\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{No closure relation used} \\
 1 & \textrm{Total reflection closure relation} 
\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{No information is stored} \\
 1 & \textrm{Groupwise escape matrices \moc{WIS} are 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}.}
\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 $1.0\times 10^{10}$.}
\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}

\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
