From 7dfcc480ba1e19bd3232349fc733caef94034292 Mon Sep 17 00:00:00 2001
From: stainer_t <thomas.stainer@oecd-nea.org>
Date: Mon, 8 Sep 2025 13:48:49 +0200
Subject: Initial commit from Polytechnique Montreal

---
 doc/IGE335/Section3.05_auto.tex | 262 ++++++++++++++++++++++++++++++++++++++++
 1 file changed, 262 insertions(+)
 create mode 100644 doc/IGE335/Section3.05_auto.tex

(limited to 'doc/IGE335/Section3.05_auto.tex')

diff --git a/doc/IGE335/Section3.05_auto.tex b/doc/IGE335/Section3.05_auto.tex
new file mode 100644
index 0000000..4d13c84
--- /dev/null
+++ b/doc/IGE335/Section3.05_auto.tex
@@ -0,0 +1,262 @@
+\subsection{The {\tt AUTO:} module}\label{sect:AUTOData}
+
+The Autosecol self-shielding module in DRAGON, called {\tt AUTO:}, allows the
+correction of the microscopic cross sections to take into account the
+self-shielding effects related to the resonant isotopes.\cite{autosecol}
+
+\vskip 0.08cm
+
+{\sl Autolib data} is a fine-group representation of microscopic cross-section data for the resonant isotopes available in a
+{\sl Draglib} or {\sl APOLIB-2} cross-section library. Each fine group in the Autolib has a lethargy width which is an integer multiple of an
+{\sl elementary lethargy width}. Elastic slowing-down scattering is assumed for the resonant isotopes.
+
+Integrating the Livolant-Jeanpierre equation over a fine group $g$, the Autosecol equation is written
+\begin{equation}
+\bff(\Omega)\cdot\bff(\nabla)\varphi_g(\bff(r),\bff(\Omega))\,+\,\Sigma_g(\bff(r))\,\varphi_g(\bff(r),\bff(\Omega))\,=\,{1\over 4\pi} \left[ \Sigma_{{\rm s},g}^+(\bff(r)) \, + \,\sum_h \Sigma_{{\rm s},j,g \leftarrow h}^{*} \, \varphi_h(\bff(r)) {\Delta u_h\over \Delta u_g} \right]
+\label{eq:auto1}
+\end{equation}
+
+\noindent where the group integrated fine structure function is written
+\begin{equation}
+\varphi_g(\bff(r))={1\over \Delta u_g}\int_{u_{g-1}}^{u_g} du\, \varphi(\bff(r),u)
+\label{eq:auto2}
+\end{equation}
+
+\noindent and where the $+$ and $*$ subscripts identify non-resonant and resonant isotopes respectively.
+
+\vskip 0.08cm
+
+The {\sl Autosecol method} consists to solve the Livolant-Jeanpierre equation over the Autolib energy mesh using a solution
+technique of the Boltzmann transport equation available in DRAGON.\cite{PIP2009} The Autosecol method
+is an accurate self-shielding technique relying on the fine-group solution of an heterogeneous transport equation. This approach may require
+substantial CPU resources in actual production cases.
+
+\vskip 0.08cm
+
+Resonant isotopes are identified as such by the \dusa{inrs} parameter, as defined in
+\Sect{LIBData}. The Autosecol 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 {\sl Autolib data} 
+recovered by the \moc{LIB:} module.
+\item Probability tables are used in the unresolved energy domain to randomly
+sample cross-section data into the Autolib fine mesh. The keyword \moc{SUBG} {\sl must} be
+set in module {\tt LIB:}.
+\item The resonant fine structure values $\varphi_g(\bff(r))$ are obtained as a solution
+of the Autosecol Eq.~(\ref{eq:auto1}) over the Autolib fine mesh;
+\item The flux can be solved using collision probabilities, or using {\sl any}
+flux solution technique for which a tracking module is available;
+\item All resonant isotopes with the same \dusa{inrs} index (see Sect.~\ref{sect:descmix1})
+are computed simultanously;
+\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{AUTO:}}
+\dusa{MICLIB} \moc{:=} \moc{AUTO:} \dusa{MICLIB\_SG} $[$ \dusa{MICLIB} $]$
+\dusa{TRKNAM} $[$ \dusa{TRKFIL} $]$ \moc{::} \dstr{descauto}
+\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 for the unresolved
+domain.
+
+\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{descauto}] structure describing the self-shielding options.
+
+\end{ListeDeDescription}
+
+\subsubsection{Data input for module {\tt AUTO:}}\label{sect:descauto}
+
+\begin{DataStructure}{Structure \dstr{descauto}}
+$[$ \moc{EDIT} \dusa{iprint} $]$ \\
+$[$ \moc{GRMIN}  \dusa{lgrmin} $]~~[$ \moc{GRMAX}  \dusa{lgrmax} $]$~~
+$[$ \moc{PASS} \dusa{ipass} $]~~[~\{$ \moc{SPH} $|$ \moc{NOSP} $\}~]$~~$[$ $\{$ \moc{TRAN} $|$ \moc{NOTR} $\}$ $]$ \\ 
+$[$ $\{$ \moc{PIJ} $|$ \moc{ARM} $\}$ $]$ \\
+$[[$ \moc{DILU} \dusa{isot\_d} \dusa{dilut} $]]$ \\
+$[$ \moc{KERN} \dusa{ialter} $]~~[$ \moc{MAXT} \dusa{maxtra} $]$ \\
+$[$~\moc{SEED} \dusa{iseed}~$]$ \\
+$[$ \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. If all \dusa{inrs} indices are set to one in module \moc{LIB:},
+these iterations are not required.
+
+\item[\dusa{ipass}] the number of iterations. The default is \dusa{ipass} $=1$ if
+\dusa{MICLIB} is created.
+
+\item[\moc{SPH}] keyword to activate the SPH equivalence scheme which
+modifies the self-shielded averaged neutron fluxes in
+heterogeneous geometries (default option).
+
+\item[\moc{NOSP}] keyword to deactivate the SPH equivalence scheme which
+modifies the self-shielded averaged neutron fluxes in heterogeneous geometries.
+
+\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 AUTO:}.
+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 AUTO:}.
+This is the default option for \moc{MCCGT:} trackings.
+
+\item[\moc{DILU}]  keyword to input an additional microscopic dilution value for a specific isotope. By default, no dilution
+source other than $\Sigma_{{\rm s},g}^+(\bff(r))$ is used.
+
+\item[\dusa{isot\_d}] {\tt character*8} alias name of the specific isotope.
+
+\item[\dusa{dilut}] dilution value in barn.
+
+\item[\moc{KERN}]  keyword to input the type of elastic slowing-down kernel.
+
+\item[\dusa{ialter}] integer value indicating the type:
+$$
+\textsl{ialter} = \left\{
+\begin{array}{ll}
+0 & \textrm{use exact elastic kernel} \\
+1 & \textrm{use an approximate kernel for the resonant isotopes.}
+\end{array} \right.
+$$
+
+\item[\moc{MAXT}]  keyword to input a maximum storage size for the slowing-down kernel values.
+
+\item[\dusa{maxtra}] integer value indicating the storage size. The default value is \dusa{maxtra} $=$ 10000.
+
+\item[\moc{SEED}] keyword used to set the initial seed integer for the random number generator used in
+the unresolved energy domain. By default, the seed integer is set from the processor clock.
+
+\item[\dusa{iseed}] initial seed integer.
+
+\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 := AUTO: 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 <<COMB0101>> <<COMB0201>> <<COMB0301>>
+                       <<COMB0401>> <<COMB0501>>
+          REGI W2 U238 <<COMB0102>> <<COMB0202>> <<COMB0302>>
+                       <<COMB0402>> <<COMB0502>>
+          REGI W3 U238 <<COMB0103>> <<COMB0203>> <<COMB0303>>
+                       <<COMB0403>> <<COMB0503>>
+          REGI W4 U238 <<COMB0104>> <<COMB0204>> <<COMB0304>>
+                       <<COMB0404>> <<COMB0504>>
+          REGI W5 U238 <<COMB0105>> <<COMB0205>> <<COMB0305>>
+                       <<COMB0405>> <<COMB0505>>
+          REGI W6 U238 <<COMB0106>> <<COMB0206>> <<COMB0306>>
+                       <<COMB0406>> <<COMB0506>>
+     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 <<COMB0101>>} to {\tt <<COMB0506>>}.
+
+\eject
-- 
cgit v1.2.3

