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\section*{\Large Preface}
\subsection*{Executive Summary}

The concept of using a muon storage ring to provide a well characterized
beam of muon and electron neutrinos (a Neutrino Factory) has been under
study for a number of years now at various laboratories throughout the
world. The physics program of a Neutrino Factory is focused on the
relatively unexplored neutrino sector. In conjunction with a detector
located a suitable distance from the neutrino source, the facility would make valuable
contributions to the study of neutrino masses and lepton mixing. A Neutrino
Factory is expected to improve the measurement accuracy of $\sin
^{2}(2\theta _{23})$ and $\Delta m_{32}^{2}$ and provide measurements of $%
\sin ^{2}(2\theta _{13})$ and the sign of $\Delta m_{32}^{2}$. It may also be able to
measure CP violation in the lepton sector.

In the U.S., a formal collaboration of some 140 scientists, the Neutrino
Factory and Muon Collider Collaboration (MC), has undertaken the study of how
to design such a machine. The MC has three ``sponsoring'' national
laboratories, Brookhaven National Laboratory (BNL), Fermi National
Accelerator Laboratory (FNAL or Fermilab), and Lawrence Berkeley National
Laboratory (LBNL), and receives funding primarily from the U.S. Department of
Energy (DOE). 

Recently, the MC has gained from the addition of
NSF-sponsored university groups, coordinated by Cornell University, and of
various universities in Illinois sponsored by the Illinois Consortium for
Accelerator Research (ICAR), coordinated by Illinois Institute of
Technology. 

In 1999, the MC aimed to define the scope of a Neutrino Factory facility by
doing an end-to-end study of the entire complex. This led, in late 1999, to
a request from the Fermilab Director, Michael Witherell, to carry out a
Feasibility Study, in cooperation with the MC, of a Neutrino Factory sited
at Fermilab. That initial Study (denoted here as ``Study-I''), organized by
Norbert Holtkamp and David Finley (Fermilab), demonstrated the feasibility
of an entry-level machine, and outlined the features of the various systems
needed to build it. However, the performance reached in that effort,
characterized in terms of the number of muon decays aimed at a detector
located 3000 km away from the muon storage ring, $N$ = 2 $\times $ 10$^{19}$
decays per ``Snowmass year'' ($\equiv 10^{7}$ s) per MW of protons on target,
was lower than anticipated.

In June 2000, a request was made by the BNL Director, John
Marburger, for the MC to participate in a second Neutrino Factory
Feasibility Study (denoted here as ``Study-II''), this time focused on a
machine sited at BNL. Study-II was to aim at a high-performance machine,
with an intensity an order of magnitude higher than achieved in Study-I.
Study-II was co-organized by the MC and BNL. The Study Leaders (see below for the organization of the work) were Satoshi Ozaki and Robert Palmer
(BNL) and Michael Zisman (LBNL). This document contains the results of
Study-II. 

In this report we first describe the exciting physics program that can be
carried out at a Neutrino Factory. The context of the experimental program
is defined in terms of the enhanced knowledge we expect to have at the time
such a facility is anticipated to come on line, roughly 2013. Then we
describe the Neutrino Factory facility, which comprises the following
systems:

\begin{itemize}
\item  Proton Driver (providing 1 MW of protons on target from an upgraded
AGS)

\item  Target and Capture (a mercury-jet target immersed in a 20-T 
superconducting solenoidal field to capture pions, product of the proton-nucleus interactions)

\item  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  Bunching and Cooling (a solenoidal focusing channel with
high-gradient rf cavities and liquid-hydrogen absorbers that bunches the 247~MeV/$c$ muons into 201.25-MHz rf buckets and cools their transverse normalized emittance from 12 mm$\cdot$rad to 2 mm$\cdot$rad)

\item  Acceleration (a superconducting linac with solenoidal focusing to
raise the muon beam energy to 2.48 GeV, followed by a four-pass
superconducting recirculating linear accelerator to provide a 20 GeV muon
beam)

\item  Storage Ring (a compact racetrack-shaped superconducting storage ring
in which 35\% of the stored 20 GeV muons decay toward a detector located
2900 km from the ring)
\end{itemize}

\noindent In addition to the Neutrino Factory facility, we describe the
features of a possible neutrino detector that could carry out the
appropriate physics program. 

Performance estimates for the facility show that an intensity of 
$N = 1.2\times 10^{20}$ decays per ``Snowmass year'' per MW of protons on target is
feasible---a factor of 6 improvement over the Study-I result, though
somewhat less than the original Study-II goal. Upgrade plans that increase
the proton driver power from 1 to 4 MW would permit a corresponding increase in the overall intensity
per year to $N = 4.8\times 10^{20}$ decays. R\&D to develop a target capable of handling this beam power would be needed. Taking the two Feasibility Studies together, we conclude that a
high-performance Neutrino Factory could easily be sited at either BNL or
Fermilab.

Reaching the facility performance estimated here will require an intensive R\&D
program; an outline of the needed activities is included in this report. To
assess the cost range of a Neutrino Factory, a top-down cost estimate has
been carried out for the major components. This estimate represents an
initial look at what is needed, and should not be construed as the kind of
detailed estimate that would result from a Conceptual Design Report. With
that caveat, we find that the cost of such a facility is about $\$1.9\,$B in 
today's dollars. This value represents only direct costs, not
including overhead or contingency allowances. Lastly, we describe a phased
approach to arriving at the complete facility. At each step, we outline the
capabilities of the facility and the corresponding scientific program that
can be pursued. We also comment on the time scales and costs that would be implied by this approach.  Such an ``evolutionary'' approach to the facility may
represent the most effective way to achieve the ultimate goal of a
high-performance Neutrino Factory, even if it stretches out the overall time line. 

It is worth noting that the Neutrino Factory facility described here can be
viewed as a first critical step on the path toward an eventual Muon
Collider. Such a collider offers the potential of bringing the energy
frontier in high energy physics within reach of a moderate sized machine.
The very fortuitous situation of having an intermediate step along this path
that offers a powerful and exciting physics program in its own right
presents an ideal opportunity, and it is hoped that the high energy physics
community will have the resources and foresight to take advantage of it.
\newpage
\subsection*{Acknowledgment}
We would like to thank the management of the Brookhaven National
Laboratory, Dr. John~Marburger and Dr. Peter~Paul, for their support,
interest and foremost for the commissioning of the Study. We would
like also to express our gratitude to Dr. A.~Sessler, spokesperson for
the Neutrino Factory and Muon Collider Collaboration, for his
continuous encouragement and technical guidance. Finally, our most
sincere thanks to all the contributors, especially those who were not members of the Collaboration. Their technical expertise was
crucial for the completion of this report.  
\newpage
\subsection*{Charge to the Study Group}
\label{charge}
\includegraphics[height=20cm]{../template/report/ps-and-eps/charge-pg1.ps}
\newpage %  ! TURN THIS ON
\includegraphics[height=20cm]{../template/report/ps-and-eps/charge-pg2.ps}
\newpage %  ! TURN THIS ON
\includegraphics[height=20cm]{../template/report/ps-and-eps/charge-pg3.ps}
%Copy of Marburger memo.
\subsection*{Organization of the Study}
\label{orga}
%\include{organization}
The organization chart  of the Study is shown in the figure
\begin{figure}[!hbt]
\begin{center}
\includegraphics[width=5.5in,angle=-90]{../template/report/ps-and-eps/studyii_flow_chart.ps}
\caption{Organization chart for Study-II.}
\end{center}
\end{figure}
\subsection*{Summary of Parameters and Performance}

In this section, we briefly summarize the overall parameters and predicted
performance of the Neutrino Factory concept developed for Study-II and
described in this document. The majority of the concepts developed here are
generic, in the sense that they do not depend upon specifics of the BNL
site. A few details, of course, do depend on the particular site chosen for
this Study.

The proton driver on which this Study is based is the BNL\ Alternating
Gradient Synchrotron (AGS). \ This machine delivers 24 GeV protons and
presently holds the world's intensity record for proton accelerators. To
create a 1 MW proton beam, the properties of the AGS dictate a ramp cycle of
150 ms up, 100 ms flat-top, and 150 ms down, with six proton bunches
extracted sequentially at 20-ms intervals during the 100-ms flat-top. This
cycle is repeated at 2.5 Hz, leading to an average pulse rate of 15 Hz, that
is, 6 bunches per cycle at 2.5 Hz. Note that the instantaneous repetition
rate is 50 Hz (20 ms bunch separation) even though the average rate is
lower. Individual proton bunches have an rms length of 3 ns.

The other site-specific aspect of the Study-II design concerns the elevation
of the facility. Local policy requires that no part of the Neutrino Factory
complex that produces radiation lie below the local BNL water table
elevation. This is not an issue for most of the facility, but it does
constrain the location of the storage ring. Because the ring must be tilted
vertically by $13.1^{\circ}$ to aim at the Waste Isolation Pilot Plant (WIPP) site in Carlsbad, NM,
some 2900 km distant, this vertical location requirement placed a premium on
having a compact storage ring, and dictated using an above-ground berm to
shield the ring.

The general design approach we follow is an outgrowth of the previous
Feasibility Study (``Study-I''). However, we have made many technical
changes from the previous design---in some cases simply to explore
alternative design options, and in other cases to specifically enhance
performance. As in the previous Study, we have chosen not to consider muon
beam polarization as a design criterion. This avoids the need to place
high-gradient rf cavities in the high-radiation environment very close to
the target. The overall layout of the facility is presented in Fig.~\ref{sch_fig}.
\begin{figure}
\begin{center}
\includegraphics[totalheight=7in]{../template/report/ps-and-eps/nufact_scheme_bnl.ps}
\caption{Schematic of the Neutrino Factory facility}
\label{sch_fig}
\end{center}
\end{figure}
\noindent Lengths of the various systems that
comprise the facility are summarized in Table~\ref{PREFACE:tb1}. 
%[{\bf use Table 1.1 from
%present version; add match between cooling and linac and check all lengths
%against Rick's numbers as these look out of date to me}].
\begin{table}[htb]
\begin{center}
\caption{Length of the main components of a Neutrino Factory.}
\label{PREFACE:tb1}
\vspace{2.5mm}
\begin{tabular}{|lcc|}
\hline
 Component   & Length & Total\\
    & (m) &(m)\\
\hline
Target &0.45 &0.45\\
Taper & 17.6&17.6\\
Drift & 18 &35.6\\
Induction 1 & 100 &135.6\\
Drift     & 3.3 &138.9\\
Mini-Cool & 13.5 &152.4\\
Drift     & 23.2 &175.6\\
Induction 2 & 80 &255.6\\
Drift     & 30 &285.6\\
Induction 3 & 80 &365.6\\
Match to Super FOFO& 12 &377.6\\
Buncher &20 $\times$ 2.75 = 55 & 432.6\\
Cooling part 1 & 16   $\times$ 2.75  = 44 &476.6   \\
Match  &    4.4 &481.0   \\
Cooling part 2 & 36   $\times$ 1.65 = 59.4 &540.4  \\
Match  &    22.04 & 562.4\\
Linac & 433 &\\
RLA arcs min. &$2\times 310$ &\\
RLA linacs & 2 $\times$ 363.5 &\\
Storage ring arcs &2 $\times$ 53&\\
Storage ring straights & 2 $\times$ 126 &\\
\hline
\end{tabular}
\end{center}
\end{table}

The specific changes made in Study-II to enhance facility performance
include:

\begin{itemize}
\item  Use of a liquid mercury target

\item  Use of three induction linac units, separated by suitable drift
lengths, to achieve nearly non-distorting phase rotation

\item  Use of a graded focusing strength along the cooling channel to keep
the beam angular spread nearly constant as the emittance decreases
\end{itemize}

\noindent As will be seen later, taken together these changes improved the
overall performance of Study-II by a factor of 6 compared with Study-I.

Other changes in the present Study that differ from Study-I include:

\begin{itemize}
\item  Use of a hollow-conductor resistive magnet insert at the target, in
place of a Bitter magnet insert

\item  Use of a Super-FOFO (``SFOFO'') cooling channel, in place of a FOFO
channel

\item  Use of a large-acceptance superconducting linac for the initial
acceleration after the cooling channel, in place of a conventional linac

\item  Use of a combined-function compact storage ring, in place of a
conventional separated-function ring
\end{itemize}

\noindent These changes, as noted above, enhance our knowledge base by
giving an expanded understanding of the parameter space available to the
designers of a Neutrino Factory.

Key parameters for the overall facility are summarized in Table~\ref{PREFACE:tb2}.
\begin{table}[!htb]
\begin{center}
\caption{Muon beam parameters along the length of the facility.}
\label{PREFACE:tb2}
\begin{tabular}{|lccccc|}
%\vspace{2.5mm}
\hline
Location & $\sigma_r$ &$\sigma_{r'}$&$\sigma_p$&$\sigma_t$&$\langle p\rangle$\\
(end of) & (cm)& (mrad)&(MeV/c)& (ns)& (GeV/c)\\
\hline
IL3 & 8.6 &95 & 118 & & 0.237\\
Matching & 5.8 & 114 & 115 & &  0.247\\
Buncher & 5.7 & 134 & 110 & 0.84 & 0.247\\
2.75~m cooling lattice & 3.0 & 87 &72 &0.55&0.222\\
1.65~m cooling lattice & 2.4 & 109 &32 &0.51 &0.204 \\
Matching &10 &29 &27 &0.97 &0.270 \\
Pre-accelerator & & &81 &0.26 &2.583\\
RLA &  &   &134&0.27 &20.105\\ 
Storage Ring&  &   &134&0.27 &20.105\\  
\hline
\end{tabular}
\end{center}
\end{table}

Based on simulation results, we expect that the facility described herein will provide $1.2\times 10^{20}$~muons decays, per ``Snowmass year'' $(10^7s)$ and per MW of proton beam incident on the target, aimed at a detector some 3000~km distant from the storage ring. This value corresponds to our baseline case of a 1-MW proton driver.

For the enhanced case of a 4-MW proton driver, discussed in Section~\ref{APP:Proton}, the muon decay rate would increase to $4.8\times 10^{20}$~muons decays, per ``Snowmass year''.