\chapter{Introduction}
\label{intro}
\section{History}

The concept of a Muon Collider was first proposed by
Budker~\cite{PREFACE:budker} and by Skrinsky~\cite {PREFACE:skrinsky}
in the 60s and early 70s. However, there was little substance to the
concept until the idea of ionization cooling was developed by Skrinsky
and Parkhomchuk~\cite{INTRO:ref3}. The ionization cooling approach was
expanded by Neuffer~\cite{INTRO:ref4} and then by Palmer~\cite
{PREFACE:palmer}, whose work led to the formation of the Neutrino
Factory and Muon Collider Collaboration (MC)~\cite{EPP:collaboration} in
1995. \footnote{A good summary of the Muon Collider concept can be found in the
Status Report of 1999~\cite{INTRO:ref5}; an earlier
document~\cite{INTRO:ref6}, prepared for Snowmass-1996, is also useful
reading. MC Notes prepared by the MC are available
on the web~\cite{INTRO:ref11}}

The concept of a neutrino source based on a pion storage ring was
originally considered by Koshkarev~\cite{INTRO:ref7}. However, the
intensity of the muons created within the ring from pion decay was too
low to provide a useful neutrino source. The Muon Collider concept
provided a way to produce a very intense muon source.  The physics
potential of neutrino beams produced by muon storage rings was
investigated by Geer in 1997 at a Fermilab workshop~\cite{rajageer,geer}
where it became evident that the neutrino beams produced by muon
storage rings needed for the muon collider were exciting on their own
merit.  The neutrino factory concept quickly captured the imagination
of the particle physics community, driven in large part by the
exciting atmospheric neutrino deficit results from the
SuperKamiokande experiment.

  As a result, the MC realized that a Neutrino
Factory could be an important first step toward a Muon
Collider and  the physics that could be addressed by a
Neutrino Factory was interesting in its own right. With this in mind,
the MC has shifted its primary emphasis toward the issues  relevant
to a Neutrino Factory.  There is also considerable international
activity on Neutrino Factories, with international conferences held at
Lyon in 1999, Monterey in 2000~\cite {INTRO:ref13}, Tsukuba in 
2001~\cite{INTRO:ref14}, and another planned for London in 2002. 


In the fall of 1999, Fermilab undertook a Feasibility Study
(``Study-I'') of an entry-level Neutrino
Factory~\cite{INTRO:ref1}. One of the aims of Study-I was to
determine to what extent the Fermilab accelerator complex could be made to 
evolve into a  Neutrino Factory. Study-I answered this question affirmatively.
Simultaneously Fermilab launched a study
of the physics that might be addressed by such a 
facility~\cite{INTRO:ref9}. More recently, Fermilab initiated a 
study to compare the
physics reach of a Neutrino Factory with that of conventional neutrino
beams~\cite{superbeams} powered by a high intensity proton driver, 
which are referred to as ``superbeams''. 
The aim  is to compare the physics reach of superbeams  with that
of a realistic Neutrino factory. Suffice it
to say, it was determined that a steady and diverse stream of  physics 
will result along this evolutionary path.

More recently, BNL organized a follow-on study (``Study-II'') on a
high-performance Neutrino Factory sited at BNL. Study-II was recently completed. 
Clearly, an important goal of Study-II was to evaluate
whether BNL was a suitable site for a Neutrino Factory. Based on the
work contained in Study-II, that question was answered affirmatively.

Studies I and II are site specific in that in each study there are a
few site-dependent parts; otherwise, they are quite generic. In
particular, Study-II uses BNL site-specific proton driver
specifications and a BNL-specific layout of the storage ring,
especially the pointing angle of the straight sections. Study-I uses
an upgraded Fermilab booster to achieve its beam intensities. The
primary substantive difference between the two studies is that
Study-II is aimed at a lower muon energy (20 GeV), but higher
intensity (for physics reach). Figure \ref{studycomp} shows a
comparison of the performance of the neutrino factory designs in Study
I and Study II~\cite{INTRO:ref9}. Both Study-I and
Study-II were carried out jointly with the 
MC~\cite{EPP:collaboration}, which has over 140 members from many
institutions in the U.S. and abroad.

 Complementing the Feasibility Studies, the MC carries on an 
experimental and theoretical R\&D
program, including work on targetry, cooling, rf hardware (both normal
conducting and superconducting), high-field solenoids, LH$_{2}$
absorber design, theory, simulations, parameter studies, and emittance
exchange~\cite{INTRO:ref12}.

\begin{figure}[tbh!]
\centerline{\includegraphics[width=4.0in]{studyIvsII.ps}}
\caption[Muon decays in  a straight section \textit{vs.} muon energy]{
Muon decays in a straight section per $10^{7}\,$s \textit{vs.} muon
energy, with fluxes required for different physics searches assuming a
50~kT detector. Simulated performance of the two studies is
indicated.\label{studycomp}}
\end{figure}



\section{General Scheme and Expected Performance}

Our present understanding of the design of a Neutrino Factory
and results for its simulated performance are
summarized here. Specific details can be found in the Study-II 
report~\cite{EPP:studyii}. 
A schematic layout is shown in
Fig.\ref{nufact-scheme-bnl}.

\begin{figure}[tbh!]
\centerline{\includegraphics[width=4.0in,angle=-90]{nufact_scheme_bnl.ps}}
\caption[Schematic of the neutrino factory-Study II version]
{Schematic of the neutrino factory-Study II
version.\label{nufact-scheme-bnl}}
\end{figure}


%\subsection{\protect\bigskip Neutrino Factory Systems}
\subsection{Neutrino Factory Systems}

In overview, the muons result from decays of pions produced when an
intense proton beam bombards a high-power production target. The
target and downstream transport channel are surrounded by
superconducting solenoids to contain the pions and muons, which are
produced with a larger spread of transverse and longitudinal momenta
than can be conveniently injected into an acceleration system. 
To produce a beam suitable
for subsequent acceleration, the energy spread is reduced by ``phase
rotation'' where the initial large energy spread and small time spread
are interchanged using induction linacs. To reduce the transverse
momentum spread, the resulting long bunch, with an average momentum of
about 250 MeV/$c$, is bunched into a 201.25 MHz bunch train and then
sent through an ionization cooling channel consisting of LH$_{2}$ energy
absorbers interspersed with rf cavities to replenish the energy lost
in the absorbers. The resulting beam is then accelerated to its final
energy using a superconducting linac to make the beam relativistic,
followed by a recirculating linear accelerator (RLA). Finally, the
muons are stored in a racetrack-shaped ring with one long straight
section aimed at a detector located at a distance of roughly 3000 km.

A list of the main ingredients of a Neutrino Factory is given below;
more details can be found in Chapter~\ref{neufact}. 
The 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.  However, the design exemplifies a general class of
Neutrino Factories for which the two Feasibility Studies have 1)
demonstrated technical feasibility, 2) established a cost baseline, and 3)
established the expected range of physics performance.

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

\item  \textbf{Target and Capture} A mercury-jet target immersed in a 20-T
superconducting solenoidal field to capture pions, produced in
proton-nucleus interactions. (A technically less-ambitious alternative in which
the target is made of graphite has also been considered.)

\item  \textbf{Decay and Phase Rotation} Three induction linacs, with
internal superconducting solenoidal focusing, to contain the muons
from pion decays and provide nearly non-distorting phase rotation; a
``minicooling'' absorber section is included after the first induction
linac.

\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 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 be added to reach 50 GeV, 
if the physics requires such high energy.

\item  \textbf{Storage Ring} A compact racetrack-shaped superconducting
storage ring in which $\approx$ 35\% of the stored muons decay 
toward a detector
located $\approx$ 2900 km from the ring.

\end{itemize}

\subsection{Predicted Performance}

Complete simulations up to the start of acceleration have been
performed using the code MARS~\cite{EPP:mars} (for pion production)
followed by ICOOL~\cite{icool} 
(for transport, phase rotation, and cooling). These results
have been confirmed by GEANT4~\cite{EPP:GEANT4}. They show an average
of 0.17 final muons per initial proton on the target, \textit{i.e.},
0.0071 $\mu /p$/GeV (considering the energy of the initial beam). This can be
compared with a value of \ 0.0011 $\mu /p$/GeV produced in Study-I. 
The gain compared with Study-I (a factor of 6) comes from:

\begin{itemize}
\item  Use of mercury, instead of carbon, as a target (1.9$\times $)

\item  Use of three, instead of one, induction linacs for phase rotation (2$%
\times $)

\item  Use of a more efficient tapered cooling channel design (1.4$\times $)

\item  Use of a larger acceptance for the acceleration channel (1.2$\times $)
\end{itemize}

Based on the improvements from Study-II, the number of muons delivered
to the storage ring per Snowmass year (10$^{7}$ s) from a
1-MW proton driver would be:

\begin{eqnarray*}
\mu /\text{year} &=&10^{14}\text{ ppp}\times 2.5\text{ Hz}\times 10^{7}\text{
s/year}\times 0.17\text{ }\mu /\text{p}\times 0.81 \\ &=&3.4\times
10^{20}
\end{eqnarray*}

\noindent where the last factor (0.81) is the calculated efficiency of the
acceleration system. Note that for the case of an upgraded 4 MW proton
driver, the muon production would increase to 1.4 $\times $ $10^{21}$
$\mu $ /year. The number of muons decaying in the production straight
section
per Snowmass year would be 35\% of this number, or 1.2 $\times $ 10$
^{20}$ decays for a 1 MW proton driver (4.8 $\times $ 10$^{20}$ decays
for a 4 MW proton driver).

Though these numbers of neutrinos are potentially available for
experiments, in the current storage-ring design the angular divergence at
both ends of the production straight section is higher than desirable for
the physics program.  In any case, we anticipate that storage-ring designs
that allow 30--40\% of the muon decays to provide useful neutrinos are
feasible.

It is worthwhile noting that a $\mu^+$ storage ring with an 
average neutrino energy of 15~GeV and 
2$\times$10$^{20}$ useful muon decays will yield 
(in the absence of oscillations) $\approx$ 30,000
charged current events/kiloton-year in a detector placed 732~km away
in the $\nu_e$ channel.  In comparison, a
1.6~MW superbeam~\cite{superbeams} from the Fermilab Main Injector 
with an average neutrino energy of 15~GeV will
yield $\approx$ 13,000 $\nu_\mu$ charged current events per kiloton-year. 
However, these superbeams have a significant $\nu_e$
contamination which will be the major background in
$\nu_\mu\rightarrow\nu_e$ appearance searches.  It is much easier to
detect the oscillation $\nu_e\rightarrow\nu_\mu$ from muon storage
rings than the oscillation $\nu_\mu\rightarrow\nu_e$ from conventional
neutrino beams, since the electron final state from conventional beams
has significant background contribution from $\pi^0$'s produced in the events.

\section{Outline of Report}

In what follows, we give a scenario for a staged approach to
constructing a Neutrino Factory and eventually a Muon
Collider. Chapter~\ref{physics} discusses the physics opportunities,
starting from conventional ``superbeams'' and going to cold muon
beams, then a Neutrino Factory with its near and far detectors, and
finally a Muon Collider. In Chapter~\ref{neufact}, we describe the
components of a Neutrino Factory, based on the Study-II
design. Chapter~\ref{higgsfact} covers our present concept of an
entry-level Higgs Factory Muon Collider. Our present understanding of
the costs of a Neutrino Factory and the financial implications of
possible staging scenarios will be described in Chapter~\ref{costs}.
Before embarking on construction of a Neutrino Factory, an R\&D
program is needed to address various technical issues. A description
of the required program and its budget requirements is presented in
Chapter~\ref{r_and_d}.  Chapter~\ref{r_and_d} also describes current
thinking about a cooling demonstration experiment that would be
carried out as an international effort. Finally, in Chapter~\ref{international} 
we provide a brief overview of the international
scope of the R\&D effort for intense muon beam accelerators.

