The AlCap experiment utilised the $\pi$E1 beamline, which provided a well-tuned, well-understood low momentum muon beam.

The magnet settings were provided by MuSun and were set to extract a 28 MeV/c momentum muon beam from the beamline. It was simple to scale this to other momenta by scaling the strengths of the magnets and it is this scale factor that is quoted in Table~\ref{tab:alcap:datasets} as the muon beam momentum.

In addition to the absolute momentum, it was possible to change the momentum bite of the beam. Most runs were taken with a $3\%$ momentum bite in order to achieve a high rate.

For the active silicon target, the choice of scale factor was based on momentum scan runs where the energy deposited by the muon beam could be seen, as shown in Figure~\ref{fig:si-mom-scan}.

\begin{figure}[htbp]
  \centering
    \includegraphics[width=0.8\textwidth]{figs/MomScanRuns.pdf}
    \caption{Plot of the pulse height (proportional to energy) of the slow pulses in the thick silicon detector when it was in the target position for different beam momenta. Distributions are normalised by peak height for ease of comparison.}
  \label{fig:si-mom-scan}
\end{figure}

In this plot, the right-hand peak is the peak due to stopped muons and the lower energy, left-hand peak is due to punch-through muons. This is confirmed by running a Monte Carlo simulation (Figure~\ref{fig:MC_punch-through-mu}). As can be seen from Figure~\ref{fig:si-mom-scan}, as the beam energy increases, the stopped muon peak also goes to higher energies, which implies that the muon beam is stopping deeper inside the target.  Above a certain energy threshold, the peak no longer rises as the muons start to punch through. 

\begin{figure}[htbp]
  \centering
  \includegraphics[width=0.9\textwidth]{figs/MC_punch-through-mu.pdf}
  \caption{Plot of Monte Carlo simulation showing the lower peak is due to muons punching through the silicon target for scale factor of 1.43.}
  \label{fig:MC_punch-through-mu}
\end{figure}

The choice of scale factor for the aluminium target runs was based on a preliminary analysis of the X-ray spectra such that the number of stopped muons was maximised. This resulted in the choices of 1.09 and 1.07 for Al100 and Al50 respectively.

Data from the muon beam were recorded during the run from the detectors
in the entrance counter. The number of hits in the $\mu$Sc and $\mu$ScA were stored and give a raw count of the number of incoming muons, and the
number passing through the hole in $\mu$ScA can then be determined
by an anti-coincidence between $\mu$Sc and $\mu$ScA. 

Also, from data taken from the wire chamber ($\mu$PC), a 2D spatial distribution of the beam exiting the beam-pipe can be plotted.
This distribution from one of the runs in the Al50 data-set is plotted in Figure~\ref{fig:mupc-data} and
shows that the beam is not entirely symmetric in the $x$-direction. This is not what
was assumed in the simulation, however, future simulations will be able to
read in this histogram and generate muons with a more realistic spatial distributions.

\begin{figure}[htbp]
  \centering
    \includegraphics[width=0.8\textwidth]{figs/mupc-data.png}
    \caption{Plot of the $x$--$y$ distribution of the beam for one run in the Al50 data-set.}
  \label{fig:mupc-data}
\end{figure}

