\section{BI system layout and installation studies}
\label{sec:Barrel_layout}
The RPC BI system aims to almost fully cover the $|\eta|<1.05$ region, with very limited unavoidable acceptance holes. Figures \ref{Rpc:Layout2} and \ref{Rpc:Layout1}shows the proposed layout scheme which is divided as usual in 16 sectors following the same naming scheme of the MDTs. The space availability and possible installation procedures for the RPC on the BI chambers have been studied in detail as it is one of the critical factors. For the large sectors between the barrel toroid coils,  the RPC can be installed on top of the existing MDT chambers.
In the small sectors, corresponding to the coils, it is proposed to extend to all BIS stations the same layout of the new BIS78 chambers, i.e. replacing the present MDT BIS chamber with an muon station integrating a small tubes MDT (sMDT) chamber and the new low-profile RPC triplets, in order to respect the present envelopes. The sMDT chambers are discussed in Section~\ref{sec:sMDT chambers}.
\begin{figure}[htbp]
\begin{center}
\includegraphics[height=0.35\textheight]{BI_layout2}

\end{center}
\caption{\label{Rpc:Layout2}The schematic BI layout in the R-$\Phi$ and R-Z cross sections. The new chamber positions are highlighted by the red boxes.}
\end{figure}
\begin{figure}[htbp]
\begin{center}

\includegraphics[height=0.35\textheight]{BI_layout1}
\end{center}
\caption{\label{Rpc:Layout1}A more detailed description of the proposed layout for the odd and the even sectors}
\end{figure}

A systematic study has been carried out by the ATLAS Technical Coordination~\cite{tatiana1} \cite{tatiana2} to evaluate the available space and the installation procedures. A summary of this study is reported in Chapter~\ref{sec:Installation}. This study produced  preliminary  drawings of the envelopes of the RPC chambers and of their support structures, taking also into account the limitations related to the need to leave space for the projective alignment lines that connect the different MDTs layers. An example for a particular sector is shown in figure~\ref{Tatiana:layout}. This permitted to start the study of different installation scenarios and to setup a Montecarlo simulation to optimize the chamber layout.
\begin{figure}[htbp]
\begin{center}
\includegraphics[height=0.7\textheight, angle=-90]{RPC_BIL_sec_01_C}
\end{center}
\caption{\label{Tatiana:layout}The layout drawing for the BIL of sector 1 side C}
\end{figure}
In Figure \ref{Rpc:layout_sim} it is shown the result of an acceptance study using simulated MDT truth hits and applying a realistic BI RPC geometry including cutouts for alignment, services, and inefficient regions near chamber edges. The chamber layout  used here is the first iteration, not yet optimized for maximizing the coverage, as it is visible in the example. This notwithstanding the total acceptance of the BI chamber is 91\%, to be compared to 95\% of the MDT chambers, which combined with the present RPC system provides already a 95\% of trigger acceptance. This type of study will be used for determining the production layout so to obtain the best possible result.
\begin{figure}[htbp]
\begin{center}
\includegraphics[height=0.4\textheight]{BI_layout_sim}
\end{center}
\caption{\label{Rpc:layout_sim}Montecarlo simulation for the BIL of sector 1 side C acceptance}
\end{figure}

The preliminary layout can be summarized as follows:
\begin{itemize}
 \item 236 RPC triplet Units of BIS and BIL type, according to the layout under study;
\item in the the 96 chambers of small sectors, an integrated muon station composed of the new RPC triplet and the corresponding sMDT, will replace the present BIS MDTs, extending to the rest of the BIS the solution implemented for the 16 BIS78 stations in Phase-I.
  \item The total covered surface is about 470 m$^{2}$, for a total detector area of 1400 m$^{2}$, one fifth of the present RPC system.
  \item the total number of FE channels will be 135000 in a conservative scenario, scaling the strip pitch with the distance from the IP, as requested by the physics performance.
  \item The total number of trigger boxes (PAD) is 400, and these PADs will be very similar to the ones being designed for the scheduled replacement of the trigger electronics in the present RPC system.
\end{itemize}

