\section{International Muon Ionization Cooling Experiment}
\label{mice}

\subsection{Motivation}

Ionization cooling of minimum-ionizing muons is an important
ingredient in the performance of a Neutrino Factory. However, it has
not been demonstrated experimentally. We seek to carry out an
experimental demonstration of cooling in a muon beam. Towards this
goal, we have developed (in collaboration with a number of physicists
from Europe and Japan interested in neutrino factories) a conceptual
design for an International Muon Ionization Cooling Experiment
(MICE). Letters of intent for MICE have beeen submitted to the Paul
Scherrer Institute in Switzerland and the Rutherford Appleton
Laboratory in England~\cite{MICE-LOI}.  A technical proposal is under
development, with completion planned in 2002.

The aim of the proposed cooling experimental demonstration is
\begin{itemize} 
\item	to show that we can design, engineer and build a section of cooling
channel capable of giving the desired performance for a neutrino
factory;
\item	to place it in a beam and measure its performance, {\em i.e.},
experimentally validate our ability to simulate precisely the passage
of muons confined within a periodic lattice as they pass through
energy absorbers and RF cavities.
\end{itemize}
The experience gained from this experimental demonstration will
provide important input to the final design of a real cooling
channel. The successful operation of a section of a muon cooling
channel has been identified (most recently by the U.S. Muon Technical
Advisory Committee~\cite{MUTAC-report}) as a key step in demonstrating
the feasibility of a Neutrino Factory or Muon Collider.

\subsection{Principle of the experiment}

Fundamentally, in a muon cooling experiment one needs to measure,
before and after the cooling channel, the phase space distribution of 
a muon beam in six dimensions~\cite{cernmice}. Such a measurement must include
the incoming and outgoing beam intensities and must avoid biases due
to the decay of muons into electrons within the channel and due to
possible contamination of the incoming beam by non-muons~\cite{summers}. 
Two techniques have been considered: i) the multi-particle method, in
which emittance and number of particles in any given volume of phase
space are determined from the global properties of a bunch; and ii)
the single-particle method, in which the properties of each particle
are measured and a ``virtual bunch" formed off-line. The full
determination of the covariance matrix in six dimensions is a delicate
task in a multi-particle experiment, and the desired diagnostics would
have to be developed specifically for this purpose; moreover, a
high-intensity muon beam bunched at an appropriate frequency would
need to be designed and built. For these reasons, the single particle
method is preferred. The single-particle approach, typical of
particle-physics experiments, is one for which experimental methods
already exist and suitable beams are already available.

In the particle-by-particle approach, the properties of each particle
are measured in magnetic spectrometers before and after the cooling
channel (Fig.~\ref{fig:MICE-measurement}). Each spectrometer measures,
at given $z$ positions, the coordinates $x, y$ of every incident
particle, as well as the time. Momentum and angles are reconstructed
by using more than one plane of measurement. For the experimental
errors not to affect the measurement of the emittance by a significant
factor, the rms resolution of the measurements must be smaller than
typically 1/10th of the rms equilibrium beam size in each of the six
dimensions~\cite{Blondel-cooling}.

\begin{figure}
\centerline{{\includegraphics[width=\linewidth]{MICE-measurement.eps}}}
\caption{Conceptual layout of MICE upstream spectrometer: 
following an initial time-of-flight (TOF) measurement, muons are 
tracked using detector planes located within a solenoidal magnetic field.
 Although in principle three $x,y$ measurements as shown suffice to 
determine the parameters of each muon's helical trajectory, in practice 
additional measurement redundancy will be employed; for example, a 
fourth measurement plane can be used to eliminate very-low-momentum
 muons that would execute multiple cycles of helical motion. 
A similar spectrometer (but with the time-of-flight measurement 
at the end) will be used downstream of the cooling apparatus.}
\label{fig:MICE-measurement}
\end{figure}

\subsection{Conceptual design}

Fig.~\ref{fig:MICE} shows the layout under consideration for MICE,
which is based on two cells of the Feasibility Study II ``Lattice 1"
cooling channel. The incoming muon beam encounters first a beam
preparation section, where the appropriate input emittance is
generated by a pair of high-$Z$ (lead) absorbers. In addition, a
precise time measurement is performed and the incident particles are
identified as muons. There follows a first measurement section, in
which the momenta, positions, and angles of the incoming particles are
measured by means of tracking devices embedded in a uniform-field
solenoid. Then comes the cooling section itself, with hydrogen
absorbers and 201 MHz RF cavities, the lattice optics being provided
by a series of superconducting coils; the pairs of coils surrounding
each absorber have opposite magnetic fields (``bucking" solenoids),
providing tight focusing. The momenta, positions, and angles of the
outgoing particles are measured within a second solenoid, equipped
with a tracking system identical to the first one. Finally, another
time-of-flight (TOF) measurement is performed together with particle
identification to eliminate those muons that have decayed within the
apparatus.

\begin{figure}
\centerline{\scalebox{0.6}{\includegraphics{MICE-fig.eps}}}
\caption{Schematic layout of MICE apparatus.}
\label{fig:MICE}
\end{figure}

\subsection{Performance}

Simulations of MICE have been carried out for a configuration
including four tracking stations per spectrometer, each station
consisting of three crossed planes of 500-micron-thick
square-cross-section scintillating fibers
(Fig.~\ref{fig:MICE-tracking}), embedded within a 5\,T solenoidal
field. Time of flight is assumed to be measured to 70\,ps rms. As
shown in Fig.~\ref{fig:MICE-resolution}, measurement resolution and
multiple scattering of the muons in the detector material introduce a
correctable bias in the measured emittance ratio of only 1\%. (For
this study the effect of the cooling apparatus was ``turned off" so as
to isolate the effect of the spectrometers.)

\begin{figure}
\centerline{\scalebox{0.7}{\includegraphics{MICE-tracking.eps}}}
\caption{A possible MICE tracking-detector configuration.}
\label{fig:MICE-tracking}
\end{figure}

\begin{figure}
\centerline{\scalebox{0.5}{\includegraphics{MICE-resolution.eps}}}
\caption{Generated and measured ratios of output to input six-dimensional 
emittance for 1000 simulated experiments, each with 1000 accepted muons.}
\label{fig:MICE-resolution}
\end{figure}

Fig.~\ref{fig:MICE-sim1} illustrates the muon-cooling performance of
the proposed MICE cooling apparatus. The normalized transverse
emittance of the incoming muon beam is reduced by about 8\%. The
longitudinal emittance increases by about the same amount, thus the
net cooling in six dimensions is also about 8\%. These are large
enough effects to be straightforwardly measured by the proposed
spectrometers.
%
\begin{figure}[htb!]
\begin{minipage}[b]{0.46\linewidth}
%emit-trans-vs-s.ps
\centering\includegraphics[width=\linewidth]{MICE-200MHz-cooling.eps}
\end{minipage}\hfill
\begin{minipage}[b]{0.46\linewidth}
%emit-long-vs-s.ps
\centering\includegraphics[width=\linewidth]{MICE-200MHz-long.eps}
\end{minipage}\hfill
\caption{Results from ICOOL simulation of MICE: normalized transverse
(left) and longitudinal (right) emittances {\em vs.}\ distance.}
\label{fig:MICE-sim1}
\end{figure}

The CERN Neutrino Factory Working Group has studied a variant of the
proposed MICE cooling apparatus, in which 88-MHz RF cavities are
employed in place of the 201-MHz devices (the 88- and 201-MHz designs
have similar cooling
performance)~\cite{Hanke-cooling}. Fig.~\ref{fig:MICE-sim2} (from the
CERN study) elucidates further experimental issues. As shown in
Fig.~\ref{fig:MICE-sim2}a, for input emittance above the equilibrium
emittance of the channel (here about 3500\,mm$\cdot$mr), the beam is
cooled, while for input emittance below equilibrium it is heated (and,
of course, for an input beam at the equilibrium emittance, the output
emittance equals the input emittance).  Fig.~\ref{fig:MICE-sim2}b
illustrates the acceptance cutoff of the cooling-channel lattice; for
input emittance above 6000\,mm$\cdot$mr, the transmission probability
falls below 100\% due to scraping of the
beam. Fig.~\ref{fig:MICE-sim2}c shows the effect of varying the beam
momentum: cooling performance improves as the momentum is
lowered~\footnote{Despite the increased cooling efficiency at low muon
momentum, simulations of an entire muon production section and cooling
channel suggest that momenta near the ionization minimum represent the
global optimum for Neutrino Factory performance.}, as quantified here
in terms of the fractional increase in the number of muons within the
phase-space volume accepted by a hypothetical acceleration section
downstream of the cooling channel. The goal of MICE includes
verification of these effects in detail in order to show that the
performance of the cooling apparatus is well understood. Subsequent
running could include tests of additional transverse cooling cells,
alternative designs, or emittance exchange cells.

\begin{figure}
\centerline{{\includegraphics[width=0.6\linewidth]{MICE-88MHz-cooling.eps}}}
\caption{Simulation results for 88-MHz variant of MICE apparatus: 
a) output emittance {\it vs.}\ input emittance, with 45$^\circ$ line (dashes) 
superimposed; b) beam transmission  {\it vs.}\ input emittance; c) 
cooling performance (see text) {\it vs.}\ input emittance for
 various beam kinetic energies (top to bottom: 140, 170, 200, 230 MeV).}
\label{fig:MICE-sim2}
\end{figure}

One critical aspect of this experiment is operation in the presence of
backgrounds due to dark currents from the rf cavities.  While it is possible to
operate the experiment using comparatively low rf gradients, it would be highly
desirable to produce cavities which would yield less dark current at higher
gradients.  This would permit more efficient use of the rf cavities and power
supplies.   We are trying to develop cavities with low dark currents.