\section{Contents of a \dir{asminfo} directory}\label{sect:asminfodir} This directory contains the multigroup collision probabilities and response matrices required in the solution of the transport equation. \subsection{State vector content for the \dir{asminfo} data structure}\label{sect:asminfostate} The dimensioning parameters for this data structure, which are stored in the state vector $\mathcal{S}^{a}_{i}$, represent: \begin{itemize} \item The type of collision probabilities considered $I_{T}=\mathcal{S}^{a}_{1}$ where \begin{displaymath} I_{T} = \left\{ \begin{array}{rl} 1 & \textrm{Scattering reduced collision probability or response matrix}\\ 2 & \textrm{Direct collision probability or response matrix} \\ 3 & \textrm{Scattering reduced directional collision probability} \\ 4 & \textrm{Direct directional collision probability} \end{array} \right. \end{displaymath} \item The type of collision probability closure relation used $I_{C}=\mathcal{S}^{a}_{2}$ (see \moc{NORM} keyword in \moc{ASM:} operator input option) \begin{displaymath} I_{C} = \left\{ \begin{array}{rl} 0 & \textrm{Total reflection closure relation} \\ 1 & \textrm{No closure relation used} \end{array} \right. \end{displaymath} \item A parameter related to the albedo leakage model $I_{\beta}=\mathcal{S}^{a}_{3}$ (see \moc{ALSB} keyword in \moc{ASM:} operator input option) \begin{displaymath} I_{\beta} = \left\{ \begin{array}{rl} 0 & \textrm{Groupwise escape matrices \moc{WIS} are stored} \\ 1 & \textrm{No information is stored} \end{array} \right. \end{displaymath} \item $\mathcal{S}^{a}_{4}$ (not used) \item The option to indicate whether response matrix or collision probability matrices are stored on the structure $I_{p}=\mathcal{S}^{a}_{5}$ (see \moc{PIJ} and \moc{ARM} keyword in \moc{ASM:} operator input option) \begin{displaymath} I_{p} = \left\{ \begin{array}{rl} 1 & \textrm{Response matrices will be stored (the \moc{ARM} keyword was selected)} \\ 2 & \textrm{Collision probability matrices will be stored (the \moc{PIJ} keyword was selected)} \end{array} \right. \end{displaymath} \item The option to indicate the type of streaming model used $I_{k}=\mathcal{S}^{a}_{6}$ (see \moc{PIJK} and \moc{ECCO} keyword in \moc{ASM:} operator input option) \begin{displaymath} I_{k} = \left\{ \begin{array}{rl} 1 & \textrm{No streaming model used (a leakage model may or may not be used)} \\ 2 & \textrm{Isotropic streaming model used (ECCO model)} \\ 3 & \textrm{Anisotropic streaming model used (TIB\`ERE model)} \end{array} \right. \end{displaymath} \item The type of collision probability normalization method used $I_{n}=\mathcal{S}^{a}_{7}$ (see \moc{PNOR} keyword in \moc{ASM:} operator input option) \begin{displaymath} I_{n} = \left\{ \begin{array}{rl} 0 & \textrm{No normalization} \\ 1 & \textrm{Gelbard normalization algorithm} \\ 2 & \textrm{Diagonal element normalization} \\ 3 & \textrm{Non-linear normalization} \\ 4 & \textrm{Helios type normalization} \end{array} \right. \end{displaymath} \item Number of energy groups $G=\mathcal{S}^{a}_{8}$ \item Number of unknown in flux system $N_{u}=\mathcal{S}^{a}_{9}$ \item Number of mixtures $N_{m}=\mathcal{S}^{a}_{10}$ \item Number of Legendre orders of the scattering cross sections used in the main transport solution. $N_{\rm ans}=\mathcal{S}^{a}_{11}$ \item Flag for the availability of diffusion coefficients. $I_{\rm diff}=\mathcal{S}^{a}_{12}$ \begin{displaymath} I_{\rm diff} = \left\{ \begin{array}{rl} 0 & \textrm{No diffusion coefficients available;} \\ 1 & \textrm{Diffusion coefficients are available.} \end{array} \right. \end{displaymath} \item Type of equation solved. $I_{\rm bfp}=\mathcal{S}^{a}_{13}$ \begin{displaymath} \mathcal{S}^{t}_{13} = \left\{ \begin{array}{rl} 0 & \textrm{Boltzmann transport equation} \\ 1 & \textrm{Boltzmann Fokker-Planck equation with Galarkin energy propagation factors} \\ 2 & \textrm{Boltzmann Fokker-Planck equation with Przybylski and Ligou energy propagation} \\ & \textrm{factors.} \end{array} \right. \end{displaymath} \end{itemize} \subsection{The main \dir{asminfo} directory}\label{sect:asminfodirmain} On its first level, the following records and sub-directories will be found in the \dir{asminfo} directory: \begin{DescriptionEnregistrement}{Main records and sub-directories in \dir{asminfo}}{8.0cm} \CharEnr {SIGNATURE\blank{3}}{$*12$} {Signature of the data structure ($\mathsf{SIGNA}=${\tt L\_PIJ\blank{7}}).} \CharEnr {LINK.MACRO\blank{2}}{$*12$} {Name of the {\sc macrolib} on which the collision probabilities are based.} \CharEnr {LINK.TRACK\blank{2}}{$*12$} {Name of the {\sc tracking} on which the collision probabilities are based.} \IntEnr {STATE-VECTOR}{$40$} {Vector describing the various parameters associated with this data structure $\mathcal{S}^{a}_{i}$, as defined in \Sect{asminfostate}.} \CharEnr {TRACK-TYPE\blank{2}}{$*12$} {Type of tracking considered ($\mathsf{CDOOR}$). Allowed values are: {\tt 'EXCELL'}, {\tt 'SYBIL'}, {\tt 'MCCG'}, {\tt 'SN'}, {\tt 'BIVAC'} and {\tt 'TRIVAC'}.} \DirlEnr {GROUP\blank{7}}{$\mathcal{S}^{a}_{8}$} {List of energy-group sub-directories. Each component of the list is a directory containing the multigroup collision probabilities and response matrices associated with an energy group. The specification of this directory is given in Sect.~\ref{sect:asminfodhdirgroup} or~\ref{sect:asminfodirgroup} depending if a double-heterogeneity is present or not. A double-heterogeneity is present if $\mathcal{S}^{t}_{40}=1$ in the {\sc tracking} object.} \end{DescriptionEnregistrement} \clearpage \subsection{The \moc{GROUP} double-heterogeneity group sub-directory}\label{sect:asminfodhdirgroup} This directory is containing the following records, corresponding to a single energy group: \begin{DescriptionEnregistrement}{Records and sub-directories in \moc{GROUP}}{7.0cm} \RealEnr {DRAGON-TXSC\blank{1}}{$N_{m}+1$}{cm$^{-1}$} {where $N_{m}=\mathcal{P}_{1}$. The total cross section $\Sigma_{m}^{g}$ for $N_{m}+1$ composite mixtures assuming that the first mixture represents void ($\Sigma_{m}^{g}=0$). A transport correction may or may not be included. The first component of this array is always equal to 0.} \RealEnr {DRAGON-S0XSC}{$N_{m}+1,N_{\rm ans}$}{cm$^{-1}$} {The within group scattering cross section $\Sigma_{0,m,w}$ (see \Sect{macrolibdirgroup}) for $N_{m}+1$ composite mixtures assuming that the first mixture represents void ($\Sigma_{0,m,w}^{g}=0$). A transport correction may or may not be included. Many Legendre orders may be given. The first component of this array, for each Legendre order, is always equal to 0.} \IntEnr {NCO\blank{9}}{${\cal M}$} {where ${\cal M}=\mathcal{P}_{2}-\mathcal{P}_{1}$. Number of composite mixtures in each macro-mixture.} \OptRealEnr {RRRR\blank{8}}{${\cal M}$}{$\mathcal{P}_{6}=1,2$}{} {Group-dependent double-heterogeneity information.} \OptRealEnr {QKOLD\blank{7}}{$\mathcal{P}_{4},\mathcal{P}_{5},{\cal M}$}{$\mathcal{P}_{6}=1$}{} {Group-dependent double-heterogeneity information related to the escape probabilities in the micro-structures.} \OptRealEnr {QKDEL\blank{7}}{$\mathcal{P}_{4},\mathcal{P}_{5},{\cal M}$}{$\mathcal{P}_{6}=1,2$}{} {Group-dependent double-heterogeneity information related to the escape probabilities in the micro-structures.} \OptRealEnr {PKL\blank{9}}{$\mathcal{P}_{4},\mathcal{P}_{5},\mathcal{P}_{5},{\cal M}$}{$\mathcal{P}_{6}=1,2$}{} {Group-dependent double-heterogeneity information related to the collision probabilities in the micro-structures.} \OptDbleEnr {COEF\blank{8}}{${\cal F},{\cal F},{\cal M}$}{$\mathcal{P}_{6}=1,2$}{} {where ${\cal F}=1+\mathcal{P}_{4}\times\mathcal{P}_{5}$. Group-dependent double-heterogeneity information.} \OptRealEnr {P1I\blank{9}}{$\mathcal{P}_{4},{\cal M}$}{$\mathcal{P}_{6}=3$}{} {Group-dependent double-heterogeneity information related to the escape probabilities through the composite.} \OptRealEnr {P1DI\blank{8}}{$\mathcal{P}_{4},{\cal M}$}{$\mathcal{P}_{6}=3$}{} {Group-dependent double-heterogeneity information related to the escape probabilities from the matrix.} \OptRealEnr {P1KI\blank{8}}{$\mathcal{P}_{4},\mathcal{P}_{5},{\cal M}$}{$\mathcal{P}_{6}=3$}{} {Group-dependent double-heterogeneity information related to the escape probabilities from the micro-structures.} \OptRealEnr {SIGA1\blank{7}}{$\mathcal{P}_{4},{\cal M}$}{$\mathcal{P}_{6}=3$}{} {Group-dependent double-heterogeneity information related to the equivalent total cross-section.} \DirEnr {BIHET\blank{7}} {Directory containing collision probability or response matrix information related to the macro-geometry (i.$\,$e., the geometry with homogenized micro-structures). The specification of this directory is given in \Sect{asminfodirgroup}. Note that the value of $N_{m}=\mathcal{P}_{2}$ in this object is set to take into account the macro-mixtures. Similarly, the value $N_{r}=\mathcal{P}_{3}$ is the number of macro-volumes.} \end{DescriptionEnregistrement} \vskip -0.5cm \subsection{The \moc{GROUP} or \moc{BIHET} group sub-directory}\label{sect:asminfodirgroup} This directory is containing the following records, corresponding to a single energy group: \begin{DescriptionEnregistrement}{Records and sub-directories in \moc{GROUP}}{7.0cm} \OptRealEnr {ALBEDO\blank{6}}{$\mathcal{S}^{M}_{8}$}{$\mathcal{S}^{M}_{8}>0$}{} {Surface ordered physical albedos in \moc{GROUP}. The number of physical albedos $\mathcal{S}^{M}_{8}$ is defined in \Sect{macrolibstate}.} \OptRealEnr {ALBEDO-FU\blank{3}}{$\mathcal{S}^{M}_{8}$}{$\mathcal{S}^{M}_{8}>0$}{} {Surface ordered physical albedo functions in \moc{GROUP}. The number of physical albedos $\mathcal{S}^{M}_{8}$ is defined in \Sect{macrolibstate}.} \RealEnr {DRAGON-TXSC\blank{1}}{$N_{m}+1$}{cm$^{-1}$} {The total cross section $\Sigma_{m}^{g}$ for $N_{m}+1$ mixtures assuming that the first mixture represents void ($\Sigma_{m}^{g}=0$). A transport correction may or may not be included. The first component of this array is always equal to 0.} \OptRealEnr {DRAGON-T1XSC}{$N_{m}+1$}{*}{cm$^{-1}$} {where $N_{m}=\mathcal{P}_{1}$. The current-weighted total cross section $\Sigma_{1,m}^{g}$ for $N_{m}+1$ composite mixtures assuming that the first mixture represents void ($\Sigma_{1,m}^{g}=0$). The first component of this array is always equal to 0.} \OptRealEnr {DRAGON-T2XSC}{$N_{m}+1$}{*}{cm$^{-1}$} {where $N_{m}=\mathcal{P}_{1}$. The second moment-weighted total cross section $\Sigma_{2,m}^{g}$ for $N_{m}+1$ composite mixtures assuming that the first mixture represents void ($\Sigma_{2,m}^{g}=0$). The first component of this array is always equal to 0.} \RealEnr {DRAGON-S0XSC}{$N_{m}+1,N_{\rm ans}$}{cm$^{-1}$} {The within group scattering cross section $\Sigma_{0,m,w}$ (see \Sect{macrolibdirgroup}) for $N_{m}+1$ mixtures assuming that the first mixture represents void ($\Sigma_{0,m,w}^{g}=0$). A transport correction may or may not be included. Many Legendre orders may be given. The first component of this array, for each Legendre order, is always equal to 0.} \OptRealEnr {DRAGON-DIFF\blank{1}}{$N_{m}+1$}{$I_{\rm diff}=1$}{cm} {Diffusion coefficients $D_{m}^{g}$ for $N_{m}+1$ mixtures assuming that the first mixture represents void ($D_{m}^{g}=1.0\times 10^{10}$). The first component of this array is always equal to $1.0\times 10^{10}$.} \OptRealEnr {FUNKNO\$USS\blank{2}}{$N_{U}$}{*}{1} {Solution of the Livolant-Jeanpierre fine-structure equation. $N_{U}$ is the number of unknowns in each subgroup and each energy group. (*) This information is present if the flux is computed within module {\tt USS:}.} \OptDirEnr {STREAMING\blank{3}}{$I_{k}=2$} {Directory containing P1 information to be used with the ECCO isotropic streaming model. This directory uses the same specification as \moc{GROUP} where P0 information is replaced with P1 information. Cross sections used in this directory are {\sl not}--transport corrected.} \end{DescriptionEnregistrement} Additional records are provided to support Boltzmann Fokker-Planck (BFP) solutions: \begin{DescriptionEnregistrement}{BFP records in \moc{GROUP}}{7.0cm} \OptRealEnr {DRAGON-ESTOP}{$N_{m}+1,2$}{$I_{\rm bfp}>0$}{MeV cm$^{-1}$} {Initial and final stopping power.} \OptRealEnr {DRAGON-EMOMT}{$N_{m}+1$}{$I_{\rm bfp}>0$}{cm$^{-1}$} {Restricted momentum transfer cross section. } \OptRealEnr {DRAGON-DELTE}{$1$}{$I_{\rm bfp}>0$}{MeV} {Energy width of the energy group.} \OptIntEnr {DRAGON-ISLG\blank{1}}{$1$}{$I_{\rm bfp}>0$} {Integer set to 0 in energy groups $< G$ and set to 1 in energy group $G$.} \end{DescriptionEnregistrement} \vskip -0.5cm \subsubsection{The \moc{trafict} dependent records on a \moc{GROUP} directory}\label{sect:traficgrpdiringdir} If a collision probability method is used, the following records will also be found on the group sub-directory: \begin{DescriptionEnregistrement}{Collision probability records in \moc{GROUP}}{7.0cm} \OptRealEnr {DRAGON-PCSCT}{$N_{r},N_{r}$}{$I_{p}=2$}{} {The scattering-reduced ($I_{T}=1,3$) collision probability matrix ${\bf W}_{g}$ or direct ($I_{T}=2,4$) collision probability matrix ${\bf p}_{g}$} \OptRealEnr {DRAGON1PCSCT}{$N_{r},N_{r}$}{$I_{k}=3$}{} {The $x-$directed P1 scattering-reduced ($I_{T}=3$) collision probability matrix ${\bf Y}_{x,g}$ or direct ($I_{T}=4$) collision probability matrix ${\bf p}_{x,g}$} \OptRealEnr {DRAGON2PCSCT}{$N_{r},N_{r}$}{$I_{k}=3$}{} {The $y-$directed P1 scattering-reduced ($I_{T}=3$) collision probability matrix ${\bf Y}_{y,g}$ or direct ($I_{T}=4$) collision probability matrix ${\bf p}_{y,g}$} \OptRealEnr {DRAGON3PCSCT}{$N_{r},N_{r}$}{$I_{k}=3$}{} {The $z-$directed P1 scattering-reduced ($I_{T}=3$) collision probability matrix ${\bf Y}_{z,g}$ or direct ($I_{T}=4$) collision probability matrix ${\bf p}_{z,g}$} \OptRealEnr {DRAGON1P*SCT}{$N_{r},N_{r}$}{$I_{k}=3$}{} {The $x-$directed matrix ${\bf p}_g^{-1}{\bf p}_{x,g}^*$} \OptRealEnr {DRAGON2P*SCT}{$N_{r},N_{r}$}{$I_{k}=3$}{} {The $y-$directed matrix ${\bf p}_g^{-1}{\bf p}_{y,g}^*$} \OptRealEnr {DRAGON3P*SCT}{$N_{r},N_{r}$}{$I_{k}=3$}{} {The $z-$directed matrix ${\bf p}_g^{-1}{\bf p}_{z,g}^*$} \OptRealEnr {DRAGON-WIS\blank{2}}{$N_{r}$}{$I_{\beta}=1$}{} {The scattering-reduced leakage matrix $W_{is}^{g}$ } \end{DescriptionEnregistrement} \goodbreak \noindent where \begin{itemize} \item the reduced collision probability matrix is defined as $${\bf p}_{g}=\{p_{ij,g}\> ;\> \forall i \ {\rm and} \ j \}$$ \item the reduced directional probability matrix, used in the first TIB\`ERE equation, is defined as $${\bf p}_{k,g}^*=\{p_{ij,k,g}^*\> ;\> \forall i \ {\rm and} \ j \} \ \ ; \ \ k=x, \ y, \ {\rm or } \ z$$ \item the reduced directional probability matrix, used in the second TIB\`ERE equation, is defined as $${\bf p}_{k,g}=\{p_{ij,k,g}\> ;\> \forall i \ {\rm and} \ j \} \ \ ; \ \ k=x, \ y, \ {\rm or } \ z \ \ \ .$$ The total cross sections used to compute this matrix are {\sl not}--transport corrected. \item the P0 scattering reduced collision probability matrix is defined as $${\bf W}_{g}=[{\bf I}-{\bf p}_{g} \ {\bf\Sigma}_{{\rm s}0,g\gets g}]^{-1} {\bf p}_{g}$$ \item the P1 scattering reduced directionnal collision probability matrix is defined as $${\bf Y}_{k,g}=[{\bf I}-{\bf p}_{k,g} \ {\bf\Sigma}_{{\rm s}1,g\gets g}]^{-1} {\bf p}_{k,g} \ \ ; \ \ k=x, \ y, \ {\rm or } \ z$$ \end{itemize} \eject \input{SectDasmsybil.tex} % Description of Sybil response matrices \input{SectDasmmccg.tex} % Description of MCCG response matrices