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\begin{document}

\title[Muscat Report]{MuScat Report - the Muon scattering experiment.}

\author{W. J. Murray
%\dag
%\footnote[3]{To
%whom correspondence should be addressed (w.murray@rl.ac.uk)}
}

\address{
%\dag\ 
W.Murray, RAL,
Chilton, Didcot, Oxon., OX11 0QX, UK,\\
(w.murray@rl.ac.uk) }


\begin{abstract}
The MuScat experiment for measuring the multiple scattering of muons in
low Z materials at momenta relevant to the cooling channel of a muon
accelerator is described. 

An engineering run in Triumf in 2000 suffered from problems with the 
delay line chambers, and a new tracking
detector, a 3 layer scintillating fibre detector which can be seen as 
a parent of one of the MICE tracker options, has been constructed.
First performance indications are given.



\end{abstract}

%Uncomment for PACS numbers title message
%\pacs{00.00, 20.00, 42.10}

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%\maketitle

\section{Introduction}
The Muscat experiment  (E875) at Triumf is designed to measure the 
multiple scattering of muons of momenta up to 200MeV/c. This process 
has never been measured, and it is very important for the optimal
design of a cooling channel for a neutrino factory or muon collider.
The motivation is discussed in section~\ref{sec:motivation}.

The history, status and prospects are also described herein.

The project is a collaboration involving people from CERN, UCLA, Birmingham,
RAL, Oxford and Imperial College, London.

\section{Motivation}
\label{sec:motivation}


The preparation of a beam of muons for a neutrino factory or collider
is likely to rely upon ionization cooling\cite{ref:cooling} to prepare the
muons for  acceleration. This entails passing the muons through
matter to reduce their $p_T$ and $p_L$ through $de/dx$ losses, and then
subsequent re-acceleration, restoring only the $p_L$. 
This cooling process is counteracted by multiple scattering, which warms 
the beam by adding random components to the $p_T$. It is probably
best performed at momenta around 200 to 300~MeV/c.

The design of the cooling
channel is a complicated affair, with a choice  to be made between
liquid hydrogen, which provides the best cooling but requires containment
and safety windows, and possibly a heavier element which might require
less additional material. This compromise, and the details of the layout, 
 require an accurate knowledge of the
cooling and warming effects of the different materials if it is to be 
made optimally.



%\begin{figure}
%\begin{center}
%\epsfxsize=4cm
%\epsfbox{aluminium.eps}
%\epsfxsize=5cm
%\epsfbox{beryllium.eps}
%\epsfxsize=4cm
%\epsfbox{lithium.eps}
%\end{center}
%\caption{\label{fig:andrievsky}Multiple scattering}
%\end{figure}


\begin{figure}[h]
\begin{center}
%$\begin{array}{c@{\hspace{1in}}c@{\hspace{1in}}c}
$\begin{array}{ccc}
%\multicolumn{1}{l}{\mbox{\bf (a)}} &
%          \multicolumn{1}{l}{\mbox{\bf (b)}} &
%                   \multicolumn{1}{l}{\mbox{\bf (c)}} \\ [-0.53cm]
\epsfxsize=2in \epsffile{aluminium.eps} &
	\epsfxsize=2in	\epsffile{beryllium.eps} &
	\epsfxsize=2in	\epsffile{lithium.eps} \\ [-5.8cm]
\multicolumn{1}{l}{\mbox{\bf a)}} &
          \multicolumn{1}{l}{\mbox{\bf b)}} &
                   \multicolumn{1}{l}{\mbox{\bf c)}} \\ [4.8cm]
%\mbox{\bf a)} & \mbox{\bf b)} & \mbox{\bf c)}
\end{array}$
\end{center}
%\caption{The caption for Figure \protect\ref{figtest-fig}}
\caption{Measurements of the scattering distribution for electrons, from 1942.}
\label{fig:andrievsky}
\end{figure}

There is no relevant data on the scattering of muons.
Figure~\ref{fig:andrievsky} shows the scattering of electrons in low-Z 
materials, with the prediction of Moliere theory overlayed. The
agreement is not overwhelming, especially for Lithium, and it
can be argued that the disagreement is growing as the Z of the
target material drops, which motivates checking this.

Multiple scattering is, of course, calculable.
The calculations are not completely trivial, because the screening
of the nuclear charge by the electron cloud requires an accurate
knowledge of the wave-function for H$_2$, or whichever molecule is
used, and in a liquid this is not the same as the wave-function in
vacuum.



\begin{figure}[h]
\begin{center}
\epsfxsize=16cm
\epsfbox{layout.eps}
\end{center}
\caption{\label{fig:sketch} The MuScat apparatus, as run in 2000. The MWPC's
have been replaced by a scintillating fibre tracker.}
\end{figure}

A cartoon of the apparatus to measure the multiple scattering is shown in
figure~\ref{fig:sketch}. 
There are two defining collimator slits, each of 2~mm in height, separated
by 1~m. An assortment of targets can be rotated into the beam at this
point, and then s further metre is allowed for the beam to diverge, allowing
a single measurement of position to yield a deflection angle.
The NaI calorimeter, Mina, is a facility of
the Triumf laboratory, used by the experiment while data-taking.


\section{History}
\label{sec:history}

The initial intention for the experiment was to check the multiple scattering
of muons using the beams available at Rutherford Appleton Laboratory, 
which have a momentum up to about 100~MeV/c. At these low momenta,
the scattering in whatever measurement system was used to characterise
the beam is significant, and it was decided to use a collimation approach
instead.

However, the pulsed muons source  at RAL is not particularly suitable for this
experiment, where single muons are analysed individually, and the beams
were heavily used, so we applied for beam-time at Triumf, which has a DC 
source. This has the
added advantage that the beam momentum can be raised to nearly 200~MeV/c, 
which is much closer to the momenta favoured for a cooling channel.

An engineering run was made in Triumf in summer 2000, using solid targets
such as aluminium, lithium and beryllium, which was generally successful. 
The collimation system worked exactly as planned and the time-of-flight
system was
able to separate pions, muons and electrons in the beam.
Unfortunately, the delay line chambers which were used to reconstruct the
outgoing particle were designed to work with  CFC's as a damping
agent, and this is now forbidden. A gas mixture was improvised using
methylal, but unfortunately too much was used, and the chambers were damaged.
The efficiency was thus not uniform, and even worse, time dependent.
Furthermore, there were some details of the performance of the
chambers which were never properly understood.
The decision was made to build a new tracking system for the main physics
run.


\begin{figure}[h]
\begin{center}
\epsfxsize=15cm
\epsfbox{pos_vac2.eps}
\end{center}
\caption{\label{fig:pos_vac} 
The distribution measured during the engineering run with no target, i.e.
the collimators only. The data is in green, and a G4 simulation in red.
Shoulders due to particles partially penetrating the collimator
jaws can be seen at $\pm$15~cm. 
}
\end{figure}


Figure~\ref{fig:pos_vac} shows the measured outgoing particle distribution
during the engineering run 
with no target present, compared with the simulation, and a simple fit to
guide the eye. The data is well described by the Geant 4 simulation, including 
both the level of the tails, and the presence and level of a shoulder
at $\pm$15cm.

\section{Scintillating Fibre Tracker}

The new tracker has three double planes of scintillating fibres, each
with 512  fibres in both x and y. The fibres are double clad Bicron 
scintillating fibre with  an external diameter
of 1~mm, and are spaced at intervals of just under 0.6~mm, so as to
cover a 30~cm squared area with good efficiency.
This is a total of 3096 fibres,  which were tensioned in a Delrin
frame and then potted into a plane of resin. A black resin is used
to reduce the effect of cross-talk or any ambient light.

To reduce costs, the readout is multiplexed. Each single plane of
512 fibres is grouped as two pairs of 256. These 256 are readout at both
ends, using a clear fibre readout bundle in which  the 256 fibres are potted
into a square arrangement, 16~mm each way. Each bundle is then brought
up to a Hamamatus R5900U photomultiplier\footnote{Hamamtsu Photonics,
325-6,Sunayama-cho,Hamamatsu City, Shizuoka Pref., 430-8587,Japan},
 which has sixteen anodes, each 16~mm by 0.85~mm, and spaced by 1~mm.
The PMT's at the two ends of the plane read the rows and columns of this
bundle respectively. In the event of one single fibre hit, this
allows the fibre number to be found. 

\begin{figure}[h]
\begin{center}
\epsfxsize=10cm
\epsfbox{bundles-lit3.eps}
\end{center}
\caption{\label{fig:bundles} The ends of two of the fibre bundles, potted
into vacuum feedthroughs, waiting for the photomultipliers to be attached.
Precision dowel holes can be seen, optically aligned to the photo-cathode.
}
\end{figure}

The three double planes are mounted in a dedicated vacuum vessel,
with twenty four fibre bundles, each coming to its own vacuum feedthrough.
Two are shown in
figure~\ref{fig:bundles}. While they are being potted the fibres naturally
try to adopt a hexagonal
packing, but need to be held in a square arrangement to match the
photomultiplier. For this reason the success rate in manufacture was only
about 50\%.

The PMT's are readout using a custom sample-and-hold system, with
a front end having a 2~$\mu$s time-constant. This means that the
incident particle flux must be kept below 10$^5$~Hz or there will 
be pile-up issues to consider. The electronic noise is very low, well 
below the level of a single photoelectron.

The complete tracker has been tested using cosmic rays and proton and pion
beams  at RAL. Pedestal uniformity is good, and there are few noisy channels.
There are no precise numbers on efficiency to date, but it is better
than 90\%. The 
mean signal size is somewhat disappointing, being between 3 and 4
photo-electrons at each end of the detector. This is however adequate,
especially when it is recalled that there are three planes in
the tracker, while only one is required to establish the outgoing
particle angle. Cosmic ray tracks have been reconstructed, demanding
3 hits in each of x and y, with an efficiency around 50\%.

The detector seems stable and should be able to make the
measurements required.

\section{Collimators}

\begin{figure}[h]
\begin{center}
\epsfxsize=16cm
\epsfbox{col-diff2.eps}
\end{center}
\caption{\label{fig:coldif} The expected particle arrival position distribution
at the detectors with no target.
The upper grey line shows the original collimation system, while the
black gives the effect of an improved 
improved passive collimation  and the solid area shows the expectation when
 using an active collimator
in addition.
  The light grey contribution at the bottom  corresponds to the effect of
 muon decays in flight.}
\end{figure}


The good agreement between simulation and data in figure~\ref{fig:pos_vac}
gives confidence that Geant 4 can be used to improve the details of the
collimation system. 
Revisions have been made to the  jaw angles, the shape and position of
additional cleaning collimators inside the collimation tube, and extra 
lead shielding has been added. These are partially because the 
collimation system was being used for momenta higher than it was originally
designed, and also due to problems identified with experience. 
Furthermore, a new active collimator has
been added to clean up some 
of the tails in the distribution.


This last comprises two scintillator bars, each 3~mm square an 24~mm long, 
which are positioned just above and just below the inlet to the final 
collimator. These should catch muons which rather than flying through
the collimation gap instead hit the front face of the lead, and then 
scatter and emerge in the final collimation jaw. Such particles have a much
larger range of angles than  normal, and would complicate the measurement
of the scattering distribution significantly.

\section{Time of flight}


\begin{figure}[h]
\begin{center}
\epsfxsize=10cm
\epsfbox{tof_1.eps}
\end{center}
\caption{\label{fig:tof} 
The time of flight distribution measured in M11 using the first
acceptance scintillator and the beam period monitor.
The clean separation of pion, muon and electron peaks can be seen.
}
\end{figure}


The beamline used at Triumf, M11, has a beam which is 80 to 90\% pions
with a contamination of 5-10\% of muons and electrons. The muon
component can be easily identified using the time of flight information
from the beam defining scintillator, as seen in figure~\ref{fig:tof}.
For the final experiment  this information will be supplemented by
 a timing signal from the SciFi tracker, which may be comparable in
accuracy when several measurements are combined. This last measurement,
being after the collimator jaws, may also be able to remove particles
which have interacted with the jaws and slowed down.

\section{Conclusions and prospects}

The MuScat experiment had a very useful engineering run, and have
proceeded to construct a brand new scintillating fibre tracker.
This has been built and is undergoing tests.

A beam allocation at Triumf for March 2003 has been made, and MuScat will
take data with liquid hydrogen and a range of solid targets there then.
Thee is much software work still to be done in understanding the fibre
tracker and working out how best to use the information from it, but
we can be confident that one year from now detailed 
multiple scattering  data will be available.

 
%\section*{References}
\vskip 2 cm
\begin{thebibliography}{99}

\bibitem{ref:cooling} 
V.V. Parkhomchuk and A. N. Skrinsky, Ionization cooling: Physics and
Applications, Proc. 12th Int. Conf. on High Energy Accelerators, 1983, 
eds. F.~T.~Cole and R.~Donaldson., \\
A. N. Skrinsky and V.V. Parkhomchuk, Sov. J. of Nucl. Physics {\bf 12},
223 (1981).,\\
D. Neuffer, ``Colliding Muon Beams at 90 GeV'', FNAL Report-FN-319, 1979.

\end{thebibliography}


\end{document}

