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diff --git a/doc/IGE335/Section3.08.tex b/doc/IGE335/Section3.08.tex new file mode 100644 index 0000000..e0abf57 --- /dev/null +++ b/doc/IGE335/Section3.08.tex @@ -0,0 +1,571 @@ +\subsection{The {\tt EDI:} module}\label{sect:EDIData} + +The \moc{EDI:} module supplies the main editing options to DRAGON. It can be +use to compute the reaction rates, average and condensed cross sections to store +this information on a file for further use. The calling specifications are: + +\begin{DataStructure}{Structure \dstr{EDI:}} +\dusa{EDINAM} \moc{:=} \moc{EDI:} $[$ \dusa{EDINAM} $]$ +\dusa{LIBNAM} $[$ \dusa{TRKNAM} \dusa{FLUNAM} $]$ \\ +~~~~~$[$ \dusa{REFGEO} $[$ \dusa{MACROGEO} $]~]~[$ \dusa{REFPIJ} $]~[$ \dusa{SURFIL} $]$ \moc{::} \dstr{descedi} +\end{DataStructure} + +\noindent +where +\begin{ListeDeDescription}{mmmmmmmm} + +\item[\dusa{EDINAM}] {\tt character*12} name of the \dds{edition} data +structure ({\tt L\_EDIT} signature) where the edition results will be stored. + +\item[\dusa{LIBNAM}] {\tt character*12} name of the read-only \dds{macrolib} or +\dds{microlib} data structure ({\tt L\_MACROLIB} or {\tt L\_LIBRARY} signature) that contains the +macroscopic cross sections (see \Sectand{MACData}{LIBData}). + +\item[\dusa{TRKNAM}] {\tt character*12} name of the read-only \dds{tracking} data +structure ({\tt L\_TRACK} signature) containing the tracking (see \Sect{TRKData}). {\bf Note:} If data +structures \dusa{TRKNAM} and \dusa{FLUNAM} are not given, a flux is recovered from the \dds{macrolib} +present in \dusa{LIBNAM} and used to perform the editions. + +\item[\dusa{FLUNAM}] {\tt character*12} name of the read-only \dds{fluxunk} data +structure ({\tt L\_FLUX} signature) containing a transport solution (see \Sect{FLUData}). + +\item[\dusa{REFGEO}] {\tt character*12} optional name of the read-only reference \dds{geometry} data +structure ({\tt L\_GEOM} signature) that was used for the original flux calculation (see \Sect{GEOData}). + +\item[\dusa{MACROGEO}] {\tt character*12} optional name of the read-only macro-\dds{geometry} data +structure ({\tt L\_GEOM} signature) that is saved in \dusa{EDINAM} and can be used in the homogenization +process or in the SPH equivalence procedure. In some cases the +module \moc{EDI:} can automatically build a macro-geometry, however it is always +possible to specify explicitly the macro-geometry to be saved in \dusa{EDINAM}. + +\item[\dusa{REFPIJ}] {\tt character*12} optional name of the read-only \dds{asmpij} data +structure ({\tt L\_PIJ} signature) that was used for the reference flux calculation (see \Sect{ASMData}). +Compulsory if keyword \moc{ALBS} is used in \Sect{descedi}. + +\item[\dusa{SURFIL}] \texttt{character*12} name of the read-only SALOME--formatted sequential {\sc ascii} +file used to store the surfacic elements of the geometry. This file is required if and only if the keyword \moc{G2S} +is set in data structure \dstr{descedi}. + +\item[\dstr{descedi}] structure containing the input data to this module +(see \Sect{descedi}). + +\end{ListeDeDescription} + +\clearpage + +\subsubsection{Data input for module {\tt EDI:}}\label{sect:descedi} + +\begin{DataStructure}{Structure \dstr{descedi}} +$[$ \moc{EDIT} \dusa{iprint} $]$ \\ +$[$ \moc{UPS} $]$ \\ +$[$ \moc{MERG} $\{$ \moc{NONE} $|$ \moc{COMP} $|$ \moc{GEO} $|$ \moc{HMIX} $|$ \\ +\hskip 0.8cm \moc{G2S} \dusa{nhom} $[[$ \moc{RECT} \dusa{xm} \dusa{xp} \dusa{ym} \dusa{yp} $]]~[[$ \moc{TRIA} \dusa{x1} \dusa{y1} \dusa{x2} \dusa{y2} \dusa{x3} \dusa{y3} $]]~[$ \moc{REMIX} (\dusa{imix2}(ii),ii=1,nhom) $]~|$ \\ +\hskip 0.8cm \moc{CELL} $[~\{$ \moc{SYBIL} $|$ \moc{EXCELL} $|$ \moc{NXT} $|$ \moc{DEFAULT} $|$ \moc{UNFOLD} $\}~]~[$ \moc{REMIX} (\dusa{imix2}(ii),ii=1,nbmix2) $]~|$ \\ +\hskip 0.8cm \moc{REGI} (\dusa{iregm}(ii),ii=1,nregio) $|$ \\ +\hskip 0.8cm \moc{MIX} $[$ (\dusa{imixm}(ii),ii=1,nbmix) $]~\}$ $]$ \\ +$[$ \moc{TAKE} $\{$ \\ +\hskip 0.8cm \moc{REGI} (\dusa{iregt}(ii),ii=1,nregio) $|$ \\ +\hskip 0.8cm \moc{MIX} (\dusa{imixt}(ii),ii=1,nbmix) $\}$ $]$ \\ +$[$ $\{$ \moc{P0W} $|$ \moc{P1W\_L} $|$ \moc{P1W\_TO} $|$ \moc{PNW\_SP} $\}$ $]$ \\ +$[$ \moc{EDI\_CURR} $]~[$ \moc{GOLVER} $]$ \\ +$[$ \moc{COND} $[~\{$ \moc{NONE} $|$ ( \dusa{icond}(ii), ii=1,ngcond) $|$ ( \dusa{energy}(ii), ii=1,ngcond) $\}~]~]$\\ +$[$ \moc{MICR} $[~\{$ \moc{ALLX} $|$ \moc{NODEPL}$\}~]~[$ \moc{NOMACR} $]~[$ \moc{ISOTXS} $[$ \moc{ASCII} $]~]$ $\{$ \moc{ALL} $|$ \moc{RES} $|$ + \dusa{nis} (\dusa{HISO}(i),i=1,\dusa{nis}) $\}$\\ +\hskip 0.8cm $[$ \moc{REAC} \dusa{nreac} (\dusa{HREAC}(i),i=1,\dusa{nreac}) $]~]$\\ +$[$ \moc{ACTI} $[$ \moc{ISOTXS} $[$ \moc{ASCII} $]~]$ $\{$ \moc{NONE} $|$ (\dusa{imixa}(ii),ii=1,nbmix) $]$ $\}$\\ +$[$ \moc{SAVE} $[$ \moc{ON} $\{$ \dusa{DIRN} $|$ \dusa{idirn} $\}$ $]$ $]$ \\ +$[$ \moc{PERT} $]$ \\ +$[$ \moc{STAT} $\{$ \moc{ALL} $|$ \moc{RATE} $|$ \moc{FLUX} $|$ \moc{DELS} $\}$ + $[$ \moc{REFE} $\{$ \dusa{DIRO} $|$ \dusa{idiro} $\}$ $]$ $]$ \\ +$[$ \moc{NOHF} $]~[$ \moc{NBAL} $]$ \\ +$[$ \moc{MAXR} \dusa{maxpts} $]$ \\ +$[~\{$ \moc{DIRE} $|$ \moc{PROD} $\}~]$ \\ +$[$ \moc{MGEO} \dusa{MACGEO} $]$ \\ +$[~\{$ \moc{NADF} $|$ \moc{ALBS} $|$ \moc{JOUT} $|$ \moc{ADFM} $|$\\ +~~~~~~~$[[$ \moc{ADF} $[$ \moc{*} $]$ \dusa{TYPE} $\{$ \moc{REGI} (\dusa{ireg}(ii),ii=1,iimax) \moc{ENDR} $|$ \moc{MIX} (\dusa{imix}(ii),ii=1,iimax) \moc{ENDM} $\}~]]~\}~]$ \\ +$[$~\moc{LEAK}~\dusa{b2}~$]$ +\end{DataStructure} + +\noindent where + +\begin{ListeDeDescription}{mmmmmmmm} + +\item[\moc{EDIT}] keyword used to modify the print level \dusa{iprint}. + +\item[\dusa{iprint}] index used to control the printing of this module. The +\dusa{iprint} parameter is important for adjusting the amount of data that is +printed by this calculation step: + +\begin{itemize} + +\item \dusa{iprint}=0 results in no output; + +\item \dusa{iprint}=1 results in the average and integrated fluxes being printed +(floating default); + +\item \dusa{iprint}=2 results in the reaction rates being printed; + +\item \dusa{iprint}=3 is identical to the previous option, but the condensed +and/or homogenized vectorial cross sections are also printed; + +\item \dusa{iprint}=4 is identical to the previous option, but the condensed +and/or homogenized transfer cross sections are also printed. + +\end{itemize} + +\item[\moc{UPS}] keyword used to specify that the reaction rates and the condensed +and/or homogenized cross sections are corrected so as to eliminate +up-scattering. This option is useful for reactor analysis codes which cannot +take into account such cross sections. Scattering ($\sigma_{{\rm s},h\gets g}$), diffusion ($\sigma_{{\rm s},g}$) +and total ($\sigma_g$) cross sections are corrected as: +\begin{eqnarray*} +\tilde\sigma_{{\rm s},h\gets g}\negthinspace\negthinspace &=&\negthinspace\negthinspace \begin{cases} 0 & {\rm if} \ h < g\\ +\sigma_{{\rm s},g\gets g} &{\rm if} \ h = g\\ +\sigma_{{\rm s},h\gets g}-\sigma_{{\rm s},g\gets h}\, {\phi_h\over \phi_g} & {\rm if} \ h > g +\end{cases} \\ +\tilde\sigma_{{\rm s},g}\negthinspace\negthinspace &=&\negthinspace\negthinspace \sum_{h=1}^G \tilde\sigma_{{\rm s},h\gets g}\, = \, \sigma_{{\rm s},g}-\sum_{h=1}^{g-1} \sigma_{{\rm s},h\gets g}-\sum_{h=g+1}^{G} \sigma_{{\rm s},g\gets h}\, {\phi_h\over \phi_g} \\ +\tilde\sigma_{g}\negthinspace\negthinspace &=&\negthinspace\negthinspace \sigma_{g}-\sum_{h=1}^{g-1} \sigma_{{\rm s},h\gets g}-\sum_{h=g+1}^{G} \sigma_{{\rm s},g\gets h}\, {\phi_h\over \phi_g} . +\end{eqnarray*} + +\item[\moc{NONE}] keyword used to deactivate the homogeneization or the condensation. + +\item[\moc{MERG}] keyword used to specify that the neutron flux is to be +homogenized over specified regions or mixtures. + +\item[\moc{REGI}] keyword used to specify that the homogenization of the neutron +flux will take place over the following regions. Here nregio$\le$\dusa{maxreg} +with \dusa{maxreg} the maximum number of regions for which solutions were +obtained. + +\item[\dusa{iregm}] array of homogenized region numbers to which are +associated the old regions. In the editing routines a value of \dusa{iregm}=0 +allows the corresponding region to be neglected. + +\item[\moc{MIX}] keyword used to specify that the homogenization of the neutron +flux will take place over the following mixtures. Here +we must have nbmix$\le$\dusa{maxmix} where \dusa{maxmix} is the maximum number +of mixtures in the macroscopic cross section library. + +\item[\dusa{imixm}] array of homogenized region numbers to which are +associated the material mixtures. In the editing routines a value of +\dusa{imixm}=0 allows the corresponding isotopic mixtures to be neglected. For a mixture in this +library which is not used in the geometry one should insert a value of 0 for the +new region number associated with this mixture. This option is also useful to homogenize the cross-section data of the second-level mixtures by combining the first-level mixtures in +a two-level computational scheme for a PWR assembly. By default, if \moc{MIX} is set and +\dusa{imixm} is not set, \dusa{imixm(ii)}$=$\dusa{ii} is assumed. + +\item[\moc{COMP}] keyword used to specify that the a complete homogenization is to +take place. + +\item[\moc{GEO}] keyword used to specify that a geometry equivalence procedure (equigeom) is to be used. Merging indices +are automatically computed by comparing the reference geometry \dusa{REFGEO} with the macro-geometry \dusa{MACROGEO}. +This capability is limited to EXCELL--type reference geometries. + +\item[\moc{G2S}] keyword used to specify that the homogenization will be based on the geometry definition available in the surfacic +file \dusa{SURFIL}. + +\item[\dusa{nhom}] number of homogeneous nodes to be defined using \moc{RECT} and/or \moc{TRIA} data structures. Many homogeneous mixtures can be defined by +repeating the \moc{RECT} and/or \moc{TRIA} data structures. + +\item[\moc{RECT}] keyword used to specify a unique homogeneous mixture based on a rectangular node. + +\item[\dusa{xm}] lower limit of the homogeneous node alonx X--axis. + +\item[\dusa{xp}] upper limit of the homogeneous node alonx X--axis. + +\item[\dusa{ym}] lower limit of the homogeneous node alonx Y--axis. + +\item[\dusa{yp}] upper limit of the homogeneous node alonx Y--axis. + +\item[\moc{TRIA}] keyword used to specify a unique homogeneous mixture based on a triangular node. + +\item[\dusa{x1}] X--coordinate of the first corner. + +\item[\dusa{y1}] Y--coordinate of the first corner. + +\item[\dusa{x2}] X--coordinate of the second corner. + +\item[\dusa{y2}] Y--coordinate of the second corner. + +\item[\dusa{x3}] X--coordinate of the third corner. + +\item[\dusa{y3}] Y--coordinate of the third corner. + +\item[\moc{HMIX}] keyword used to specify that the homogenization region will be selected using the information provided by the \moc{HMIX} option in the \moc{GEO:} module (see \Sect{descPP}). In this case, all the regions associated with a virtual homogenization mixture will be homogenized. If the virtual homogenization mixtures were not defined in the geometry, the real mixtures are used instead (see \moc{MIX} keyword in \Sect{descPP}). This option is valid only for \moc{NXT:} based \dds{tracking} data structure (this option uses the information stored on the reference \dds{TRKNAM} data structure). + +\item[\moc{CELL}] keyword used to specify that the a cell-by-cell homogenization +(with or without SPH equivalence) is to take place. The macro-geometry and the merging indices are automatically +computed and the macro-geometry named {\tt MACRO-GEOM} is created on the root directory of \dusa{EDINAM}. This +capability is limited to reference geometries previously tracked by EURYDICE (see \Sect{SYBILData}) or NXT (see +\Sect{NXTData}). + +\item[\moc{SYBIL}] the macro-geometry produced by \moc{CELL} is tracked by {\tt SYBILT:} module. + +\item[\moc{EXCELL}] the macro-geometry produced by \moc{CELL} is tracked by {\tt EXCELT:} module. + +\item[\moc{NXT}] the macro-geometry produced by \moc{CELL} is tracked by {\tt NXT:} module. + +\item[\moc{DEFAULT}] the macro-geometry produced by \moc{CELL} is tracked by another module (default option). + +\item[\moc{UNFOLD}] the macro-geometry produced by \moc{CELL} is unfolded and tracked with the \moc{DEFAULT} option. This option is +useful with fine power reconstruction techniques. + +\item[\moc{REMIX}] the homogenization produced by option \moc{MERG} \moc{G2S} or \moc{MERG} \moc{CELL} (cell-by-cell) is further +homogenized according to \dusa{imix2} indices. This option is useful to integrate the assembly gap into the boundary cells. By default, one homogenized region is created +for each region of the macro-geometry. + +\item[\dusa{imix2}] array of rehomogenized region numbers to which are associated the regions indices created {\sl after} +the \moc{MERG} \moc{G2S} or \moc{MERG} \moc{CELL} homogenization was performed. In the editing routines a value of \dusa{imix2}=0 allows the corresponding +region to be neglected. Here, nbmix2 is equal to the number of mixtures in the geometry before the \moc{REMIX} operation is performed (equal to the number +of cells in the macro-geometry if \moc{MERG} \moc{CELL} was set). + +\item[\moc{TAKE}] keyword used to specify that the neutron flux is to be edited +over specified regions or mixtures. + +\item[\moc{REGI}] keyword used to specify that the editing of the neutron flux will +take place over the following regions. Here nregio$\le$\dusa{maxreg} +with \dusa{maxreg} the maximum number of regions for which solutions were +obtained. + +\item[\dusa{iregt}] regions where the editing will take place. The new region +numbers associated with these editing regions are numbered sequentially. + +\item[\moc{MIX}] keyword used to specify that the editing of the neutron +flux will take place over the following mixtures. Here +we must have nbmix$\le$\dusa{maxmix} where \dusa{maxmix} is the maximum number +of mixtures in the macroscopic cross section library. + +\item[\dusa{imixt}] mixtures where the editing will take place. +Each mixture set here must exists in the reference geometry. + +\item[\moc{P0W}] keyword used to specify that the $P_\ell$, $\ell\ge 1$ information is to be +homogenized and condensed using the scalar flux. This is the default option. + +\item[\moc{P1W\_L}] keyword used to specify that the $P_\ell$, $\ell\ge 1$ information is to be +homogenized and condensed using a current recovered from a consistent $P_1$ or +from a consistent heterogeneous $B_1$ model. + +\item[\moc{P1W\_TO}] keyword used to specify that the $P_\ell$, $\ell\ge 1$ information is to be +homogenized and condensed using the Todorova flux\cite{todorova}, defined as +$$ +\phi_1(\bff(r),E)={\phi(\bff(r),E)\over \Sigma_i(E)-\Sigma_{{\rm s1},i}(E)} +$$ +\noindent where $\Sigma_i(E)$ and $\Sigma_{{\rm s1},i}(E)$ are the macroscopic total and $P_1$ scattering +cross sections in the mixture $i$ containing the point $\bff(r)$. This option is not recommended. + +\item[\moc{PNW\_SP}] keyword used to specify that the $P_\ell$, $\ell\ge 1$ information is to be +homogenized and condensed using a weighting spectra based on the APOLLO3 averaging formula\cite{condPn}, defined as +$$ +\phi_\ell(\bff(r),E)={ \displaystyle\sum_{m=-\ell}^\ell \phi_\ell^m(\bff(r),E) \left<\phi_\ell^m\right>_{G,M} \over \displaystyle\sum_{m=-\ell}^\ell \left<\phi_\ell^m\right>_{G,M} } +$$ +where $\phi_\ell^m(\bff(r),E)$ are the spherical harmonic $\ell$-th moment of the flux with $E \in G$ and $\bff(r) \in M$. Here, $G$ is the +condensed macrogroup and $M$ is the homogenized mixture. + +\item[\moc{EDI\_CURR}] keyword used to specify the generation of integrated net currents (homogenized and condensed) in the macrolib along each axis. +This option is only provided with SN and MOC discretizations. By default, only integrated fluxes are generated. + +\item[\moc{GOLVER}] keyword used to specify the use of the Golfier-Vergain diffusion coefficient formula. This formula is written +$$D_{i,g}={\alpha_g\over 3\Sigma_{{\rm tr},i,g}}$$ + +\noindent with the Golfier-Vergain factors $\alpha_g$ defined as +$$\alpha_g={\sum_i \int_{u_{g-1}}^{u_g} du \, {\displaystyle\phi_i(u) \over \displaystyle\left(\Sigma_i(u)-\Sigma_{{\rm s1},i}(u) \right) } +\over \sum_i {\displaystyle\phi_{i,g} \over \displaystyle\Sigma_{{\rm tr},i,g}} }$$ + +and where the multigroup transport cross sections are defined as +$$\Sigma_{{\rm tr},i,g}={\int_{u_{g-1}}^{u_g} du \left(\Sigma(u) -\Sigma_{{\rm s1},i}(u) \right) \phi_i(u) +\over \int_{u_{g-1}}^{u_g} du \, \phi_i(u) }.$$ + +By default, the diffusion coefficients are obtained by condensation of the fine-group leakage coefficients $d_i(u)$: +$$D_{i,g}={\int_{u_{g-1}}^{u_g} du \, d_i(u) \, \phi_i(u) \over \int_{u_{g-1}}^{u_g} du \, \phi_i(u) }.$$ + +\item[\moc{COND}] keyword used to specify that a group condensation of the flux is to be performed. + +\item[\dusa{icond}] array of increasing energy group limits that will be associated with +each of the ngcond condensed groups. The final value of +\dusa{icond} will automatically be set to \dusa{ngroup} while the values of +\dusa{icond}$>$\dusa{ngroup} will be droped from the condensation. +We must have ngcond$\le$\dusa{ngroup}. By default, if \moc{COND} is set and \dusa{icond} +is not set, all energy groups are condensed together. + +\item[\dusa{energy}] array of decreasing energy limits (in eV) that will be +associated with each of the ngcond condensed groups. We must have ngcond$\le$\dusa{ngroup+1}. +Note that if an energy limit is located between two energy groups, the condensation +group will include this associated energy group. In the case where two energy +limits fall within the same energy group the lowest energy will be droped. +Finally the maximum and minimum energy limits can be skipped since they will be +taken automatically from the information available in the library. + +\item[\moc{MICR}] keyword used to specify that the condensation and homogenization +procedure will be used to associate microscopic cross sections to the isotopes +present in the homogenized regions. The macroscopic cross sections and the +diffusion coefficients are weighted by the multigroup fluxes appearing in the +regions where the isotopes are present. The resulting nuclear properties are +saved on \dusa{EDINAM} when the \moc{SAVE} keyword is present. + +\item[\moc{ALLX}] keyword used to register the region number of each isotope before merging, in the +embedded library. The homogeneized information is therefore registered for each isotope in the merging +region, as depicted by the formulas below. This procedure is useful to produce particular databases, +in order to perform micro-depletion calculations in diffusion with DONJON. + +\item[\moc{NODEPL}] keyword used to suppress all depletion information from the output microlib. + +\item[\moc{NOMACR}] keyword used to suppress the calculation of a residual isotope. + +\item[\moc{ALL}] keyword used to specify that all the isotopes present in the +homogenized region are to be kept individual and processed. + +\item[\moc{RES}] keyword used to specify that all the isotopes present in the +homogenized region will be merged as a single residual isotope. + +\item[\dusa{nis}] number of isotopes present in the homogenized +region to be processed. + +\item[\dusa{HISO}] array of {\tt character*8} isotopes alias names to be processed. + +\item[\moc{REAC}] keyword used to specify the reaction names to be included in the output microlib. By default, all available reactions +are included in the output microlib. + +\item[\dusa{nreac}] number of reactions to be included in the output microlib. + +\item[\dusa{HREAC}] array of {\tt character*8} reaction names to be included in the output microlib. + +\item[\moc{ACTI}] keyword used to specify that microscopic activation +data will be edited for the isotopes associated with the specified mixture. This +information correspond to the microscopic cross section associated with each +isotope in a given macro-group and macro-region assuming a concentration +for this isotope of 1.0 $\times{\it cm}^{-3}$ in each region. This keyword is +followed by nacti material mixture indices, where +nacti$\le$\dusa{maxmix}. + +\item[\moc{NONE}] keyword used to specify that no isotope present in the +homogenized region is to be used as activation data. + +\item[\dusa{imixa}] array of material mixture indices which contains the +isotopes for which activation data is to be generated. +\dusa{nmix}$\le$\dusa{maxmix}. Even mixture not used in the geometry +can be considered here. + +\item[\moc{ISOTXS}] keyword used to specify that the set of microscopic cross +section generated by the \moc{MICR} and \moc{ACTI} command will also +be saved on a microscopic group neutron cross section library in the ISOTXS-IV +format. This will generate a file for each final region specified by the +\moc{TAKE} or \moc{MERG} keyword, numbered consecutively ({\tt IFILE}). The name +of the file ({\tt NISOTXS}) is built using the command + +\begin{verbatim} +WRITE(NISOTXS,'(A6,I6.6)') 'ISOTXS',IFILE +\end{verbatim} + +\item[\moc{ASCII}] keyword used to specify that the ISOTXS file is created in ascii format. +By default, it is created in binary format. + +\item[\moc{SAVE}] keyword used to specify that the fluxes, the macroscopic and +microscopic cross sections and the volumes corresponding to homogenized regions +are to be saved on \dusa{EDINAM}. A \dds{macrolib} is store on a subdirectory +of \dds{edition}. + +\item[\moc{ON}] keyword used to specify on which directory of \dusa{EDINAM} this +information is to be stored. + +\item[\dusa{DIRN}] name of the directory on which the above information is to +be stored. + +\item[\dusa{idirn}] number associated with a directory of \dusa{EDINAM} on +which the above information is to be stored. To each number \dusa{idirn} is +associated a directory name \moc{CDIRN}={\tt 'REF-CASE'//CN} where {\tt CN} is a +{\tt character*4} variable defined by {\tt WRITE(CN,'(I4)')} \moc{idirn}. + +\item[\moc{PERT}] keyword used to specify that first order perturbations for +the microscopic cross sections are to be saved on \dusa{EDINAM}. + +\item[\moc{STAT}] keyword used to specify that a comparison between the current and +a reference set of reaction rates and/or integrated fluxes is to be performed. + +\item[\moc{ALL}] keyword used to specify that the relative differences in the +reaction rates and the integrated fluxes are to be printed. + +\item[\moc{RATE}] keyword used to specify that the relative differences in the +reaction rates are to be printed. + +\item[\moc{FLUX}] keyword used to specify that the relative differences in the +integrated fluxes are to be printed. + +\item[\moc{DELS}] keyword used to specify that the absolute differences in the +macroscopic cross section are to be printed. + +\item[\moc{REFE}] keyword used to specify the directory of \dusa{EDINAM} where the +reference data requires for the comparison is stored. When this keyword is +absent, the last reaction rates and integrated fluxes saved on \dusa{EDINAM} are +used. + +\item[\dusa{DIRO}] name of the directory from which the reference information +is taken. + +\item[\dusa{idiro}] number associated with an directory of \dusa{EDINAM} on +which the reference information is stored. To each number \dusa{idirn} is +associated a the directory \moc{CDIRN}={\tt 'REF-CASE'//CN} where {\tt CN} is a +{\tt character*4} variable defined by {\tt WRITE(CN,'(I4)')} \moc{idirn}. + +\item[\moc{NOHF}] keyword used to suppress the calculation and edition of the H-factors (sum of all +the cross sections producing energy times the energy produced by each reaction). +Note that this calculation may be time-consuming. By default, the H-factors are +computed and edited if keyword \moc{DEPL} and associated data is set in module {\tt LIB:}. + +\item[\moc{NBAL}] keyword used to specify the editing of the four factors computed +from a group balance. In this case, the user must specify explicitly a three +group condensation. + +\item[\moc{MAXR}] keyword used to specify the number of components in +region-related dynamically allocated arrays. If the default value is +not sufficient, an error message is issued. + +\item[\dusa{maxpts}] user-defined maximum number of components. + +\item[\moc{DIRE}] use the direct flux to perform homogenization or/and +condensation (default value). + +\item[\moc{PROD}] use the product of the direct and adjoint flux to perform homogenization or/and +condensation. This option is used only in specialized applications such as in the {\sc clio} perturbative +analysis formula.\cite{clio} The homogenization and condensation equations are presented in Sect.~\ref{sect:prod}. +{\bf Note:} The \dusa{FLUNAM} object must contain both an adjoint and a direct flux solution. + +\item[\moc{MGEO}] keyword used to define the name of the macro-geometry, which must appear among the RHS. The macro-geometry is recovered automatically +by interface modules such as \moc{COMPO:} (see \Sect{COMPOData}) or manually by a CLE-2000 statement such as +\begin{verbatim} +GEONAM := EDINAM :: STEP UP 'MACRO-GEOM' ; +\end{verbatim} +\noindent where {\tt GEONAM} and {\tt EDINAM} are {\tt L\_GEOM} and {\tt L\_EDIT} LCM objects, respectively. + +\item[\dusa{MACGEO}] character*12 name of the macro-geometry. + +\item[\moc{NADF}] keyword used to desactivate boundary editions. + +\item[\moc{ALBS}] keyword used to specify that the boundary flux is to be obtained from relation +$\phi_{\rm surf}=4J_{\rm out}/S$ where $J_{\rm out}$ is the outgoing interface current. The albedo of +the geometry are to be taken into account in the complete homogenization process. Thus the \moc{MERG} +and \moc{COMP} options must be specified. The boundary fluxes are obtained from a calculation using the collision +probabilities. This option requires a geometry with \moc{VOID} (see \Sect{descBC}) external boundary conditions to +be closed using \moc{ALBS} in module \moc{ASM:} (see \Sect{descasm}).\cite{ALSB2} + +\item[\moc{JOUT}] keyword used to recover multigroup boundary current information ($J_{\rm out}$ and $J_{\rm in}$). This keyword +is only compatible with \moc{MCCGT:} or interface current trackings (within \moc{SYBILT:} or \moc{SALT:}) and if keyword \moc{ARM} is set in module \moc{ASM:} +(see \Sect{descasm}). The outgoing/ingoing interface currents are recovered by direct homogenization and condensation of the +flux unknown components corresponding to external boundary and used with the current iteration method in Eurydice or from a MOC +calculation. The boundary flux required by the SPH method is to be obtained from relation $\phi_{\rm surf}=4J_{\rm out}/S$ where +$J_{\rm out}$ is the outgoing interface current. The net boundary current is to be obtained from relation +$J_{\rm net}=J_{\rm out}-J_{\rm in}$. + +\item[\moc{ADFM}] keyword used to specify that the ADF information is recovered from macrolib in RHS object \dusa{LIBNAM}. ADF information can +be defined as explained in Sect.~\ref{sect:descxs} of module {\tt MAC:} and recovered in module {\tt EDI:} for further processing. + +\item[\moc{ADF}] keyword used to specify that boundary editions are required. Averaged fluxes are +computed over boundary regions. + +\item[\moc{*}] keyword used to specify that boundary fluxes are divided by average assembly fluxes so as to produce {\sl assembly discontinuity factors} +(ADF). By default, boundary fluxes are recovered and saved in the boundary edit without further treatment. + +\item[\dusa{TYPE}] {\tt character*8} name of the boundary edit corresponding to +regions \dusa{ireg} or mixtures \dusa{imix}. Any user-defined name can be used, but some +standard names are recognized by module \moc{SPH} (see \Sect{descsph}). Standard names are: $=$ \moc{FD\_C}: +corner flux edition; $=$ \moc{FD\_B}: surface (assembly gap) flux edition; $=$ \moc{FD\_H}: +row flux edition. These are the first row of surrounding cells in the assembly. + +\item[\dusa{ireg}] index of a region of the reference geometry belonging to boundary edition. + +\item[\dusa{imix}] index of a material mixture of the reference geometry belonging to boundary edition. + +\item[\moc{LEAK}] keyword used to introduce leakage in the embedded {\sc macrolib}. This option should only be used for non-regression tests. The {\sc microlib} is not modified. + +\item[\dusa{b2}] the imposed buckling corresponding to the leakage. + +\end{ListeDeDescription} + +\subsubsection{Homogenization and condensation with the flux} + +The cross sections are homogenized over macro-volumes $V_{\rm merg}$ and condensed over +macro groups $E_{\rm merg}$. We also use $V_i$ to identify the subset of $V_{\rm merg}$ where +the isotope $i$ is defined. The module {\tt EDI:} produces the following homogenized/condensed information: + +\begin{description} +\item[integrated volume:] +$$ +\overline V=\int_{V_{\rm merg}} dV +$$ + +\item[macroscopic cross section of type $\bff(x)$:] +$$ +\overline \Sigma_x = {\int_{V_{\rm merg}} dV \int_{E_{\rm merg}} dE \, \Sigma_x(\bff(r),E) \, \phi(\bff(r),E) +\over \int_{V_{\rm merg}} dV \int_{E_{\rm merg}} dE \, \phi(\bff(r),E)} +$$ + +\item[number density for isotope $\bff(i)$:] +$$ +\overline N_i= {1\over \overline V} \int_{V_i} dV N_i(\bff(r)) +$$ +\noindent where $N_i(\bff(r))$ is the space-dependent number density of isotope $i$. + +\item[neutron flux:] +$$ +\overline\phi = {1\over \overline V} \, \int_{V_{\rm merg}} dV \int_{E_{\rm merg}} dE \, \phi(\bff(r),E) +$$ + +\item[microscopic cross section of type $\bff(x)$ for isotope $\bff(i)$:] +\begin{eqnarray*} +\overline \sigma_{x,i} \negthinspace\negthinspace &=& \negthinspace\negthinspace { 1 \over \overline N_i} \, {\int_{V_i} dV \int_{E_{\rm merg}} dE \, N_i(\bff(r)) \, \sigma_{x,i}(\bff(r),E) \, \phi(\bff(r),E) +\over \int_{V_{\rm merg}} dV \int_{E_{\rm merg}} dE \, \phi(\bff(r),E)} \\ +&=& \negthinspace\negthinspace { 1 \over \overline N_i\, \overline\phi \, \overline V} \, \int_{V_i} dV \int_{E_{\rm merg}} dE \, N_i(\bff(r)) \, \sigma_{x,i}(\bff(r),E) \, \phi(\bff(r),E) \ \ . +\end{eqnarray*} +\end{description} + +\subsubsection{Homogenization and condensation with the flux and adjoint flux}\label{sect:prod} + +If the \moc{PROD} keyword is set in data structure \ref{sect:descedi}, the adjoint flux is introduced as a weighting function in the +homogenization and condensation formulas. In this case, the module {\tt EDI:} produces the following homogenized/condensed information: + +\begin{description} + +\item[adjoint neutron flux:] +$$ +\overline\phi^* = {1\over \overline\phi\, \overline V} \, \int_{V_{\rm merg}} dV \int_{E_{\rm merg}} dE \, \phi^*(\bff(r),E)\, \phi(\bff(r),E) +$$ + +\item[microscopic transfer cross section for isotope $\bff(i)$:] +$$ +\overline \sigma_{{\rm s},i} ={ 1 \over \overline N_i\, (\overline\phi^*)' \, \overline\phi \, \overline V} \, \int_{V_i} dV \int_{E'_{\rm merg}} dE' \,\int_{E_{\rm merg}} dE \, N_i(\bff(r)) \, \sigma_{{\rm s},i}(\bff(r),E' \leftarrow E) \, \phi^*(\bff(r),E') \, \phi(\bff(r),E) +$$ +\noindent with +$$ +(\overline\phi^*)' = {1\over (\overline\phi)' \, \overline V} \, \int_{V_{\rm merg}} dV \int_{E'_{\rm merg}} dE' \, \phi^*(\bff(r),E')\, \phi(\bff(r),E') +$$ + +\item[microscopic cross section of type $\bff(x)\neq$ f for isotope $\bff(i)$:] +$$ +\overline \sigma_{x,i} ={ 1 \over \overline N_i\, \overline\phi^* \, \overline\phi \, \overline V} \, \int_{V_i} dV \int_{E_{\rm merg}} dE \, N_i(\bff(r)) \, \sigma_{x,i}(\bff(r),E) \, \phi^*(\bff(r),E) \, \phi(\bff(r),E) +$$ + +\item[microscopic $\nu$ times fission cross section for isotope $\bff(i)$:] +$$ +\overline\nu\overline\sigma_{{\rm f},i} ={ 1 \over \overline N_i\, \overline\phi \, \overline V} \, \int_{V_i} dV \int_{E_{\rm merg}} dE \, N_i(\bff(r)) \, \nu\sigma_{{\rm f},i}(\bff(r),E) \, \phi(\bff(r),E) +$$ + +\item[fission spectra for isotope $\bff(i)$:] +$$ +\overline\chi_{i} ={ 1 \over \overline{\cal F}_i \overline\phi^* \, \overline V} \, \int_{V_i} dV \int_{E_{\rm merg}} dE \, \chi_{i}(\bff(r),E) \, {\cal F}_i(\bff(r)) \phi^*(\bff(r),E) +$$ + +\noindent where ${\cal F}_i(\bff(r))$ is the energy-integrated fission rate for isotope $\bff(i)$, defined as +$$ +{\cal F}_i(\bff(r))=\int_\infty dE \, N_i(\bff(r)) \, \nu\sigma_{{\rm f},i}(\bff(r),E) \, \phi(\bff(r),E) +$$ + +\noindent and +$$ +\overline{\cal F}_i={1\over \overline V} \int_{V_i} dV \, {\cal F}_i(\bff(r)) \ . +$$ +\end{description} + +Both the macrolib and microlib information is affected by the adjoint weighting. However, users should be advised that this operation may have some +undesirable effects on the fission spectrum normalization. Its use must therefore be limited to specialized applications where the adjoint weighting +is theoretically required. This is the case, for example, with the {\sc clio} perturbative analysis method.\cite{clio} + +\eject |