\chapter{Costs and Staging Options}

\label{costs}

\section{Costs}

\subsection{Methodology}

We have specified each system of the Study-II Neutrino Factory in sufficient
detail to obtain a ``top-down'' cost estimate for it. Clearly this estimate
is not the complete and detailed cost estimate that would come from
preparing a full Conceptual Design Report (CDR). However, there is
considerable experience in designing and building accelerators with similar
components, so we have a substantial knowledge base from which costs can be
derived. The costs summarized here were obtained mainly in that way.

Where available, we have used costs from existing components---scaled as
needed to reflect essential changes---to represent the expected costs to
fabricate what we need. This applies to the Proton Driver, the
superconducting and normal conducting magnets and their power supplies, the
rf cavities, and conventional facilities and utilities. In some cases, we
were able to take advantage of experience in designing similar components in
a different context. For example, the target facility we require closely
resembles that needed for the Spallation Neutron Source (SNS) project at
ORNL, for which detailed CDR-level designs already exist and construction is
under way. The superconducting target solenoid is not a standard device, but
there is a magnet of similar size and field strength, designed for the ITER
project, that serves as a convenient scaling model. In the case of rf power
sources, we made use of the multi-beam klystron (MBK) example developed at
DESY for TESLA, along with expertise in developing other high-power tubes at
U.S. Laboratories. For devices such as the MBK, which are a significant
extrapolation from existing hardware, allowance was made for a substantial
development program, whose cost was amortized over the initial complement of
devices needed for the Neutrino Factory.

\subsection{Facility Costs}

The Neutrino Factory design we describe here favors feasibility over cost
reduction. Thus, we do not claim to present a fully cost-optimized design,
nor one that has been reviewed from the standpoint of ``value engineering.''
\ In that sense, there is hope that a detailed design study will \textit{
reduce} the costs compared with what we estimate here. We have put in an
allowance of 10\% for each of the systems to account for things we have not
considered in detail at this stage. \ Only direct costs are included here,
that is, the estimates do not contain allowances for EDIA, laboratory
overhead burdens, or contingency. The breakdown by system is summarized in
Table~\ref{costtotal}; these costs are given in FY01 dollars. However, to
facilitate comparison with the Feasibility Study-I estimate, in the last
column of Table~\ref{costtotal} we converted our costs to FY00 dollars,
using the DOE-approved inflation factor of 2.5\%.

It is interesting to compare our estimate with that of Study-I; in this
study, we have improved the performance by a factor of six over that reached
in Study-I, at a total cost (estimated in the same way for both designs) of
about 3/4 of that in the original study. This is an encouraging trend and,
as noted, we have some hope that it will continue.

\begin{table}[tbp]
\caption[Construction costs for Study-II Neutrino Factory]{Summary of
construction cost totals for Study-II Neutrino Factory. All costs are in
FY01 dollars unless otherwise noted.}
\begin{center}
\begin{tabular}{lcccc}
\hline
{\small System} & {\small Sum} & {\small Others$^{a}$} & {\small Total} & 
{\small Reconciliation$^{b}$} \\ 
& {\small (\$M)} & {\small (\$M)} & {\small (\$M)} & {\small (FY00 \$M)} \\ 
\hline
{\small Proton Driver} & \multicolumn{1}{r}{168.0} & \multicolumn{1}{r}{16.8}
& \multicolumn{1}{r}{184.8} & \multicolumn{1}{r}{180.0} \\ 
{\small Target Systems} & \multicolumn{1}{r}{92.0} & \multicolumn{1}{r}{9.2}
& \multicolumn{1}{r}{101.2} & \multicolumn{1}{r}{98.0} \\ 
{\small Decay Channel} & \multicolumn{1}{r}{4.6} & \multicolumn{1}{r}{0.5} & 
\multicolumn{1}{r}{5.1} & \multicolumn{1}{r}{5.0} \\ 
{\small Induction Linacs} & \multicolumn{1}{r}{319.0} & \multicolumn{1}{r}{
31.9} & \multicolumn{1}{r}{350.9} & \multicolumn{1}{r}{343.0} \\ 
{\small Bunching} & \multicolumn{1}{r}{69.0} & \multicolumn{1}{r}{6.9} & 
\multicolumn{1}{r}{75.9} & \multicolumn{1}{r}{74.0} \\ 
{\small Cooling Channel} & \multicolumn{1}{r}{317.0} & \multicolumn{1}{r}{
31.7} & \multicolumn{1}{r}{348.7} & \multicolumn{1}{r}{340.0} \\ 
{\small Pre-accel. linac} & \multicolumn{1}{r}{189.0} & \multicolumn{1}{r}{
18.9} & \multicolumn{1}{r}{207.9} & \multicolumn{1}{r}{203.0} \\ 
{\small RLA} & \multicolumn{1}{r}{355.0} & \multicolumn{1}{r}{35.5} & 
\multicolumn{1}{r}{390.5} & \multicolumn{1}{r}{381.0} \\ 
{\small Storage Ring} & \multicolumn{1}{r}{107.0} & \multicolumn{1}{r}{10.7}
& \multicolumn{1}{r}{117.7} & \multicolumn{1}{r}{115.0} \\ 
{\small Site Utilities} & \multicolumn{1}{r}{127.0} & \multicolumn{1}{r}{12.7
} & \multicolumn{1}{r}{139.7} & \multicolumn{1}{r}{136.0} \\ \hline\hline
{\small Totals} & \multicolumn{1}{r}{1,747} & \multicolumn{1}{r}{175} & 
\multicolumn{1}{r}{1,922} & \multicolumn{1}{r}{1,875} \\ \hline
\multicolumn{5}{l}{$^{a}${\small Others is 10\% of each system to account
for missing items,}} \\ 
\multicolumn{5}{l}{\small as was used in Study-I.} \\ 
\multicolumn{5}{l}{$^{b}${\small Reconciliation represents the Study-II
costs given in FY00}} \\ 
\multicolumn{5}{l}{\small dollars to permit direct comparison with Study-I
costs.} \\ 
\multicolumn{5}{l}{\small The inflation factor used (1/1.025) is per DOE
official rates.}
\end{tabular}
\end{center}
\label{costtotal}
\end{table}

\section{Staging Options\label{StagingOps}}

During the HEPAP sub-panel presentations on Neutrino Factory R\&D that took
place at BNL on April 19, 2001, the MC was asked to discuss the time scale
for arriving at a Muon Collider, and to outline possible staging options
that would lead to a high-performance Neutrino Factory and, at a later date,
a Muon Collider. The discussion below supplements our response to these
questions.

The collaboration has now completed two detailed ``Feasibility Studies'' of
Neutrino Factories. These studies included end-to-end simulations of the
non-conventional parts of the facilities, and sufficient engineering studies
to form the basis for defensible R\&D plans. The schedule presented
indicated that, with adequate R\&D support, construction of a Neutrino
Factory could begin in 2007. Depending upon available resources, this could
be either a complete high-performance Neutrino Factory capable of searching
for CP violation in the lepton sector, or a more modest first step that
would address many outstanding neutrino oscillation questions, and would be
upgradeable in a staged manner to a high-performance facility.

Expanding on the staging possibilities that could be considered as we
proceed toward a Neutrino Factory, we note that there are a number of
options:

\begin{enumerate}
\item  A high-intensity Proton Driver that could be used to provide an
upgraded conventional neutrino ``superbeam'' and also to support a new round
of kaon experiments if desired. We believe construction of the Proton
Driver, based on either the BNL AGS or the FNAL proton source, could begin
in 2--3 years and be completed within 4--5 years from today.

\item  A very high intensity, low energy, muon source making about 10$^{21}$
muons per year available for stopped muon experiments. This might enable $
\mu $ $\rightarrow $ e conversion, for example, to be probed with a
sensitivity exceeding that of the MECO experiment by several orders of
magnitude, and could also support a broad physics community beyond
high-energy physics. We believe construction of the muon facility could
begin 7--8 years from now, or even sooner (in parallel with construction of
the proton source) if it were deemed to have sufficiently high priority.
\end{enumerate}

In addition to the MC work on a Neutrino Factory, we are committed to
developing the technology required for a Muon Collider. Indeed, it was our
interest in Muon Colliders that led us initially to study the production of
intense muon beams. By focusing on the easier problem of the Neutrino
Factory, we have made more rapid progress and, at the same time, established
many of the technologies needed for the Collider. However, this approach has
resulted in a considerable difference in our level of understanding of the
two types of facility.

Unlike the situation for the Neutrino Factory, we do not yet have a complete
scenario, with parameters and chosen technologies, for the Collider. As a
result, we have no end-to-end simulations, little engineering, and no cost
estimates. Many of the required components are natural extensions of those
used in a Neutrino Factory, but some are specific to the Collider (e.g.,
emittance exchange and the Collider ring itself), and many involve large
extrapolations from the Neutrino Factory parameter regime (e.g., the total
amount of cooling, the final beam emittance, the charge per bunch). There
are ideas of how a Collider scenario might look, and there has been
substantial progress on possible technologies for some of these components
(e.g., a ring cooler that would give emittance exchange, and lithium lens
cooling to the required very small final emittance). However, these studies
are far from complete. Thus, we are not yet in a position to conduct the
``feasibility'' study that would be needed to make a complete R\&D plan for
this new and exciting machine.

Before we can reach the feasibility study stage, we must establish robust
technical solutions to emittance exchange, issues related to the high bunch
charges, techniques for cooling to the required final emittances, and the
design of a very low $\beta $* collider ring. We are confident that
solutions exist along the lines we have been investigating, but at present
we do not have enough R\&D support to adequately pursue both the Collider
studies and the Neutrino Factory design studies. Unless and until we obtain
such support, it is hard to predict how long it will take to solve the
emittance exchange and other collider-specific problems---it could be very
soon, or it could be a much longer time.

In view of the above, it should be clear that any estimated time scale
quoted for a Muon Collider has considerable uncertainty. The MC has
previously presented one time scale, based on particular assumptions that
the R\&D for the Collider would mainly follow that for the Neutrino Factory.
Clearly, with more optimistic assumptions a significantly faster time scale
might be possible. We have gone through the exercise of considering such
schedules, and they have the potential to reduce the time to start physics
at a Muon Collider by many years. \ On the other hand, it is also
possible---given the conceptual and technical uncertainties and the current
limits on funding---that the real time scale will be longer.

We in the MC are eager to advance to the stage of building a Muon Collider
on the earliest possible time scale. However, for that to happen there is an
urgent need to greatly increase support for our R\&D so that we can address
the vital issues.

As discussed above, it seems quite possible---perhaps even likely---that the
Neutrino Factory would be built in stages, both for programmatic and for
cost reasons. In what follows we outline a possible staging concept that
provides good physics opportunities with reasonable cost increments. The
staging scenario we consider here is not unique, nor is it necessarily
optimized. Discussions at Snowmass will serve to sharpen the thoughts of the
physics community on what is an optimal staging scenario. Depending on the
results of our technical studies and the results of continued searches for
the Higgs boson, it is hoped that the Neutrino Factory is really the
penultimate stage, to be followed later by a Muon Collider (Higgs Factory).
We assume this scenario in the staging discussion that follows.

Because the physics program would be different at different stages, it is
impractical at this time to consider detector costs. \ Therefore, none of
the costs listed in Section \ref{StagingOps} include any detector costs. To
better represent the incremental costs of a staged approach, utility costs,
which are called out separately in Table \ref{costtotal}, have been
apportioned among the various stages.

\subsection{Stage 1}

In the first stage, we envision a Proton Driver and a Target Facility to
create superbeams. The Driver could begin with a 1 MW beam level (Stage 1)
or could be designed from the outset to reach 4 MW (Stage 1a). (Since the
cost differential between 1 and 4 MW is not large, we do not consider any
intermediate options here.) Because the Proton Driver design is site
specific, cost estimates are slightly different for the BNL and FNAL
options. The Target Facility cost we take from Study-II (see Table \ref
{costtotal}). It is assumed, as was the case for both Study-I and Study-II,
that the Target Facility is built from the outset to accommodate a 4 MW
beam. \ Based on the Study-II results, a 1 MW beam would provide about $
1.2\times 10^{14}$ $\mu $/s ($1.2\times 10^{21}$ $\mu $/year) and a 4 MW
beam about $5\times 10^{14}$ $\mu $/s ($5\times 10^{21}$ $\mu $/year) into a
solenoid channel.

Costs for Stage 1 are summarized in Table \ref{costs1}. If a horn were used
in place of the Study-II solenoid capture system, the intensities may
decrease but the potential cost savings might be in the range of \$30--40M.
This option has not been explored in our Studies to date, and we have not
yet assessed the feasibility of using a horn for the 4 MW scenario. As noted
earlier, the costs in Table \ref{costs1} are only facility costs and do not
include detectors.

In addition to the neutrino program, this stage will also benefit $\pi $, $K$
, and $\overline{p}$ programs, as discussed in~\cite{proton-physics,low-pbar}

\begin{table}[tbp]
\caption[Stage 1 cost estimates]{Stage 1 cost estimates.}
\begin{center}
\begin{tabular}{lllc}
\hline
& BNL option & FNAL 16-GeV option & FNAL 8-GeV option \\ 
& \multicolumn{1}{c}{(\$M)} & \multicolumn{1}{c}{(\$M)} & (\$M) \\ 
\cline{2-4}
1 MW & \multicolumn{1}{c}{310} & \multicolumn{1}{c}{330} & 250 \\ 
4 MW & \multicolumn{1}{c}{400} & \multicolumn{1}{c}{410} & 330 \\ \hline
\end{tabular}
\end{center}
\label{costs1}
\end{table}

\subsection{Stage 2}

In Stage 2, we envision a muon beam that has been phase rotated (to give a
reasonably low momentum spread) and transversely cooled. \ In the notation
of Study-II, this stage takes us to the end of the cooling channel. Thus, we
have access to a muon beam with a central momentum of about 200 MeV/$c$, a
transverse (normalized) emittance of 2.7 mm-rad and an rms energy spread of
about 4.5\%. The intensity of the beam would be about $4\times 10^{13}$ $\mu 
$/s ($4\times 10^{20}$ $\mu $/year) at 1 MW, or $1.7\times 10^{14}$ $\mu $/s
($1.7\times 10^{21}$ $\mu $/year) at 4 MW. The \textit{incremental} cost of
this option is \$840M, based on assuming the cooling channel length adopted
in Study-II. If more intensity were needed, and if less cooling could be
tolerated, the length of the cooling channel could be reduced. \ As an
example, stopping at the end of Lattice 1 instead of the end of Lattice 2
would decrease the incremental cost by about \$180M, with the penalty of
roughly doubling the transverse emittance.

\subsection{Stage 3}

In Stage 3, we envision using the Pre-acceleration Linac to raise the beam
energy to roughly 2.5 GeV. \ The incremental cost of this option is about
\$220M. At this juncture, it may be appropriate to consider a small storage
ring, comparable to the $g-2$ ring at BNL, to be used for the next round of
muon $g-2$ experiments. This ring would, in some sense, be a throw-away
device. \ No cost estimate has been made for this ring, but it would be
expected to cost a few tens of millions. For the present purpose, we take
the cost of such a ring, which we refer to as Stage 3a, as \$30M.

\subsection{Stage 4}

At Stage 4, we envision having a complete Neutrino Factory operating with a
20 GeV storage ring. The incremental cost of this stage, which includes the
RLA and the storage ring, is \$550M. If it were necessary to provide a 50
GeV muon beam as Stage 4a, an additional RLA and a larger storage ring would
be needed. \ The incremental cost to go from Stage 4 to Stage 4a would be an
additional \$700--800M.

Table \ref{Stagecosts} summarizes the incremental costs for each stage of a
Neutrino Factory, exclusive of detector costs.

\begin{table}[tbp]
\caption[Incremental costs for Neutrino factory stages]{Estimated
incremental costs for various possible project stages leading to a Neutrino
Factory, based on the cost estimate from Table \ref{costtotal}. Utility
costs were prorated among the various stages.}
\begin{center}
\begin{tabular}{lc}
\hline
Stage & Incremental Cost \\ 
& (\$M) \\ \cline{2-2}
1 (1 MW Proton Driver) & 250--330 \\ 
1a (4 MW Proton Driver) & 80 \\ 
2 (Cooled muons, 200 MeV/$c$) & 660--840 \\ 
3 (2.5 GeV muons) & 220 \\ 
3a ($g-2$ storage ring) & 30 \\ 
4 (20-GeV Neutrino Factory) & 550 \\ 
4a (50-GeV Neutrino Factory) & 700--800 \\ \hline
\end{tabular}
\end{center}
\label{Stagecosts}
\end{table}

\subsection{Stage 5}

In Stage 5, we can envision an entry level Muon Collider to operate as a
Higgs Factory. No cost estimate has yet been prepared for this stage, so we
mention here only the obvious ``cost drivers.'' First, the initial muon beam
must be prepared as a single bunch of each charge. This may involve an
additional ring for the proton driver to coalesce proton bunches into a
single pulse. The cooling will have to be significantly augmented. First, a
much lower transverse emittance is needed, and second, it will be necessary
to provide emittance exchange to maintain a reasonable transmission of the
muons. The additional cooling will permit going to smaller solenoids and
higher frequency rf systems (402.5 or perhaps 805 MHz), which should lower
the incremental cost somewhat. Next, we will need considerably more
acceleration, though with smaller energy acceptance and aperture
requirements than at present. Lastly, we will need a very low $\beta ^{\ast
} $ lattice for the storage ring, along with mitigation of the potentially
copious background levels near the interaction point. In this case the
detector is, in effect, part of the Collider and cannot be ignored in terms
of its cost impact.

Of the items mentioned, it is likely that the additional cooling and the
additional acceleration are the most significant cost drivers. Future work
will define the system requirements better and permit a cost estimate of the
same type provided for Studies-I and -II.


