIMSE} $|$ \moc{WIMSAECL} $|$ \moc{NDAS} $|$ \moc{APLIB3} $\}$ \moc{FIL:} \dusa{NAMEFIL} \\ +\hskip 0.6cm $|$ \moc{LIB:} $\{$ \moc{APLIB2} $|$ \moc{APXSM} $\}$ \moc{FIL:} \dusa{NAMEFIL} \dstr{descdeplA2} \\ +\hskip 0.6cm $|$ \dusa{ndepl} \dstr{descdepl} $\}$ $]$ \\ +\moc{CATL} $[[$ \dstr{descmix2} $]]$ \\ +{\tt ;} +\end{DataStructure} + +\noindent +Alternatively if keyword \moc{BURN} or \moc{MAXS} is given, \dstr{desclib} takes the form: + +\begin{DataStructure}{Structure \dstr{desclib}} +$[$ \moc{EDIT} \dusa{iprint} $]$ \\ +$\{$ \moc{BURN} $\{$ \dusa{iburn} $|$ \dusa{tburn} $\}~|$ \moc{MAXS} $\}$ +$[[$ \dstr{descmix2} $]]$ \\ +{\tt ;} +\end{DataStructure} +\noindent where the RHS data structure is a \dds{burnup} (\dusa{EVORHS}) or a \dds{microlib} (\dusa{LIBRHS}) data structure. \dstr{desclib} options are: + +\begin{ListeDeDescription}{mmmmmm} + +\item[\moc{EDIT}] keyword used to modify the print level \dusa{iprint}. + +\item[\dusa{iprint}] index used to control the printing in this operator. It +must be set to 0 if no printing on the output file is required while values +$>$0 will increase in steps the amount of information transferred to the output +file. If \dusa{iprint}$\ge$10, the depletion chain is printed in the format of +structure \dstr{descdepl}. If \dusa{iprint}$\ge$20, the depletion chain is also +printed in the format of structure \dstr{descdeplA2}. + +\item[\moc{MXIS}] keyword used to redefine the maximum number of isotopes per +mixture. + +\item[\dusa{nmisot}] the maximum number of isotopes per +mixture. By default up to 300 different isotopes per mixture are permitted. + +\item[\moc{NMIX}] keyword used to define the number of material mixtures. This +data is required if \dusa{MICLIB} is created. + +\item[\dusa{nmixt}] the maximum number of mixtures (a mixture +is characterized by a distinct set of macroscopic cross sections). + +\item[\moc{CALENDF}] keyword to set the accuracy of the CALENDF probability +tables. + +\item[\dusa{ipreci}] integer set to 1, 2, 3 or 4. The highest the value, the +more accurate are the probability tables. The default value is \dusa{ipreci}=4. + +\item[\moc{CTRA}] keyword to specify the type of transport correction that +should be generated and stored on the \dds{microlib}. The transport correction is to be +substracted from the total and isotropic ($P_0$) within-group scattering cross sections. A leakage correction, equal +to the difference between current-- and flux--weighted total cross sections ($\sigma_{1}-\sigma_{0}$) +is also applied in the \moc{APOL}, \moc{OLDW} and \moc{LEAK} cases. All the operators that +will read this \dds{microlib} will then have access to transport corrected +cross sections. The default is no transport correction. + +\item[\moc{NONE}] keyword to specify that no transport correction should be +used in this calculation. + +\item[\moc{APOL}] keyword to specify that an APOLLO type transport correction +based on the linearly anisotropic ($P_1$) within-group scattering cross sections is to be set. This correction assumes that +the micro-reversibility principle is valid for all energy groups. This type of +correction uses $P_1$ scattering information present on the library. + +\item[\moc{WIMS}] This type of correction uses directly a transport-correction +provided on the library. +Such information is available in WIMSD4, WIMSE and WIMS--AECL libraries. This is +the new recommended option with WIMS-type libraries. {\sl This option has no effect on +libraries that does not contain transport correction information.} + +\item[\moc{OLDW}] keyword to specify that a WIMS type transport +correction based on the $P_1$ scattering cross sections is to be +set. This correction +assumes that the micro-reversibility principle is valid only for groups energies +less than 4.0 eV. For the remaining groups a $1/E$ current spectrum is considered +in the evaluation of the transport correction. This type of correction uses +$P_1$ scattering information present on the library. + +\item[\moc{LEAK}] A leakage correction is applied to the total and +$P_0$ within-group scattering cross sections. No transport correction is +applied in this case. + +\item[\moc{ANIS}] keyword to specify the maximum level of anisotropy for the +scattering cross sections. + +\item[\dusa{naniso}] number of Legendre orders for the representation of the +scattering cross sections. Isotropic scattering is represented by +\dusa{naniso}=1 while \dusa{naniso}=2 represents linearly anisotropic +scattering. Generally the linearly anisotropic ($P_1$) scattering contributions are +taken into account via the transport correction (see \moc{CTRA} keyword) in the +transport calculation. For $B_{1}$ or $P_{1}$ leakage calculations, the linearly +anisotropic scattering cross sections are taken into account explicitly. The +default value is \dusa{naniso}=2. + +\item[\moc{STERN}] keyword to specify the application of the Sternheimer density correction for charged particles. + +\item[\dusa{nstern}] index used to control the Sternheimer correction application. Sternheimer correction applied for both restricted total stopping power +and heat deposition cross section ({\tt H-FACTOR}) is represented by \dusa{nstern} $=1$. A complete desactivation of the Sternheimer correction is obtained +by setting \dusa{nstern} $=0$. By default, the Sternheimer density correction is applied for both quantities. Notes: 1) The Sternheimer density correction should be +applied for both quantities except for specific charged particles cross sections perturbations analysis; 2) The Sternheimer density correction should be +applied on macroscopic cross sections. However, the heat deposition cross section contains a microscopic collisional stopping power which has not been +corrected in ELECTR module of NJOY. This is why the charged particle {\tt H-FACTOR} data $-$ recovered from microscopic libraries produced by ELECTR, but not +those produced by CEPXS-BFP $-$ should be corrected in DRAGON5. + +\item[\moc{ADJ}] keyword to specify the production of adjoint macroscopic +cross sections. By default, direct cross sections are produced. + +\item[\moc{PROM}] keyword to specify that prompt neutrons are to be considered +for the calculation of the fission spectrum. By default, the contribution due to +delayed neutrons is considered. This option is only compatible with a +\moc{MATXS} or \moc{MATXS2} format library. + +\item[\moc{CDEPCHN}] keyword to enable the automatic completion of burnup chains. + +\item[\moc{DDEPCHN}] keyword to avoid the automatic completion of burnup chains. + +\item[\moc{SKIP}] keyword to recover the user--defined microlib data without processing +any library (i.e., without temperature and/or dilution interpolation). + +\item[\moc{INTR}] keyword to perform a temperature and dilution interpolation +of the microscopic cross sections present in the libraries. The bin-type +cross-section data is not processed. This is the default option. + +\item[\moc{SUBG}] keyword to activate the calculation of the physical probability +tables using the tempera\-tu\-re-interpolated cross-section data as +input.\cite{subg,nse2004} The bin-type cross-section data is not processed. + +\item[\moc{PT}] keyword to activate the calculation of the CALENDF-type +mathematical probability tables ({\sl without} slowing-down correlated weight matrices) +using the bin-type cross-section data as input.\cite{pt} This option is +compatible with the Sanchez-Coste self-shielding method and with the subgroup projection method (SPM).\cite{SPM09} + +\item[\moc{PTMC}] this option is similar to the \moc{PT} procedure. Here, the base points of the probability tables corresponding +to fission and scattering cross sections and to components of the transfer scattering matrix are also obtained using the CALENDF approach. + +\item[\moc{PTSL}] keyword to activate the calculation of the CALENDF-type +mathematical probability tables and slowing-down correlated weight matrices +using the bin-type cross-section data as input.\cite{nse2004} + +\item[\moc{RSE}] keyword to activate the generation of information for the resonance spectrum expansion (RSE) method.\cite{rse2021} + +\item[\dusa{svdeps}] rank accuracy $\epsilon_{\rm svd}$ of the singular value decomposition. Singular values $w_i \le \epsilon_{\rm svd}\Delta u_{\rm elem}$ are set to zero. +$\Delta u_{\rm elem}$ is the elementary lethargy width of the Autolib. The default value is \dusa{svdeps}=1.0 $\times 10^{-3}$. + +\item[\moc{NEWL}] keyword to activate the calculation of a microlib +containing temperature-interpo\-la\-ted cross-section data. The bin-type +cross-section data is also interpolated. Probability tables are not computed. + +\item[\moc{MACR}] keyword to force the calculation of the embedded +macrolib. By default, the embedded macrolib is computed, {\sl except if} one of the +key words \moc{SKIP}, \moc{INTR}, \moc{SUBG}, \moc{PT} or \moc{NEWL} is used. + +\item[\moc{ADED}] keyword to specify the input of additional cross sections to +be treated by DRAGON. These cross sections are not needed to solve the transport +equation but are recognized by the \moc{EDI:} and utility operators. + +\item[\dusa{nedit}] number of types of additional cross sections. + +\item[\dusa{HEDIT}] {\tt character*6} name of an additional +cross-section type. This name also corresponds to vectorial reactions in a +\moc{MATXS} and +\moc{MATXS2} format library. For example: + +\moc{NWT0}/\moc{NWT1}=$P_0/P_1$ library weight functions.\\ +\moc{NTOT0}/\moc{NTOT1}=$P_0/P_1$ neutron total cross sections.\\ +\moc{NELAS}=Neutron elastic scattering cross sections (MT=2).\\ +\moc{NINEL}=Neutron inelastic scattering cross sections (MT=4).\\ +\moc{NG}=Neutron radiative capture cross sections (MT=102).\\ +\moc{NFTOT}=Total fission cross sections (MT=18).\\ +\moc{NUDEL}=Number of delayed secondary neutrons (Nu-D / MT=455).\\ +\moc{NFSLO}=$\nu*$slow fission cross section.\\ +\moc{NHEAT}=Heat production cross section.\\ +\moc{CHIS}/\moc{CHID}=Slow/delayed fission spectrum.\\ +\moc{NF}/\moc{NNF}/\moc{N2NF}/\moc{N3NF}=$\nu*$partial fission cross sections (MT=19, 20, 21 and 38).\\ +\moc{N2N}/\moc{N3N}/\moc{N4N}=(n,2n), (n,3n), (n,4n) cross sections (MT=16, 17 and 37).\\ +\moc{NP}/\moc{NA}=(n,p) and (n,$\alpha$) transmutation cross sections (MT=103 and 107). + +By default, DRAGON will always attempt to recover the additional cross sections +\moc{NG}, \moc{NFTOT}, \moc{NHEAT} and \moc{N2N} which are required for the depletion +calculations. + +\item[\moc{DEPL}] keyword to specify that the isotopic depletion (burnup) +chain is to be read. For a given \moc{LIB:} execution only one isotopic +depletion chain can be read. + +\item[\moc{MIXS}] keyword to specify that the mixture description is to be +read. For a given \moc{LIB:} execution more than one cross-section library can +be read. + +\item[\moc{LIB:}] keyword to specify the type of library from which the +isotopic depletion chain or microscopic cross section is to be read. It is +optional when preceded by the keyword \moc{DEPL} in which case the isotopic +depletion chain is read from the standard input file. + +\item[\moc{DRAGON}] keyword to specify that the isotopic depletion chain or +the microscopic cross sections are in the {\sc draglib} format. + +\item[\moc{MATXS}] keyword to specify that the microscopic cross sections are +in the MATXS format of NJOY-II and NJOY-89 (no depletion data available for +libraries using this format). + +\item[\moc{MATXS2}] keyword to specify that the microscopic cross sections are +in the MATXS format of NJOY-91 (no depletion data available for libraries using +this format). The MATXS file is a binary sequential file by default. If the name +\dusa{NAMEFIL} has a leading ``{\tt \_}'' character, the MATXS file is expected to be +BCD-formatted, as produced by NJOY. + +\item[\moc{WIMSD4}] keyword to specify that the isotopic depletion chain and the +microscopic cross sections are in the WIMSD4 format, as produced by module {\tt wimsr} of NJOY with flag +{\tt iverw} $=4$. This format is supported by the WLUP project.\cite{wlup} + +\item[\moc{WIMSE}] keyword to specify that the isotopic depletion chain and the +microscopic cross sections are in the WIMSE format, as produced by module {\tt wimsr} of NJOY with flag +{\tt iverw} $=5$. + +\item[\moc{WIMSAECL}] keyword to specify that the isotopic depletion chain and the +microscopic cross sections are in the WIMS-AECL format. + +\item[\moc{NDAS}] keyword to specify that the isotopic depletion chain and the +microscopic cross sections are in the NDAS format, as used in recent versions of WIMS-AECL. + +\item[\moc{APLIB1}] keyword to specify that the microscopic cross sections are +in the APOLLO-1 format. There are no depletion chains available for libraries using this +format. + +\item[\moc{APLIB2}] keyword to specify that the microscopic cross sections are +in the APOLLO-2 direct access format. There are no depletion chains available for libraries +using this format. However, fission yields, radioactive decay constants and +energy released per fission or radiative capture are recovered from the file. +Only versions of the APOLIB-2 libraries subsequent or equal to CEA93-V4 can be +processed. The list of isotopes (standard and self-shielded) available in an APOLIB-2 +is printed by setting the print flag to a value \dusa{iprint}$\ge$10. + +\item[\moc{APXSM}] keyword to specify that the microscopic cross sections are +in the APOLIB-XSM format, the output format of N2A2 utility. There are no depletion chains available for libraries +using this format. However, fission yields, radioactive decay constants and +energy released per fission or radiative capture are recovered from the file. +The list of isotopes (standard and self-shielded) available in an APOLIB-XSM +is printed by setting the print flag to a value \dusa{iprint}$\ge$10. + +\item[\moc{APLIB3}] keyword to specify that the microscopic cross sections are +in the APOLIB-3 format, the output format of the Galilee system. An ENDF/B evaluation is +represented by three HDF5 files: +\begin{description} +\item[\dusa{NAME1}:] HDF5 file containing infinite dilution information +\item[\dusa{NAME2}:] HDF5 file containing resonance self-shielding information +\item[\dusa{NAME3}:] HDF5 file containing depletion chains, branching ratio, fission yields and energy deposition information. +\end{description} +After \moc{DEPL}, the \moc{FIL:} keyword is followed by the concatenation of \dusa{NAME1} and \dusa{NAME3} with a colon character ({\tt :}) between +the two names. After \moc{MIXS}, the \moc{FIL:} keyword is followed by the concatenation of \dusa{NAME1} and \dusa{NAME2} with a colon character ({\tt :}) between +the two names. The list of isotopes (standard and self-shielded) available in an APOLIB-3 +is printed by setting the print flag to a value \dusa{iprint}$\ge$10. + +\item[\moc{MICROLIB}] keyword to specify that the microscopic cross sections are +in a {\sc microlib}-formatted object, as produced by DRAGON. This format is similar to the {\sc draglib} +format where the isotopes are stored in elements of list {\tt ISOTOPESLIST} instead of been stored +as independent sub-directories. + +\item[\moc{FIL:}] keyword to specify the name of the file where is stored the +isotopic depletion data. + +\item[\dusa{NAMEFIL}] {\tt character*64} name of the library +where the isotopic depletion chain or the microscopic cross sections are stored. + +Library names in {\sc draglib} format are limited to 12 characters. + +An \moc{APLIB3} library name is the concatenation of two names with a colon character ({\tt :}) between them: +\begin{verbatim} + DEPL LIB: APLIB3 FIL: CLA99CEA93:CLA99CEA93_EVO + MIXS LIB: APLIB3 FIL: CLA99CEA93:CLA99CEA93_SS +\end{verbatim} + +A \moc{NDAS} library is made of two or more files. These file names must be concatenated in a single +\dusa{NAMEFIL} name, using colons as separators. The {\sc ascii} index file is always the first, +followed by optional patch files, and terminated by the main direct-access binary file. The +following sample data line corresponds to a {\sc ndas} library without patch: +\begin{verbatim} + MIXS LIB: NDAS FIL: E65LIB6.idx:E65LIB6.sdb +\end{verbatim} + +\item[\dusa{ndepl}] number of isotopes in the depleting chain. + +\item[\dstr{descdepl}] input structure describing the +depletion chain (see \Sect{descdepl}). + +\item[\dstr{descdeplA2}] simplified input structure describing the +depletion chain in cases where an APOLIB-2 or APOLIB-XSM file is used (see \Sect{descdepl}). + +\item[\moc{CATL}] keyword to perform the following operations: +\vspace{-0.15cm} +\begin{itemize} +\item create a new microlib or recover an existing \dds{microlib} in modification mode, +\item catenate with a RHS \dds{microlib} in read-only mode, +\item create the embedded \dds{macrolib}. +\end{itemize} + +\item[\moc{MAXS}] keyword to specify that the mixture density on \dusa{MICLIB} +are to be modified. If \dusa{MICRHS} is present and \dstr{descmix2} is absent, a +direct one to one correspondence between the isotope on both libraries is +assumed. If \dusa{MICRHS} and \dstr{descmix2} are present, only the +mixture on the library file specified by \dstr{descmix2} are updated using +information from the \dusa{MICRHS}. If \dusa{MICRHS} is absent and +\dstr{descmix2} is present, only the mixture on \dusa{MICLIB} specified by +\dstr{descmix2} are updated. This option is useful for implementing two-level +computational schemes similar to REL-2005. + +\item[\moc{BURN}] keyword to specify that the mixture density on \dusa{MICLIB} +are to be updated using information taken from \dusa{EVORHS}. If \dstr{descmix2} +is absent, a direct one to one correspondence between the isotope on +\dusa{EVORHS} and \dusa{MICLIB} is assumed. If \dstr{descmix2} is present, only +the mixture specified by \dstr{descmix2} are updated using information from +\dusa{EVORHS}. This option is useful for performing branching calculations. + +\item[\dusa{iburn}] burnup step from the burnup file to use. This step must be +already present on the burnup file. + +\item[\dusa{tburn}] burnup time in days from the burnup file to use. This time +step must be already present on the burnup file. + +\item[\dstr{descmix1}] input structure describing the +isotopic and physical properties of a given mixture (see \Sect{descmix1}). + +\item[\dstr{descmix2}] input structure describing perturbations to the +isotopic and physical properties of a given mixture (see \Sect{descmix2}). + + +\end{ListeDeDescription} + +Note that it is possible to recompute the embedded macrolib in an existing microlib +named {\tt MICRO} by writing +\begin{verbatim} +MICRO := LIB: MICRO :: MACR MIXS ; +\end{verbatim} + +\subsubsection{Depletion data structure}\label{sect:descdepl} + +The structure \dstr{descdepl} describes the heredity of the radioactive decay +and the neutron activation chain to be used in the isotopic depletion +calculation. +\begin{DataStructure}{Structure \dstr{descdepl}} +\moc{CHAIN} \\ +$[[$ \dusa{NAMDPL} $[$ \dusa{izae} $]$ \\ +\hskip 1.0cm $[[~\{$ \moc{DECAY} \dusa{dcr} $|$ \\ +\hskip 2.0cm \dusa{reaction} $[$ \dusa{energy} $]~\}~]]$ \\ +\hskip 1.0cm $[~\{$ \moc{STABLE} $|$ \\ +\hskip 2.0cm \moc{FROM} $[[~\{$ \moc{DECAY} $|$ \dusa{reaction} $\}$ +$[[$ \dusa{yield} \dusa{NAMPAR} $]]~]]~\}~]~]]$\\ +\moc{ENDCHAIN} +\end{DataStructure} + +\vspace{-0.15cm} + +\noindent +with: + +\begin{ListeDeDescription}{mmmmmm} + +\item[\moc{CHAIN}] keyword to specify the beginning of the depletion chain. + +\item[\dusa{NAMDPL}] {\tt character*12} name of an isotope (or isomer) of the +depletion chain that appears in the cross-section library. + +\item[\dusa{izae}] optional six digit integer representing the isotope. The first two +digits represent the atomic number of the isotope; the next three indicate its +mass number and the last digit indicates the excitation level of the nucleus (0 +for a nucleus in its ground state, 1 for an isomer in its first exited state, +etc.). For example, $^{238}$U in its ground state will be represented by +\dusa{izae}=922380. + +\item[\moc{DECAY}] indicates that a decay reaction takes place either for +production of this isotope or its depletion. + +\item[\dusa{dcr}] radioactive decay constant (in $10^{-8}$ s$^{-1}$) of the +isotope. By default, \dusa{dcr}=0.0. + +\item[\dusa{reaction}] {\tt character*6} identification of a neutron-induced +reaction that takes place either for production of this isotope, its depletion, +or for producing energy. Example of reactions are following: + +\begin{ListeDeDescription}{mmmmmmmm} +\item[\moc{NG}] indicates that a radiative capture reaction takes place either +for production of this isotope, its depletion or for producing energy. + +\item[\moc{N2N}] indicates that the following reaction is taking place: +$$ n +^{A}X_Z \to 2 n + ^{A-1}X_Z$$ + +\item[\moc{N3N}] indicates that the following reaction is taking place: +$$ n +^{A}X_Z \to 3 n + ^{A-2}X_Z$$ + +\item[\moc{N4N}] indicates that the following reaction is taking place: +$$ n +^{A}X_Z \to 4 n + ^{A-3}X_Z$$ + +\item[\moc{NP}] indicates that the following reaction is taking place: +$$ n +^{A}X_Z \to p + ^AY_{Z-1}$$ + +\item[\moc{NA}] indicates that the following reaction is taking place: +$$ n +^{A}X_Z \to ^4{\rm He}_2 + ^{A-3}X_{Z-2}$$ + +\item[\moc{NFTOT}] indicates that a fission is taking place. +\end{ListeDeDescription} + +\item[\dusa{energy}] energy (in MeV) recoverable per neutron-induced +reaction of type \dusa{reaction}. If the energy associated to radiative capture +is not explicitely given, it should be added to the energy released per fission. +If {\tt H-FACTOR} information is available for isotope \dusa{NAMDPL}, \dusa{energy} +contains only decay energy of lumped isotopes produced by \dusa{reaction} of \dusa{NAMDPL}. +By default, \dusa{energy}=0.0 MeV. + +\item[\moc{STABLE}] non depleting isotope. Such an isotope may produces +energy by neutron-induced reactions (such as radiative capture). + +\item[\moc{FROM}] indicates that this isotope is produced from decay or +neutron-induced reactions. + +\item[\dusa{yield}] branching ratio or production yield expressed in fraction. + +\item[\dusa{NAMPAR}] {\tt character*12} name of the a parent isotope +(or isomer) that appears in the cross-section library. + +\item[\moc{ENDCHAIN}] keyword to specify the end of the depletion chain. + +\end{ListeDeDescription} + +\vskip 0.15cm + +If the keyword \moc{APLIB2} or \moc{APXSM} was used in structure \dstr{desclib}, part of the +depletion data is recovered from the APOLIB file: the fission yields, the +radioactive decay constants and the energy released per fission or radiative +capture. Moreover, the following simplified structure is used to provide the +remaining depletion data: + +\begin{DataStructure}{Structure \dstr{descdeplA2}} +\moc{CHAIN} \\ +$[[$ \dusa{NAMDPL} $[$ \moc{FROM} $[[$ $\{$ \moc{DECAY} $|$ \dusa{reaction} $\}$ +\dusa{yield} \dusa{NAMPAR} $]]$ $]$ $]]$\\ +\moc{ENDCHAIN} +\end{DataStructure} + +\vskip 0.15cm + +In this case, the following rules apply: +\begin{itemize} +\item We should provide the names \dusa{NAMDPL} of {\sl all} the depleting +isotopes (i.e. isotopes with a time-dependent number density), including the +pseudo fission products (PFP). +\item The fission father reactions (\moc{NFTOT}) are not given. +\item The stable isotopes are automatically recovered from the +APOLIB file. They are not given in structure \dstr{descdeplA2}. +\item An isotope is considered to be stable if it is not present in +structure \dstr{descdeplA2}, has no father and no daughter, +but can release energy by fission or radiative capture. +\item It is possible to truncate the isotope name \dusa{NAMDPL} at the +underscore. For example, {\tt D2O\_3\_P5} can be simply written {\tt D2O}. +\item Only the radioactive decay constants of the isotopes present in +structure \dstr{descdeplA2} are recovered from the APOLIB file. The +radioactive decay constants of the other isotopes are set to zero. +\end{itemize} + +\subsubsection{Mixture description structure}\label{sect:descmix1} + +The structure \dstr{descmix1} is used to describe the isotopic composition and +the physical properties, such as the temperature and density, of a mixture. + +\begin{DataStructure}{Structure \dstr{descmix1}} +\moc{MIX} $[$ \dusa{matnum} $]$ $\{$ \\ +\hskip 1.0cm $[$\dusa{temp} $[$ \dusa{denmix} $]~]~~[~\{$ \moc{NOEV} $|$ \moc{EVOL} $\}~]~~[~\{$ \moc{NOGAS} + $|$ \moc{GAS}$\}~]$\\ +\hskip 2.0cm $[[~[$ \dusa{NAMALI} \moc{=} $]$ \dusa{NAMISO} \dusa{dens} $[~\{$ \dusa{dil} + $|$ \moc{INF} $\}~]$\\ +\hskip 2.0cm $[~[$ \moc{CORR} $]$ \dusa{inrs} $]~[$ \moc{DBYE} \dusa{tempd} $]~[$ \moc{SHIB} \dusa{NAMS} $]$ \\ +\hskip 2.0cm $[$ \moc{THER} \dusa{ntfg} \dusa{HINC} $[$ \moc{TCOH} \dusa{HCOH} $]~[$ \moc{RESK} $]~]$ \\ +\hskip 2.0cm $[$ \moc{IRSET} $\{$ \dusa{gir} $|~\{$ \moc{PT} $|$ \moc{PTMC} $|$ \moc{PTSL} $|$ \moc{RSE} $\}~\}~\{$ +\dusa{nir} $|$ \moc{NONE} $\}~]~~[~\{$ \moc{NOEV} $|$ \moc{EVOL} $|$ \moc{SAT} $\}~]~]]$ \\ +\hskip 1.0cm $|$ \\ +\hskip 1.0cm \moc{COMB} $[[$ \dusa{mati} \dusa{relvol} $]]~\}$ +\end{DataStructure} + +\vspace{-0.15cm} + +\noindent +where: + +\begin{ListeDeDescription}{mmmmmm} + +\item[\moc{MIX}] keyword to specify the number identifying the next mixture to +be read. + +\item[\dusa{matnum}] mixture identifier. The maximum value that \dusa{matnum} +may have is \dusa{nmixt}. When \dusa{matnum} is absent, the mixtures are +numbered successively starting from 1 if no mixture has yet been specified or +from the last mixture number specified + 1. + +\item[\dusa{temp}] absolute temperature (in Kelvin) of the isotopic mixture. +It is optional only when this mixture is to be updated, in which case the old +temperature associated with the mixture is used. + +\item[\dusa{denmix}] mixture density in $g \ cm^{-3}$. + +\item[\dusa{NAMALI}] {\tt character*8} alias name for an isotope to be used +locally. When the alias name is absent, the isotope name used locally is +identical to the first 8-character isotope name on the library. + +\item[\moc{=}] keyword to specify to which isotope in a library is associated +the previous alias name. + +\item[\dusa{NAMISO}] {\tt character*12} name of an isotope present in the +library which is included in this mixture. + +\item[\dusa{dens}] isotopic concentration of the isotope \dusa{NAMISO} in the +current mixture in $10^{24}cm^{-3}$. When the mixture density \dusa{denmix} +is specified, the relative weight percentage of each of the isotopes in this +mixture is to be provided. + +\item[\dusa{dil}] group independent microscopic dilution cross section (in +barns) of the isotope \dusa{NAMISO} in this mixture. It is possible to +recalculate a group dependent dilution for an isotope by the use of the +\moc{SHI:} or \moc{TONE:} operator (see \Sect{SHIData} and \Sect{TONEData}). In this case, the dilution is only used +as a starting point for the self-shielding iterations and has no effect on the +final result. If the dilution is not given or is larger than $10^{10}$ barns, +an infinite dilution is assumed. + +\item[\moc{INF}] keyword to specify that a dilution of $10^{10}$ barns is to +be associated with this isotope. This value represents an infinite dilution (the +isotope is present in trace amounts only). It is possible to +recalculate a group dependent dilution for an isotope by the use of the +\moc{SHI:} operator (see \Sect{SHIData}) or \moc{TONE:} operator (see \Sect{TONEData}). In this case, the dilution is only used +as a starting point for the self-shielding iterations and has no effect on the +final result. If the dilution is not given an infinite dilution is assumed. + +\item[\moc{CORR}] keyword to specify that the resonances of an isotope are correlated +with those of other isotopes with the same \dusa{inrs} index. This option is only +available with the {\sl Ribon extended} model\cite{nse2004} or wth the {\sl subgroup +projection method} (SPM)\cite{SPM09} in energy groups where +this model is set. If this option is selected for +an isotope, it must be set for all isotopes with the same \dusa{inrs} index. By default, +the resonances of distinct isotopes are assumed to be uncorrelated. + +\item[\dusa{inrs}] index of the resonant region associated with this isotope. +By default \dusa{inrs}=0 and the isotope is not a candidate for self-shielding. +When \dusa{inrs}$\ne$0, the isotope can be self-shielded where it is assumed that a given +isotope distributed with different concentrations in a number of mixtures and +having the same value of \dusa{inrs} will share the same fine flux. +Should we wish to self-shield both the clad and the fuel it is important +to assign a different \dusa{inrs} number +to each. If a single type of fuel is located in different mixture in +{\sl onion-peel fashion}, it is necessary to attribute a single \dusa{inrs} value +to this fuel. + +\item[\moc{DBYE}] keyword to specify that the absolute temperature of the +isotope is different from that of the isotopic mixture. This option is useful to +define Debye-corrected temperature. + +\item[\dusa{tempd}] absolute temperature (in Kelvin) of the isotope. By +default \dusa{tempd}=\dusa{temp}. + +\item[\moc{SHIB}] keyword to specify that the name of the isotope containing +the information related to the self-shielding is different from the initial name +of the isotope. This option is not required if a MATXS or a {\sc draglib} file is used. + +\item[\dusa{NAMS}] {\tt character*12} name of a record in the library +containing the self-shielding data. This name is required if the dilution is +not infinite or a non zero resonant region is associated with this isotope and \dusa{NAMS} +is different from \dusa{NAMISO}. This record must be contained in the same +library file as record \dusa{NAMISO}. + +\item[\moc{THER}] keyword to specify that the thermalization and resonant elastic +scattering kernel effects are to be included with the cross sections when using a +\moc{MATXS} or \moc{MATXS2} format library. + +\item[\dusa{HINC}] {\tt character*6} name of the incoherent thermalization +effects which will be taken into account. The incoherent effects are those that +may be described by the $S(\alpha,\beta)$ scattering law. The value \moc{FREE} +is used to simulate the effects of a gas. + +\item[\moc{TCOH}] keyword to specify that coherent thermalization effects +will be taken into account. + +\item[\dusa{HCOH}] {\tt character*6} name of the coherent thermalization +effects which will be taken into account. The coherent effects are the +{\sl vectorial reactions} in the \moc{MATXS} or \moc{MATXS2} format library where +the name is terminated by the `\$' suffix. They are generally available for +graphite, beryllium, beryllium oxide, polyethylene and zirconium hydroxide. + +\item[\moc{RESK}] keyword to specify that resonant elastic scattering kernel effects +will be taken into account. + +\item[\dusa{ntfg}] number of energy groups that will be affected by the +thermalization and resonant elastic scattering kernel effects. + +\item[\moc{IRSET}] keyword to specify an intermediate resonance (IR) +approximation or the {\sl Ribon extended} model for some energy groups. By default, an +IR approximation with the value of the Goldstein-Cohen parameter found on the library +is used. If no value is found on the library, a statistical (ST) model\cite{st} is set in +all groups by default. The ``{\tt IRSET PT 1}'' option is set by default if keyword \moc{PT} +is selected in structure \dstr{desclib}. The same rule applies for \moc{PTMC}, \moc{PTSL} or +\moc{RSE}. + +\item[\dusa{gir}] imposed Goldstein-Cohen IR parameter. A Goldstein-Cohen IR parameter +$0 \le \lambda_g\le 1$ is set in energy group $g$. A value of 1.0 stands for +a statistical (ST) approximation. A value of 0.0 stands for an infinite mass +(IM or WR) approximation. + +\item[\moc{PT}] keyword to enable the calculation of CALENDF--type probability tables in some energy groups. The +slowing-down correlated weight matrices are {\sl not} computed. This type of probability tables is consistent +with the Sanchez-Coste self-shielding method and with the subgroup projection method (SPM).\cite{SPM09} + +\item[\moc{PTMC}] keyword to enable the calculation of CALENDF--type probability tables, similar to the \moc{PT} +procedure. Here, the base points of the probability tables corresponding +to fission and scattering cross sections and to components of the transfer scattering matrix are also obtained using the CALENDF approach. + +\item[\moc{PTSL}] keyword to enable the calculation of CALENDF--type probability tables, consistent +with the Ribon extended model, in some energy groups. + +\item[\moc{RSE}] keyword to enable the calculation of RSE--type probability tables in some energy groups. + +\item[\dusa{nir}] the intermediate resonance (IR) approximation or the Ribon extended +model is imposed for energy groups with an index equal or greater than \dusa{nir}. +A statistical (ST) model is set in other groups. + +\item[\moc{NONE}] keyword to specify that a statistical (ST) model is set in +all groups. + +\item[\moc{NOEV}] keyword to force a mixture or a nuclide to be non-depleting (even in +cases where it is potentially depleting). Note that the mixture or nuclide keeps its +capability to produce energy. By default, the depleting isotopes are +automatically regognized as depleting. + +\item[\moc{EVOL}] keyword to force a mixture or a nuclide to be depleting. By default, only fission products and +fissile isotopes are depleting. + +\item[\moc{NOGAS}] keyword to specify that a mixture has a solid or liquid state (used for stopping power correction). +This is the default option. + +\item[\moc{GAS}] keyword to specify that a mixture has a gaseous state (used for stopping power correction). + +\item[\moc{SAT}] keyword to force a nuclide to be at saturation. By default, the saturation approximation is +automatically set as a function of the half life and capture cross sections of the isotope. + +\item[\moc{COMB}] keyword to specify that this mixture is reset with a +combination of previously defined mixtures. + +\item[\dusa{mati}] number associated with a previously defined mixture. In +order to insert some void in a mixture use \dusa{mati}=0. If the mixture is not +already defined one assumes that it represents a voided mixture. + +\item[\dusa{relvol}] relative volume $V_{i}$ occupied by mixture +\dusa{mati}=$i$ in \dusa{matnum}. Two cases can be considered, namely that +where the density $\rho_{i}$ of each mixture \dusa{mati} is provided along with +the weight percent for each isotope $J$ ($W_{i}^{j}$) and the case where the +explicit concentration $N_{i}^{j}$ of each isotope in a \dusa{mati} was provided +(it is forbidden to combined two mixtures with different isotopic content +description). In the case where the initial mixtures are defined using densities +$\rho_{i}$, the density ($\rho_k$) and volume ($V_{k}$) of the final mixture +will become: + $$V_{k}=\sum_{i} V_{i} $$ + $$\rho_{k}=\frac{1}{V_{k}} \sum_{i}\rho_{i}V_{i}$$ +and the weight percent will be changed in a consistent way, namely + $$W_{k,J}=\frac{\rho_{i}V_{i}W_{i,J}}{\rho_{k} V_{k} } $$ +When the explicit concentration are given we will use: + $$N_{k,J}=\frac{V_{i}N_{i,J}}{V_{k} } $$ + +\vskip 0.08cm + +There is a very common usage of keyword \moc{COMB}. In the following example, a new mixture with index 42 +is defined in such a way to be identical to an existing mixture with index 25. +\begin{verbatim} + MIX 42 COMB 25 1.0 +\end{verbatim} + +\end{ListeDeDescription} + +Note that in the structure \dstr{descmix1} one only needs to describe the +isotopes initially present in each mixture. DRAGON will then automatically +associate with each depleting mixture the additional isotopes required by the +available burnup chain. Moreover, the microscopic cross-section library +associated with these new isotopes will be the same as that of their parent +isotope. For example, suppose that mixture 1 contains isotope {\tt U235} which +is to be read on the DRAGON-formatted library associated with file {\tt +DRAGLIB}. Assume also that the depletion chain, which is written on the +WIMS--AECL format library associated with file {\tt WIMSLIB}, states that isotope +{\tt U236} (initially absent in the mixture) can be generated form {\tt U235} by +neutron capture. Then, one can either specify explicitly from which library file +the microscopic cross sections associated with isotope {\tt U236} (zero +concentration) are to be read, or omit {\tt U236} from the mixture description +in which case DRAGON will assume that the microscopic cross sections associated +with isotope {\tt U236} are to be read from the same library as the cross +section for isotope {\tt U235}. Note that the isotopes added automatically will +remain at infinite dilution. + +\vskip 0.15cm + +If the \moc{SHI:} or \moc{TONE:} module is used for performing self-shielding calculation, +the self-shielding data for an isotope takes the form +\begin{verbatim} + U235 = U235 5.105E-5 1 +\end{verbatim} +\noindent where the last index indicates the self-shielding region (1 in this case). + +\vskip 0.15cm + +If the {\tt USS:} module implementing the subgroup method is used, +additional self-shielding data is required: +\begin{itemize} +\item Physical probability tables are used (keyword {\tt SUBG}). Consider the following data: +\begin{verbatim} + U235 = U235 5.105E-5 1 IRSET 0.0 81 +\end{verbatim} +The data ``{\tt IRSET 0.0 81}'' indicates that a Goldstein-Cohen parameter +$\lambda_g$ equal +to 0.0 is used for all energy groups with an index equal or greater than 81. A value +of $\lambda_g=1.0$ corresponding to a statistical model is used by default. + +\item Mathematical probability tables (with slowing-down correlated weight matrices) are used (keyword {\tt PTSL}) +{\sl or} mathematical probability tables with the subgroup projection method (SPM)\cite{SPM09} are used (keyword {\tt PT} +or {\tt PTMC}). Consider the following data: +\begin{verbatim} + U235 = U235 5.105E-5 1 IRSET PT 5 +\end{verbatim} +The Goldstein-Cohen approximation is not used with mathematical (CALENDF) probability tables. The data ``{\tt IRSET PT 5}'' +indicates that the CALENDF probability tables are used for energy groups with an index equal +or greater than 5, {\sl with the exception of the energy groups where no Autolib data +is available} and a statistical model (with physical probability tables) is used for energy groups with an index smaller +than 5. A statistical model is also imposed in groups where no Autolib data is available. + +\vskip 0.15cm + +The following data: +\begin{verbatim} + U235 = U235 5.105E-5 1 IRSET PT NONE +\end{verbatim} +\noindent is useful to impose the statistical model (with physical probability tables) in all energy groups. This is equivalent of selecting +the {\tt SUBG} keyword in structure \dstr{desclib}. + +\vskip 0.15cm + +Mathematical (CALENDF) probability tables are used in each energy group where Autolib data is available if the following data is set: +\begin{verbatim} + U235 = U235 5.105E-5 1 IRSET PT 1 +\end{verbatim} +\noindent {\sl This latter definition is equivalent to the default behavior obtained using} +\begin{verbatim} + U235 = U235 5.105E-5 1 +\end{verbatim} +\end{itemize} + +\vskip 0.25cm +\goodbreak + +\subsubsection{Mixture modification description structure}\label{sect:descmix2} + +The structure \dstr{descmix2} is used to describe the modifications in the isotopic composition of a mixture. + +\begin{DataStructure}{Structure \dstr{descmix2}} +$\{$ \moc{MIX} \dusa{matnum} $[$ \dusa{matold} $]$ $[$ \dusa{relden} $]$ +$[$ \dusa{NAMALI} \dusa{dens} $]~[~\{$ \moc{NOEV} $|$ \moc{EVOL} $\}~]~|$ \moc{ALL} $\}$ +\end{DataStructure} + +\vspace{-0.15cm} + +\noindent +where: + +\begin{ListeDeDescription}{mmmmmm} + +\item[\moc{MIX}] keyword to specify the number identifying the next mixture to +be updated. + +\item[\dusa{matnum}] mixture identifier on \dusa{MICLIB}. + +\item[\dusa{matold}] mixture identifier on \dusa{MICRHS}. By default, \dusa{matold}$=$\dusa{matnum}. + +\item[\dusa{relden}] relative density of updated mixture. The concentration +of each isotope in the mixture is to be multiplied by this factor whether it +comes from \dusa{MICLIB}, from \dusa{MICRHS} or is +specified explicitly using \dusa{dens}. + +\item[\dusa{NAMALI}] {\tt character*8} alias name for an isotope on +\dusa{MICLIB} to be modified. + +\item[\dusa{dens}] isotopic concentration of the isotope \dusa{NAMISO} in the +current mixture in $10^{24}cm^{-3}$. When \dusa{relden} is specified, the +isotopic concentration becomes \dusa{dens}$\times$\dusa{relden}. + +\item[\moc{NOEV}] keyword to force a mixture to be non-depleting (even in +cases where it is potentially depleting). Note that the mixture keeps its +capability to produce energy. + +\item[\moc{EVOL}] keyword to force a mixture to be depleting. By default, only +mixtures containing fission products and/or fissile isotopes are depleting. + +\item[\moc{ALL}] keyword to copy all isotopes from \dusa{MICRHS} into \dusa{MICLIB}. Isotopes in \dusa{MICRHS} +must be assigned to mixture indices not existing in \dusa{MICLIB}. + +\end{ListeDeDescription} + +\vskip 0.2cm + +\subsubsection{Cross sections in Dragon}\label{sect:xs} +Multigroup cross sections in Draglibs files are of two types: +\begin{itemize} +\item Vectorial cross sections $\sigma_{x,g}$ +\item Matrix cross sections $\sigma_{x,g\leftarrow h}.$ +\end{itemize} +\begin{enumerate} +\item Total cross sections $\sigma_g$ are provided in ENDF evaluations as {\tt MT} $=1$. They are redundent with other information in the same evaluation. The vectorial total cross section is defined as +\begin{eqnarray} +\nonumber \sigma_g\negthinspace &=&\negthinspace \sigma_{{\rm e},g}+\sigma_{{\rm in},g}+\sigma_{{\rm (n,2n)},g}+\sigma_{{\rm (n,3n)},g}+\sigma_{{\rm (n,4n)},g}+\sigma_{{\rm f},g}+\sigma_{{\rm p},g}+\sigma_{\gamma,g} ++\sigma_{{\rm d},g}+\sigma_{{\rm t},g}+\sigma_{\alpha,g}\\ +&+&\negthinspace \sigma_{2\alpha,g}+\sigma_{{\rm (n,np)},g}+\sigma_{{\rm any},g} +\end{eqnarray} +\noindent where $\sigma_{{\rm e},g}$ and $\sigma_{{\rm in},g}$ are the elastic and inelastic scattering cross sections and where the matrix cross sections are transformed into vectorial cross sections using +\begin{equation} +\sigma_{x,g}=\sum_h \sigma_{x,h\leftarrow g} \ , \ \ {\rm except \ for \ (n,}x{\rm n) \ reactions.} +\end{equation} +\item Inelastic scattering cross sections are sum over {\tt MT} 51 to 91 in the ENDF evaluation: +\begin{equation} +\sigma_{{\rm in},g}=\sum_{{\sl mt}=51}^{91} \sigma_{{\sl mt},g}=\sum_{{\sl mt}=51}^{91} \sum_h \sigma_{{\sl mt},h\leftarrow g} . +\end{equation} +\item (n,$x$n) vectorial cross sections are divided by the secondary neutron multiplicity: +\begin{equation} +\sigma_{{\rm (n,2n)},g}={1\over 2}\sum_h \sigma_{{\rm (n,2n)},h\leftarrow g} \ , \ \ \sigma_{{\rm (n,3n)},g}={1\over 3}\sum_h \sigma_{{\rm (n,3n)},h\leftarrow g} \ , \ \ \sigma_{{\rm (n,4n)},g}={1\over 4}\sum_h \sigma_{{\rm (n,4n)},h\leftarrow g} . +\end{equation} +\item {\tt SCAT} matrix reactions in Dragon are defined as +\begin{eqnarray} +\nonumber \sigma_{{\tt scat},h\leftarrow g} \negthinspace\negthinspace &=& \negthinspace\negthinspace \sigma_{{\rm e},h\leftarrow g}+\sigma_{{\rm (n,2n)},h\leftarrow g}+\sigma_{{\rm (n,3n)},h\leftarrow g}+\sigma_{{\rm (n,4n)},h\leftarrow g} ++\sum_{{\sl mt}=51}^{91} \sigma_{{\sl mt},h\leftarrow g} \\ +&+& \negthinspace\negthinspace \sigma_{{\rm any},h\leftarrow g} \, . +\end{eqnarray} +\item Vectorial {\sl neutronic scattering} ({\tt SIGS}) in Dragon is defined as +\begin{equation} +\sigma_{{\tt sigs},g}=\sum_h \sigma_{{\tt scat},h\leftarrow g} +\end{equation} +\noindent so that the {\sl neutronic absorption}, used to compute the $K_\infty$ is +\begin{eqnarray} +\nonumber \sigma_g-\sigma_{{\tt sigs},g}\negthinspace &=&\negthinspace \sigma_{{\rm f},g}+\sigma_{{\rm p},g}+\sigma_{\gamma,g} ++\sigma_{{\rm d},g}+\sigma_{{\rm t},g}+\sigma_{\alpha,g}+\sigma_{2\alpha,g}+\sigma_{{\rm (n,np)},g}\\ +&-&\negthinspace \sigma_{{\rm (n,2n)},g}-2\sigma_{{\rm (n,3n)},g}-3\sigma_{{\rm (n,4n)},g} +\label{eq:eq1} +\end{eqnarray} +\noindent where all these terms are available in the Dragon microlib under the following names:\\ +\vskip 0.1cm +\begin{tabular}{| l | l | l |} +\hline +Dragon name & $\sigma_x$ & type \\ +\hline +{\tt NTOT0} & $\sigma_g$ & total \\ +{\tt SIGS00} & $\sigma_{{\tt sigs},g}$ & neutronic scattering \\ +{\tt NFTOT} &$\sigma_{{\rm f},g}$ & fission \\ +{\tt NP} & $\sigma_{{\rm p},g}$ & (n,p) \\ +{\tt NG} & $\sigma_{\gamma,g}$ & (n,$\gamma$) \\ +{\tt ND} &$\sigma_{{\rm d},g}$ & (n,d) \\ +{\tt NT} &$\sigma_{{\rm t},g}$ & (n,t) \\ +{\tt NA} &$\sigma_{\alpha,g}$ & (n,$\alpha$) \\ +{\tt N2A} &$\sigma_{2\alpha,g}$ & (n,2$\alpha$) \\ +{\tt NNP} &$\sigma_{{\rm (n,np)},g}$ & (n,np) \\ +{\tt NX} &$\sigma_{{\rm any},g}$ & (n,anything) \\ +{\tt N2N} &$\sigma_{{\rm (n,2n)},g}$ & (n,2n) \\ +{\tt N3N} &$\sigma_{{\rm (n,3n)},g}$ & (n,3n) \\ +{\tt N4N} &$\sigma_{{\rm (n,4n)},g}$ & (n,4n) \\ +\hline +\end{tabular} +\item The {\sl infinite multiplication factor} $K_\infty$ in a Dragon mixture is defined as +\begin{equation} +K_\infty={\sum\limits_g \nu\Sigma_{{\rm f},g}\bar\phi_g \over \sum\limits_g \left(\Sigma_g-\Sigma_{{\tt sigs},g}\right)\bar\phi_g} +\end{equation} +\noindent where $\nu\Sigma_{{\rm f},g} $, $\Sigma_g$ and $\Sigma_{{\tt sigs},g}$ are the macroscopic $\nu$-fission, total and +neutronic scattering cross sections, and $\bar\phi_g$ is the neutron flux. + +\end{enumerate} + +\eject |