\subsection{The {\tt USS:} module}\label{sect:USSData} The universal self-shielding module in DRAGON, called {\tt USS:}, allows the correction of the microscopic cross sections to take into account the self-shielding effects related to the resonant isotopes. These isotopes are identified as such by the \dusa{inrs} parameter, as defined in \Sect{LIBData}. The universal self-shielding module is based on the following models: \begin{itemize} \item The Livolant-Jeanpierre flux factorization and approximations are used to uncouple the self-shielding treatment from the main flux calculation; \item The resonant cross sections are represented using probability tables computed in the \moc{LIB:} module (the keyword \moc{SUBG} or \moc{PTSL} {\sl must} be used). Two approaches can be used to compute the probability tables: \begin{enumerate} \item Physical probability tables can be computed using a RMS approach similar to the one used in Wims-7 and Helios.\cite{subg} In this case, the slowing-down operator of each resonant isotope is represented as a pure ST\cite{st}, ST/IR or ST/WR approximation; \item Mathematical probability tables\cite{pt} and slowing-down correlated weight matrices can be computed in selected energy groups using the {\sl Ribon extended} approach.\cite{nse2004} In this case, an elastic slowing-down model is used and a mutual self-shielding model is available. \end{enumerate} \item The resonant fluxes are computed for each band of the probability tables using a subgroup method if \moc{SUBG}, \moc{PT}, \moc{PTMC} or \moc{PTSL} keyword is set in module \moc{LIB:}; \item The resonance spectrum expansion (RSE) method is used if \moc{RSE} keyword is set in module \moc{LIB:}; \item The flux can be solved using collision probabilities, or using {\sl any} flux solution technique for which a tracking module is available; \item The resonant isotopes are computed one-a-time, starting from the isotopes with the lower values of index \dusa{inrs}, as defined in \Sect{LIBData}; If many isotopes have the same value of \dusa{inrs}, the isotope with the greatest number of resonant nuclides is self-shielded first. One or many outer iterations can be performed; \item The distributed self-shielded effect is automatically taken into account if different mixture indices are assigned to different regions inside the resonant part of the cell. The rim effect can be computed by dividing the fuel into "onion rings" and by assigning different mixture indices to them. \item A SPH (superhomog\'en\'eisation) equivalence is performed to correct the self-shielded cross sections from the non-linear effects related to the heterogeneity of the geometry. \end{itemize} \vskip 0.2cm The general format of the data for this module is: \begin{DataStructure}{Structure \dstr{USS:}} \dusa{MICLIB} \moc{:=} \moc{USS:} \dusa{MICLIB\_SG} $[$ \dusa{MICLIB} $]$ \dusa{TRKNAM} $[$ \dusa{TRKFIL} $]$ \moc{::} \dstr{descuss} \end{DataStructure} \noindent where \begin{ListeDeDescription}{mmmmmmmm} \item[\dusa{MICLIB}] {\tt character*12} name of the \dds{microlib} that will contain the microscopic and macroscopic cross sections updated by the self-shielding module. If \dusa{MICLIB} appears on both LHS and RHS, it is updated; otherwise, \dusa{MICLIB} is created. \item[\dusa{MICLIB\_SG}] {\tt character*12} name of the \dds{microlib} builded by module \moc{LIB:} and containing probability table information (the keyword \moc{SUBG} {\sl must} be used in module {\tt LIB:}). \item[\dusa{TRKNAM}] {\tt character*12} name of the required \dds{tracking} data structure. \item[\dusa{TRKFIL}] {\tt character*12} name of the sequential binary tracking file used to store the tracks lengths. This file is given if and only if it was required in the previous tracking module call (see \Sect{TRKData}). \item[\dstr{descuss}] structure describing the self-shielding options. \end{ListeDeDescription} Each time the \moc{USS:} module is called, a sub-directory is updated in the \dds{microlib} data structure to hold the last values defined in the \dstr{descuss} structure. The next time this module is called, these values will be used as floating defaults. \subsubsection{Data input for module {\tt USS:}}\label{sect:descuss} \begin{DataStructure}{Structure \dstr{descuss}} $[$ \moc{EDIT} \dusa{iprint} $]$ \\ $[$ \moc{GRMIN} \dusa{lgrmin} $]~~[$ \moc{GRMAX} \dusa{lgrmax} $]$~~ $[$ \moc{PASS} \dusa{ipass} $]~~[$ \moc{NOCO} $]~~[$ \moc{NOSP} $]$~~$[$ $\{$ \moc{TRAN} $|$ \moc{NOTR} $\}$ $]$ \\ $[$ $\{$ \moc{PIJ} $|$ \moc{ARM} $\}$ $]$ \\ $[$ \moc{MAXST} \dusa{imax} $]~[$ \moc{FLAT} $]$ \\ $[$ \moc{CALC} \\ ~~~~$[[$ \moc{REGI} \dusa{suffix} $[[$ \dusa{isot} $\{$ \moc{ALL} $|$ (\dusa{imix}(i),i=1,\dusa{nmix}) $\}$ $]]$ \\ ~~~~$]]$ \\ \moc{ENDC} $]$ \\ {\tt ;} \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 amount of output produced by this tracking module will vary substantially depending on the print level specified. \item[\moc{GRMIN}] keyword to specify the minimum group number considered during the self-shielding process. \item[\dusa{lgrmin}] first group number considered during the self-shielding process. By default, \dusa{lgrmin} is set to the first group number containing self-shielding data in the library. \item[\moc{GRMAX}] keyword to specify the maximum group number considered during the self-shielding process. \item[\dusa{lgrmax}] last group number considered during the self-shielding process. By default, \dusa{lgrmax} is set is set to the last group number containing self-shielding data in the library. \item[\moc{PASS}] keyword to specify the number of outer iterations during the self-shielding process. \item[\dusa{ipass}] the number of iterations. The default is \dusa{ipass} $=2$ if \dusa{MICLIB} is created. \item[\moc{NOCO}] keyword to ignore the directives set by {\tt LIB} concerning the mutual resonance shielding model. This keyword has the effect to replace the mutual resonance shielding model in the subgroup projection method (SPM) by a full correlation approximation similar to the technique used in the ECCO code. This keyword can be used to avoid the message \begin{verbatim} USSIST: UNABLE TO FIND CORRELATED ISOTOPE ************. \end{verbatim} \noindent that appears with the SPM if the correlated weights matrices are missing in the microlib. \item[\moc{NOSP}] keyword to deactivate the SPH equivalence scheme which modifies the self-shielded averaged neutron fluxes in heterogeneous geometries. The default option is to perform SPH equivalence. \item[\moc{TRAN}] keyword to activate the transport correction option for self-shielding calculations (see \moc{CTRA} in \Sectand{MACData}{LIBData}). This is the default option. \item[\moc{NOTR}] keyword to deactivate the transport correction option for self-shielding calculations (see \moc{CTRA} in \Sectand{MACData}{LIBData}). \item[\moc{PIJ}] keyword to specify the use of complete collision probabilities in the subgroup and SPH equivalence calculations of {\tt USS:}. This is the default option for \moc{EXCELT:} and \moc{SYBILT:} trackings. This option is not available for \moc{MCCGT:} trackings. \item[\moc{ARM}] keyword to specify the use of iterative flux techniques in the subgroup and SPH equivalence calculations of {\tt USS:}. This is the default option for \moc{MCCGT:} trackings. \item[\moc{MAXST}] keyword to set the maximum number of fixed point iterations for the ST scattering source convergence. \item[\dusa{imax}] the maximum number of ST iterations. The default is \dusa{imax} $=50$ ($=20$ with the RSE method). A non-iterative response matrix approach is available with the subgroup projection method (SPM) by setting \dusa{imax} $=0$. \item[\moc{FLAT}] keyword to force the flat-flux initialization of subgroup fluxes if \dusa{MICLIB} is open in modification mode. \item[\moc{CALC}] keyword to activate the simplified self-shielding approximation in which a single self-shielded isotope is shared by many resonant mixtures. \item[\moc{REGI}] keyword to specify a set of isotopes and mixtures that will be self-shielded together. All the self-shielded isotopes in this group will share the same 4--digit suffix. \item[\dusa{suffix}] {\tt character*4} suffix for the isotope names in this group \item[\dusa{isot}] {\tt character*8} alias name of a self-shielded isotope in this group \item[\moc{ALL}] keyword to specify that a unique self-shielded isotope will be made for the complete domain \item[\dusa{imix}] list of mixture indices that will share the same self-shielded isotope \item[\dusa{nmix}] number of mixtures that will share the same self-shielded isotope \item[\moc{ENDC}] end of \moc{CALC} data keyword \end{ListeDeDescription} \vskip 0.15cm Here is an example of the data structure corresponding to a production case where only $^{238}$U is assumed to show distributed self-shielding effects: \begin{verbatim} LIBRARY2 := USS: LIBRARY TRACK :: CALC REGI W1 PU239 ALL REGI W1 PU241 ALL REGI W1 PU240 ALL REGI W1 PU242 ALL REGI W1 U235 ALL REGI W1 U236 ALL REGI W1 PU238 ALL REGI W1 U234 ALL REGI W1 AM241 ALL REGI W1 NP237 ALL REGI W1 ZRNAT ALL REGI W1 U238 <> <> <> <> <> REGI W2 U238 <> <> <> <> <> REGI W3 U238 <> <> <> <> <> REGI W4 U238 <> <> <> <> <> REGI W5 U238 <> <> <> <> <> REGI W6 U238 <> <> <> <> <> ENDC ; \end{verbatim} \vskip 0.15cm In this case, $^{238}$U is self-shielded within six distributed regions (labeled {\tt W1} to {\tt W6}) and each of these regions are merging volumes belonging to five different fuel rods. The mixture indices of the 30 resonant volumes belonging to the fuel are CLE-2000 variables labeled {\tt <>} to {\tt <>}. \eject