\section{Cost Reduction Options}
%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Introduction}
For this study, an effort has been made to select specific and
feasible technologies giving acceptable performance at reasonable
cost. Nonetheless there are many
alternative ideas that could be considered. In this chapter we discuss
options that might lower the cost, improve performance, or be
used as alternatives. In some cases, cost
reductions may be possible with little sacrifice of performance; other
 choices would hurt performance, but by amounts that might be justifiable 
by the savings achieved. Some newer technologies might raise performance and
lower costs simultaneously.

%The discussion is arranged in component order, with the main motivation 
%for each modification (Cost, Performance, or Alternative) preceding
%the subsection titles.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Capture Solenoid}
\subsubsection{Cost: Choice of Capture Field}
Figure~\ref{muvsB} shows the efficiency for muon production \textit{vs.} the
axial peak field of the capture magnet. Maximum performance is
achieved with the baseline value of 20~T, but the drop in efficiency
is small for moderate reductions in this field. A drop from 20~T to 18~T 
would have an almost insignificant effect ($\approx 2$\%) and even a reduction
to 15~T causes only $\approx 9$\% reduction. The savings, even for a reduction to 18
T could be significant.
\begin{figure}[htb!]
\begin{center}
%\input{bb.fig}
\includegraphics*[bb=113 285 433 548,clip]{../template/report/ps-and-eps/jcg-bb.ps}
\caption{Efficiency \textit{vs.} capture field.}
\label{muvsB}
\end{center}
\end{figure}
\subsubsection{Cost/Performance:  Use of Wrapped Insulation}
Figure~\ref{coileff} shows the field \textit{vs.} power consumption for three
different insert coil technologies (see Section~\ref{TGT:hollow-mag}.) The lowest curve is for the
baseline design using MgO insulated hollow conductor giving 6~T with 12~MW. 
\begin{figure}[htb!]
\begin{center}
\includegraphics*[width=6cm]{../template/report/ps-and-eps/bvsmw.eps}
%\hskip1.5in\special{bmp:incert_eff.bmp y=2in } ASK BOB WEGGEL FOR THIS FILE
\caption[Efficiency of three types of inserts in 20~T magnet]{Efficiency of three types of inserts in 20~T magnet; lowest curve: mineral-insulated hollow conductor as developed for the JHF; middle curve: higher-performance hollow conductor under development; top curve: Bitter coil.}
\label{coileff}
\end{center}
\end{figure}
The dotted line above is for a wrapped ceramic insulation as being
developed at CTD, Inc.~\cite{wrapped}. With this conductor, for the same
power consumption, the field from the hollow conductor would rise from
6 to 7.6~T, thus lowering the field needed from the superconducting
coil from 14~T to 12.4~T, and offering significant
savings. Alternatively, the gain in performance could be used to
reduce the power consumption, or some combination of these two options could be considered.
\subsection{Bitter Magnet}
\label{APP-Bitter}
The upper dashed line in Fig.~\ref{coileff} is for a Bitter
magnet.
%\input{appendix-ac} 
%Bitter-Magnet Alternative to Hollow-Conductor Insert for Pion Capture Magnet

The Bitter magnet design is the invention of Prof. Francis Bitter of
MIT, who in the late 1930's first used such magnets to
generate 10~T in a 5~cm bore. 
The design has the potential to be a
very efficient insert for the pion capture magnet. The windings of a
Bitter magnet are sets of thin annular plates, each like a big washer,
slit along a radius, as in a lock washer. In each plate a voltage
difference between the two edges of the slit forces the current to
flow circumferentially, the long way around from one edge of the slit
to the other, before entering the next plate. Tie rods or components
of the magnet housing keep the plates in good registration and provide
the axial clamping for good electrical contact over the sectors in
which current transfers from one plate to the next.  

The Bitter design
has many virtues. It possesses great inherent strength and permits the
use of a wide range of conductors, such as heavily cold-worked copper,
with excellent combinations of strength and electrical
conductivity. Therefore the conductor can resist the huge tensile hoop
stresses that arise in generating intense fields. The fraction of
conductor in a Bitter magnet typically is much higher than in a magnet
built from hollow conductors. One reason is that only a thin film
between adjacent plates suffices to confine the current to its desired
path, because the potential difference between adjacent plates is only
a few volts. Another reason is that cooling passages may be very
small, because they are so short. This is true especially if one cools
the magnet radially, by means of shallow grooves etched into one face
of each plate (or each pair of plates; one can mate each etched plate
with an unetched one). The cooling passage length in such a magnet is
its ``build'' (outer radius minus inner radius). If, instead, one chooses
to cool the magnet axially, through holes punched in each plate and
insulator, the cooling passage length will be the magnet length. For
the pion capture insert coil, axial passages are several times longer
than radial ones---but still short, by an order of magnitude, relative
to those in a magnet employing hollow conductors (See, Section~\ref{TGT:hollow-mag}). The favorable
cooling geometry enables Bitter magnets to operate at very high power
densities. Another virtue of the Bitter magnet design is the ease with
which desired field profiles can be achieved by employing turns of
the appropriate thickness in each of many axial zones. One need only
change the thickness of plates comprising a turn, or change the number
of plates making up each turn.  

Figure~\ref{APP-BITTER:fg1} plots the relative costs
of various systems, each with the peak field of its associated
superconducting magnet. The set labeled ``unshielded" employs a Bitter
magnet whose bore accommodates just the pion capture beam tube and
radial clearance for an annulus to bring water to the radial cooling
passages. The annulus is tapered from the upstream to the downstream
end, in order to maintain a water velocity in the annulus of about 10~m/s. 
The annular height is at most 1.8 cm. For the set labeled
``shielded" the bore accommodates 10 cm of shielding with water-cooled
tungsten carbide, just as for the magnet with hollow conductors. Each
magnet has an outer diameter of 80 cm if shielded, 40 cm if not---values
close to the optimum.  
\begin{figure}[!htb]
\begin{center}
\includegraphics[width=3.5in]{../template/report/ps-and-eps/Bitter-graph1.eps}
\caption[Relative cost of pion capture magnet]{Relative cost of pion capture magnet, as function of the
power consumed by its Bitter magnet, with and without 10 cm of
shielding with water-cooled tungsten carbide. Decreasing the power of
the Bitter magnet by a factor of four from the 8-10 MW maximum plotted
here entails a $\approx 50$\% increase in system cost; the needed field
contribution from the superconducting magnet rises from $\approx 12$~T to $\approx 15$~T.}
\label{APP-BITTER:fg1}
\end{center}
\end{figure}

To consider a Bitter magnet for the
insert to the pion capture system will require an R\&D program that validates 
three issues: 
\begin{itemize}
\item verification  that radiation will not immediately
induce arcing so severe that a substantial fraction of current flows
through the arc instead of through the copper windings 
\item development of  an insulator---undoubtedly a ceramic---that will 
withstand not only the intense radiation emanating from the target but also the
environment of a Bitter magnet. (Even without radiation this
environment involves  high clamping pressure, high
temperature and high water velocities.) 
\item verification that conductors will not deteriorate too much in strength 
and ductility when irradiated for at least a few months.
\end{itemize}
 If so, one can save many megawatts of power consumption
and/or many millions of dollars of capital cost in superconducting
magnets---a tantalizing prospect for economy for the Neutrino Factory.

%This technology, which has a very high fraction of its volume
%available to carry current, is more efficient and less expensive than hollow
%conductor technology. It is not proposed for the baseline because a
%suitable radiation resistant insulation would need development, and
%even with such insulation it is expected to have a limited lifetime.

%Conventional Bitter magnets employ thin wet organic sheet insulation
%between turns. Ceramic insulation would have to be substituted, but
%this too would be wet. In the high radiation environment the
%conductors may corrode. R\&D is needed to establish if this is a real
%concern (see Section~\ref{APP-Bitter}) and to assess the lifetime implications.
%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Phase Rotation}
\label{alternative-phase-rotation}
\subsubsection{Cost:  Combining Induction Linacs 2 and 3}
In the baseline design there are 3 induction linacs. The first linac
must be separate from the other two in order to achieve non-distorting
phase rotation, but the second and third linacs are separate only in
order that they each be unipolar. A single second linac with a bipolar
pulse approximately equal to the sum of the two opposite polarity
pulses would perform equally well. This appears possible and would be 
somewhat less expensive.
\subsubsection{Cost:  Fewer Induction Linacs}

\begin{figure}[!hbt]
\begin{center}
{\small
%\hskip.3in
\includegraphics*[bb=160 353 420 526]{../template/report/ps-and-eps/jcg-baserot.ps}
\qquad
%\hskip.3in 
\includegraphics*[bb=170 354 420 530]{../template/report/ps-and-eps/jcg-cc13rot.ps}
}
\caption[Final energy {\it vs.} time: baseline]{Final energy {\it vs} time for different phase rotation systems: a) baseline; b) with IL2 removed.}
\label{phaserots1}
\end{center}
\end{figure}
\begin{figure}[!hbt]
\begin{center}
{\small
%\hskip.3in
\includegraphics*[bb=170 354 420 530]{../template/report/ps-and-eps/jcg-cc23rot.ps}
%\hskip.3in
\qquad
\includegraphics*[bb=170 354 420 530]{../template/report/ps-and-eps/jcg-cc3rot.ps}
}
\caption[Final energy \textit{vs.} time: IL1 and IL2 removed]{Final energy {\it vs} time for different phase rotation systems: c) without IL1;   d) without IL1 and IL2.}
\label{phaserots2}
\end{center}
\end{figure}
\clearpage
\begin{figure}[!hbt]
\begin{center}
%\input{cc.fig}
\includegraphics*[bb=96 258 426 500,clip]{../template/report/ps-and-eps/jcg-cc.ps}
\caption[Efficiency \textit{vs.} length of induction linacs ]{Efficiency \textit{vs.} length of induction linacs. The $\mu$/p ratio that characterizes the performance of the front end is measured at the end of the cooling channel.}
\label{muvsind}
\end{center}
\end{figure}
Further cost savings could be achieved if one or more of the linacs
 were eliminated and the remaining linacs re-optimized. This has been
 studied assuming a fixed geometrical layout, so that the option of upgrading 
to the original baseline design is retained. Figures~\ref{phaserots1} and 
~\ref{phaserots2} show
 3 such cases, together with the baseline design. Figure~\ref{muvsind}
 shows the muon production efficiency (at the end of the cooling channel) for 
the four cases, plotted
 against the sum of the lengths of the remaining linacs. The losses in
 efficiency are large if  the first linac is eliminated, but less
 severe (11\%) if only the second linac is removed. Removing IL2 would provide a cost saving of about 4\%, so its presence is favorable from a cost-benefit standpoint.

\subsection{Cooling}
\subsubsection{Cost:  Less Cooling}

Figure~\ref{muvscool} shows the muon production into the defined accelerator acceptance as a function of length.
Table~\ref{muvscooltab} shows the values for three cooling lengths.
It is seen that a reduction in cooling length from 108 to 88~m, which would offer significant savings, reduces the performance by only 3.4\%. Looked at in terms of marginal costs, however, we note that the baseline scenario still appears cost effective.
\begin{table}[!hbt]
\begin{center}
\caption{Efficiency for three cooling lengths.}
\vspace{1mm}
\begin{tabular}{|c|ccc|}
\hline
Cooling length&  $\mu$/p& Loss& Savings   \\
     (m) & &(\%)&(\%)\\
\hline
108&0.174&0&0\\
88&0.168&3.4&2.5\\
68 & 0.150& 13.8&6.7\\
%48 & 0.124  &29   \\
\hline
\end{tabular}
\label{muvscooltab}
\end{center}
\end{table}

\begin{figure}[!hbt]
\begin{center}
%\input{s7ecfig.fig}
\includegraphics*[bb=139 321 447 541,clip]{../template/report/ps-and-eps/jcg-s7ecfig.ps}
\caption{Efficiency \textit{vs.} length of cooling.}
\label{muvscool}
\end{center}
\end{figure}

\subsubsection{ Cost: Fixed Field Alternating Gradient}
Fixed Field Alternating Gradient (FFAG) acceleration offers the
possibility of savings. There would be no multiple arcs,
and no switchyards: the lattice would have a large enough momentum
acceptance to circulate the muons from initial to final energy. The
number of turns could now be raised, limited only by muon decay
considerations, thus lowering the needed rf acceleration per turn.

Lattices have been designed with momentum acceptances of more than a factor of
2-3. Injection and extraction would be performed using kickers.
Designs being studied at KEK~\cite{kekffag} employ low frequency, low
accelerating gradient rf and accept relatively large decay loss. Work
in the US~\cite{usffag} has concentrated mainly on higher gradient
superconducting rf with fewer turns and less loss. The main problem in
this approach is assuring that the rf phase is set correctly at each pass. The
ideal solution is a ring that is exactly isochronous, but the best
current designs are less than ideal and require phase control of the
rf corresponding to frequency variations of the order of
$10^{-4}$. This would be easy for conventional rf, but is difficult in
a superconducting cavity. The use of ferrites weakly coupled to such
cavities is being studied.
\subsection{Summary}
Although we believe that the current Study-II baseline represents a
feasible and reasonably costed high performance design, there are many
possibilities for cost reduction that could be considered for an initial implementation.
\begin{thebibliography}{99}
\bibitem{wrapped}J.~Rice, DoE SBIR Phase I Final Report, \textsl{Ceramic Insulation for Heavy Ion Fusion and Other High Radiation Magnets}, DoE Grant No. DE-FG03-00ER82979 (2000).

 \bibitem{kekffag}Y.~Mori, \textsl{KEK FFAG Program}, presented at NUFACT01\\
\verb+http:\\www-prism.kek.jp/nufact01/May25/WG3/25wg3_mori.pdf+.

\bibitem{usffag}C.~Johnstone, \textsl{US FFAG Program}, unpublished.
\end{thebibliography}


%\end{document}
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