\subsection{Accelerator Acceptance. \label{accaccsec}}
The acceleration of the muons represents a major cost of the
system. This cost could be reduced if the longitudinal and/or
transverse acceptances could be reduced. And, conversely, the
performance could be improved if these acceptances could be
increased. The performance \textit{vs.} acceptances are plotted in 
Fig.~\ref{accaccfig}. It is seen
that a significant gain in performance could be achieved with greater
transverse acceptance, but that the baseline longitudinal aperture already 
accepts almost all muons.
%\begin{table}[!hbt]
%\begin{center}
%\caption{Performance \textit{vs.} accelerator acceptances.}
%\begin{tabular}{|p{2.5}p{2.5}|cc|}
%\hline
%  longitudinal acceptance &   transverse acceptance & $ \mu/p$& $ \mu/p^*$ \\
%     (mm)  &        (mm$\cdot$~rad)&&\\
%\hline
%      -        &   -  &         0.231 &\\
%\hline
%     150      &    5    &       0.074 &\\
%        150       &       10      &       0.136    &\\     
%\bf  150     &\bf 15      &\bf 0.174&\\
%        150       &       20      &       0.194    &       0.20\\
%     150      &       25      &       0.205    &       0.216\\
%     150       &       30      &       0.213    &       0.23 \\ 
%\hline
%     50 &       15      &       0.09&\\
%     100        &       15       &       0.153&\\
%\bf  150     &\bf 15      &\bf 0.174&\\
%        200     &       15      &       0.177&\\
%        300     &    15      &       0.179 &\\
%\hline
%\end{tabular}
%$*$ with shorter cooling to maximize $\mu/p.$
%\end{center}
%\label{perftb}
%\end{table}
\begin{figure}[!hbt]
%\vskip0.75in
%\vskip1.in
%\input{accacc.fig}
\includegraphics[width=4.5in]{accacc.ps}
\begin{center}
\caption[Performance \textit{vs.} accelerator acceptance]{Performance \textit{vs.} accelerator acceptance: a) (left) transverse (upper line includes re-optimization of cooling length); b) (right) longitudinal. The baseline parameters are indicated by the circles.}
\label{accaccfig}
\end{center}
\end{figure}
\subsection{Dogbone Configuration}
A parametric study of costs~\cite{ref:dogbone} has been done on
conventional racetrack and dogbone RLAs. The method used a
semi-automatic longitudinal motion design, minimizing the energy
spread. The costs were taken from the Feasibility Study-I: linac
costs proportional to energy gain (C=35~$\Delta E$~per GeV) and  arc
costs proportional to length and energy spread (C=0.18 $\Delta
E~\delta p/p$~per GeV and \%.)  The cost units are such that the two RLAs
of Study-I cost 500 units.

For the conventional racetrack design (Fig.~\ref{racetrack},) the method shows that a cost minimum is achieved with 6 turns (Fig.~\ref{rlacosts}). However, four passes have been chosen for several practical reasons, including the difficulties of designing a switchyard with greater than 4 paths. If these problems could be overcome, then a cost saving of approximately 7\% might be achieved.

\begin{figure}[!hbt]
\begin{center}
\includegraphics[width=1.2in, angle=90]{../template/report/ps-and-eps/racetrack.ps}
\caption{Schematic of conventional racetrack RLA.}
\label{racetrack}
\end{center}
\end{figure}


\begin{figure}[!hbt]
\begin{center}
\includegraphics[width=1.2in, angle=90]{../template/report/ps-and-eps/dogbone.ps}
\caption{Schematic of dogbone RLA.}
\label{dogbone}
\end{center}
\end{figure}


\begin{figure}[!htb]
\begin{center}
\vskip.5in
\includegraphics[width=4in]{../template/report/ps-and-eps/costs-a.ps}
\caption{Relative costs of RLA's \textit{vs.} number of passes.}
\label{rlacosts}
\end{center}
\end{figure}

An alternative geometry for the RLA is the dogbone
(Fig.~\ref{dogbone}). In this geometry there is only one linac, with
the beam passing through it in alternate directions. 
%The minimum cost
%in this case is found to be at 7 linac passes and is 11\% less than the
%optimized racetrack and 18\% less than the baseline. 
Despite the
larger number of passes, the number of paths on any one side of a
switchyard is only four---no more than in the baseline. The savings in
a dogbone arise primarily from the ability to reduce the length of the
arcs when the momentum is lower. (If all the arcs were forced into a
single tunnel, the gains would be lost.) A serious study based on actual costs will be needed to quantify the benefits of alternative accelerator approaches. This should include the use of FFAG ( Fixed-Field Alternating Gradient) rings. However, the main motivation for an FFAG, its large longitudinal acceptance, seems moot based on Fig.~\ref{accaccfig}.