Neutrino Factory and Muon Collider R\&D
Steve Geer
European, Japanese, and US Neutrino Factory designs are presented. The main R\&D issues and associated R\&D programs, future prospects, and the additional issues that must be addressed to produce a viable Muon Collider design, are discussed.
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\documentclass{preprint}

\begin{document}

\title{Neutrino Factory and Muon Collider R\&D}

\author{Steve Geer}

\address{Fermi National Accelerator Laboratory, P.O. Box 500, Batavia, 
IL 60510, USA\\E-mail: sgeer@fnal.gov}



\twocolumn[\maketitle\abstract{
European, Japanese, and US Neutrino Factory designs are presented. 
The main R\&D issues and associated R\&D programs, 
future prospects, 
and the additional issues that must be addressed to produce a viable 
Muon Collider design, are discussed. 
}]




\section{Introduction}
\label{Intro}

The development of a 
very intense muon source capable of producing a millimole of muons per 
year would enable a Neutrino Factory~\cite{sgprd}, 
and perhaps eventually a Muon Collider~\cite{mucollider}, to be built. 
In the last two years Neutrino Factory physics studies~\cite{nufact-physics} 
have mapped out an exciting Neutrino Factory physics program. 
In addition, Neutrino Factory feasibility studies~\cite{study1,study2,studyJ}  
have yielded designs that appear to be ``realistic'' provided the 
performance parameters for the critical components can be achieved. 
Some of the key components will need a vigorous R\&D program to meet the 
requirements. Neutrino Factory R\&D activities in Europe~\cite{europe-RD}, 
Japan~\cite{studyJ,japan-RD}, and the US~\cite{us-RD} 
are ongoing and have, in fact, resulted in three promising 
variants of the basic Neutrino Factory design. 
In the following the various Neutrino Factory schemes are briefly described. 
The main R\&D issues, and the ongoing R\&D programs are summarized, and 
R\&D results presented. 
Finally, the additional issues that must be addressed before a 
Muon Collider can be proposed are briefly discussed.   

\section{Neutrino Factory Schemes}

In all of the present Neutrino Factory schemes  
an intense multi-GeV proton source is used to make 
low energy charged pions. The pions are confined within  
a large acceptance decay channel. The daughter muons 
produced from $\pi^\pm$ decays are also confined within the channel, 
but they occupy a large phase-space volume, 
and this presents the main challenge in designing Neutrino Factories 
and Muon Colliders.

In the US and European designs the strategy is to first 
reduce the energy spread of the muons by  manipulating the 
longitudinal phase-space they occupy using a technique 
called ``phase rotation''. 
The transverse phase-space occupied by the muons is then reduced 
using ``ionization cooling~\cite{cool}''. After phase rotation and 
ionization cooling the resulting muon phase space fits within 
the acceptance of a normal type of accelerator. In the Japanese scheme 
an alternative strategy is pursued, in which the large muon phase-space 
is accommodated using so called FFAG's, which are very large acceptance 
accelerators. Finally, in all three schemes the muons are accelerated 
to the desired final energy (typically in the range from 20 - 50~GeV), 
and injected into a storage ring with either two or three long straight 
sections. Muons decaying within the straight sections produce intense 
neutrino beams. If the straight section points downwards, the resulting 
beam is sufficiently intense to produce thousands of neutrino interactions 
per year in a reasonably sized detector on the other side of the 
Earth~\cite{sgprd}~!

\subsection{US Scheme}

In the last 18 months there have been two Neutrino Factory ``Feasibility'' 
Studies~\cite{study1,study2} in the US. Within these studies  
engineering designs have been developed and detailed simulations 
performed for each piece of the Neutrino Factory complex. 
Study I was initiated by the Fermilab Director, and 
conducted between October 1999 and April 2000. 
%
\begin{figure}%1
%\vspace{-2.0cm}
\centering
\epsfxsize260pt
\epsffile{fig1.ps}
%\vspace{-6.5cm}
\caption{US Neutrino Factory schematic from design study I~[4].}
\label{fig:US}
\end{figure}
%
The Study I design 
was for a 50~GeV Neutrino Factory with the neutrino beams pointing 
down 13$^\circ$ below the horizon, corresponding to a baseline of 2900~km. 
A schematic is shown in Figure~\ref{fig:US}. 
The proton source for Study I~\cite{pstudy} was assumed to be 
a 16~GeV synchrotron producing 3~ns long bunches, operating at 15~Hz, 
and providing a 1.2~MW beam ($4.5 \times 10^{14}$ protons per sec) on 
an 80~cm long carbon target located within a 20~T solenoid. The solenoid 
radially confines essentially all of the produced $\pi^\pm$. Downstream 
of the target and target solenoid the pions propagate down a 50~m long 
decay channel consisting of a 1.25~T super-conducting solenoid which 
confines the $\pi^\pm$ and their daughter muons within a warm bore of 60~cm. 
At the end of the decay channel 95\% of the initial $\pi^\pm$ have decayed
and, per incident proton, there are $\sim 0.2$ muons with energies $< 500$~MeV 
captured within the beam transport system.  
The muon system downstream of the decay channel is designed to produce a 
bunched  cold muon beam with a central momentum of 200~MeV/c (T = 120~MeV). 
Beyond the decay channel. the first step is to reduce the muon energy 
spread using a 100~m long induction linac which accelerates the late low 
energy particles and de-accelerates the early high energy particles 
(phase rotation). 
After the induction linac, a 2.45~m long liquid hydrogen absorber is 
used to lower the central energy of the muons. 
Muons with energies close to the central value are then captured 
within bunches using a 201~MHz RF system within a 60~m long channel. 
Throughout the induction linac, liquid hydrogen absorber, 
and bunching system the muons are confined 
radially using a solenoid field of a few Tesla. 
The buncher produces a string of muon bunches, captured 
longitudinally, but still occupying a very large transverse phase-space.  
Downstream of the buncher the muons are cooled transversely within a 
120~m long ionization cooling channel. The phase-space occupied by 
the muon bunches will then fit with the acceptance of an acceleration 
system consisting of a linac that accelerates the muons to 3~GeV, and two 
recirculating linear accelerators (RLA's) that raise the muon energies 
to 50~GeV. The muons are then injected into a storage ring. The ring is 
tilted downwards at the desired angle ($13^\circ$), has a 
circumference of 1800~m, and has two 600~m long straight sections. 
One third of the injected muons will decay in the downward pointing 
straight section. A detailed simulation of the Study I design shows that
this scheme will produce about $6 \times 10^{19}$ muon decays per 
operational year (defined as $2 \times 10^7$ seconds) 
in the downward pointing straight-section, which is a factor of 3 less 
than the initial design goal for the study. The resulting beam intensity 
would be sufficient for a so-called ``entry-level'' Neutrino Factory, 
but insufficient for a ``high-performance'' machine. 

Study II was initiated by the BNL Directorate, and built upon the work done 
during Study I. The Study II was effort focussed 
on improving the Neutrino Factory design to achieve higher beam intensities. 
The main improvements came from using 
(i) a 4~MW proton source, 
(ii) a liquid Hg target, 
(iii) an improved induction linac design, 
and (iv) an improved cooling channel design. 
Detailed simulations of the Study II design predicted $2 \times 10^{20}$ 
muon decays per operational year (defined as $1 \times 10^7$ seconds) 
in the downward pointing straight-section, thus achieving the initial 
goal. 
%
\begin{figure}%1
%\vspace{-2.0cm}
%\centering
\epsfxsize190pt
\epsffile{fig2.ps}
%\vspace{-3.5cm}
\caption{European Neutrino Factory schematic~[12].}
\label{fig:CERN}
\end{figure}

\subsection{European Scheme}

The European Neutrino Factory design~\cite{cern} has many similarities to the 
US design. However, the European studies have explored alternative 
technology choices for several key subsystems. A schematic is shown 
in Fig.~\ref{fig:CERN}. The European 
studies have focused on a design in which:
(i) The proton driver consists of a 2.2 GeV super-conducting linac  
(rather than a higher energy synchrotron), followed by an accumulator 
ring designed to produce short proton pulses~\cite{europe-p}. 
The beam power is 4 MW. 
(ii) In addition to a liquid metal jet, a target consisting of water 
cooled Ta spheres is also being considered. 
(iii) The charged pions are focussed using a magnetic horn (rather than 
a high-field solenoid) with a 4~cm waist radius, and a peak current 
of 300~kA. 
(iv) After a 30~m drift, the muon energy spread is reduced using 44~MHz 
RF cavities (rather than induction an linac).
(v) The ionization cooling channel (described later) uses 44~MHz and 88~MHz RF
cavities. These are lower frequency cavities than employed in the US scheme. 
(vi) A bowtie-shaped storage ring (rather than a simple race-track design) 
has been considered for the final muon ring. 

Simulations of the European design predict that the resulting neutrino 
beams will have intensities comparable to the corresponding beams from 
the US design. A comprehensive design study at the level of those in the 
US is not yet complete. It seems plausible that, at the end of the day, 
the optimal European/US-type Neutrino Factory design will inherit 
some of the technical choices being explored in the European studies, 
and some of those explored in the US studies. 
%
\begin{figure}%1
%\vspace{-2.0cm}
\centering
\epsfxsize190pt
%\figurebox{16pc}{16pc}{}
\fbox{
\epsffile{fig3.ps}
}
%\vspace{-6.5cm}
\caption{Japanese Neutrino Factory schematic~[8].}
\label{fig:Japan}
\end{figure}

\subsection{Japanese Scheme}

The Japanese Neutrino Factory scheme is shown in Fig.~\ref{fig:Japan}. 
The front end of the design consists of a 50 GeV proton synchrotron providing 
a 4~MW beam (corresponding to an upgraded JHF complex) incident on a 
target within a 12~T solenoid. This is followed by a 
large acceptance pion decay channel. However, instead of manipulating and 
cooling the phase space occupied by the muons exiting the decay channel, 
very large acceptance FFAG (Fixed Field Alternating Gradient) accelerators 
are used to raise the beam energy before injecting into a storage ring 
with long straight sections. The predicted neutrino yield from this scheme 
seems to be comparable to the corresponding predicted yields from the 
US/European designs, although more detailed simulations will be needed 
to confirm this. 

Although the Japanese Neutrino Factory scheme might benefit from the addition 
of some muon cooling, in principle the use of FFAGs evades the 
need to cool the muons before injecting them into an accelerator. This 
simplification comes at the price of a more challenging accelerator, 
requiring complicated large aperture magnets and broad-band low frequency 
high gradient RF cavities. Modern design 
tools have made practical the task of designing the FFAG magnets, and 
a small proof-of-principle (POP) FFAG accelerator~\cite{pop} has been 
built and successfully operated. 
A second test FFAG, designed to accelerate protons to 150~MeV, 
is under construction.
Furthermore, with some US participation, 
an R\&D program is underway in Japan to develop the required cavities. 
It is too early to conclude whether the promising Japanese Neutrino Factory 
scheme will lead to a more cost effective solution than the European/US-type 
designs. It may even be that the optimum solution consists of 
a combination of the two concepts, with some 
phase space manipulation and cooling, but using large acceptance FFAGs 
for the acceleration.
%
\begin{figure}%1
%\vspace{-2.0cm}
\centering
\epsfxsize200pt
\epsffile{fig4.ps}
%\vspace{-6.5cm}
\caption{Proof of Principle (POP) FFAG accelerator~[14].}
\label{fig:POP}
\end{figure}

\section{Pion production \& Target R\&D}

To produce a sufficient number of useful $\pi^\pm$, 
and hence a sufficient number of muons, all Neutrino Factory 
schemes begin with a MW-scale proton driver, a pion production target, and 
a collection system optimized to capture as many $\pi^\pm$ as 
possible. 
To establish confidence in the predicted $\pi^\pm$ fluxes downstream of 
the target several secondary particle production experiments are 
underway~\cite{E910,harp,P907}. 
In addition, a target R\&D program is being pursued 
to develop targets that can operate within MW-scale proton beams~\cite{E951}.
%
\begin{figure}%1
%\vspace{-2.0cm}
\centering
\epsfxsize200pt
\epsffile{fig5.ps}
%\vspace{-6.5cm}
\caption{MARS predictions for the yield of pions captured within a Neutrino 
Factory pion decay channel, shown as a function of the primary proton 
beam energy~[4]. 
More explicitly, the number of $\pi^+ + \mu^+$ (filled symbols) 
and $\pi^- + \mu^-$ (open symbols) within an energy interval 
30~MeV $< E < 230$~MeV is shown 9~m downstream of an 
80~cm long 0.75~cm radius carbon 
target within a 20~T solenoid, and tilted 50~mrad with respect to the solenoid 
axis. Triangles show the yields divided by the primary proton energy.
}
\label{fig:yields}
\end{figure}

\subsection{Pion production experiments}

Figure~\ref{fig:yields} shows, as a function of the primary proton beam 
energy, predicted charged pion yields for $\pi^+$ and $\pi^-$ captured 
within a decay channel downstream of a Neutrino Factory target system. 
Over a broad interval of proton beam energies, at fixed beam power the 
yields are approximately independent of beam energy. Hence, a wide variety 
of multi-GeV MW-scale proton drivers can be considered when designing a 
Neutrino Factory. 
The E910 experiment at BNL~\cite{E910} has recently measured $\pi^+$ and $\pi^-$ 
yields for several targets and different incident proton beam energies. Some  
of the results are shown in Fig.~\ref{fig:E910}. 
Note that (i) the measurements 
are in fair agreement with MARS calculations~\cite{E910}, 
and (ii)  the pion yields 
peak in the region 300 - 500~MeV/c. Hence, Neutrino Factory designs 
tend to have $\pi^\pm$ collection systems optimized to capture particles 
with momenta in this range. 
In the next few years we can anticipate further particle production 
measurements from the HARP 
experiment~\cite{harp} at CERN, and the proposed P907 experiment~\cite{P907} 
at Fermilab. This will enable the relevant $\pi^\pm$  
production measurements to be cross-checked and extended to cover the 
entire region of interest for Neutrino Factory designs. 
%
\begin{figure}%1
%\vspace{-2.0cm}
\centering
\epsfxsize200pt
\epsffile{fig6.ps}
%\vspace{-6.5cm}
\caption{Pion production measurements from the BNL E910 experiment, compared 
with MARS predictions~[15].}
\label{fig:E910}
\end{figure}

\subsection{Target R\&D}

Entry-Level Neutrino Factories providing a few $\times 10^{19}$ useful 
muon decays per year require proton beams with beam powers of $\sim 1$~MW, 
and short proton bunches, typically a few ns long. It is believed that 
carbon targets can operate with these beam parameters. This has been tested 
at BNL by the E951 Collaboration~\cite{target}. 
Two different types of carbon rod were 
exposed to the AGS beam and strain gauge data taken. The beam induced 
longitudinal pressure waves and transverse reflections were both measured. 
The strains in the two types of rod differed by an order of magnitude, 
the most promising rod being made from an anisotropic carbon-carbon 
composite.

High performance Neutrino Factories providing O($10^{20}$) useful 
muon decays per year require proton beams with beam powers of $\sim 4$~MW.
Targets must be 
developed to operate in these extreme conditions. Solid targets will melt 
unless very efficient cooling strategies can be developed. Rotating metal 
bands~\cite{band_target} and water cooled Ta spheres~\cite{sphere_target} 
are being considered, but the presently favored 
solution is to avoid problems with target melting and integrity by using 
a liquid Hg jet. In the US and Japanese schemes the target is in a high-field 
solenoid. Hence, the main R\&D issues are (i) can a Hg jet be injected within 
a high-field solenoid without magneto-hydrodynamic effects disrupting the 
jet, (ii) after the jet has been destroyed by one proton pulse will it 
re-establish itself before the next pulse, and (iii) can the disrupted 
jet be safely contained within the target system.
%
\begin{figure}%1
%\vspace{-2.0cm}
\centering
\epsfxsize130pt
\epsffile{fig7a.ps}
\epsfxsize130pt
\epsffile{fig7b.ps}
%\vspace{-6.5cm}
\caption{CERN-Grenoble tests in which a liquid Hg jet is injected 
into a solenoid providing 0 field (top picture) and 13~T 
(bottom picture)~[13].}
\label{fig:grenoble}
\end{figure}
%
\begin{figure}%1
%\vspace{-2.0cm}
\centering
\epsfxsize200pt
\epsffile{fig8.ps}
%\vspace{-6.5cm}
\caption{Schematic of the E951 system to test a Hg jet in the BNL AGS 
beam~[19].}
\label{fig:E951}
\end{figure}
%
\begin{figure*}
%\vspace{-2.0cm}
\centering
\epsfxsize34pc
\epsffile{fig9.ps}
\vspace{0.5mm}
\caption{BNL E951 results~[19]. 
The sequence of pictures shows the Hg jet at the 
time of impact (t=0) of the AGS beam, and at t = 0.75~ms, 2~ms, 7~ms, 
and 18~ms. Time increases from left to right.}
\label{fig:e951-results}
\end{figure*}

To address these questions, R\&D has begun at CERN and by the E951 
collaboration at BNL. Photographs of a liquid Hg jet injected into 
a high-field solenoid at Grenoble are shown in Fig.~\ref{fig:grenoble}. 
The presence of a 13~T solenoid field seems to damp surface tension waves, 
improving the characteristics of the jet. This is clearly good news. 
The E951 liquid Hg jet setup~\cite{target} in the BNL AGS beam is shown in 
Fig.~\ref{fig:E951}. Figure~\ref{fig:e951-results} shows a sequence of 
pictures of the 1~cm diameter Hg jet taken by a high speed camera from the 
time of impact of $4 \times 10^{12}$ protons in a 150~ns long pulse 
from the 24~GeV BNL AGS. Jet dispersal is delayed for about $40\mu$s, and 
it takes several ms before the jet, which has an 
initial velocity of 2.5~m/sec, is completely disrupted. The velocity of 
the out-flying Hg filaments, which appears to scale with beam intensity, 
has been measured to be $\sim 10$~m/sec for a deposited energy of 25~J/g. 
These velocities are fairly modest, implying that the disrupted jet can 
be easily contained within the target system. Furthermore, the Hg jet 
dispersal is mostly in the transverse direction, and after disruption 
it has been found that the jet quickly re-establishes itself. 

Initial results with Hg jets are promising. However, high performance 
Neutrino Factories will require Hg jets with much higher velocities 
($\sim 20$~m/sec) to be developed and tested. The next steps in the 
E951 R\&D program will 
require beam tests with a factor of a few higher beam intensities, and 
finally beam tests in which the Hg jet is injected into a 20~T solenoid.
%
\begin{figure*}
%\vspace{-2.0cm}
\centering
\epsfxsize30pc
%\figurebox{16pc}{32pc}{}
\epsffile{fig10.ps}
%\vspace{-6.5cm}
\caption{SFOFO cooling channel design~[5]. A 5.5~m long section 
is shown, consisting of two 
200 MHz four-cell cavities interleaved with three liquid 
hydrogen absorbers.}
\label{fig:sfofo}
\end{figure*}

\section{Muon Cooling R\&D}

Before the muons can be accelerated   
the transverse phase-space they occupy must be reduced 
so that the muon beam fits within the acceptance of an accelerator. 
This means the muons must be ``cooled'' by at least a factor of a few in each 
transverse plane, and this must be done fast, before the muons decay. 
Stochastic-- and electron--cooling are too slow. 
It is proposed to use a new cooling technique, namely 
``ionization cooling''~\cite{cool}. 

In an ionization cooling channel the muons 
pass through an absorber in which they lose transverse-- and 
longitudinal--momentum by {\it dE/dx} losses. The longitudinal momentum 
is then replaced using an RF cavity, and the process is 
repeated many times, reducing the transverse momenta. This  
cooling process will compete with transverse heating due to 
Coulomb scattering. To minimize the effects of scattering we chose 
low--Z absorbers placed in the cooling channel 
lattice at positions of low--$\beta_\perp$ so that the typical radial 
focusing angle is large. If the focusing angle is much larger 
than the average scattering angle then scattering will not have much 
impact on the cooling process.


\subsection{US Cooling Channel Design}

Studies I and II used two simulation tools developed by the 
Neutrino Factory and Muon Collider Collaboration: (i) A specially developed 
tracking code ICOOL~\cite{ICOOL}, and 
(ii) A GEANT based program with accelerator 
components (e.g. RF cavities) implemented. Out of these design and 
simulation studies, two promising cooling channel designs have emerged: 
\begin{description}
\item{(i)} The ``SFOFO'' lattice in which the absorbers are 
placed at low--$\beta_\perp$ locations 
within high-field solenoids. The field rapidly decreases from a 
maximum to zero at the absorber center, and then increases to a maximum 
again with the axial field direction reversed. 
Figure~\ref{fig:sfofo} shows the design for a 5.5~m long section of the 
$\sim 100$~m long cooling channel. The section shown has 30~cm long 
absorbers with a radius of 15~cm, within a system of solenoids with 
a peak axial field of 3.5~T. 
Towards the end of the cooling channel the maximum field is 
higher (5~T) and the lattice period shorter (3.3~m).  
The RF cavities operate at 201~MHz and provide a peak gradient of 17~MV/m. 
Detailed simulations predict that the SFOFO channel increases  
the number of muons within the accelerator acceptance  
by a factor of 3-5 (depending 
on whether a large- or very-large acceptance accelerator is used).
\item{(ii)} The ``DFLIP'' lattice in which the solenoid field remains constant
over large sections of the channel, reversing direction only twice. 
In the early part of the channel the muons lose mechanical angular momentum 
until they are propagating parallel to the axis. After the first field 
flip the muons have, once again, mechanical angular momentum, and 
hence move along helical trajectories with Lamour centers along the 
solenoid axis. Further cooling removes the mechanical angular momentum, 
shrinking the beam size in the transverse directions. 
The field in the early part of the channel is 3~T, increasing to 7~T for
the last part. Detailed simulations 
show the performances of the DFLIP and SFOFO channels are comparable.
\end{description}
Earlier less detailed studies~\cite{mucollider} 
have shown that a much larger cooling factor will be required for a 
muon collider. This will require an extended cooling channel, using 
higher frequency (e.g. 805 MHz) cavities, higher field solenoids, 
and possibly liquid lithium lenses~\cite{LiLens}.

\subsection{MUCOOL R\&D}

Muon cooling channel design and development is being pursued within the 
US by the MUCOOL collaboration~\cite{MUCOOL}. The mission of the MUCOOL collaboration 
includes bench--testing all cooling channel components, and eventually 
beam--testing a cooling channel section. The main component issues 
that must be addressed before a cooling channel can be built are 
(i) can sufficiently high gradient RF cavities be built and operated 
in the appropriate magnetic field and radiation environment, 
(ii) can liquid hydrogen absorbers with thin enough windows be built 
so that the $dE/dx$ heating can be safely removed, and (iii) can the 
lattice solenoids be built to tolerance and be affordable? 
The MUCOOL collaboration 
has embarked on a design--, prototyping--, and testing--program that  
addresses these questions. This R\&D is expected to proceed over the next 
3~years.
%
\begin{figure}%1
%\vspace{-2.0cm}
\centering
\epsfxsize190pt
\epsffile{fig11.ps}
%\vspace{-6.5cm}
\caption{High power 805 MHz cavity test in the MUCOOL Lab G test 
area, Fermilab~[25].}
\label{fig:labg}
\end{figure}
%
\begin{figure*}
%\vspace{-2.0cm}
\centering
\epsfxsize31pc
%\figurebox{16pc}{32pc}{}
\epsffile{fig12.ps}
%\vspace{-6.5cm}
\caption{Measurements of the deflection of a Be foil in an 805 MHz cavity 
at LBNL~[26]. The measured deflections are shown as a function of the heat 
dissipated in the foil, and are compared with predictions from two 
finite element analysis calculations.}
\label{fig:foil}
\end{figure*}

\subsection*{805 MHz RF Tests}

Early design work for a Muon Collider resulted in a Muon Collider 
cooling channel design 
that required 805~MHz cavities operating in a 5T 
solenoid, with the cavities providing a peak gradient on axis   
of $\sim30$~MV/m. This deep potential well is needed to keep the 
muons bunched as they propagate down the channel. 
This requirement led to two cavity concepts: 
(a) an open cell design, and (b) a design in which the 
penetrating nature of the muons is exploited by closing the RF aperture 
with a thin conducting Be window (at fixed peak power this doubles 
the gradient on axis).
 
The MUCOOL collaboration has pursued an aggressive 805 MHz cavity 
development program, which is now advanced. 
A 12~MW high power test facility has been built and operated at 
Fermilab (Lab G). The Lab G facility enables 
805 MHz cavities to be tested  within a 5T solenoid. 
The main results to date are: 
(i) An open cell cavity suitable for a muon cooling channel has been 
designed, an aluminum model built and measured, and a prototype copper 
cavity built, tuned, and successfully tested at full power in the Lab G 
facility (Fig.~\ref{fig:labg}). Dark current produced by the cavity has 
been identified as an important R\&D issue~\cite{dark_current}. 
(ii) A Be foil cavity has been designed at LBNL, a low power test cavity 
built and measured, and foil deflection studies made~\cite{BeWindows} 
to ensure the cavity 
does not detune when the foil is subject to RF heating. 
The foil deflection is reasonably well understood for small displacements 
(Fig.~\ref{fig:foil}). A high power copper 
cavity with Be-foil windows is under construction at LBNL and the 
University of Mississippi, and will be tested at Lab G when ready.
 
\subsection*{201 MHz Cavity Development}

The cooling channel designs developed for the US Neutrino Factory studies 
require 201~MHz RF cavities providing a gradient on axis of $\sim 17$~MV/m. 
Preliminary cavity designs have been made. There are two concepts, 
both of which close the cavity aperture. The options are to use (a) a thin 
Be foil, exploiting the work done for the 805 MHz cavity, or 
(b) use a grid of hollow conducting tubes. Preliminary mechanical tests 
for both the grid and foil concepts are planned, and should proceed 
during the next few months. A 201~MHz prototype cavity will then be 
constructed, and should be ready for high power tests in about 2 years.
%
\begin{table*}[]
\caption{LH$_2$ absorber parameters in Neutrino Factory design study II~[5].}
\begin{center}
%\vspace{0.6 cm}
\begin{tabular}{l|cccccc}
\hline \hline
 &Length&Radius&Number&Heat (kW)&Window Thick&Max. Pres-\\
 Absorbers&(cm)  &(cm)  &Needed&Deposited&-ness ($\mu$m)&sure (atm)\\
\hline
Early&35&18&16&$\sim 0.3$&360&1.2\\
Late &21&11&36&$\sim 0.1$&220&1.2\\
\hline\hline
\end{tabular}
\label{tab:1}
\end{center}
\end{table*}
%
%
\begin{figure*}%1
%\vspace{-2.0cm}
\centering
\epsfxsize10pc
\epsffile{fig13a.ps}
\epsfxsize22pc
\epsffile{fig13b.ps}
\vspace{0.5mm}
\caption{KEK prototype absorber. The liquid hydrogen is to be mixed 
by convection and cooled with a local heat exchanger. A simulation of 
the convection, performed at IIT, is shown on the right.}
\label{fig:convection}
\end{figure*}

\subsection*{Absorber Development}

The cooling channel liquid hydrogen absorbers must have 
very thin windows to minimize multiple scattering, and must tolerate 
heating of O(100~W) from the ionization energy deposited by the 
traversing muons. Absorber parameters for the Neutrino Factory 
study II cooling channel design are listed in Table~\ref{tab:1}.

To adequately remove the heat from the absorbers requires transverse 
mixing of the liquid hydrogen. There are two design concepts that are 
being pursued~\cite{Dan}: (i) Forced flow design. The LH$_2$ is 
injected into the 
absorber volume through nozzles, and cooled using an external 
loop and heat exchanger. (ii) Convection design. Convection 
is driven by a heater
at the bottom of the absorber volume, and heat removed by a heat exchanger
on the outer surface of the absorber. A forced flow absorber 
prototype is being designed at the Illinois Institute of Technology (IIT) 
and will be constructed in the coming year. A convection prototype, 
designed by IIT, KEK, and the University of Osaka, is being constructed 
in Japan (Fig.~\ref{fig:convection}). 
Both absorbers will be tested at Fermilab when complete.

A first prototype 15~cm radius aluminum absorber window has been made at the 
University of Mississippi on a CNC milling machine and lathe. The 
window has a central thickness of 130~$\mu$m. The window thickness 
and profile were measured at FNAL and found 
to be within 5\% of the nominal envelope. This 
verifies the manufacturing procedure. The window has been tested~\cite{Dan} 
under pressure in a setup at Northern Illinois University 
in which it was mounted on a backplate 
and water injected between window and plate. Strain gauge and 
photogrammetric 
measurements were made as a function of pressure, and the results compared 
with FEA predictions. The onset of inelastic deformation 
was predicted at 29~psig, 
a pinhole leak appeared at 31~psig, and rupture occurred at 44~psig. 
The windows required for a cooling channel absorber can be about 
twice as thick as the first prototype window. The results to date are 
therefore encouraging. Further window studies and tests are proceeding.
%
\begin{figure*}%1
%\vspace{-2.0cm}
\centering
\epsfxsize30pc
\epsffile{fig14.ps}
\vspace{0.5mm}
\caption{Absorber window test, showing an array of dots 
projected onto the window for photogrammetric measurements of its 
shape as it deforms under pressure~[27].}
\label{fig:absorber}
\end{figure*}
%
\begin{figure}%1
%\vspace{-2.0cm}
\centering
\epsfxsize200pt
\epsffile{fig15.ps}
%\vspace{-6.5cm}
\caption{CERN 88~MHz cavity~[29] to be prepared for high power tests.}
\label{fig:88mhz}
\end{figure}

\subsection{European Cooling R\&D Program}

The European cooling channel design~\cite{Alessandra} 
is similar in concept to the US design, 
but is based on 44~MHz and 88~MHz cavities~\cite{cern_cavities} 
rather than 201~MHz cavities. 
To minimize the radii of the solenoids used to confine the muons 
within the channel, the cavities have been designed to wrap around 
the solenoids. A full engineering design of this concept will be 
required to understand its feasibility. 
The initial transverse cooling is performed using 44~MHz cavities with 
four 1~m long RF cells between each 24~cm long LH$_2$ absorber. 
The beam is then accelerated from 200~MeV to 300~MeV, and the cooling 
is continued using 88~MHz cavities with eight 0.5~m long cells 
between each 40~cm long LH$_2$ absorber. The channel parameters are 
summarized in Table~\ref{tab:2}. Simulations of the channel performance 
with detailed field-maps have not yet been made. However, simulations 
using simpler field maps yield promising results: the effect of the 
channel is to increase the number of muons within the acceptance of the 
subsequent accelerating system by a factor of about 20. Whether or not 
the predicted  
increased yield is significantly degraded when full simulations are 
performed remains to be seen. In the meantime, a prototype 88~MHz cavity 
is being prepared at CERN (Fig.~\ref{fig:88mhz}) 
for high power tests within the coming year. 
%
\begin{table}
%\renewcommand{\baselinestretch}{2}
\caption{\label{tab:2} CERN cooling channel design parameters~[28]. 
}
\begin{center}
%\vspace{0.6 cm}
\begin{tabular}{l|cc}
\hline \hline
 &Channel 1&Channel 2\\
\hline
Length& 46~m& 112~m\\
Diameter&60~cm&30~cm\\
Sol. Field&2.0~T&2.6~T\\
RF Freq.&44~MHz&88~MHz\\
RF Gradient&2~ MV/m&4~MV/m\\
Beam Energy&200~MeV&300~MeV\\
\hline\hline
\end{tabular}
\end{center}
\end{table}

\subsection{Cooling Experiments}

A sequence of muon cooling-related experiments is being planned. 
The first, the MUSCAT experiment~\cite{muscat}, 
is already under way at TRIUMF. 
The second, the MUCOOL Component Test Experiment, is under 
construction at the Fermilab Linac. The third, an International 
Cooling Experiment~\cite{MICE}, is in the planning stage. The fourth, an 
eventual String Test Experiment, will be planned in the future.

\subsection*{MUSCAT}

The goal of the MUSCAT experiment at TRIUMF is the precise measurement of 
low energy (130, 150, and 180~MeV/c) 
muon scattering in a variety of materials that might be found 
within a cooling channel. In a second phase, the experiment will also 
measure straggling. Scattering measurements for Li, Be, 
C, Al, CH$_2$, and Fe have already been made. Preliminary results 
seem to be in good agreement with expectations~\cite{muscat}. Further analysis 
is in progress. Measurements with LH$_2$ are expected in the 
future.

\subsection*{MUCOOL Component Test Experiment}

A MUCOOL test area located at the end of the Fermilab 400~MeV Linac 
was proposed in the Fall of 2000, and is currently under construction. 
The project is being pursued in two phases. In Phase 1 a LH$_2$ absorber 
test facility is being built, which will enable the first prototype 
absorbers to be filled. In Phase 2  
a linac beam will be brought to the absorber area, and the 5T solenoid 
will be moved from Lab G so that the absorber can be tested in a magnet 
whilst exposed to a proton beam. The beam intensity and spot size 
will be designed to mimic the total ionization energy deposition 
and profile that corresponds to the passage of $10^{12} - 10^{13}$ muons 
propagating through a cooling channel. In addition, 201~MHz RF power 
will be piped to the test area from a nearby test-stand, enabling 
high-power tests to be made of a prototype 201~MHz cooling channel 
cavity exposed to the proton beam.

\subsection*{International Cooling Experiment}

A Europe-Japan-US International Cooling Experiment is currently being 
planned~\cite{MICE}. The goals are to (i) place a cooling channel section in a muon 
beam, and (ii) demonstrate our ability to precisely simulate the passage 
of muons confined within a periodic lattice as they pass through 
LH$_2$ absorbers and high-gradient RF cavities. In the envisioned 
experiment muons are measured one at a time at the input and output of the 
cooling section, and the precise response of the muons to the cooling 
section is determined. The main challenge to the design of this type 
of experiment arises from the prolific X-ray and dark current 
environment created by the 
RF cavities. This is currently under study at Lab~G and elsewhere. 
If it is found that single particle detectors can function in this 
hostile environment, we anticipate a proposal being submitted 
sometime in 2002.

\section{Muon Acceleration and Storage}

The acceleration system has been identified as one of the cost drivers 
for a Neutrino Factory. In the US and European schemes the main acceleration 
systems use SC cavities. The US scheme, for example, uses 201~MHz SCRF 
delivering gradients of 15~MV/m with Q~$\sim 5 \times 10^9$. Although 
higher frequency SCRF cavities are no longer novel, 201~MHz is a relatively 
low frequency and the cavities are therefore large. 
The associated R\&D issues are related 
to microphonics, fabrication and cleaning techniques and, because of the 
large stored energy, quench protection. Furthermore, the cavities must 
tolerate whatever stray magnetic fields they see within the accelerating 
lattice. To address these issues a 201~MHz SC cavity is being constructed 
at CERN and sent to Cornell for high-power testing. 

No major R\&D issues have been identified for the final muon storage ring. 
Building a ring tilted at a large angle raises interesting, but not 
insurmountable, construction challenges~\cite{study1,study2}.

\section{Muon Collider Issues}

A Neutrino Factory, although motivated by its own physics program, 
would also provide a solid step in developing the technology 
that would be required to eventually build a Muon Collider. 
However, additional issues must be addressed before a Muon Collider 
could be proposed. In particular:
\begin{description}

\item{(i)} Muon Cooling: 
The 6-D cooling factor required for a Muon Collider 
is O($10^6$) compared with the more modest factor of O(100) for a Neutrino 
Factory. Muon cooling for a Muon Collider 
will require additional technology. In particular, present 
Muon Collider muon cooling schemes require the longitudinal phase-space to be reduced 
using ``emittance exchange'' in which some of the reduction in the 
transverse phase-space is traded for a reduction in the muon energy spread. 
Although progress towards a viable emittance exchange scheme has been made 
over the last two years, a convincing design has not yet emerged. In addition, 
to obtain the final transverse emittances required for a Muon Collider 
will require a cooling channel with stronger radial focusing than is likely 
to be achieved with affordable high-field solenoids. A new technology  
(liquid lithium lenses~\cite{LiLens}, optical stochastic 
cooling~\cite{Optical}, ... ) is required. 

\item{(ii)} Cost-effective acceleration:
Acceleration is a cost driver for a Neutrino Factory, which requires 
muons accelerated to 20-50~GeV. If a multi-TeV Muon Collider is to be 
affordable an efficient cost-effective acceleration system must be 
developed. 

\item{(iii)} Single muon bunches:
The Neutrino Factory does not require the muons to be packaged into a 
small number of bunches. However, to maximize the luminosity, the 
muons for a Muon Collider should be packaged into one $\mu^+$ and one 
$\mu^-$ bunch per cycle. This will require a more challenging bunching scheme 
and raises additional issues associated 
with having more intense muon bunches (e.g. space charge effects).

\item{(iv)} Detector backgrounds:
Decaying muons within the Muon Collider ring create an intense flux of 
energetic electrons in the neighborhood of the detector. This has been 
studied in detailed~\cite{MUCOL-DET}, and elaborate shielding strategies have 
been shown to reduce the backgrounds down to levels that appear to be acceptable.

\end{description}

Assuming that solutions can be found on paper for these Muon Collider design 
challenges, I believe it will take many extra years of R\&D to develop the 
additional technology required for a Multi-TeV Muon Collider. However, 
the best way to eventually build a cost-effective multi-TeV lepton collider 
is far from clear, and R\&D addressing Muon Collider issues is worthy of a 
significant investment by the community.

\section{Summary and Prospects}

Muon sources capable of delivering a millimole of muons per year 
seem feasible, and would enable Neutrino Factories, and perhaps 
eventually Muon Colliders, to be built. Neutrino Factory designs 
have been developed in Europe, Japan, and the US. Three promising 
schemes are being studied, and a healthy R\&D program is underway 
to develop the required technologies. The most challenging R\&D 
questions are associated with targets for MW-scale proton beams, 
and the development of an ionization cooling channel. Additional 
challenges must be overcome before a Muon Collider can be proposed.

With the present level of support, we can expect much progress 
in Neutrino Factory R\&D over the next few years. However, the future 
level of support is uncertain, and I believe 
a significant increase (factor of two ?) in the R\&D support will 
be needed, sustained over a handful of years, if we are ever to 
arrive at a ``Technical Design Report''. In addition, there must be 
good international collaboration to enable the most promising design 
to be eventually chosen, and pursued. There is already a healthy 
dialogue between the European, Japanese, and US R\&D teams, 
and some cross-participation in the various R\&D programs. 
This international collaboration would greatly benefit from an increase 
in support to enable, for example,  an international ionization 
cooling experiment. 

Finally, it should be noted that Neutrino Factory R\&D is being pursued 
by engineers, accelerator physicists, and particle physicists 
from Laboratories and Universities in Europe, Japan and the US. There 
are a broad range of interesting sub-projects to be pursued, and with 
adequate support, the prospects seem bright.

\section*{Acknowledgments}
This talk is based upon the work of many people. I am particularly 
indebted to material provided to me from my colleagues in Europe and 
Japan, most notably B. Autin, H. Haseroth, Y. Kuno, and Y. Mori. In 
addition I am indebted to all the members of the US Neutrino Factory and 
Muon Collider Collaboration, and those outside of the collaboration who have 
participated in the two US Neutrino Factory studies. My own 
humble contribution to the  work was 
supported at the Fermi National Accelerator Laboratory, which is operated 
by Universities Research Association, under contract No. DE-AC02-76CH03000 
with the U.S. Department of Energy.


\begin{thebibliography}{00}

% \bibitem{label}
% Text of bibliographic item

% notes:
% \bibitem{label} \note

% subbibitems:
% \begin{subbibitems}{label}
% \bibitem{label1}
% \bibitem{label2}
% If there is a note, it should come last:
% \bibitem{label3} \note
% \end{subbibitems}

%[1]
\bibitem{sgprd}
S. Geer, Phys. Rev. {\bf D57}, 6989 (1998). 

%[2]
\bibitem{mucollider}
G.I. Budker, AIP Conf. Proc. {\bf 352} (AIP, New York, 1996) p.4;
A.N. Skrinsky, AIP Conf. Proc. {\bf 352} (AIP, New York, 1996) p.6;
C.M. Ankenbrandt et al. (Muon Collider Collabration), 
``$\mu^+\mu^-$ Collider: A Feasibility Study'', Snowmass 96, BNL-52505; 
ibid. Phys. Rev. ST Accel. Beams 2, 081001 (1999).

%[3]
\bibitem{nufact-physics}
B. Autin, A. Blondel, J. Ellis (editors), CERN yellow report 99-02.,
C. Albright et al., (Eds. S. Geer and H. Schellman), 
``Physics at a Neutrino Factory'', Report to the 
Fermilab Directorate, May 10, 2000, hep-ex/0008064., see also 
the proceedings of NUFACT99 (Lyon, France), NUFACT00 (Monterey, US), 
and NUFACT01 (Tsukuba, Japan). There are many other neutrino factory 
physics papers. Amongst the most cited are:
A. De Rujula, M.B. Gavela, P. Hernandez, Nucl.Phys.B547:21-38,1999; 
V. Barger, S. Geer, R. Raja, K. Whisnant, Phys.Rev.D62:013004,2000., and 
A. Cervera et al., Nucl.Phys.B579:17-55,2000, Erratum-ibid.B593:731,2001.

%[4]
\bibitem{study1}
T. Anderson et al. (Eds: N. Holtkamp and D. Finley), 
``A Feasibility Study of a Neutrino Source Based on a Muon Storage Ring'', 
FERMILAB-Pub-00/108-E (2000). 

%[5]
\bibitem{study2}
M. Goodman et al. (Eds: S.~Ozaki, R.~Palmer, M.~Zisman, J.~Gallardo), 
``Feasibility Study II of a Muon-Based Neutrino Source'', 
BNL-52623, June 2001.

%%[6]
\bibitem{studyJ}
NufactJ Working Group (Eds. Y. Kuno, Y. Mori), 
``A Feasibility Study of a Neutrino Factory in Japan'', see 
http:// www-prism.kek.jp/ nufactj/ index.html

%%[7]
\bibitem{europe-RD}
R. Garoby and B. Autin, presentions at the Neutrino Factory Workshop NUFACT01, 
Tsukuba, Ibaraki, Japan, May 24-30, 2001; 
B. Autin, ``European R\&D for Neutrino Factory'', 
CERN Neutrino Factory Note 101, 
see http://molat.home.cern.ch/molat/ neutrino/nfnotes.html

%%[8]
\bibitem{japan-RD}
S. Machida,  presented at the Neutrino Factory Workshop NUFACT01, 
Tsukuba, Ibaraki, Japan, May 24-30, 2001. 

%%[9]
\bibitem{us-RD}
R. Raja et al; ``The Program in Muon Physics: Superbeams, Cold 
Muon Beams, Neutrino Factory and Muon Collider'', 
Contributed to APS / DPF / DPB Summer Study on the Future of 
Particle Physics (Snowmass 2001), Snowmass, Colorado, 30 Jun - 21 Jul 2001;
hep-ex/0108041 

%%[10]
\bibitem{cool}
A.N. Skrinsky and V.V. Parkhomchuk, Sov. J. of Nuclear Physics, 
12, 3 (1981); D.~Neuffer, Particle Accelerators 14, 75 (1983).

%%[11]
\bibitem{pstudy}
R. Alber et al. (Eds. W. Chou, A. Ankenbrandt, and E. Malamud), 
``The Proton Driver Design Study'', 
FERMILAB-TM-2136, Dec 2000.

%%[12]
\bibitem{cern}
H. Haseroth (CERN). CERN-PS-2000-064-PP.

%%[13]
\bibitem{europe-p}
B. Autin (CERN). CERN-PS-2000-067-PP, 
Workshop on High Intensity Muon Sources, Tsukuba, Japan, 1-4 Dec 1999; 
B. Autin et al.,
CERN-PS-2000-011-AE, Jun 2000. 4pp., 
7th European Particle Accelerator Conference, Vienna, Austria, 26-30 Jun 2000.
B. Autin et al., CERN-2000-012, Dec 2000. 89pp. 

%%[14]
\bibitem{pop}
Y. Mori, Nuclear Instruments and Methods in Physics Research Section A, 
Vol. 451 (1) (2000) p. 300.

%%[15]
\bibitem{E910}
I.~Chemakin et al. (E910 Collab.), 
``Inclusive Soft Pion Production from 12.3 and 17.5 GeV/c Protons on 
Be, Cu, and Au'', nucl-ex/0108007. 

%%[16]
\bibitem{harp}
Proposal to Study Hadron Production for the Neutrino Factory and for the 
Atmospheric Neutrino Flux'', 
CERN-SPSC/99-35, SPSC/P315, 15 November, 1999 
HARP Web Page: http://harp.web.cern.ch/harp/

%%[17]
\bibitem{P907}
P907: ``Proposal to measure particle production in the Meson area using Main Injector
primary and secondary beams'', 
Y.Fisyak et al., R.Raja (spokesperson),
http://ppd.fnal.gov/experiments/ e907/e907.htm

%%[18]
\bibitem{E951}
J. Alessi et al. (E951 Collab.), 
``Proposal: An R\&D Program for Targetry and Capture at a Muon Collider 
Source'', September 28, 1998.

%%[19]
\bibitem{target}
A. Hassenein et al., 
``An R\&D Program for Targetry and Capture at a Neutrino Factory and Muon 
Collider Source'',
Proc. Neutrino Factory Workshop NUFACT01, 
Tsukuba, Ibaraki, Japan, May 24-30, 2001.

%%[20]
\bibitem{band_target}
B. King et al; 
``A Rotating Inconel Band Target for Pion Production at a Neutrino Factory'',
MUCOOL Note 199, 
see http://www-mucool.fnal.gov/htbin/ mcnote1LinePrint

%%[21]
\bibitem{sphere_target}
P.~Sievers, ``A Stationary Target for the CERN Neutrino Factory'', 
CERN Neutrino Factory Note 65. 
See http: // molat.home.cern.ch/molat/neutrino/nfnotes.html

%%[22]
\bibitem{ICOOL}
R. Fernow, ``Fortran Program to Simulate Ionization Cooling'', 
unpublished.

%%[23]
\bibitem{LiLens}
B. Bayanov et al., ``Liquid Lithium Lens for Fermilab Antiproton Source'', 
Budker INP 98-23; 
B. Bayanov et al., ``Design and Construction Technology for a 15~cm 
Long Liquid Lithium Lens'', Budker Institute of Nuclear Physics, 1998.

%%[24]
\bibitem{MUCOOL}
The MUCOOL Web Page can be found at 
http://www.fnal.gov /projects /muon$_-$ collider /cool/ cool.html

%%[25]
\bibitem{dark_current}
J.~Norem et al., 
``Preliminary Lab G Dark~Current~Results'', 
MUCOOL Note 226~at
http://www-mucool.fnal.gov /htbin / mcnote1LinePrint

%%[26]
\bibitem{BeWindows}
N. Hartman, Derun Li, and J. Corlett, 
``Thin Beryllium Windows - Analysis and Design Status'', 
MUCOOL Note 180, 
see http://www-mucool.fnal.gov/ htbin/ mcnote1LinePrint

%%[27]
\bibitem{Dan}
D. Kaplan et al., ``Progress in Absorber R\&D for Muon Cooling'', 
physics/ 0108027; 
D. Kaplan et al., ``Progress in Absorber R\&D 2: Windows'', 
physics/ 0108028.

%%[28]
\bibitem{Alessandra}
A. Lombardi, ``A 40-80 MHz System for Phase Rotation and Cooling'', 
CERN Neutrino Factory Notes 20 and 34, 
see http://molat.home.cern.ch/molat/ neutrino/nfnotes.html

%%[29]
\bibitem{cern_cavities}
R. Garoby and F. Gerigk, 
``Cavity Design for the CERN Muon Cooling Channel'', 
CERN Neutrino Factory Note 87, 
see http://molat.home.cern.ch/molat/ neutrino/nfnotes.html

%%[30]
\bibitem{muscat}
B. Autin, talk given at NUFACT01.

%%[31]
\bibitem{MICE}
K. Hanke, talk given at NUFACT01, and 
http://hep04.phys.iit.edu/cooldemo/. 
The cooling experiment was first proposed in the Fermilab P907 proposal:
C.Ankenbrandt et al., ``Proposal: Ionization Cooling R\&D Program 
for a High Luminosity Muon Collider'', April 15, 1998 
(see http: // www.fnal.gov/projects/muon$_-$ collider/cool/ proposal/ proposal.html).

%%[32]
\bibitem{Optical}
A. Zholents, M. Zolotorev, and W. Wan; Phys. Rev. Special Topics - 
Accelerators and Beams, {\bf 4}, 031001 (2001).

%%[33]
\bibitem{MUCOL-DET}
Muon Collider Collaboration, in Proceedings of the 1996 Snowmass Study, 
Chapter 9 of the Muon Collider Feasibility Study.

\end{thebibliography}

\end{document}



%%%%%%%%%%%%%% End of ws-p10x7.tex %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

hep-ex0111016.extracted_bib
\begin{thebibliography}{00}

% \bibitem{label}
% Text of bibliographic item

% notes:
% \bibitem{label} \note

% subbibitems:
% \begin{subbibitems}{label}
% \bibitem{label1}
% \bibitem{label2}
% If there is a note, it should come last:
% \bibitem{label3} \note
% \end{subbibitems}

%[1]
\bibitem{sgprd}
S. Geer, Phys. Rev. {\bf D57}, 6989 (1998). 

%[2]
\bibitem{mucollider}
G.I. Budker, AIP Conf. Proc. {\bf 352} (AIP, New York, 1996) p.4;
A.N. Skrinsky, AIP Conf. Proc. {\bf 352} (AIP, New York, 1996) p.6;
C.M. Ankenbrandt et al. (Muon Collider Collabration), 
``$\mu^+\mu^-$ Collider: A Feasibility Study'', Snowmass 96, BNL-52505; 
ibid. Phys. Rev. ST Accel. Beams 2, 081001 (1999).

%[3]
\bibitem{nufact-physics}
B. Autin, A. Blondel, J. Ellis (editors), CERN yellow report 99-02.,
C. Albright et al., (Eds. S. Geer and H. Schellman), 
``Physics at a Neutrino Factory'', Report to the 
Fermilab Directorate, May 10, 2000, hep-ex/0008064., see also 
the proceedings of NUFACT99 (Lyon, France), NUFACT00 (Monterey, US), 
and NUFACT01 (Tsukuba, Japan). There are many other neutrino factory 
physics papers. Amongst the most cited are:
A. De Rujula, M.B. Gavela, P. Hernandez, Nucl.Phys.B547:21-38,1999; 
V. Barger, S. Geer, R. Raja, K. Whisnant, Phys.Rev.D62:013004,2000., and 
A. Cervera et al., Nucl.Phys.B579:17-55,2000, Erratum-ibid.B593:731,2001.

%[4]
\bibitem{study1}
T. Anderson et al. (Eds: N. Holtkamp and D. Finley), 
``A Feasibility Study of a Neutrino Source Based on a Muon Storage Ring'', 
FERMILAB-Pub-00/108-E (2000). 

%[5]
\bibitem{study2}
M. Goodman et al. (Eds: S.~Ozaki, R.~Palmer, M.~Zisman, J.~Gallardo), 
``Feasibility Study II of a Muon-Based Neutrino Source'', 
BNL-52623, June 2001.

%%[6]
\bibitem{studyJ}
NufactJ Working Group (Eds. Y. Kuno, Y. Mori), 
``A Feasibility Study of a Neutrino Factory in Japan'', see 
http:// www-prism.kek.jp/ nufactj/ index.html

%%[7]
\bibitem{europe-RD}
R. Garoby and B. Autin, presentions at the Neutrino Factory Workshop NUFACT01, 
Tsukuba, Ibaraki, Japan, May 24-30, 2001; 
B. Autin, ``European R\&D for Neutrino Factory'', 
CERN Neutrino Factory Note 101, 
see http://molat.home.cern.ch/molat/ neutrino/nfnotes.html

%%[8]
\bibitem{japan-RD}
S. Machida,  presented at the Neutrino Factory Workshop NUFACT01, 
Tsukuba, Ibaraki, Japan, May 24-30, 2001. 

%%[9]
\bibitem{us-RD}
R. Raja et al; ``The Program in Muon Physics: Superbeams, Cold 
Muon Beams, Neutrino Factory and Muon Collider'', 
Contributed to APS / DPF / DPB Summer Study on the Future of 
Particle Physics (Snowmass 2001), Snowmass, Colorado, 30 Jun - 21 Jul 2001;
hep-ex/0108041 

%%[10]
\bibitem{cool}
A.N. Skrinsky and V.V. Parkhomchuk, Sov. J. of Nuclear Physics, 
12, 3 (1981); D.~Neuffer, Particle Accelerators 14, 75 (1983).

%%[11]
\bibitem{pstudy}
R. Alber et al. (Eds. W. Chou, A. Ankenbrandt, and E. Malamud), 
``The Proton Driver Design Study'', 
FERMILAB-TM-2136, Dec 2000.

%%[12]
\bibitem{cern}
H. Haseroth (CERN). CERN-PS-2000-064-PP.

%%[13]
\bibitem{europe-p}
B. Autin (CERN). CERN-PS-2000-067-PP, 
Workshop on High Intensity Muon Sources, Tsukuba, Japan, 1-4 Dec 1999; 
B. Autin et al.,
CERN-PS-2000-011-AE, Jun 2000. 4pp., 
7th European Particle Accelerator Conference, Vienna, Austria, 26-30 Jun 2000.
B. Autin et al., CERN-2000-012, Dec 2000. 89pp. 

%%[14]
\bibitem{pop}
Y. Mori, Nuclear Instruments and Methods in Physics Research Section A, 
Vol. 451 (1) (2000) p. 300.

%%[15]
\bibitem{E910}
I.~Chemakin et al. (E910 Collab.), 
``Inclusive Soft Pion Production from 12.3 and 17.5 GeV/c Protons on 
Be, Cu, and Au'', nucl-ex/0108007. 

%%[16]
\bibitem{harp}
Proposal to Study Hadron Production for the Neutrino Factory and for the 
Atmospheric Neutrino Flux'', 
CERN-SPSC/99-35, SPSC/P315, 15 November, 1999 
HARP Web Page: http://harp.web.cern.ch/harp/

%%[17]
\bibitem{P907}
P907: ``Proposal to measure particle production in the Meson area using Main Injector
primary and secondary beams'', 
Y.Fisyak et al., R.Raja (spokesperson),
http://ppd.fnal.gov/experiments/ e907/e907.htm

%%[18]
\bibitem{E951}
J. Alessi et al. (E951 Collab.), 
``Proposal: An R\&D Program for Targetry and Capture at a Muon Collider 
Source'', September 28, 1998.

%%[19]
\bibitem{target}
A. Hassenein et al., 
``An R\&D Program for Targetry and Capture at a Neutrino Factory and Muon 
Collider Source'',
Proc. Neutrino Factory Workshop NUFACT01, 
Tsukuba, Ibaraki, Japan, May 24-30, 2001.

%%[20]
\bibitem{band_target}
B. King et al; 
``A Rotating Inconel Band Target for Pion Production at a Neutrino Factory'',
MUCOOL Note 199, 
see http://www-mucool.fnal.gov/htbin/ mcnote1LinePrint

%%[21]
\bibitem{sphere_target}
P.~Sievers, ``A Stationary Target for the CERN Neutrino Factory'', 
CERN Neutrino Factory Note 65. 
See http: // molat.home.cern.ch/molat/neutrino/nfnotes.html

%%[22]
\bibitem{ICOOL}
R. Fernow, ``Fortran Program to Simulate Ionization Cooling'', 
unpublished.

%%[23]
\bibitem{LiLens}
B. Bayanov et al., ``Liquid Lithium Lens for Fermilab Antiproton Source'', 
Budker INP 98-23; 
B. Bayanov et al., ``Design and Construction Technology for a 15~cm 
Long Liquid Lithium Lens'', Budker Institute of Nuclear Physics, 1998.

%%[24]
\bibitem{MUCOOL}
The MUCOOL Web Page can be found at 
http://www.fnal.gov /projects /muon$_-$ collider /cool/ cool.html

%%[25]
\bibitem{dark_current}
J.~Norem et al., 
``Preliminary Lab G Dark~Current~Results'', 
MUCOOL Note 226~at
http://www-mucool.fnal.gov /htbin / mcnote1LinePrint

%%[26]
\bibitem{BeWindows}
N. Hartman, Derun Li, and J. Corlett, 
``Thin Beryllium Windows - Analysis and Design Status'', 
MUCOOL Note 180, 
see http://www-mucool.fnal.gov/ htbin/ mcnote1LinePrint

%%[27]
\bibitem{Dan}
D. Kaplan et al., ``Progress in Absorber R\&D for Muon Cooling'', 
physics/ 0108027; 
D. Kaplan et al., ``Progress in Absorber R\&D 2: Windows'', 
physics/ 0108028.

%%[28]
\bibitem{Alessandra}
A. Lombardi, ``A 40-80 MHz System for Phase Rotation and Cooling'', 
CERN Neutrino Factory Notes 20 and 34, 
see http://molat.home.cern.ch/molat/ neutrino/nfnotes.html

%%[29]
\bibitem{cern_cavities}
R. Garoby and F. Gerigk, 
``Cavity Design for the CERN Muon Cooling Channel'', 
CERN Neutrino Factory Note 87, 
see http://molat.home.cern.ch/molat/ neutrino/nfnotes.html

%%[30]
\bibitem{muscat}
B. Autin, talk given at NUFACT01.

%%[31]
\bibitem{MICE}
K. Hanke, talk given at NUFACT01, and 
http://hep04.phys.iit.edu/cooldemo/. 
The cooling experiment was first proposed in the Fermilab P907 proposal:
C.Ankenbrandt et al., ``Proposal: Ionization Cooling R\&D Program 
for a High Luminosity Muon Collider'', April 15, 1998 
(see http: // www.fnal.gov/projects/muon$_-$ collider/cool/ proposal/ proposal.html).

%%[32]
\bibitem{Optical}
A. Zholents, M. Zolotorev, and W. Wan; Phys. Rev. Special Topics - 
Accelerators and Beams, {\bf 4}, 031001 (2001).

%%[33]
\bibitem{MUCOL-DET}
Muon Collider Collaboration, in Proceedings of the 1996 Snowmass Study, 
Chapter 9 of the Muon Collider Feasibility Study.

\end{thebibliography}