\chapter{The AlCap Run 2013}
\label{cha:the_alcap_run_2013}
\thispagestyle{empty}
The first run of the AlCap experiment was performed at the $\pi$E1 beam line
area, PSI from November 26 to December 23,
2013. The goal of the run was to measure protons rate and spectrum following
muon capture on aluminium.

\section{Experimental set up}
\label{sec:experimental_set_up}
The low energy muons from the $\pi$E1 beam line were stopped in thin aluminium
and silicon targets, and charged particles emitted were measured by two pairs
of silicon detectors inside of a vacuum vessel
(\cref{fig:alcap_setup_detailed}).  A stopped muon event is defined by
a group of upstream detectors and a muon veto plastic scintillator. 
The number of stopped muons is monitored by a germanium detector placed outside
of the vacuum chamber. In addition, several plastic scintillators were used to
provide veto signals for the silicon and germanium detectors. Two liquid
scintillators for neutron measurements were also tested in this run.  
\begin{figure}[btp] 
	\centering
	\includegraphics[width=0.65\textwidth]{figs/alcap_setup_detailed} 
	\caption{AlCap detectors: two silicon packages inside the vacuum vessel, 
    muon beam detectors including plastic scintillators and a wire chamber, 
    germanium detector and veto plastic scintillators.}
	\label{fig:alcap_setup_detailed} 
\end{figure} 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Muon beam and vacuum chamber}
Muons in the $\pi$E1 beam line are decay products of pions created
as a \SI{590}{\mega\electronvolt} proton beam hits a thick carbon target. The
beam line was designed to deliver muons with momenta ranging from
\SIrange{10}{500}{\mega\electronvolt\per\cc} and momentum spread from
\SIrange{0.26}{8.0}{\percent}~\cite{Foroughli.1997}. These parameters can be
selected by changing various magnets and slits shown in
\cref{fig:psi_piE1_elements}.

%(E-target in \cref{fig:psi_exp_hall_all}). 
%\begin{figure}[p]
  %\centering
    %\includegraphics[height=0.85\textheight]{figs/psi_exp_hall_all}
  %\caption{Layout of the PSI experimental hall, $\pi$E1 experimental area is
	%marked with the red circle. \\Image taken from
	%\url{http://www.psi.ch/num/FacilitiesEN/HallenplanPSI.png}}
  %\label{fig:psi_exp_hall_all}
%\end{figure}

\begin{figure}[btp]
  \centering
    \includegraphics[width=0.7\textwidth]{figs/psi_piE1_elements}
  \caption{The $\pi$E1 beam line}
  \label{fig:psi_piE1_elements}
\end{figure}

One of the main requirements of the AlCap experiment was a low energy muon beam
with narrow momentum bite in order to achieve a high fraction of stopping muons
in the very thin targets. In this Run 2013, muons from
\SIrange{28}{45}{\mega\electronvolt\per\cc} and momentum spread of 1\% and
3\%were used. 

For part of the experiment the target was replaced with one of the silicon
detector packages allowed an accurate momentum and range calibration 
%(via range-energy relations)
of the beam at the target. \Cref{fig:Rates} shows the measured muon rates
as a function of momentum for two different momentum bites.
\Cref{fig:Beam} shows an example of the resulting energy spectra.
\begin{figure}[btp] 
	\centering
	\includegraphics[width=0.6\textwidth]{figs/Rates.png} 
	\caption{Measured muon rate (kHz) at low momenta. Momentum bite of 3 and 1 \%
	FWHM, respectively.} 
	\label{fig:Rates} 
\end{figure}   

\begin{figure}[btp]
	\centering 
	\includegraphics[width=0.9\textwidth]{figs/beam.pdf} 
	\caption{Energy deposition at \SI{36.4}{/c} incident muon beam in an
    \SI{1500}{\micro\meter}-thick active target. The peak at low energy is due
    to beam electrons, the peaks at higher energies are due to muons. Momentum
    bite of 1 and 3\% FWHM on left and right hand side, respectively.} 
  \label{fig:Beam} 
\end{figure}  

The targets and charged particle detectors are installed inside the vacuum
chamber as shown in \cref{fig:alcap_setup_detailed}.  The muon beam enters
from the right of the image and hits the target, which is placed at the
centre of the vacuum chamber and orientated at 45 degrees to the beam axis.
The side walls and bottom flange of the vessel provide several
vacuum-feedthroughs for the high voltage and signal cables for the silicon and
scintillator detectors inside the chamber.
In addition, the chamber is equipped with several lead collimators
%so that muons that are not captured in the target would quickly decay.
to quickly capture muons that do not stop in the actual target. 
%\begin{figure}[btp]
	%\centering
	%\includegraphics[width=0.55\textwidth]{figs/SetupOverview.jpg}
	%\caption{Vacuum chamber in beam line}
	%\label{fig:SetupOverall}
%\end{figure}

%It is known fact that there is a risk of sparkling between the electrodes of
%a silicon detector in the low vacuum region of $10^{-3}$ mbar.
%An interlock mechanism was installed to prevent the bias of the
%silicon detectors from being applied before the safe vacuum level. 
For a safe operation of the silicon detector, a vacuum of \SI{e-4}{\milli\bar}
was necessary.  With the help of the vacuum group of PSI, we could consistently
reach the required vacuum level within 45 minutes after closure of the
chamber's top flange.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\subsection{Silicon detectors} 
The main detectors for proton measurement in the Run 2013 were four large area
silicon detectors. The silicon detectors were grouped into two detector
packages located symmetrically at 90 degrees of the nominal muon beam path, SiL
and SiR in \cref{fig:alcap_setup_detailed}. Each arm consists of: one
$\Delta$E counter, a \SI{65}{\micro\meter}-thick silicon detector, divided into
4 quadrants; one E counter made from \SI{1500}{\micro\meter}-thick silicon; and
one plastic scintillator to identify electrons or high energy protons that
pass through the silicon. The area of each of these silicon detectors and the
scintillators is $50\times50 \textrm{mm}^2$. There is a dead layer of
\SI{0.5}{\micro\meter} on each side of the silicon detectors according to the
manufacturer Micron Semiconductor
\footnote{\url{http://www.micronsemiconductor.co.uk/}}.

The detectors were named according to their positions relative to the muon
view: the SiL package contains the thin
detector SiL1 and thick detector SiL2; the SiR package has SiR1 and SiR2
accordingly. Each quadrant of the thin detectors were also numbered from 1 to
4, i.e. SiL1-1, SiL1-2, SiL1-3, SiL1-4, SiR1-1, SiR1-2, SiR1-3,
SiR1-4.

Bias for the four silicon detectors was supplied by an ORTEC 710 NIM module,
which has a vacuum interlock input to prevent biasing before the safe vacuum
level has been reached. Typical voltage to fully depleted the detectors were
\SI{-300}{\volt} and \SI{-10}{\volt} for the thick and thin silicon detectors
respectively. The leakage currents at the operating voltages are less than
\SI{1.5}{\micro\ampere} for the thick detectors, and about
\SI{0.05}{\micro\ampere} for the thin ones (see \cref{fig:si_leakage}).
\begin{figure}[btp]
  \centering
    \includegraphics[width=0.85\textwidth]{figs/si_leakage}
  \caption{Leakage currents of the silicon detectors under bias.}
  \label{fig:si_leakage}
\end{figure}

The fact that a detector were fully depleted was checked by putting
a calibration source $^{241}\textrm{Am}$ at its ohmic side, and observing the
output
pulse height on an oscilloscope. One would expect that the maximum pulse height
increases as the bias is raised until the voltage of fully depleted. The effect
can also be seen on the pulse height spectrum as in
\cref{fig:sir2_bias_alpha}.
\begin{figure}[btp]
  \centering
    \includegraphics[width=0.75\textwidth]{figs/sir2_bias_alpha}
  \caption{$^{241}\textrm{Am}$ spectra in cases of fully depleted (top), and
    partly depleted (bottom).}
  \label{fig:sir2_bias_alpha}
\end{figure}

%It is known that the noise level of a silicon detector increases linearly with
%its capacity. So both noise and pick-up suppression had been carefully
%optimised in the real PSI accelerator environment, particularly for the thin
%silicon detectors which have a large capacity of 1~\nano\farad~in each
%quadrant.
%After improving the feed-through flanges during the set-up phase of the
%experiment with isolated ground connections, good electronic resolution of
%55--76~\kilo\electronvolt\ FWHM was achieved in the thin silicon detectors.
%So achieving good energy resolution was particularly challenging
%for the thin silicon detector, as each quadrant had a large capacity of
%1~\nano\farad. Both
%noise and pick-up suppression had been carefully optimized in the real PSI
%accelerator environment.
%Optimization of the fast timing signals proved another challenge.
%The energy calibration for the silicon detectors were done
%by several means:
%\begin{enumerate}
	%\item An $^{241}\textrm{Am}$ alpha source: the  main alpha
		%particles have energies of 5.484~\mega\electronvolt\ (85.2\%) and
		%5.442~\mega\electronvolt\ (12.5\%). The source emits 79.5
		%$\alpha\per\second$ in 2$\pi$~\steradian. 
	%\item Test pulse with a fixed amplitude: the preamplifiers used for the
    %silicon detectors are come with the manufacturer's specification on the
    %response, namely a 66 \milli\volt\ fed into the test input will produce an
    %output equivalent to that of a 1 \mega\electronvolt\ energy deposition.  
	%\item Minimum ionisation particles
		%(MIPs): electrons in the beam are MIPs with a nominal deposit energy of
		%388~\electronvolt\per\micro\meter\ Si. This is only applicable for thick
		%silicon detectors because the energy deposit is large enough and the energy
		%resolution is good enough. During the run, this peak was observed to make
    %sure the stability of the electronics.
	%\item Muons with different momenta: the thick silicon detectors were placed
		%at the target position during beam tuning period, allowed an accurate
		%momentum and range calibration. This also only works with thick silicon
		%detectors.
%\end{enumerate}
% subsection silicon_detectors (end)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Upstream counters}
\label{sub:upstream_counters}
The upstream detector consists of three counters: a \SI{500}{\micro\meter}-thick
scintillator muon trigger counter (\Pmu{}SC); a muon anti-coincidence counter
(\Pmu{}SCA) surrounding the trigger counter with a hole
of 35 \si{\milli\meter}\ in diameter to define the beam radius; and a multi-wire
proportional chamber (\Pmu{}PC) that uses 24 X wires and 24 Y wires at
2~\si{\milli\meter}~intervals. 

The upstream detectors provide signal of an incoming muon as coincident hits on
the muon trigger and the wire chamber in anti-coincident with the muon
anti-coincidence counter.
This set of detectors along with their read-out system
belong to the MuSun experiment, which operated at the same beam line just
before our run. Thanks to the MuSun group, the detectors were well-tuned and
ready to be used in our run without any modification.

% subsection upstream_counters (end)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\subsection{Germanium detector}
%\begin{figure}[btp] 
	%\centering
	%\includegraphics[width=0.9\textwidth]{figs/neutron.png} 
	%\caption{Setup of two
	%liquid scintillators outside the vacuum envelope for neutron detection.}
	%\label{fig:neutron}
%\end{figure}
We used a germanium detector to normalise the number of stopped muons by
measuring characteristics muon X-rays from the target material. The primary
X-rays of interest are the 346.828~keV line for aluminium targets, and the
400.177 line for silicon targets. The energies and intensities of the X-rays
listed in \cref{tab:xray_ref} follow measurement results from
Measday and colleagues~\cite{MeasdayStocki.etal.2007}.
\begin{table}[btp]
  \begin{center}
    \begin{tabular}{c l l l l }
      \toprule
      \textbf{Elements}  & \textbf{Transition}
      & \textbf{Energy} & \textbf{Intensity}\\
      \midrule 
      $^{27}\textrm{Al}$ &  $2p-1s$ & $346.828 \pm 0.002$ & $79.8\pm 0.8$\\
         &  $3p-1s$ & $412.87  \pm 0.05$ &  $7.62\pm 0.15$\\
      \midrule
      $^{28}\textrm{Si}$ &  $2p-1s$ & $400.177 \pm 0.005$ & $80.3\pm 0.8$\\
       &  $3p-1s$ & $476.80 \pm 0.05$ & $7.40 \pm 0.20$\\
      \bottomrule
    \end{tabular}
  \end{center}
  \caption{Reference values of major muonic X-rays from aluminium and silicon.}
  \label{tab:xray_ref}
\end{table}

The germanium detector is
a GMX20P4-70-RB-B-PL, n-type, coaxial high purity germanium detector produced
by ORTEC. The detector was optimised for low energy gamma and X-rays
measurement with an ultra-thin entrance window of 0.5-mm-thick beryllium and
a 0.3-\si{\micro\meter}-thick ion implanted contact (\cref{fig:ge_det_dimensions}).
This detector is equipped with a transistor reset preamplifier which,
according to the producer, enables it to work in an ultra-high rate environment
up to $10^6$ counts\si{\per\second} at \SI{1}{\mega\electronvolt}. 
\begin{figure}[btp]
  \centering
    \includegraphics[width=0.9\textwidth]{figs/ge_det_dimensions}
  \caption{Dimensions of the germanium detector}
  \label{fig:ge_det_dimensions}
\end{figure}

The detector was installed outside of the vacuum chamber at 32 cm from the
target, seeing the target through a 10-mm-thick aluminium window, behind
a plastic scintillator counter used to veto electrons. Liquid nitrogen
necessary for the operation of the detector had to be refilled every 8 hours.
A timer was set up in the data acquisition system to remind this.

\subsection{Plastic and liquid scintillators}
\label{sub:plastic_scintillators}
Apart from the scintillators in the upstream group, there were four other
plastic scintillators used as veto counters for:
\begin{itemize}
  \item punch-through-the-target muons, ScVe
  \item electrons and other high energy charged particles for germanium
    detector (ScGe) and  silicon detectors (ScL and ScR)
\end{itemize}
The ScL, ScR and ScVe were installed inside the vacuum vessel and  were
optically connected to external PMTs by light-guides at the bottom flange. 

We also set up two liquid scintillation counters for neutron measurements in
preparation  for the next beam time where the neutron measurements will be
carried out.
% subsection plastic_scintillators (end)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Front-end electronics and data acquisition system}
The front-end electronics of the AlCap experiment was simple since we employed
a trigger-less read out system with waveform digitisers and flash ADCs
(FADCs). As shown in \cref{fig:alcapdaq_scheme}, all plastic
scintillators signals were amplified by PMTs, then fed into the digitisers. The
signals from silicon and germanium detectors were preamplified, and
subsequently shaped by spectroscopy amplifiers and timing filter amplifiers
(TFAs) to provide energy and timing information.
\begin{figure}[btp]
  \centering
    \includegraphics[width=0.99\textwidth]{figs/alcapdaq_scheme}
  \caption{Schematic diagram of the electronics and DAQ used in the Run 2013}
  \label{fig:alcapdaq_scheme}
\end{figure}

The germanium detector has its own transistor reset preamplifier
installed very close to the germanium crystal. Two ORTEC Model 142
preamplifiers were used for the thick silicon detectors. The timing outputs of
the preamplifiers were fed into three ORTEC Model 579 TFAs.
We used an ORTEC Model 673 to shape the germanium signal with 6~\si{\micro\second}
shaping time.

A more modern-style electronics was used for thin silicon detectors where the
preamplifier, shaping and timing amplifiers were implemented on one compact
package, namely a Mesytec MSI-8 box. This box has 8 channels, each channel
consists of one preamplifier board and one shaper-and-timing filter board which
can be fine-tuned independently. The shaping time was set to 1~\si{\micro\second}\
for all channels.

The detector system produced signals that differs significantly in time scale,
ranging from very fast (about 40~\si{\nano\second}\ from scintillators) to very slow
(several \si{\micro\second}\ from shaping outputs of semiconductor detectors). This
lead to the use of several sampling frequencies from 17~\si{\mega\hertz}\ to
250~\si{\mega\hertz}, and three types of digitisers were employed:
\begin{itemize}
  \item custom-built 12-bit 170-MHz FADCs which was designed for the
    MuCap experiment. Each FADC board has dimensions the same as those of
    a single-width 6U VME module, but is hosted in a custom built crate due to
    its different power supply mechanical structure. The FADC communicates with
    a host computer through a 100-Mb/s Ethernet interface using a simple
    Ethernet-level protocol. The protocol only allows detecting
    incomplete data transfers but no retransmitting is possible due to the
    limited size of the module's output buffer. The FADCs accept clock signal
    at the frequency of  50~\si{\mega\hertz}\ then multiply that internally up to
    170~\si{\mega\hertz}.  Each channel on one board can run at different sampling
    frequency not dependent on other channels. The FADC has 8 single-ended
    LEMO inputs with 1~\si{\volt} pp dynamic range. 
  \item a 14-bit 100-MS/s CAEN VME FADC waveform digitiser model V1724. The
    module houses 8 channels with 2.25~Vpp dynamic range on single-ended MCX
    coaxial inputs. The digitiser features an optical link for transmission of
    data to its host computer. All of 8 channels run at the same sampling
    frequency and have one common trigger.
  \item a 12-bit 250-MS/s CAEN desktop waveform digitizer model DT5720. This
    digitiser is similar to the V1724, except for its form factor and maximum
    sampling frequency. Although there is an optical link available, the module
    is connected to its host computer through a USB 2.0 interface where data
    transfer rate of 30 MB/s was determined to be good enough in our run
    (actual data rate from this digitiser was typically about 5 MB/s during the
    run). Communication with both CAEN digitisers was based on CAEN's
    proprietary binary drivers and libraries.
\end{itemize}
All digitisers were driven by external clocks which were derived from the same
500-\si{\mega\hertz}\ master clock, a high precision RF signal generator Model SG382
of Stanford Research System.

The silicon detectors were read out by FADC boards feature network-based data
readout interface. To maximize the data throughput, each of the four FADC
boards was read out through separate network adapter. 
The CAEN digitisers were used to read out
the germanium detector (timing and energy, slow signals) or scintillator
detectors (fast signals). For redundancy, all beam monitors (\Pmu{}SC, \Pmu{}SCA
and \Pmu{}PC) were also read out by a CAEN time-to-digital converter (TDC)
model V767 which was kindly provided by the MuSun experiment. 

The Data Acquisition System (DAQ) of the AlCap experiment, so-called AlCapDAQ,
provided the readout of front-end electronics, event assembling, data logging,
hardware monitoring and control, and the run database of the experiment
(\cref{fig:alcapdaq_pcs}). It was based on MIDAS framework~\footnote{
MIDAS is a general purpose DAQ software system developed at PSI and TRIUMF:\\
\url{http://midas.triumf.ca}} and consisted of two circuits, {\em i})
a detector circuit for synchronous data readout from the front-end electronics
instrumenting detectors, and {\em ii}) a slow control circuit for asynchronous
periodic hardware monitoring (vacuum, liquid nitrogen
filling).  The detector circuit consisted of three computers, two front-end
computers and one computer serving both as a front-end and as a back-end
processor. The slow circuit consisted of one computer. All computers were
running Linux operating system and connected into a private subnetwork. 

%\hl{TODO: storage and shift monitor}

\begin{figure}[btp]
  \centering
    \includegraphics[width=0.95\textwidth]{figs/alcapdaq_pcs}
  \caption{AlCapDAQ in the Run 2013. The {\ttfamily fe6} front-end is
    a VME single board computer belongs to the MuSun group, reads out the
    upstream detectors.}
  \label{fig:alcapdaq_pcs}
\end{figure}

The data were collected as dead-time-free time segments of 110~ms, called
``block'', followed by about 10-ms-long time intervals used to complete data
readout and synchronize the DAQ. Such data collection approach was chosen to
maximize the data readout efficiency. During each 110-ms-long period, signals
from each detector were digitized independently by threshold crossing. The data
segment of each detector data were first written into on-board memories of
front-end electronics and either read out in a loop (CAEN TDCs and CAEN
digitizers) or streamed (FADCs) into the computer memories. The thresholds were
adjusted as low as possible and individually for each detector.  The time
correlation between detectors would be established in the analysis stage.

At the beginning of each block, the time counter in each digitiser is reset to
ensure time alignment across all modules. The period of 110~ms was chosen to be:
{\em i}) long enough compared to the time scale of several \si{\micro\second}\
of the physics of interest, {\em ii}) short enough so that there is no timer
rollover on any digitiser (a FADC runs at its maximum speed of
\SI{170}{\mega\hertz} could handle up to about \SI{1.5}{\second} with its
28-bit time counter).

To ease the task of handling data, the data collecting period was divided into
short runs, each run stopped when the logger had recorded 2 GB of data.
The data size effectively made each run last for about 5 minutes. The DAQ
automatically starts a new run with the same parameters after about 6 seconds.
The short period of each run also allows the detection, and helps to reduce the
influence of effects such as electronics drifting, temperature fluctuation.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Detector calibration}
\label{sec:detector_calibration}
The calibration was done mainly for the silicon and germanium detectors
because they would provide energy information. The plastic scintillators were
only checked by oscilloscopes to make sure that the minimum ionisation
particles (MIPs) could be observed. The upstream plastic scintillation
counters and wire chamber, as mentioned, were well-tuned by the MuSun group.

\subsection{Silicon detector}
\label{sub:silicon_detector}
The energy calibration for the silicon detectors were done routinely during the
run, by:
\begin{itemize}
  \item a \SI{79.5}{\becquerel} $^{241}\textrm{Am}$ alpha source.  The most
    prominent alpha particles have energies of \SI{5.484}{\MeV} (85.2\%)
    and \SI{5.442}{\MeV} (12.5\%).  The alpha particles from the source
    would lose about \SI{66}{\kilo\eV} in the \SI{0.5}{\um}-thick dead layer,
    and the peak would appear at \SI{5418}{\kilo\eV} (\cref{fig:toyMC_alpha}); 
  
  \item and a tail pulse generator, A tail pulse with amplitude of
    \SI{66}{\milli\volt}~was used to simulate the response of the silicon
    detectors' preamplifiers to a particle with \SI{1}{\MeV} energy deposition;

  \item During data taking period, electrons in the beam were were also used
    for energy calibration of thick silicon detectors where energy deposition
    is large enough.  The muons at different momenta provided another mean of
    calibration in the beam tuning period. 
\end{itemize}

\begin{figure}[htb]
  \centering
    \includegraphics[width=0.6\textwidth]{figs/toyMC_alpha}
  \caption{Energy loss of the alpha particles after a dead layer of
    \SI{0.5}{\um}.}
  \label{fig:toyMC_alpha}
\end{figure}

The calibration coefficients for the silicon channels are listed in
\cref{tab:cal_coeff}.

\begin{table}
  \begin{center}
    \pgfplotstabletypeset[
    % separator
    col sep=comma,
    % columns displayed
    display columns/0/.style={column name = \textbf{Detector}, string type,
      column type=l},
    display columns/1/.style={column name = \textbf{Slope}, column type=c,
      dec sep align},
    display columns/2/.style={column name = \textbf{Offset}, column type=r,
      dec sep align},
    % format the line breaks
    every head row/.style={
      before row={\toprule},
      after row={\midrule},
      columns/Detector/.style={column type=c},
      columns/Slope/.style={column type=c},
      columns/Offset/.style={column type=c}
    },
    every last row/.style={after row=\bottomrule},
    ]{raw/si_cal_effs.csv}
    \caption{Calibration coefficients of the silicon detector channels}
    \label{tab:cal_coeff}
  \end{center}
\end{table}
% subsection silicon_detector (end)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Germanium detector}
\label{sub:germanium_detector}
The germanium detector was calibrated using a $^{152}\textrm{Eu}$
source
\footnote{Energies and intensities of gamma rays are taken from the
  X-ray and Gamma-ray Decay Data Standards for Detector Calibration and Other
  Applications, which is published by IAEA at \\
  \url{https://www-nds.iaea.org/xgamma_standards/}}, 
the recorded pulse height spectrum is shown in \cref{fig:ge_eu152_spec}. The
source was placed at the target position so that the absolute efficiencies can
be calculated. The peak centroids and areas were obtained by fitting a Gaussian
peak on top of a first-order polynomial background. The only exception is the
\SI{1085.84}{\keV} line because of the interference of the \SI{1089.74}{\keV}
gamma, the two were fitted with two Gaussian peaks on top of a first-order
polynomial background.

The relation between pulse height in ADC value and energy is found to be: 
\begin{equation}
  \textrm{ E [keV]} = 0.1219 \times \textrm{ADC} + 1.1621
\end{equation}
The energy resolution (full width at half maximum - FWHM) was better than
2.6~\si{\keV}\ for all the $^{152}\textrm{Eu}$ peaks. It was
a little worse at 3.1~\si{\keV}~for the annihilation photons at
511.0~\si{\keV}.

\begin{figure}[htb]
  \centering
    \includegraphics[width=0.70\textwidth]{figs/ge_eu152_spec}
  \caption{Energy spectrum of the $\rm^{152}\textrm{Eu}$ calibration source
    recorded by the germanium detector. The most prominent peaks of
    $^{152}\textrm{Eu}$ along with their energies are
    annotated in red; the 1460.82 \si{\keV}~line is background from
    $^{40}\textrm{K}$; and the annihilation 511.0~\si{\keV}~photons
    come both from the source and the surrounding environment.}
  \label{fig:ge_eu152_spec}
\end{figure}

\begin{figure}[htb]
  \centering
    \includegraphics[width=0.89\textwidth]{figs/ge_ecal_fwhm}
  \caption{Germanium energy calibration and resolution.}
  \label{fig:ge_fwhm}
\end{figure}

Following corrections for the peak areas are considered:
\begin{enumerate}
  \item Correction for counting loss due to finite response time of the
    detector system, where two gamma rays arrive at the detector within a time
    interval short compared to that response time. This correction is
    significant in our germanium system because of the current pulse
    information extracting method does not count the second pulse.
  \item Correction of counting time loss in the reset periods of the transistor
    reset preamplifier.  A preamplifier of this type would reset itself after
    accumulating a predetermined amount of charge. During a reset, the
    preamplifier is insensitive so this can be counted as dead time.
  \item True coincidence summing correction: two cascade gamma rays hit the
    detector at the same time would cause loss of count under the two
    respective peaks and gain under the sum energy peak. 
  \item Correction for self-absorption of a gamma ray by the source itself.
\end{enumerate}

The corrections for the first two mechanisms can be estimated by examining
pulse length and intervals between two consecutive pulses in the germanium
detector (\cref{fig:ge_cal_rate_pulselength}). The average pulse
length is \SI{45.7}{\um}, the average count rate obtained from the decay rate
of the interval spectrum is \SI{240}{\per\s}.

The correction factor for the finite response time of the detector system is
calculated as:
\begin{align}
  k_{\textrm{finite response time}} &= e^{2\times \textrm{(pulse length)} 
    \times \textrm{(count rate)}}\\ 
  &= e^{2\times 47.5\times10^{-6} \times 241} \nonumber\\
  &= 1.02 \label{eqn:finite_time_response}
\end{align}

The resets of the preamplifier show up as a peak around \SI{2}{\ms},
consistent with specification of the manufacturer. Fitting the peak on top of
an exponential background gives the actual reset pulse length of
\SI{1947.34}{\us} and the number of resets during the calibration runs is
2335.0. The total time loss for resetting is hence: 
$1947.34\times 10^{-6} \times 2335.0 = 4.55$ \si{\s}. That is a 0.14\% loss
for a measuring time of \SI{3245.5}{\s}. This percentage loss is insignificant
compared with the loss in \eqref{eqn:finite_time_response} and the statistical
uncertainty of peak areas so correction for amplifier resets is not applied. 

\begin{figure}[htb]
  \centering
    \includegraphics[width=0.95\textwidth]{figs/ge_cal_rate_pulselength}
  \caption{Germanium detector pulse length (left) and intervals between pulses
  on that detector (right). The peak around \SI{2}{\ms} corresponds to the
  resets of the preamplifier. The peak at \SI{250}{\us} is due to triggering
  by the timing channel which is on the same digitiser.}
  \label{fig:ge_cal_rate_pulselength}
\end{figure}

The true coincidence summing probability is estimated to be very small, about
\num{5.4d-6}, thanks to the far geometry of the calibration. The absorption in
the source cover made of \SI{22}{\mg\per\cm^2} polyethylene is less than
\num{4d-4} for a \SI{100}{\keV} photon. Therefore these two corrections are
omitted.

The absolute efficiencies of the reference gamma rays show agreement with those
obtained from a Monte Carlo (MC) study where a point source made of $^{152}$Eu
is placed at the target position (see \cref{fig:ge_eff_cal}). A comparison
between efficiencies in case of the point-like source and a finite-size
source is also done by MC simulation.  As shown in \cref{fig:ge_eff_cal}, the
differences are in line with the uncertainties of the measured efficiencies.
%The dimensions of the latter are set to
%resemble the distribution of muons inside the target: Gaussian spreading
%\SI{11}{\mm} vertically, \SI{13}{\mm} horizontally, and \SI{127}{\um} in
\begin{figure}[htb]
  \centering
    \includegraphics[width=0.40\textwidth]{figs/ge_eff_cal}
    \includegraphics[width=0.40\textwidth]{figs/ge_eff_mc_finitesize_vs_pointlike_root}
  \caption{Absolute efficiency of the germanium detector, the fit was done with
    7 energy points from 244~keV, the shaded area is
    95\% confidence interval of the fit.}
  %because it is known that the linearity between
    %$ln(\textrm{E})$ and $ln(\textrm{eff})$ holds better. 
  \label{fig:ge_eff_cal}
\end{figure}
The absolute efficiencies of the referenced points, and calculated efficiencies
at X-rays of interest are listed in \cref{tab:xray_eff}.
\begin{table}[htb]
  \begin{center}
    \pgfplotstabletypeset[
    % separator
    col sep=comma,
    % columns displayed
    % column type={S} means leave formatting to siunitx
    display columns/0/.style={column name = \textbf{Photons (\si{\keV})}, 
      string type,
      column type={S[table-format=4.3, table-alignment=center]}},
    display columns/1/.style={column name = \textbf{Efficiency}, 
      string type,
      column type={S[parse-numbers = true, 
        round-precision=3,
        round-mode=figures,
        fixed-exponent=-4,
        scientific-notation=fixed,
        table-format=1.2e-1,
        %table-omit-exponent,
        ]}}, 
    display columns/2/.style={column name = \textbf{Uncertainty}, 
      string type,
      column type={S[parse-numbers = true, 
        round-precision=3,
        round-mode=figures,
        fixed-exponent=-5,
        scientific-notation=fixed,
        table-format=1.3e-1,
        %table-omit-exponent,
        ]}}, 
    % format the line breaks
    every head row/.style={
      before row={\toprule},
      after row={
        %\textbf{\si{\keV}} & \textbf{\num{E-4}} & \textbf{\num{E-4}}\\
        \midrule},
      columns/0/.style={column type=r},
      columns/1/.style={column type=c},
      columns/2/.style={column type=c}
    },
    every last row/.style={after row=\bottomrule},
    every nth row={8}{before row={\midrule}},
    ]{raw/ge_eff.csv}
  \end{center}
  \caption{Absolute efficiencies of the germanium detector in case of
    a point-like source placed at the centre of the target (upper half), and
    the calculated efficiencies for the X-rays of interest (lower half).}
  \label{tab:xray_eff}
\end{table}

% subsection germanium_detector (end)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\subsection{Beam tuning and muon momentum scanning}
%\label{sub:muon_momentum_scanning}
%Before taking any data, we carried out the muon momentum scanning to understand
%the muon beam, as well as calibrate the detector system. The nominal muon
%momentum used in the Run 2013 had been tuned to 28~MeV\cc\ before the run. By
%changing simultaneously the strength of the key magnet elements in the $\pi$E1
%beam line with the same factor, the muon beam momentum would be scaled with the
%same factor.

%The first study was on the range of muons in an active silicon target. The SiL2
%detector was placed perpendicular to the nominal beam path, after an oval
%collimator. The beam momentum scaling factor was scanned from 1.10 to 1.60,
%muon momenta and energies in the measured points are listed in
%\cref{tab:mu_scales}.
%\begin{table}[htbp]
  %\begin{center}
    %\begin{tabular}{c c c c}
      %\toprule
      %\textbf{Scaling} & \textbf{Momentum} & \textbf{Kinetic energy}
      %& \textbf{Momentum spread}\\ 
      %\textbf{factor} & \textbf{(MeV\per\cc)} & \textbf{(MeV)}
      %& \textbf{(MeV\per\cc, 3\% FWHM)}\\ 
      %\midrule 
      %1.03 &   28.84 &     3.87&    0.87\\
      %1.05 &   29.40 &     4.01&    0.88\\
      %1.06 &   29.68 &     4.09&    0.89\\
      %1.07 &   29.96 &     4.17&    0.90\\
      %1.10 &   30.80 &     4.40&    0.92\\
      %1.15 &   32.20 &     4.80&    0.97\\
      %1.20 &   33.60 &     5.21&    1.01\\
      %1.30 &   36.40 &     6.09&    1.09\\
      %1.40 &   39.20 &     7.04&    1.18\\
      %1.43 &   40.04 &     7.33&    1.20\\
      %1.45 &   40.60 &     7.53&    1.22\\
      %1.47 &   41.16 &     7.73&    1.23\\
      %1.50 &   42.00 &     8.04&    1.26\\
      %\bottomrule
    %\end{tabular}
  %\end{center}
  %\caption{Muon beam scaling factors, energies and momenta.}
  %\label{tab:mu_scales}
%\end{table}

% subsection muon_momentum_scanning (end)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% section detector_calibration (end)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Data sets and statistics}
\label{sec:data_sets}

The main goal of this Run 2013 was to measure the rates and energy spectra of
protons following muon capture on aluminium. Also for normalisation and cross
checking against the existing experimental data, two types of measurements with
different targets were carried out for silicon targets: 
\begin{itemize}
  \item[(a)] an active, thick target similar to the set up
    used by Sobottka and Wills~\cite{SobottkaWills.1968}. This provides
    a cross-check against the existing experimental data. The silicon detector
    package at the right hand side was moved to the target position with the
    thick detector facing the muon beam in this set up.
  \item[(b)] a passive, thin target and heavy charged particles were observed
    by the two silicon packages. The measurement serves multiple purposes:
    confirmation that the particle identification by dE/dx actually works,
    separation of components of heavy charged particles emitted from the
    silicon target.
\end{itemize}

As the emitted protons deposit a significant amount of energy in the target
material, thin targets and thus excellent momentum resolution of the low energy
muon beam are critical, aluminium targets of 50-\si{\micro\meter}\ and
100-\si{\micro\meter}\ thick were used. Although a beam with low momentum
spread of 1\% is preferable, it was used for only a small portion of the run
due to the low beam rate (see \cref{fig:Rates}). The beam momentum for each
target was chosen to maximise the number of stopped muons. The collected data
sets are shown in \cref{tb:stat}.

\begin{table}[btp!]
  \begin{center}
    \vspace{0.15cm}
    \begin{tabular}{l c c c}
      \toprule
      \textbf{Target} &\textbf{Momentum}	&	\textbf{Run time} & \textbf{Number}\\
      \textbf{and thickness}&\textbf{scaling factor}	&	\textbf{(h)} &\textbf{of muons}\\
      \midrule
      Si 	1500 \si{\micro\meter}& 1.32& 3.07& $2.78\times 10^7$\\
      & 1.30& 12.04& $2.89 \times 10^8$\\ 
      & 1.10& 9.36& $1.37 \times 10^8$ \\
      \midrule
      Si 	62 \si{\micro\meter} & 1.06& 10.29& $1.72 \times 10^8$\\
      \midrule
      Al 	100 \si{\micro\meter}& 1.09& 14.37&$2.94 \times 10^8$\\
      & 1.07&  2.56& $4.99 \times 10^7$\\
      \midrule
      Al 	50 \si{\micro\meter} & 1.07& 51.94& $8.81 \times 10^8$\\
      \bottomrule
    \end{tabular}
  \end{center}
  \caption{Run statistics. Momentum scaling factors are normalised to
    \SI{28}{\MeV\per\cc}.}
  \label{tb:stat} 
\end{table}

% section data_sets (end)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Analysis framework} 
\subsection{Concept}
\label{sub:concept}
Since the AlCapDAQ is a trigger-less system, it stored all waveforms of the
hits occured in 100-ms-long blocks without considering their physics
significance The analysis code therefore must be able to extract parameters of
the waveforms, then organises the pulses into physics events correlated to
stopped muons (\cref{fig:muon_event}). In addition, the analyser is
intended to be usable as a real-time component of a MIDAS DAQ, where simple
analysis could be done online for monitoring and diagnostic during the run.

\begin{figure}[btp] 
	\centering
	\includegraphics[width=0.9\textwidth]{figs/muon_event.pdf} 
	\caption{Concept of the AlCap analysis code: pulses from individual detector
    in blocks of time are analysed, then sorted centred around stopped muons.} 
  \label{fig:muon_event} 
\end{figure}  

The analysis framework of the AlCap consists of two separate programs.
A MIDAS-based analyser framework, \alcapana{}, processes the raw data and
passes its ROOT data output to a second
stage, \rootana{}, where most of the physics analysis is performed. 
Both programs were designed to be modularised, which allowed us to develop
lightweight analysis modules that were used online to generate plots quickly,
while more sophisticated modules can be applied in offline analysis.

The DAQ system generated MIDAS files which stores the data as a stream of MIDAS
``banks''. In the AlCapDAQ, each bank corresponds to a single channel on
a digitizer and was named according to a predefined convention. The map between
detector channels and MIDAS bank names was stored in the MIDAS online database
(ODB), along with other settings such as sampling frequencies, timing offsets,
thresholds and calibration coefficients of each channel. 
%These can then be
%accessed by both \alcapana{} and \rootana{} for either online or offline
%analysis.  

The first step
of the analysis framework is to convert the raw MIDAS data into waveforms,
series of digitised samples continuous in time corresponding to pulses from the
detector. The waveform is called \tpulseisland{}s, which contain the bank name,
the ADC values of the samples and the time stamp of the first sample. This
conversion is performed in \alcapana{} and the resulting objects are stored in
a ROOT output file as a {\ttfamily TTree}.  

The next step of the analysis is to obtain summary parameters of the pulses
from the digitized samples. The parameters of primary interest are the
amplitude and time of the peak and the integral of the pulse. This extraction
of parameters is done by a \rootana{} module, and the objects produced by this
stage are called \tanalysedpulse{}s. Currently, we have a usable and simple
algorithm that takes the pulse parameters from the peak of the waveform. In
parallel, a pulse finding and template fitting code is being developed because
it would provide more accurate pulse information. The first iteration of this
code has been completed and is being tested.  
\begin{figure}[btp]
  \centering
    \includegraphics[width=0.85\textwidth]{figs/analysis_scheme}
  \caption{Concept of the analysis framework in \rootana{}}
  \label{fig:rootana_scheme}
\end{figure}

After obtaining pulse parameters for individual channel, the pairing up of
fast and slow pulses from the same physical detector needs to be done. This
entails looping through all fast and slow pulses from each detector,
checking for correlated pulses in time and amplitude,  creating 
{\ttfamily TDetectorPulse}s. The {\ttfamily TDetectorPulse}s allow better
understanding of the hits on the detector by combining timing information from
the fast channel and amplitude information from the slow channel. It also helps 
reduce the impact of pile-up on the amplitude measurement, where the
improved time resolution of the fast channels can be used to  separate the
overlapping amplitudes in the slow channels. The pulse pairing are applicable to
the silicon and germanium channels only. The scintillator channels provide only
fast timing signals which can be used as {\ttfamily TDetectorPulse}s directly.

The detector pulses are subsequently used to identify particles that hit the
detectors. These particle hits are still stored in the time-ordered tree
corresponds to the 110 ms block length from the AlCapDAQ. By iterating through
the tree to find stopped muons and taking any hits within a certain window
around this muon from every detector, a stopped-muon-centred tree shown in
\cref{fig:muon_event} can be produced. This will make it much easier to
look for coincidences and apply cuts, thereby bringing  the end
goal of particle numbers and energy distributions.

% subsection concept (end)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\subsection{Online analyser}
\label{sub:online_analyser}
The online analyser was developed and proved to be very useful during the run.
A few basic modules were used to produce plots for diagnostic purposes
including: persistency view of waveforms, pulse height
spectra, timing correlations with respect to the upstream counters. The
modules and their purposes are listed in \cref{tab:online_modules}.
\begin{table}[btp]
  \begin{center}
    \begin{tabular}{l p{6cm}}
      \toprule
      \textbf{Module name} & \textbf{Functions}\\
      \midrule 
      common/MUnCompressRawData               & decompress raw MIDAS data\\
      \midrule 
      FADC/MOctalFADCProcessRaw & \multirow{3}{6cm}{convert raw data to
        {\ttfamily TPulseIsland}s}\\ v1724/MV1724ProcessRaw& \\
      dt5720/MDT5720ProcessRaw&\\
      \midrule 
      muSC\_muPC/MCaenCompProcessRaw& \multirow{4}{6cm}{decompress data from
        {\ttfamily fe6}, make coincidence in upstream counters} \\
      muSC\_muPC/MMuPC1AnalysisC&\\
      muSC\_muPC/MMuPC1AnalysisMQL&\\
      muSC\_muPC/MMuSCAnalysisMQL&\\
      \midrule 
      diagnostics/MCommonOnlineDisplayPlots& produce plots of interest\\
      \midrule 
      FADC/MOctalFADCBufferOverflow& \multirow{2}{6cm}{diagnostics for FADCs}\\
      FADC/MOctalFADCPacketLoss&\\
      \midrule 
      common/MExpectedIslands&\multirow{4}{6cm}{diagnostics in general}\\
      common/MMuSCTimeDifferences&\\
      common/MNumberIslands&\\
      common/MPulseLengths&\\
      \midrule 
      common/MTreeOutput& save {\ttfamily TPulseIsland}s tree\\
      \bottomrule
    \end{tabular}
  \end{center}
  \caption{Online analysis modules in the Run 2013.}
  \label{tab:online_modules}
\end{table}

The \alcapana{} served the plots on port 9090 of the {\ttfamily abner}
via the ROOT socket protocol. We then used a ROOT-based program called
{\ttfamily online-display} to display the plots on the shift terminal
({\ttfamily alcap}). The {\ttfamily online-display} simply executed ROOT macros
which retrieved plots from the ROOT server, sorted then drew them in 
groups such as upstream counters, silicon arms. It could also periodically
update the plots to reflect real-time status of the detector system. 
%Screen
%shots of the {\ttfamily online-display} with several plots are shown in
%\cref{fig:online_display}.

%\hl{Screen shots}
\subsection{Offline analyser}
\label{sub:offline_analyser}
Some offline analysis modules has been developed during the beam time and could
provide quick feedback in confirming and guiding the decisions at the time. For
example, the X-ray spectrum analysis was done to confirm that we could observe
the muon capture process and to help in choosing optimal momenta which
maximised the number of stopped muons.  

Although the offline analyser is still not fully available yet, several modules
are ready(\cref{tab:offline_modules}). An initial analysis is possible using
the existing modules thanks to the modularity of the analysis framework. 

\begin{table}[htb]
  \begin{center}
    \begin{tabular}{l p{8cm}}
      \toprule
      \textbf{Module name} & \textbf{Functions}\\
      \midrule
      MakeAnalysedPulses  & make a pulse with parameters extracted from
      a waveform\\
      MaxBinAPGenerator   & simplest algorithm to get pulse information\\
      TSimpleMuonEvent    & sort pulses occur in a fixed time window around the
      muon hits\\
      ExportPulse \& PulseViewer & plot waveforms for diagnostics\\
      PlotAmplitude       & plot pulse height spectra\\
      PlotAmpVsTdiff      & plot pulse correlations in timing and amplitude\\
      EvdE                & plot \sdEdx histograms\\
      \bottomrule
    \end{tabular}
  \end{center}
  \caption{Available offline analysis modules.}
  \label{tab:offline_modules}
\end{table}

The MakeAnalysedPulses module takes a raw waveform, calculates the pedestal
from a predefined number of first samples, subtracts this pedestal taking
pulse polarity into account, then calls another module to extract pulse
parameters. At the moment, the simplest module, so-called MaxBinAPGenerator,
for pulse information calculation is in use. The module looks for the
sample that has the maximal deviation from the baseline, takes the deviation as
pulse amplitude and the time stamp of the sample as pulse time. The procedure
is illustrated on \cref{fig:tap_maxbin_algo}. This module could not handle
pile-up or double pulses in one \tpulseisland{} in \cref{fig:tap_maxbin_bad}.
\begin{figure}[htb]
  \centering
    \includegraphics[width=0.85\textwidth]{figs/tap_maxbin_algo}
  \caption{Pulse parameters extraction with MaxBinAPGenerator.}
  \label{fig:tap_maxbin_algo}
\end{figure}
\begin{figure}[htb]
  \centering
    \includegraphics[width=0.47\textwidth]{figs/tap_maxbin_bad}
    \includegraphics[width=0.47\textwidth]{figs/tap_maxbin_bad2}
  \caption{Double pulse and pile up are taken as one single pulse by the
    MaxBinAPGenerator}
  \label{fig:tap_maxbin_bad}
\end{figure}

The TSimpleMuonEvent first picks a muon candidate, then loops through all
pulses on all detector channels, and picks all pulses occur in
a time window of \SI{\pm 10}{\si{\us}} around each candidate to build
a muon event. A muon candidates is a hit on the upstream plastic scintillator
with an amplitude higher than a threshold which was chosen to reject MIPs. The
period of \SI{10}{\si{\us}} is long enough compared to the mean life time of
muons in the target materials
(\SI{0.758}{\si{\us}} for silicon, and \SI{0.864}{\si{\us}}
for aluminium~\cite{SuzukiMeasday.etal.1987}) so practically all of emitted
charged particles would be recorded in this time window.
%\begin{figure}[htb]
  %\centering
    %\includegraphics[width=0.85\textwidth]{figs/tme_musc_threshold}
  %\caption{Pulse height spectrum of the $\mu$Sc scintillator}
  %\label{fig:tme_musc_threshold}
%\end{figure}

A pile-up protection mechanism is employed to reject multiple muons events: if
there exists another muon hit in less than \SI{15}{\us} from the
candidate then both the candidate and the other muon are discarded. This
pile-up protection would cut out less than 11\% total number of events because
the beam rate was generally less than \SI{8}{\kilo\hertz}.

%In runs with active silicon targets, another requirement is applied for the
%candidate: a prompt hit on the target in $\pm 200$ \si{\ns}\ around the
%time of the $\mu$Sc pulse. The number comes from the observation of the
%time correlation between hits on the target and the $\mu$Sc
%(\cref{fig:tme_sir_prompt_rational}).
%\begin{figure}[htb]
  %\centering
    %\includegraphics[width=0.85\textwidth]{figs/tme_sir_prompt_rational}
  %\caption{Correlation in time between SiR2 hit and muon hit}
  %\label{fig:tme_sir_prompt_rational}
%\end{figure}

To make sure that we will analyse good data, a low level data quality checking
was done on the whole data sets. The idea is plotting the variations of basic
parameters, such as noise level, length of raw waveforms, pulse rate, time
correlation to hits on the muon counter on each channel during the data
collecting period. Runs with significant difference from the averaging 
values were further checked for possible causes, and would be discarded if such
discrepancy was too large or unaccounted for. Examples of such trend plots are
shown in \cref{fig:lldq}.
\begin{figure}[htb]
  \centering
    \includegraphics[width=0.47\textwidth]{figs/lldq_noise}
    \includegraphics[width=0.47\textwidth]{figs/lldq_tdiff}
  \caption{Example trend plots used in the low level data quality checking:
    noise level in FWHM (left) and time correlation with muon hits (right). The
    noise level was basically stable in in this data set, except for one
    channel. On the right hand side, this sanity check helped find out the
    sampling frequency was wrongly applied in the first tranche of the data
    set.}
  \label{fig:lldq}
\end{figure}
% subsection offline_analyser (end)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Monte Carlo simulation}
\label{sec:monte_carlo_simulation}

A full Monte Carlo (MC) simulation of the experimental set up has been developed
based on Geant4~\cite{Agostinelli.etal.2003}. The geometrical implementation
was as detailed as possible and could be modified via configuration script at
run time. Descriptions of the muon beam came from the beam line optic
calculation provided by the accelerator experts at PSI.

The MC model greatly assisted the design of the experiment, such as alignment
of the detectors with respect to the target, and shielding of scattered muons.
It also helps make sense of observed results during the run and data
analysing. 

% chapter the_alcap_run_2013 (end)