% Mike's new version, received Jan.9
\section{ Neutrino Factory}

\label{neufact}

In this Section we describe the various components of a Neutrino Factory,
based on the most recent Feasibility Study (Study-II)~\cite{EPP:studyii}
that was carried out jointly by BNL and the MC. We also describe the stages
that could be constructed incrementally to provide a productive physics
program that evolves eventually into a full-fledged Neutrino Factory.
Details of the design described here are based on the specific scenario of
sending a neutrino beam from Brookhaven to a detector in Carlsbad, New
Mexico. More generally, however, the design exemplifies a Neutrino Factory
for which our two Feasibility Studies demonstrated technical feasibility
(provided the challenging component specifications are met), established a
cost baseline, and established the expected range of physics performance. As
noted earlier, this design typifies a Neutrino Factory that could fit
comfortably on the site of an existing laboratory, such as BNL or FNAL.

A list of the main ingredients of a Neutrino Factory is given below: 

\begin{itemize}
\item  \textbf{Proton Driver:} Provides 1--4 MW of protons on target from an
upgraded AGS; a new booster at Fermilab would perform equivalently.

\item  \textbf{Target and Capture:} A high-power target immersed in a 20-T
superconducting solenoidal field to capture pions produced in proton-nucleus
interactions.

\item  \textbf{Decay and Phase Rotation:} Three induction linacs, with
internal superconducting solenoidal focusing to contain the muons from pion
decays, that provide nearly non-distorting phase rotation; a
``mini-cooling'' absorber section is included after the first induction
linac to reduce the beam emittance and lower the beam energy to match the
downstream cooling channel acceptance.

\item  \textbf{Bunching and Cooling:} A solenoidal focusing channel, with
high-gradient rf cavities and liquid-hydrogen absorbers, that bunches the
250~MeV/c muons into 201.25-MHz rf buckets and cools their transverse
normalized rms emittance from 12 mm$\cdot $rad to 2.7 mm$\cdot $rad.

\item  \textbf{Acceleration:} A superconducting linac with solenoidal
focusing to raise the muon beam energy to 2.48 GeV, followed by a four-pass
superconducting RLA to provide a 20 GeV muon beam; a second RLA could
optionally be added to reach 50 GeV, if the physics requires this.

\item  \textbf{Storage Ring:} A compact racetrack-shaped superconducting
storage ring in which $\approx $35\% of the stored muons decay toward a
detector located about 3000 km from the ring.
\end{itemize}

\subsection{Proton Driver}

The proton driver considered in Study-II is an upgrade of the BNL
Alternating Gradient Synchrotron (AGS) and uses most of the existing
components and facilities; parameters are listed in Table~\ref{Proton:tb1}.
To serve as the proton driver for a Neutrino Factory, the existing booster
is replaced by a 1.2-GeV superconducting proton linac. The modified layout
is shown in Fig.~\ref{Proton:bnl}. 
\begin{figure}[tbh]
\begin{center}
\includegraphics[width=5.5in]{Proton_driver_bnl.eps}
\end{center}
\caption{AGS proton driver layout.}
\label{Proton:bnl}
\end{figure}
\begin{figure}[tbh]
\begin{center}
\includegraphics[width=5.5in]{Proton_driver_fnal.eps}
\end{center}
\caption{FNAL proton driver layout from Ref. \protect\cite{FNALbooster}.}
\label{Proton:fnal}
\end{figure}
The AGS repetition rate is increased from 0.5 Hz to 2.5 Hz by adding power
supplies to permit ramping the ring more quickly. No new technology is
required for this---the existing supplies are replicated and the magnets are
split into six sectors rather than the two used presently. The total proton
charge (10$^{14}$ ppp in six bunches) is only 40\% higher than the current
performance of the AGS. However, due to the required short bunches, there is
a large increase in peak current and concomitant need for an improved vacuum
chamber; this is included in the upgrade. The six bunches are extracted
separately, spaced by 20 ms, so that the target, induction linacs, and rf
systems that follow need only deal with single bunches at an instantaneous
repetition rate of 50 Hz (average rate of 15 Hz). The average proton beam
power is 1 MW. A possible future upgrade to 2 $\times $10$^{14}$ ppp and 5
Hz could give an average beam power of 4 MW. At this higher intensity, a
superconducting bunch compressor ring would be needed to maintain the rms
bunch length at 3 ns.

If the facility were built at Fermilab, the proton driver would be a newly
constructed 16-GeV rapid cycling booster synchrotron~\cite{FNALbooster}. The
planned facility layout is shown in Fig.~\ref{Proton:fnal}. The initial beam
power would be 1.2 MW, and a future upgrade to 4 MW would be possible. The
Fermilab design parameters are included in Table~\ref{Proton:tb1}. A less
ambitious and more cost-effective 8-GeV proton driver option has also been
considered for Fermilab \cite{FNALbooster}; this too might be the basis for
a proton driver design.

\begin{table}[tbh]
\caption{Proton driver parameters for BNL and FNAL designs.}
\label{Proton:tb1}
\begin{center}
\begin{tabular}{|l|c|c|}
\hline
& BNL & FNAL \\ \cline{2-3}
Total beam power (MW) & 1 & 1.2 \\ 
Beam energy (GeV) & 24 & 16 \\ 
Average beam current ($\mu $A) & 42 & 72 \\ 
Cycle time (ms) & 400 & 67 \\ 
Number of protons per fill & $1\times 10^{14}$ & $3\times 10^{13}$ \\ 
Average circulating current (A) & 6 & 2 \\ 
No. of bunches per fill & 6 & 18 \\ 
No. of protons per bunch & $1.7\times 10^{13}$ & $1.7\times 10^{12}$ \\ 
Time between extracted bunches (ms) & 20 & 0.13 \\ 
Bunch length at extraction, rms (ns) & 3 & 1 \\ \hline
\end{tabular}
\end{center}
\end{table}

\subsection{Target and Capture}

A mercury jet target is chosen to give a high yield of pions per MW of
incident proton power. The 1-cm-diameter jet is continuous, and is tilted
with respect to the beam axis. The target layout is shown in Fig.~\ref{tgtc}.  
\begin{figure}[tbh]
\begin{center}
%\input{tgtc.fig}
\includegraphics*[width=4in]{tgt2.ps}
\end{center}
\caption[Target, capture solenoids and mercury containment ]{Target, capture
solenoids and mercury containment.}
\label{tgtc}
\end{figure}
We assume that the thermal shock from the interacting proton bunch fully
disperses the mercury, so the jet must have a velocity of 20--30 m/s to be
replaced before the next bunch. Calculations of pion yields that reflect the
detailed magnetic geometry of the target area have been performed with the
MARS code~\cite{MARSstudyii}. To avoid mechanical fatigue problems, a
mercury pool serves as the beam dump. This pool is part of the overall
target---its mercury is circulated through the mercury jet nozzle after
passing through a heat exchanger.

Pions emerging from the target are captured and focused down the decay
channel by a solenoidal field that is 20 T at the target center, and tapers
down, over 18 m, to a periodic (0.5-m) superconducting solenoid channel ($%
B_{z}$ = 1 .25 T) that continues through the phase rotation to the start of
bunching. The 20-T solenoid, with a resistive magnet insert and
superconducting outer coil, is similar in character to the higher field (up
to 45 T), but smaller bore, magnets existing at several laboratories \cite
{ITERmag}. The magnet insert is made with hollow copper conductor having
ceramic insulation to withstand radiation. MARS~\cite{MARSstudyii}
simulations of radiation levels show that, with the shielding provided, both
the copper and superconducting magnets could have a lifetime greater than 15
years at 1 MW.

In Study-I, the target was a solid carbon rod. At high beam energies, this
implementation has a lower pion yield than the mercury jet, and is expected
to be more limited in its ability to handle the proton beam power, but
should simplify the target handling issues that must be dealt with. At lower
beam energies, say 6 GeV, the yield difference between C and Hg essentially
disappears, so a carbon target would be a competitive option with a lower
energy driver. Present indications \cite{Ref:ORNLtgt} are that a
carbon-carbon composite target can be tailored to tolerate even a 4 MW
proton beam power---a very encouraging result. Other alternative approaches,
including a rotating Inconel band target, and a granular Ta target are also
under consideration, as discussed in Study-II \cite{EPP:studyii}. Clearly
there are several target options that could be used for the initial facility.

\subsection{Phase Rotation}

Pions, and the muons into which they decay, are generated in the target over
a very wide range of energies, but in a short time pulse ($\approx $3 ns
rms). This large energy spread is ``phase rotated,'' using drifts and
induction linacs, into a pulse with a longer time duration and a lower
energy spread. The muons first drift and spread out in time, after which the
induction linacs decelerate the early ones and accelerate the later ones.
Three induction linacs (with lengths of 100, 80, and 80 m) are used in a
system that reduces distortion in the phase-rotated bunch, and permits all
induction units to operate with unipolar pulses. The 1.25-T beam transport
solenoids are placed inside the induction cores to avoid saturating the core
material, as shown in Fig.~\ref{CandPR:fg1}. 
\begin{figure}[tbh]
\begin{center}
\includegraphics*[width=4in]{Phase_Rot1.eps}
\end{center}
\caption[Induction cell and mini-cooling solenoid]{Cross section of the
induction cell and mini-cooling solenoids.}
\label{CandPR:fg1}
\end{figure}
The induction units are similar to those being built for DARHT~\cite{daarht}.

Between the first and second induction linacs, two LH$_{2}$ absorbers (each
1.7 m long and 30 cm radius), with a magnetic field reversal between them,
are introduced to reduce the transverse emittance and lower the beam energy
to a value matched to the downstream cooling channel acceptance
(``mini-cooling''). The beam at the end of the phase rotation section has an
average momentum of about 250 MeV/c and an rms fractional energy spread of 
approximately 4.4\%.

\subsection{Buncher}

The long beam pulse (400 ns) after the phase rotation is then bunched at
201.25 MHz prior to cooling and acceleration at that frequency. The bunching
is done in a lattice identical to that at the start of the cooling channel,
and is preceded by a matching section from the 1.25-T solenoids into this
lattice. The bunching has three stages, each consisting of rf (with
increasing acceleration) followed by drifts (with decreasing length). In the
first two rf sections, second-harmonic 402.5-MHz rf is used together with
the 201.25 MHz primary frequency to improve the capture efficiency. The
402.5-MHz cavities are designed to fit into the bore of the focusing
solenoids, in the location corresponding to that of the LH$_{2}$ absorber in
the downstream cooling channel.

\subsection{Cooling}

Transverse emittance cooling is achieved by lowering the beam energy in LH$_{2}$ absorbers, interspersed with rf acceleration to keep the average
energy constant. Transverse and longitudinal momenta are lowered in the
absorbers, but only the longitudinal momentum is restored by the rf. The
emittance increase from Coulomb scattering is minimized by maintaining the
focusing strength such that the angular spread of the beam at the absorber
locations is large. This is achieved by keeping the focusing strength
inversely proportional to the emittance,\textit{\ i.e.}, increasing it as
the emittance is reduced. A modified Focus-Focus (SFOFO)~\cite{EPP:refsfofo}
lattice is employed. The solenoidal fields in each cell alternate in sign,
and the field shape is chosen to maximize the momentum acceptance ($\pm $%
22\%). To maintain the tapering of the focusing, it was necessary to reduce
the cell length from 2.75 m in the initial portion of the channel to 1.65 m
in the final portion. A layout of the shorter cooling cell is shown in Fig.~\ref{RF:fg18.Q}.

\begin{figure}[hbt!]
\begin{center}
\includegraphics[width=4in]{rf_fg19.eps}
\end{center}
\caption{Cooling channel Lattice 2, two cavities per cell.}
\label{RF:fg18.Q}
\end{figure}

Figure~\ref{EmittCool} shows a simulation of cooling; the transverse 
emittance falls
along the length of the channel. The increase in the number of muons that
fit within the acceptance of the downstream acceleration channel is shown in
Fig.~\ref{YieldCool}. 
\begin{figure}[tbh]
\begin{center}
%\leavevmode
\includegraphics*[width=100mm]{Emitt2D-211.eps}
\end{center}
\caption[The longitudinal and transverse emittances]{The longitudinal and
transverse emittances, obtained with the Geant4~\cite{GEANT4} simulation code, as a
function of channel length. The length of the 
lattice  was extended by $\approx $%
20~m to investigate the ultimate performance of the cooling channel.}
\label{EmittCool}
\end{figure}
\begin{figure}[tbh]
\begin{center}
\includegraphics*[width=100mm]{MuOPInAcc-211.eps}
\end{center}
\caption[$\protect\mu /p$ yield ratio for the two transverse emittance
cuts]{ Geant4 simulations of the muon-to-proton yield ratio for two
transverse emittance cuts, clearly showing that the channel cools,
\textit{i.e.}, the density in the center of the phase space region
increases.  $\protect\mu /$p$_{15}$ ($\protect\mu /$p$_{9.75}$) is the
muon to proton yield after a cut of 15 (9.75) mm on the transverse
phase space.  Since the relevant yield $\protect\mu /$p$_{15}$ no
longer increases for $z\geq 110$~m, the channel length was set to
108~m.}
\label{YieldCool}
\end{figure}

\subsection{Acceleration}

Parameters of the acceleration system are listed in Table~\ref{tab:acc:parm}. A 20-m SFOFO matching section, using normal conducting rf systems, matches
the beam optics to the requirements of a 2.5 GeV superconducting rf linac
with solenoidal focusing. The linac is in three parts. The first part has a
single 2-cell rf cavity unit per period. The second part, as a longer period
becomes possible, has two 2-cell cavity units per period. The last section,
with still longer period, accommodates four 2-cell rf cavity units per
period. Figure~\ref{fig:acc:cryomod} shows the three cryomodule types that
make up the linac. 
\begin{figure}[tbh]
\centering\includegraphics[angle=270,width=4.0in]{accel-010307-f03.eps}
\caption[Layouts of cryomodules.]{Layouts of short (top), intermediate
(middle) and long (bottom) cryomodules. Blue lines are the SC walls of the
cavities. Solenoid coils are indicated in red.}
\label{fig:acc:cryomod}
\end{figure}

This linac is followed by a single, four-pass recirculating linear
accelerator (RLA) that raises the energy from 2.5 GeV to 20 GeV. The RLA
uses the same layout of four 2-cell superconducting rf cavity structures as
the long cryomodules in the linac, but utilizes quadrupole triplet focusing,
as indicated in Fig.~\ref{fig:acc:rlalinac}. The arcs have an average radius
of 62 m. The final arc has a dipole field of 2 T. 
\begin{figure}[!tbh]
\centering\includegraphics[angle=270,width=4.0in]{accel-010307-f28.eps}
\caption{Layout of an RLA linac period.}
\label{fig:acc:rlalinac}
\end{figure}

In Study-I, where the final beam energy was chosen to be 50 GeV, a second
RLA is needed. This second RLA is similar to the RLA just described, but
considerably larger.

\begin{table}[tbh]
\caption{Main parameters of the muon accelerator.}
\label{tab:acc:parm}
\begin{center}
\begin{tabular}{|l|c|}
\hline
Injection momentum (MeV/c)/Kinetic energy (MeV) & 210/129.4 \\ 
Final energy (GeV) & 20 \\ 
Initial normalized transverse acceptance (mm-rad) & 15 \\ 
\quad rms normalized transverse emittance (mm-rad) & 2.4 \\ 
Initial longitudinal acceptance, $\Delta pL_{b}/m_{\mu }$ (mm) & 170 \\ 
\quad momentum spread, $\Delta p/p$ & $\pm 0.21$ \\ 
\quad bunch length, $L_{b}$ (mm) & $\pm 407$ \\ 
\quad rms energy spread & 0.084 \\ 
\quad rms bunch length (mm) & 163 \\ 
Number of bunches per pulse & 67 \\ 
Number of particles per bunch\textbf{/}per pulse & $4.4\times 10^{10}$ 
\textbf{/}$3\times 10^{12}$ \\ 
Bunch frequency\textbf{/}accelerating frequency (MHz) & 201.25\textbf{/}
201.25 \\ 
Average beam power (kW) & 150 \\ \hline
\end{tabular}
\end{center}
\end{table}

\subsection{Storage Ring}

After acceleration in the RLA, the muons are injected into the upward-going
straight section of a racetrack-shaped storage ring with a circumference of
358 m. Parameters of the ring are summarized in Table~\ref{SRING:tb}.
High-field superconducting arc magnets are used to minimize the arc length
and maximize the fraction (35\%) of muons that decay in the downward-going
straight, generating neutrinos headed toward the detector located some 3000
km away.

All muons are allowed to decay; the maximum heat load from their decay
electrons is 42 kW (126 W/m). This load is too high to be dissipated in the
superconducting coils. For Study-II, a magnet design has been chosen that
allows the majority of these electrons to exit between separate upper and
lower cryostats, and be dissipated in a dump at room temperature. To
maintain the vertical cryostat separation in focusing elements, skew
quadrupoles are employed in place of standard quadrupoles. In order to
maximize the average bending field, Nb$_{3}$Sn pancake coils are employed.
One coil of the bending magnet is extended and used as one half of the
previous (or following) skew quadrupole to minimize unused space. Figure~\ref
{EPP:fgsection} shows a layout of the ring as it would be located at BNL.
(The existing 110-m-high BNL smokestack is shown for scale.) For
site-specific reasons, the ring is kept above the local water table and is
placed on a roughly 30-m-high berm. This requirement places a premium on a
compact storage ring.

\begin{table}[tb]
\caption{Muon storage ring parameters.}
\label{SRING:tb}
\begin{center}
\begin{tabular}{|l|l|}
\hline
Energy (GeV) & 20 \\ 
Circumference (m) & 358.18 \\ 
Normalized transverse acceptance (mm-rad) & 30 \\ 
Energy acceptance (\%) & 2.2 \\ 
\hline
\multicolumn{2}{c}{\underline{Arc}} \\ 
\hline
Length (m) & 53.09 \\ 
No. cells per arc & 10 \\ 
Cell length (m) & 5.3 \\ 
Phase advance ($\deg $) & 60 \\ 
Dipole length (m) & 1.89 \\ 
Dipole field (T) & 6.93 \\ 
Skew quadrupole length (m) & 0.76 \\ 
Skew quadrupole gradient (T/m) & 35 \\ 
$\beta _{\text{max}}$ (m) & 8.6 \\
\hline 
\multicolumn{2}{c}{\underline{Production Straight}} \\ 
\hline
Length (m) & 126 \\ 
$\beta _{\text{max}}$ (m) & 200 \\ \hline
\end{tabular}
\end{center}
\end{table}

For Study-I, a conventional superconducting ring was utilized to store the
50 GeV muon beam. The heat load from muon decay products in this scenario is
managed by having a liner inside the magnet bore to absorb the decay
products. This approach is likewise available for BNL, provided some care is
taken to keep the ring compact; acceptable lattice solutions have been found
for this option as well.

An overall layout of the Neutrino Factory on the BNL site is shown in Fig.~\ref{bnlsite}.  
Figure~\ref{fnalsite} shows the equivalent picture for a facility on the
Fermilab site. In this latter case, the layout includes the additional RLA
and longer storage ring needed to reach 50 GeV. Clearly the footprint of a
Neutrino Factory is reasonably small, and such a machine would fit easily on
the site of either BNL or Fermilab. 
\begin{figure}[tbh]  %% figure 21
\begin{center}
\includegraphics[width=4.0in]{mole-hill.eps}
\end{center}
\caption[Top view and cross section through ring and berm]{Top view and
cross section through 20-GeV ring and berm. The existing 110-m tower, drawn
to scale, gives a sense of the height of the ring on the BNL landscape.}
\label{EPP:fgsection}
\end{figure}
\begin{figure}[tbh]  %% figure 22
\begin{center}
\includegraphics[width=0.9\linewidth]{bnl-location-old.eps}
\end{center}
\caption[Schematic of a Neutrino Factory at Brookhaven]{Schematic of a
20-GeV Neutrino Factory at BNL.}
\label{bnlsite}
\end{figure}
\begin{figure}[tbh]  %% figure 23
\begin{center}
\includegraphics[width=4in,angle=270]{fnal-location.eps}
\end{center}
\caption[Schematic of a Neutrino Factory at Fermilab]{Schematic of a 50-GeV
Neutrino Factory at Fermilab.}
\label{fnalsite}
\end{figure}

\subsection{Detector}

The Neutrino Factory, plus its long-baseline detector, will have a physics
program that is a logical continuation of current and near-future neutrino
oscillation experiments in the U.S., Japan, and Europe. Moreover, detector
facilities located in experimental areas near the neutrino source will have
access to integrated neutrino intensities $10^{4}$--$10^{5}$ times larger
than previously available ($10^{20}$ neutrinos per year compared with $10^{15}$--$10^{16}$).

The detector site taken for Study-II is the Waste Isolation Pilot Plant
(WIPP) in Carlsbad, New Mexico. The WIPP site is approximately 2900~km from
BNL. Space is potentially available for a large underground physics facility
at depths of 740--1100~m, and discussions are under way between DOE and the
UNO project~\cite{DET:uno} on the possible development of such a facility.

\subsubsection{Far Detector}

Specifications for the long-baseline Neutrino Factory detector are rather
typical for an accelerator-based neutrino experiment. However, the need to
maintain a high neutrino rate at these long distances requires detectors
3--10 times more massive than those in current neutrino experiments.
Clearly, the rate of detected neutrinos depends on two factors---the source
intensity and the detector size. In the final design of a Neutrino Factory,
these two factors would be optimized together.

Two options are considered for the WIPP site: a 50 kton
steel--scintillator--proportional-drift-tube (PDT) detector or a
water-Cherenkov detector. The PDT detector would resemble MINOS. Figure~\ref
{fg:steelwipp} shows a 50-kton detector with dimensions $8~\text{m}\times 8~%
\text{m}\times 150$~m. A detector of this size would record up to $4\times
10^{4}$ $\nu _{\mu }$ events per year. 
\begin{figure}[tbh]
\begin{center}
\includegraphics[width=3.5in]{steelwipp6.eps}
\end{center}
\caption[A possible 50 kton Steel/Scintillator/PDT detector at WIPP]{A
possible 50-kton steel-scintillator-PDT detector at WIPP.}
\label{fg:steelwipp}
\end{figure}

A large water-Cherenkov detector would be similar to SuperKamiokande, but
with either a magnetized water volume or toroids separating smaller water
tanks. The detector could be the UNO detector~\cite{DET:uno}, currently
proposed to study both proton decay and cosmic neutrinos. UNO would be a
650-kton water-Cherenkov detector segmented into a minimum of three tanks
(see Fig.~\ref{fg:unodet}). It would have an active fiducial mass of
440~kton and would record up to $3\,\times \,10^{5}$ $\nu _{\mu }$ events
per year from the Neutrino Factory beam. 
\begin{figure}[tbh]
\begin{center}
\includegraphics[width=3.0in]{unodet1.eps}
\end{center}
\caption[Block schematic of the UNO detector]{Block schematic of the UNO
detector, including initial design parameters.}
\label{fg:unodet}
\end{figure}

Another possibility for a Neutrino Factory detector is a massive
liquid-argon magnetized detector~\cite{landd} that would also attempt to
detect proton decay, as well as solar and supernova neutrinos.

\subsubsection{Near Detector}

As noted, detector facilities located on-site at the Neutrino Factory would
have access to unprecedented intensities of pure neutrino beams. This would
enable standard neutrino physics studies, such as ${\sin }^{2}\theta _{W}$,
structure functions, neutrino cross sections, nuclear shadowing and pQCD to
be performed with much higher precision than previously obtainable. In
addition to its primary physics program, the near detector can also provide
a precise flux calibration for the far detector, though this may not be
critical given the ability to monitor the storage ring beam intensity
independently.

A compact liquid-argon TPC (similar to the ICARUS detector~\cite{ICARUS}),
cylindrically shaped with a radius of 0.5 m and a length of 1~m, would have
an active mass of $10^{3}$ kg and a neutrino event rate \textsl{O}(10~Hz).
The TPC could be combined with a downstream magnetic spectrometer for muon
and hadron momentum measurements. At these neutrino intensities, it is even
possible to have an experiment with a relatively thin Pb target (1~$L_{rad}$), followed by a standard fixed-target spectrometer containing tracking
chambers, time-of-flight, and calorimetry, with an event rate ${\cal O}$(1~Hz).

\subsection{Staging Options}

\label{StagingOps}

It seems quite possible---perhaps even likely---that the Neutrino Factory
would be built in stages, both for programmatic and for cost reasons. Here
we outline a possible staging concept that provides good physics
opportunities at each stage. The staging scenario we consider is not unique,
nor is it necessarily optimized. 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
possibility 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 details.

\subsubsection{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 expected to be large, we do not
consider any intermediate options here.) 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.

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}.

\subsubsection{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 nomenclature 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. 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 in the Study-II cooling channel would result in an
increase of transverse emittance by roughly a factor of two. This is an 
appropriate stage to mount an experiment to search for a non-zero 
muon electric dipole moment.

\subsubsection{Stage 3}

In Stage 3, we envision using the Pre-acceleration Linac to raise the beam
energy to roughly 2.5 GeV. 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.

\subsubsection{Stage 4}

At Stage 4, we envision having a complete Neutrino Factory operating with a
20-GeV storage ring. This stage includes the RLA and the storage ring. 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.

\subsubsection{Stage 5}

In Stage 5, we could envision an entry-level Muon Collider operating as a
Higgs Factory. Because the initial muon beam must be prepared as a single
bunch of each charge, an additional ring for the proton driver to coalesce
proton bunches into a single pulse is anticipated. The cooling will have to
be significantly augmented. First, a much lower transverse emittance is
needed, and second, it will be necessary to provide longitudinal cooling
(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 provide more
cost-effective cooling. 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
collider 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 ring, and its design must be an integral part of the
overall ring design.