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%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 their spectrum following muon capture on aluminium.
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=0.55\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}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsubsection{Muon beam and vacuum chamber}
The muon beam of low energy at \SIrange{28}{45}{\MeV\per\cc}, and narrow
momentum spread of 3\% were used.
\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 recorded by
our silicon detector.
\begin{figure}[btp]
\centering
\includegraphics[width=0.65\textwidth]{figs/Rates.png}
\caption{Measured muon rates at low momenta during the Run 2013. Beam rates
at 1 \% FWHM momentum bite were about 3 times smaller than the rates at
3 \% FWHM.}
\label{fig:Rates}
\end{figure}
\begin{figure}[btp]
\centering
\includegraphics[width=1.00\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. The
electron peak are the same in both plots as beam electrons are minimum
ionisation particles and passed though the detector easily. The muon peak
at the 3 \% FWHM momentum bite is notably broader than that at 1 \% FWHM
setting.}
\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 \cref{fig:alcap_setup_detailed} 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
to quickly capture muons that do not stop in the actual target.
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.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsubsection{Silicon detectors}
The main detectors for charged particles measurement are 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}
% subsubsection silicon_detectors (end)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsubsection{Upstream counters}
\label{sub:upstream_counters}
The upstream detector consists of three counters: a \SI{500}{\micro\meter}-thick
scintillator muon trigger counter ($\mu$SC); a muon anti-coincidence counter
($\mu$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 ($\mu$PC) that uses 24 X wires and 24 Y wires at
2~\si{\milli\meter}~intervals.
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.
% subsubsection upstream_counters (end)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsubsection{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. The germanium crystal is
\SI{52.5}{\mm} in diameter, and \SI{55.3}{\mm} in length. The axial well has
a diameter of \SI{9.9}{\mm} and \SI{47.8}{\mm} deep.
%(\cref{fig:ge_det_dimensions}).
%\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, viewing 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.
\subsubsection{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.
% subsubsection plastic_scintillators (end)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsubsection{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 the same dimensions 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 ($\mu$SC, $\mu$SCA
and $\mu$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 the 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 started 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.

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*.out
*.log
*.aux
*.toc
progress*.pdf
*.blg
*.bbl

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%\subsubsection{plan}
%\begin{itemize}
%\item two stage: alcapana then rootana
%\item alcapana is online analysis as well as primary midas -> root conversion
%\item rootana is the main offline analysis
%\item Waveform Analysis
%\begin{itemize}
%\item Pulse Candidate Finder
%\item Amplitude: MaxBin
%\item Timing: Constant Fraction
%\item Calibration: Timing offsets, Pedestals, Energy scales
%\end{itemize}
%\item Event Correlating: Fast and Slow coincidence
%\item Event Correlating: Muon events
%\end{itemize}
\begin{figure}[htbp]
\centering
\includegraphics[width=0.7\textwidth]{figs/WaveformAnalysis.png}
\caption{Illustration of the waveform analysis techniques used in Rootana.}
\label{fig:waveform_reco_demo}
\end{figure}
%The analaysis of the Alcap data is split between two main stages, known as
%Alcapana and Rootana.
The AlCap DAQ delivers data as compressed MIDAS files. These are then
handled in two stages. In the first stage (Alcapana),
some preliminary analysis is
performed and the MIDAS files unpacked into a ROOT format. These are then
passed through the second stage (Rootana) for physics analysis.
\subsubsection{Alcapana}
The MIDAS files produced by the DAQ contain both the digitised
waveform outputs
and the run-time DAQ configuration. Alcapana is the first point in the
processing chain to look at this data and performs two roles: 1) it
provides some preliminary, semi-online analysis, 2) it converts the
MIDAS data into a ROOT format.
The analysis produces simple histograms of quantities such as amplitude,
timing, and pulse island length. It also creates persistency-style
overlays of each
waveform in the event. These histograms are placed in an output file which can
then be loaded into a simple ROOT-based GUI where results can be displayed
rapidly and help to understand the data quality.
%Much of this was implemented during the run and by the end the alcapana
%analysis and displays formed a strong and user-friendly tool-kit.
Since each digitiser is run in a self-trigger mode within a MIDAS block, the
output waveforms contain, in principle, a single pulse stored as a vector of
ADC samples. The waveform digitisers stamp each pulse with a trigger time-stamp relative to the
start of the MIDAS block. Each of these time-stamped ADC vectors is referred
to as a Pulse Island. Occasionally a
real pulse may be split over two Pulse Islands. Therefore, during the
unpacking in Alcapana Pulse Islands are with adjacent time-stamps are
checked to concatenated into a single pulse when necessary.
The treatment of the $\mu$PC detector is slightly different as it is readout using a discriminator and TDC, and so does not use the same waveform format for raw data.
\subsubsection{Rootana}
Most of the physics analysis is performed in Rootana. The framework is
designed to be easily configured by dividing the analysis into
modules which can be called and reconfigured at run-time through a
configuration file. Most processing chains begin with waveform analysis so
the module for this delegates the work to runtime selectable `generators' which
implement the actual waveform analysis. Then the program searches for
correlations or coincidences between different detectors in order
to produce the final physics results.
\subsubsection*{Waveform Analysis}
The general approach to waveform analysis
uses the following methodology:
\begin{description}
\item [1. Find Pulse Candidates:] Remove pulse islands which are just noise and
divide pile-up pulses into two separate pulse islands.
%
%\item [2. Subtract Pedestal]
%
\item [2. Amplitude and Time reconstruction:] Use the Max Bin method (sometimes
Peak Sample method) to extract the amplitude followed by a Constant Fraction Timing
process using a linear interpolation between the two bins closest to the
peak-sample which crosses a given fraction of the pulse's amplitude. See Fig.
\ref{fig:waveform_reco_demo} for an illustration of these techniques.
%
\item [3. Apply Calibration Constants:] Account for cable delays and
similar effects in
the timing and convert the amplitude to energy. The constants
are obtained from a prior data pass which calculates the timing and
pedestal data, or from a dedicated calibration datasets in the case of energy
constants.
\end{description}
We are investigating alternative methods of waveform analysis using
pulse-averaging in order to produce a template followed by fitting or
convolution of the
original waveform. Since the analysis shown below has not used these
methods,
they will not be described here.
\subsubsection*{Pulse Correlation}
There are two types of pulse correlation used in the analysis:
1) correlation of
pulses between the fast and slow filtered read-out channels of a
single detector,
and 2) correlation of pulses between all detectors. The first method
provides a
cross check on the data quality, but results in a reduction of the overall
dynamic range of the detector since the correlation is only meaningful for
pulses with energies within the intersection of the individual
dynamic ranges of each channel.
The second method is used when pulses are correlated between
detectors. It
is implemented
by restructuring the dataset into what are known as ``Muon Events''. Individual
pulses on the $\mu$Sc are used as a reference point and all pulses which occur
within a certain time window (typically 15~\textmu s) are collected together into
a single muon event. Should two or more $\mu$Sc pulses occur within this window,
the event is marked as a muon pile-up event. It is then trivial to scan
over each muon event, applying various cuts, in order to build a
spectrum of interest.
Since the bulk of the correlation work is done by inspecting the timing of
pulses on different channels, the accuracy of the time offsets due to
cable delays is particularly important.

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We request a total beam time of one month in the $\pi$E1.2 area. The preferred running period
would be to start on October 26. We need at least 14 days free access to
the area to mount and commission the experiment. The division of beam time is
listed in Table \ref{table:nonlin}.
The proton measurements use a vacuum chamber which
surrounds a thin stopping target and silicon detectors. A germanium detector
views the target through a vacuum window. It provides the muon stopping rate
in the target by measuring the rate \atrn{2p}{1s} muonic X-rays.
The gamma and neutron measurements will use a thick target in air,
with minimal material near the target. The target has sufficient
thickness to fully stop the beam, and will allow an increase of the beam
momentum with a subsequent higher stopping rate.
\begin{table}[ht]
\caption{Beam Request} % title of Table
\centering % used for centering table
\begin{tabular}{l c c c} % centered columns (4 columns)
\addlinespace
\toprule
\bf Task or Target & \bf Measurement & \bf Beam Time (days) \\
\midrule
% inserts single horizontal line
Beam Tuning & & 2 \\ % inserting body of the table
Experiment commission & & 3 \\
Silicon & proton & 4 \\
Aluminium & proton & 3 \\
Titanium & proton & 3 \\
Background & proton & 1 \\
Aluminium & $\gamma$,n & 2 \\% [1ex] % [1ex] adds vertical space
Silicon & $\gamma$,n & 1.5 \\% [1ex] % [1ex] adds vertical space
Titanium & $\gamma$,n & 1.5 \\% [1ex] % [1ex] adds vertical spac
Lead & $\gamma$,n & 0.33 \\% [1ex] % [1ex] adds vertical space
Stainless Steel & $\gamma$,n & 0.33 \\% [1ex] % [1ex] adds vertical space
Tungsten & $\gamma$,n & 0.33 \\% [1ex] % [1ex] adds vertical space
H2O & $\gamma$,n & 0.5 \\
Polyethylene & $\gamma$,n & 0.5 \\% [1ex] % [1ex] adds vertical space
\midrule %inserts single line
\midrule %inserts single line
\bf Total& & \bf 23 \\
\bottomrule %inserts single line
\end{tabular}
\label{table:nonlin} % is used to refer this table in the text
\end{table}

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/.DS_Store/1.1.1.1/Thu Jan 8 07:32:47 2015//
/Makefile/1.1.1.1/Thu Jan 8 07:32:47 2015//
/nature.bst/1.1.1.1/Thu Jan 8 07:32:47 2015//
D/figs////
/Geant_simulation.tex/1.1/Sun Jan 18 04:02:35 2015//
/.cvsignore/1.2/Mon Jan 19 07:15:05 2015//
/DAQ.tex/1.7/Mon Jan 19 07:15:05 2015//
/GeantSimulation.tex/1.8/Mon Jan 19 07:15:05 2015//
/MuonBeam.tex/1.10/Mon Jan 19 07:15:05 2015//
/SummaryMeasurements.tex/1.6/Mon Jan 19 07:15:05 2015//
/progress14.bib/1.8/Mon Jan 19 07:15:05 2015//
/AnalysisFramework.tex/1.12/Tue Jan 27 15:51:25 2015//
/BeamRequest.tex/1.13/Tue Jan 27 15:51:25 2015//
/ChargedParticleAnalysis.tex/1.13/Tue Jan 27 15:51:25 2015//
/Gammas.tex/1.29/Tue Jan 27 15:51:25 2015//
/Improvements.tex/1.8/Tue Jan 27 15:51:25 2015//
/NeutronAnalysis.tex/1.7/Tue Jan 27 15:51:25 2015//
/Neutrons.tex/1.12/Tue Jan 27 15:51:25 2015//
/Overview.tex/1.16/Tue Jan 27 15:51:25 2015//
/PartialAnalysis.tex/1.12/Tue Jan 27 15:51:25 2015//
/Protons.tex/1.9/Tue Jan 27 15:51:25 2015//
/Setup.tex/1.26/Tue Jan 27 15:51:25 2015//
/XrayAnalysis.tex/1.28/Tue Jan 27 15:51:25 2015//
/progress14.bbl/1.9/Tue Jan 27 15:51:25 2015//
/progress14.blg/1.12/Tue Jan 27 15:51:25 2015//
/progress14.pdf/1.27/Tue Jan 27 15:51:30 2015//
/progress14.tex/1.21/Tue Jan 27 15:51:30 2015//

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alcap@muon.npl.washington.edu:/home/alcap/cvsAlCap

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%Ben and Nam, 1 p, just intro, different analysis active silicon and
%passive Al
%\subsubsection{plan}
%\begin{itemize}
%\item Method:
%\begin{itemize}
%\item Coincidence between thick and thin silicon
%\item Since thin silicon is very thin ( $\sim65~\mu$m ) assume that energy deposited in thin is $E_{\mathrm{thin}}\propto \frac{dE}{dx}$
%\item Then build dE/dx vs E plot from $E_{\mathrm{thin}}$ vs $E_{\mathrm{thick}} + E_{\mathrm{thin}}$
%\item Cuts: muSc coincidence, remove muon pile-up, muSc is muon like, thick and thin coincidence, minimum and maximum energy cuts on thick and thin
%\item Vacuum to prevent scattering of low-energy charged particles
%\end{itemize}
%\item Analysed data-sets:
%\begin{itemize}
%\item Al100 - Fully unfolded
%\item Al50 - Folded spectrum, comparison to MC using Al100 unfolded spectrum
%\item Active SiR2 - Folded but with large background from lack of back wall shielding. Require additional Active Target coincidence
%\end{itemize}
%\item Backgrounds:
%\begin{itemize}
%\item Pile-up (particularly since only Slow Silicon is used due to calibration data)
%\item Muons stopping in silicon
%\item Random coincidence (particularly in Active Si dataset)
%\end{itemize}
%\end{itemize}
\begin{figure}[htbp]
\centering
\includegraphics[width=0.35\textwidth]{figs/SiPackage.jpg}
\caption{One of the silicon packages used for the charged particle
measurement. The thin detector is on the near-side to the target, whereas
the thick detector sits at the back.}
\label{fig:SiPackage}
\end{figure}
The measurement of charged particles makes use of 4 silicon detectors, two
thick and two thin. One thick and one thin detector are placed back to back
as shown in Fig.~\ref{fig:SiPackage} so that charged particles pass first
through the thin silicon and stop in the thick (provided their
kinetic energy is not too high, around \SI{18}{MeV}).
The energy deposited in the thin silicon can be decribed as
\begin{equation}
E_\mathrm{thin} = \frac{dE}{dx} \Delta x
\end{equation}
By comparing this to the total energy deposited by the particle,
$E_\mathrm{total} = E_\mathrm{thin}+ E_\mathrm{thick}$,
we can build up a typical $\dfrac{dE}{dx}$ curve which allows us to perform
particle identification (PID) based on the two energy measurements.
Since most of the particles being studied are low in energy ($E_k <
\SI{15}{MeV}$) the target and chamber are placed in a vacuum chamber
to reduce scattering and absorption in air. This increases efficiency,
and gives a better estimate of the initial energy.
The analysis of charged particle data uses the muon centred tree approach
described above with the following cuts:
\begin{itemize}
\item {\bf MuSc coincidence.} Hits in the detector should be related to an
incoming muon,
\item {\bf Thick and thin coincidence.} Required for PID,
\item {\bf MuSc is muon like.} Make sure the coincident $\mu$Sc hit was from a muon and
not a beam-electron or otherwise,
\item {\bf Muon pile-up.} Ensures the detected hit is definitely from the right
muon, important when studying the timing of the processes.
\item {\bf Energy cuts on thick and thin.}
\end{itemize}
Of the data taken during R2013, the two aluminium datasets (Al50 and Al100)
have been studied the most. Additionally, data was also taken using one of the
detectors as the target itself which gives additional information as to the
stopping distribution and acceptances. This silicon dataset (ActiveSi) has only been
partially analysed at this stage. Table \ref{tab:ChargedParticleDatasets} shows
a summary of the datasets analysed.
\begin{table}[htbp]
\centering
\caption{Status of the charged particle analysis for different datasets}
\begin{tabular}{p{0.2\textwidth}p{0.7\textwidth}}
\addlinespace
\toprule
\bf Dataset & \bf Analysis status and approach \\ %[0.5ex]
\midrule
Al100 & Fully unfolded \\
\addlinespace
Al50 & Spectrum at detector, comparison to MC using Al100 unfolded spectrum \\
\addlinespace
Active SiR2 & Spectrum at detector but with large background from lack of back wall shielding. Requires additional Active Target coincidence \\
\bottomrule
\end{tabular}
\label{tab:ChargedParticleDatasets}
\end{table}
Possible backgrounds to the analysis come from muons scattering into the
detector and stopping in the front face of the thin silicon, random coincidences
between events in the thick and thin detectors, and waveform pile-up caused by
two or more less energetic particles arriving at the same time.
Muons stopping in the front of the thin silicon are an issue since those that
capture on a silicon nucleus in the detector will emit charged particles which
could---if they pass through the thin and stop in the thick---overlap with the
distribution of the charged particles coming from the target. Since the
lifetime of silicon is very close to that of aluminium, timing cuts cannot be used to remove this background. Estimates from Monte Carlo however suggest
there is only 5\% contamination at maximum.

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\subsection{Frontend Electronics and Data Acquisition System}
The frontend electronics of the AlCap experiment includes; 1) A CAEN
time-to-digital converter (TDC) model V767 which reads the $\mu$PC and
2) Several types of waveform digitisers (WFD) recording raw pulse
waveforms. A 12-bit 250-MS/s CAEN digitiser model DT5720 was used to
record fast pulses from the entrance muon counters (a thin plastic
scintillator $\mu$Sc to provide a time reference; a
scintillator detector $\mu$ScA to veto muons from beam halo; and
a thick scintillator detector to veto muons which did not stop in
the target).
A 14-bit 100-MS/s CAEN digitiser model V1724 was used to instrument
the germanium detector.
Custom-built 12-bit 170-MS/s flash analogue-to-digital converters
(FADCs),
previously used for the MuCap experiment, were used to instrument the
neutron detector, all silicon detectors and the remaining
scintillator detectors.
The germanium detector and all silicon detectors use two parallel readout channels.
One channel has a very fast preamp shaping time, to be used for precise time resolution on the order of a few nanoseconds. The other channel uses a longer shaping time which results in a better energy resolution.
The two readout channels are acquired and written to disk independently and recombined offline.
For the scintillator detectors, which are just used for veto, a slow signal was not necessary so each was read out by a single channel.
To synchronise the different detectors, AlCap follows the approach
successfully exploited by other muon experiments at PSI (MuCap and MuSun).
The data collection is organised into $\sim100$-ms-long time segments
where the length of the time segments was optimised.
During each segment, signals from all detectors are recorded
independently
by threshold crossing and were time-stamped relative to the start of
the segment.
The clock signals for all electronics modules are derived from a
common source, which allows us to time-correlate different detectors
in the offline analysis. It also provides an opportunity to conduct
various background studies, and exercise different veto selection conditions.
The data acquisition system (DAQ) of the AlCap experiment is based on the MIDAS framework.
It provides the readout of the frontend electronics into data blocks, data logging, hardware monitoring and control, and the run database of the experiment.
Each data block (also known as a MIDAS block) contains data from all detectors from a given time segment.
In R2013, the DAQ consisted of two frontend computers, one backend computer (which was also used to run several frontend processes), one slow control computer, and one computer for the offline data analysis.
%%% Local Variables:
%%% mode: latex
%%% TeX-master: t
%%% End:

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For the proposed run, we plan two types of photon measurements.
%\begin{enumerate}
%\item Measurement of the low energy ($<7$ MeV) gamma and muonic X-ray
% spectra produced when muons stop in candidate target materials, using
% a high resolution germanium detector (FWHM $\sim2$ keV).
%\item Measurement of the high energy photon and electron spectra ($E>30$ MeV)
% produced when muons stop in candidate materials, using $5\times5$
% LSYO-crystal calorimeter array.
%\end{enumerate}
\subsubsection{Low energy ($E<7$ MeV) photons}
Using a high resolution germanium detector we will measure the number of
muonic X-rays emitted from the AlCap targets and will investigate
nuclear gammas emitted in muon capture, as an alternative method to
normalize the number of stopped muons in the Mu2e/COMET experiments.
The emphasis of the first AlCap run (R2013) was to measure the proton
emission spectra on aluminium and silicon targets, which
required placing very thin targets in a vacuum along with the
silicon surface detectors. The setup was excellent for proton measurements
but was not optimal for the measurement of
gammas. A significant fraction of the muon beam stopped in the lead collimator
and other materials located inside the vacuum just upstream of the target,
which led to background in the gamma spectra, for example from
muon capture on lead.
In the proposed upcoming run, we will eliminate the vacuum chamber and
any lead near the muon beam, and place an isolated target in air.
The target would be made sufficiently thick to stop muons at 40 \si{
MeV\per\cc}, which will provide a much higher stopping rate.
%The proposed run would use a muon beam with higher momentum
%than the 29 \si{MeV\per\cc} used for the thin target runs where the stopping
%flux is much higher.
Since all incoming muons will stop in the target,
backgrounds due to stops in shielding material will be significantly reduced.
We also plan add shielding around the Ge detector to add
protection from ambient radiation background.
\paragraph{Aluminium}
%We first discuss the specific case of aluminium.
The number of \atrn{2p}{1s} muonic X-ray transitions per stopped muon is
experimentally determined to be 79(1)\% in aluminium (from the literature).
%The measurement of this rate
%with a high resolution germanium detector provides
%the normalisation for the number of stopped muons in AlCap.
In principle these X-rays can be used to monitor the number of stopped
muons in the Mu2e/COMET experiments. In practice, it remains a
significant challenge for Mu2e/COMET to measure the X-rays. Both Mu2e and
COMET will employ intense pulsed proton and thus pulsed muon beams.
A background in the form of an intense pulse of low energy beam
electrons arrives at the target less
than 100~ns before the muons stop, and produce a ``flash''
of low energy bremsstrahlung. The commercial germanium detectors will
be saturated by the high rates of gammas produced in the flash,
and will not recover in time to measure the X-rays.
Commercially available scintillating crystals are capable of handling much
higher rates but have about x10 poorer resolution (LaBr3(Ce)~3\% at 662~keV)
when compared to Ge.
%In AlCap R2013, thanks to the excellent energy resolution of
%the germanium, we were able to distinguish between the \atrn{2p}{1s} line and a
%nearby background peak due to muons stopping in lead.
In the proposed 2015
run, we will have a thick target without lead shielding. Thus we can evaluate
whether the energy regions near the \atrn{2p}{1s} X-rays are
sufficiently free of
background peaks and noise to permit the use of a faster but lower energy resolution crystal, such as LaBr3, instead of
germanium in the Mu2e/COMET experiments.
Given the challenge of measuring the X-rays for normalisation in Mu2e/COMET,
AlCap will investigate alternatives.
One scenario for Mu2e would be to use a gamma ray from the decay of a nucleus
produced promptly during muon capture. When a muon captures on Al,
it produces $^{27}$Mg about 10-15\% of the time, via the reaction
$\mu^-+ {}^{27}_{13}\mbox{Al}\rightarrow {}^{27}_{13}\mbox{Mg}^*+\nu_{\mu}$. The $^{27}$Mg decays
with a 9.5 minute half-life, emitting an 844 keV gamma 72\% of the time.
(See section \ref{sec:XRayAnalysis} for analysis of this peak in R2013.)
In Mu2e, the beam cycle is such that proton pulses arrive for 0.4 s,
followed by no beam for 0.9 s. A beam shutter would close to protect
the gamma detector (germanium is the likely candidate) from high rates
and radiation damage during beam on,
then it would open during the beam off, when the 844 keV gammas
would be detected.
%In Run 1, we found evidence of the presence
%of the 844 keV peak, however the background was large and we were not able
%to approach the goal of 10\% uncertainty in the number of 844 keV gammas
%per muon stop.
In the proposed 2015 ALCap run, we plan to measure the 844 keV
gammas with 10\% uncertainty.
This measurement will be done with a thick target in air with a minimum
of material near the stopping target. This should
allow us to dramatically increase the stopped muon rate compared to R2013.
We estimate it can be done in one 36 hour measurement.
At the same time, we will study another Mu2e/COMET normalisation alternative,
the use of a 1.8~MeV gamma that is emitted promptly when the muon is captured
on the aluminium nucleus. The gamma is therefore emitted with the lifetime of the muonic
aluminium atom, 864~ns. The gamma ray comes from the chain
$\mu^- + {}^{27}_{13}\mbox{Al}\rightarrow {}^{26}_{12}\mbox{Mg}^*+n+\nu_{\mu}$ followed by the
prompt decay $^{26}_{12}\mbox{Mg}^* \rightarrow {}^{26}_{12}\mbox{Mg}+\gamma$. This gamma is
produced in 50\% of captures.
Detection of the 1.8~MeV~gamma with germanium will be much easier than detecting
the X-rays, since with the Mu2e/COMET pulsed proton beams
it can be delayed 500~ns or more after the proton pulse.
The gamma detector would have to be designed to recover from the 'flash’ in
about 500~ns, and preliminary indications are that this is feasible for
germanium.
If the gamma detector requires a longer time to recover, the measurement
could be delayed more, with the limit being the time of the next proton
pulse 1700~ns later.
\paragraph{Titanium}
Though aluminium is the likely target for Mu2e/COMET,
titanium is an alternate that must be similarly characterised.
The additional task of establishing the $2p\to 1s$ rate per stopped muon
is necessary since this has not been previously
measured, though the
relative intensities of the Lyman and Balmer lines are known~\cite{Kessler:1967}.
A collection of candidate delayed gamma rays from activated nuclei
after capture are appealing for the same reasons as mentioned above for
aluminium. The most interesting come from the capture daughters $^{48}$Sc (44 hours)
and $^{46}$Sc(84 days); both have a yield comparable to
the similar reaction yielding
$^{27}$Mg in aluminium, but emit four gammas with near 100\% intensity.
The gamma rays are
listed in Table \ref{tab:gammas:tidelayed}. The long lifetime of the $^{46}$Sc precludes seeing its decay gammas at AlCap,
however it is of potential use in the much longer-running Mu2e and
COMET experiments and is therefore included here for completeness.
Because of the number of peaks
and their intensities, a measurement time comparable to that planned
for the $^{27}$Mg peak with the aluminium target, 1.5 days,
will be enough to get the necessary statistics
on the $^{48}$Sc peaks.
Observing gamma rays emitted promptly following muon capture also
appears possible.
There are four of interest with intensities of the order 10\% and these are
listed in Table~\ref{tab:gammas:tipromptcapture}. Note that there are other
possible measurements to make, but surveying the literature leads us to
believe the candidates discussed here are the most promising.
\begin{table}
\centering
\caption{After muon nuclear capture in titanium, activated scandium
is produced. One of these has a lifetime much longer than any
measurement time
scales on AlCap, making detecting these gammas impractical. Gammas from
the shorter
lifetime isotope however can be measured in AlCap.
Signature $\gamma$s are produced upon
decay that may prove useful for normalisation in both AlCap and
Mu2e/COMET. Branching ratios after capture~\cite{Evans:1973} refer to how often the isotope is
produced per muon capture. Intensities refer to how often the
$\gamma$ is emitted after the isotope decays.}
\begin{tabular}{c c c c c}
\addlinespace
\toprule
\bf Capture Product & \bf Branching Ratio & \bf Lifetime & \bf Energy & \bf Intensity \\
\bf Isotope & \bf (\%) & & \bf (keV) & \bf (\%) \\
\midrule
$^{48}$Sc & 11.1(9) & 43.7 h & \phantom{1}983.52 & 100\phantom{.0} \\
& & & 1037.6\phantom{0} & \phantom{1}97.6 \\
& & & 1312.1\phantom{0} & 100\phantom{.0} \\
\addlinespace
$^{46}$Sc & 8.1(10) & 83.8 d & \phantom{1}889.28 & 100\phantom{.0} \\
& & & 1120.5\phantom{0} & 100\phantom{.0} \\
\bottomrule
\end{tabular}
\label{tab:gammas:tidelayed}
\bigskip
\caption{(Excerpt of table in \cite{Evans:1973}.) Gammas that are produced
promptly when a muon nuclear captures
on titanium. The intensity is in terms of per-$\mu$-capture.
A number of promising $\gamma$s are given off that may be useful for
normalisation in AlCap and Mu2e/COMET.}
\begin{tabular}{c c c}
\addlinespace
\toprule
\bf Resultant Isotope & \bf Energy (keV) & \bf Intensity (\%)\\
\midrule
$^{48}$Sc & 121.41(4) & 10.5(9)\phantom{1} \\
& 130.94(4) & 10.4(9)\phantom{1} \\
& 370.29(5) & 12.2(8)\phantom{1} \\
\addlinespace
$^{47}$Sc & 807.79(8) & 13.0(15) \\
\bottomrule
\end{tabular}
\label{tab:gammas:tipromptcapture}
\end{table}
Simulations have been done to confirm which lines will be prominent enough to be useful.
By overlaying the simulated peaks onto real Al data (which contains a relevant
sample of background gamma lines),
it is obvious where certain problems will
arise when trying to count these peaks. The X-rays are shown in Figure
\ref{fig:gammas:ti_xrays}, and already we see a lead X-ray may prove
problematic without
proper shielding setup. The $\gamma$s prompt with muon nuclear capture
are in Figure
\ref{fig:gammas:ti_semiprompt} and those from the decay of activated capture
daughters
are in Figure \ref{fig:gammas:ti_delayed}.
Though the poor statistics associated with the R2013 data set
and signal-to-noise
ratio may seem discouraging, with the planned much
improved background suppression
and stopping rates
we expect these peaks to be seen solidly above background in the proposed
AlCap run in 2015.
\begin{figure}
\centering
\includegraphics[width=1.\linewidth]{figs/ti_xray}
\caption{The simulated Ti X-rays (black) were filled over the Al100 data.
Assuming the same number of muon stops as in the data and 100\%
$2p\to1s$ intensity, we see
for the most part the X-rays are readily identifiable. The first
Lyman line, however, would be much easier seen
were it not for the muonic lead X-ray immediately to the left.}
\label{fig:gammas:ti_xrays}
\end{figure}
\begin{figure}
\centering
\includegraphics[width=1.\linewidth]{figs/ti_semiprompt}
\caption{Similar to figure \ref{fig:gammas:ti_xrays}, except
above the simulated Ti signals are $\gamma$s prompt
with muonic nuclear capture. Clearly the signal-to-noise
ratio is poor, though we are confident our improvements in
the next AlCap run will allow these peaks to stand out.}
\label{fig:gammas:ti_semiprompt}
\end{figure}
\begin{figure}
\centering
\includegraphics[width=1.\linewidth]{figs/ti_delayed}
\caption{Similar to figures \ref{fig:gammas:ti_xrays} and
\ref{fig:gammas:ti_semiprompt}, except above are the $\gamma$s from
the decay of the product isotopes after muon nuclear capture in Ti
($^{48}$Sc and $^{46}$Sc)
This plot has assumed each isotope is in equilibrium with the beam,
which can only be achieved with beam on time
equivalent to the isotope's lifetime. Therefore the gammas from
the decay of $^{46}$Sc, with an 84 day half life, will not be visible in AlCap,
however the $^{48}$Sc (44 hours) decays are expected to be visible with a 1.5 day run.}
\label{fig:gammas:ti_delayed}
\end{figure}
\paragraph{Backgrounds}
Finally, it is important to understand the background lines that may exist
in the final Mu2e and COMET experiments. In AlCap Run 1 an unexpected gamma
peak from muons stopping in the stainless steel (SS) chamber appeared very
close to the \atrn{2p}{1s} aluminium X-ray of interest.
By directly measuring, in AlCap, the X-rays and gammas produced by muons
stopping in material that will be abundant in Mu2e/COMET, we can get ahead
of these issues early on.
\subsubsection{High Energy ($E>10$ MeV) Photons and Electrons}
The INFN Frascati group will provide a LYSO calorimeter array in order to
measure higher energy photons and electrons. It will operate parasitically
with a stand-alone DAQ, during the proposed thick target runs when the
neutrons and low-energy gammas will also be measured.
The array consists of LYSO crystals
with dimensions $3 \times 3 \times 13~\textrm{cm}$ in a $5\times5$ array, read out with $1 \times 1~\textrm{cm}$
Hamamatsu APDs and waveform digitisers.
The high energy photons will include those from radiative muon capture (RMC)
and from
radiative muon decay.
RMC is expected to dominate above about 80 MeV.
(See Figure \ref{fig:RMC-RMD-DIO})
\begin{figure}
\centering
\includegraphics[width=0.5\textwidth]{figs/RMC-RMD-DIO.jpg}
\caption{Simulated energy spectra of electrons and photons emitted from
muonic aluminium. Electron spectrum from muon decay in orbit
(red). Photon spectrum from radiative muon capture
(blue). Photon spectrum from radiative muon decay in orbit
(green).}
\label{fig:RMC-RMD-DIO}
\end{figure}
Based on published branching ratios, we expect about 5000 RMC events
above 57~MeV from the aluminium target.
The resulting high energy photon spectra will be evaluated for their suitability
for normalisation in the Mu2e and COMET experiments.
We will also detect the spectrum of electrons from ordinary muon decay, which
are identified by requiring a time coincidence between the LYSO signal
and a signal from a scintillator placed in front of the LYSO.

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A Monte Carlo simulation of the experiment has been developed using the GEANT4 toolkit. A visualisation of the implemented geometry is shown in Figure~\ref{fig:geant-vis}.
\begin{figure}[htbp]
\centering
\subfigure{
\includegraphics[scale=0.4,trim=100 50 100 100,clip]{figs/geant-vis}
\label{g4}
}
~%
\subfigure{
\mbox{
\includegraphics[scale=0.20,trim=200 0 200 0,clip]{figs/geant-vis_eventDisplay}
}
\label{g4_ed}
}
\caption{Visualisations from the AlCap Monte Carlo simulation. Left: The implemented geometry for an aluminium target. Right: An event display where a muon stops in the target, emitting a proton which is stopped in the right silicon detector package.}
\label{fig:geant-vis}
\end{figure}
The simulation is written in such a way that most aspects of it can be easily modified by editing various text files that exist for the geometry, the initial particle distribution and the output variables.
%The geometry configure files define and place all volumes. Some of these are placed within each other but ultimately they all placed within the ``world'' volume. By editing this file, properties of each volume can be changed to suit the simulation study being done. For example, the thickness and material of the target can be changed to simulate the experimental set-up of a different dataset. In addition, it is in this file that the volumes that are designated the ``sensitive'' volumes are defined. It is in these volumes where the properties of particles are read out.
The initial particle distribution configure files (also called the generator configure files) are used to define the particles that are created at the beginning of the experiment. These files contain the particle type, starting position, and initial momentum. The distributions of these latter two can be defined as a simple random uniform or Gaussian distributions or a distribution stored in a ROOT histogram can be used. This is especially useful if a previous simulation has generated a more realistic distribution that should be used. For example, after running a simulation where muons are fired at the target, a 3D histogram of the muon stopping positions can be created and used in future simulations.
%Finally, the output configure file defines the variables that are read out of the simulation. This includes, for example, each particle's momentum and energy deposited in the sensitive volumes as defined in the geometry configure file. Also, certain condition can be specified in this configure file so that only particles passing a certain cut will be recorded which can aid in reducing the output file size and allowing more statistics for a specific result.

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A Monte Carlo simulation of the experiment was developed using the GEANT4 toolkit. A visualisation of the implemented geometry is shown in Figure~\ref{fig:geant-vis}.
\begin{figure}[htbp]
\centering
\subfigure{
\includegraphics[scale=0.4,trim=100 50 100 100,clip]{figs/geant-vis}
\label{g4}
}
~%
\subfigure{
\fbox{
\includegraphics[scale=0.20,trim=200 0 200 0,clip]{figs/geant-vis_eventDisplay}
}
\label{g4_ed}
}
\caption{Visualisations from the AlCap Monte Carlo simulation. Left: The implemented geometry for an aluminium target. Right: An event display where a muon stops in the target, emitting a proton which is stopped in the right silicon detector package.}
\label{fig:geant-vis}
\end{figure}
The simulation is written so that most aspects can be easily
modified by editing various text files which describe
the geometry, the initial particle distribution, and the output variables.
%The geometry configure files define and place all volumes. Some of these are placed within each other but ultimately they all placed within the ``world'' volume. By editing this file, properties of each volume can be changed to suit the simulation study being done. For example, the thickness and material of the target can be changed to simulate the experimental set-up of a different dataset. In addition, it is in this file that the volumes that are designated the ``sensitive'' volumes are defined. It is in these volumes where the properties of particles are read out.
The initial particle distribution configure-files
(also called the generator configure files) are used to define the
particles which are created at the beginning of the experiment. These
files contain the particle type, starting position, and initial
momentum. The distributions of the latter two can be defined as
simple random uniform or Gaussian distributions, or a stored
distribution in a ROOT histogram. The later is is especially useful if a
particular simulation is found which provides a more realistic
distribution. For example, after running a simulation where muons
are thrown at the target, a 3D histogram of the muon stopping positions can be created and used in future simulations.
%Finally, the output configure file defines the variables that are read out of the simulation. This includes, for example, each particle's momentum and energy deposited in the sensitive volumes as defined in the geometry configure file. Also, certain condition can be specified in this configure file so that only particles passing a certain cut will be recorded which can aid in reducing the output file size and allowing more statistics for a specific result.

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The AlCap 2013 run demonstrated that the setup was capable of
performing this demanding charged particle experiment and led to
preliminary results. In R2015 we plan to improve several aspects which
will reduce the systematic uncertainty and improve the quality of the
final result.
\begin{itemize}
\item
\textbf{Beam profile measurements at target location.}
We intend to assemble a small probe
which can be inserted to measure the beam profile at the target
position for all measurements. Two possible methods are under
consideration: the first uses a series of crossed scintillating fibres
read-out with MPPCs, the second uses a single fibre which is scanned
across the beam.
\item
\textbf{Beam and detector geometry in the vacuum chamber.} We plan an
improved mechanics and surveying method for determining the relative
target and detector positions.
\item
\textbf{Improved silicon detector frontend.} We plan to suppress noise
and increase the stability of the Si detector readout, by placing
the preamplifiers inside the vacuum chamber. In addition, the shaping
constants of the fast preamplier outputs were not optimised, which
led to significant noise or undershoots in those signals.
\item
\textbf{DAQ.} The FADCs experienced data losses in high rate situations,
e.g. when using the silicon detector as active target. This data
quality issue will be eliminated by purchasing, and carefully
testing, new wave form digitisers from CAEN or SIS.
\item
\textbf{Ge detector.} The time resolution of the Ge detector was
only 66 ns FWHM, larger than specified (10 ns). This problem will addressed
with careful comparisons of analogue and digitised readout chains in our university labs.
\end{itemize}

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pdflatex $(file)
bibtex $(file)
pdflatex $(file)
pdflatex $(file)
clean:
rm -f *.aux *.dvi

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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}

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In R2013, two BC501 neutron
counters ($5''$ diameter and $5''$ depth) were borrowed from the
MuSun experiment, and placed outside the vacuum chamber on
both sides of the muon beam and centred on the stopping
target. Neutron spectra between 1 to about 20 MeV were obtained. The lower
threshold is limited by pulse shape discrimination (PSD) which
identifies neutron from photon events. Calibration of the detector
energy primarily used Cs-137 and Co-60, however these sources proved
inadequate. The Cs-127 Compton edge was too low in energy to be useful
and the Co-60 has two overlapping Compton edges. An average of the
two edge energies was used for calibration. An AmBe source was
originally intended to provide a known neutron spectrum and it did prove
useful in providing a 4.19 MeV gamma line for calibration. A ratio of the fast to slow
integrated waveform components
was used to provide neutron/gamma discrimination.
Discrimination is excellent above 1 MeVee, Figure~\ref{psdplot_2013}.
Analysis of the R2013 data demonstrated that a waveform digitiser of
at least 250 MHz sampling rate is needed to optimise the pulse shape
discrimination. A raw neutron spectrum is shown in Figure
~\ref{neutron_spectrum}. Initial work on unfolding the
spectrum has begun and is described in a later section. \\
\begin{figure}[btp]
\centering
\includegraphics[width=0.55\textwidth]{figs/PSD1}
\caption{Pulse shape discrimination between
neutrons (top band) and gammas (bottom band). The true neutron
energy is approximately twice the energy deposited in
MeVee.} \label{psdplot_2013}
\end{figure}
\begin{figure}[btp]
\centering
\includegraphics[width=0.55\textwidth]{figs/Neutron_Spectrum}
\caption{Raw neutron spectrum from an $Al$
target. The horizontal axis is electron equivalent energy
which is approximately a factor of 2 greater than the recoil
proton energy, which is of course folded by the detector
response function. \label{neutron_spectrum}. }
\end{figure}

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\subsubsection{Goals}
We propose to obtain the neutron emission spectrum due to muon
capture on Al, Ti, and H$_{2}$O. The focus will be on
Al. Ti remains a secondary target and capture on O would
be interesting as existing neutron data is of
reasonable quality, and shows a prominent peak near 5 MeV,
purportedly due to a giant resonance excitation. The unfolded neutron
energies would lie between 1 to somewhat over 10 MeV.
\subsubsection{Geometry/Detectors}
The main emphasis of R2013 was on the detection of charged
particle emission after muon capture, however, some neutron
emission data were collected and used to develop analysis
codes, efficiencies, and rates. In R2015, the basic
experimental setup will be
modified from that of R2013, by removing the vacuum chamber
and hanging the stopping target in
air by thin wires from a large frame far from the
beam line. Thus while the associated beamline components remain, the
vacuum chamber, veto scintillators, and their readout electronics are
removed. The target is rotated approximately $45^\circ$ with
respect to the beam line to minimise the target material
through which emitted particles travel to reach the
detectors.
We will borrow two neutron BC501 detectors ($5'' \times
2''$) from the Triangle Universities Nuclear Laboratory (TUNL)
for the proposed experiment. They are placed horizontally at
distances approximately 30 cm from the target. If the
LYSO array is used, it can be placed beneath the target and the
target rotated around the horizontal as well as the vertical
axis. A beam momentum of approximately \SI{40}{MeV\per\cc} and rate of
40 kHz is anticipated. The stopping thickness in an Al
target is approximately 0.2 cm (2000 $\mu$m), and with a
target rotation the Al target dimensions would be
$10\times10\times(0.1\textrm{\,--\,}0.2) \textrm{cm}^3$.
\subsubsection{Electronics}
Analysis of the R2013 data demonstrated that a waveform digitizer of
at least 250 MHz sampling rate is needed to optimise the pulse shape
discrimination (PSD) allowing separation of neutron from gamma events.
%Figure~\ref{psdplot_2013} shows the pulse shape discrimination
%Figure~\ref{fig:neutron-psd} shows the pulse shape discrimination
%achieved in a R2013 run.
Data will be acquired using the MIDAS
framework and stored in MIDAS banks for offline analysis. Real time
spectra will be available for online analysis and will be monitored
from the counting house via the software tools developed during 2013
run.
\subsubsection{Calibration}
The neutron counters will be calibrated periodically using radioactive
sources ($^{22}$Na, $^{137}$Cs, $^{22}$Na, AmBe). Data will be taken
with $^{137}$Cs daily to monitor the gain of detector system. Also,
data will be taken with beam-off to obtain a measure of
backgrounds. The AmBe source is particularly useful to set the gain
for higher energy neutrons as it has a Compton edge at 4.19 MeV, as
well as neutron emission up to 10 MeV. The neutron detectors will be
characterized at TUNL using $^7$Li(p,n)$^7$Be reaction and
time-of-flight~\cite{gonzales2009}.
In 2014 a similar detector was calibrated at TUNL, although the proton
beam energy was restricted keeping neutron energies below 5 MeV.
The results of this characterization
are being used to calibrate a MC simulation of the response
function, NRESP7~\cite{dietze1982}, in order to simulate the
detector response function for an arbitrary incident neutron
energy. The MC can then be used to obtain the folding matrix for the
detector for any detected energy.
The true neutron energy distribution must be obtained by
spectrum unfolding techniques~\cite{matzke1994}, and this
requires the knowledge of response of the detectors to
neutrons in the relevant energy range of the experiment. Thus the
detectors to be used in R2015 will be calibrated prior to their use at
PSI. As the neutron spectrum of AmBe is known, the measured spectrum will be unfolded after the unfolding function is determined and will be compared to the known
AmBe spectrum.
\subsubsection{Rates}
%Analysis of error propagation in unfolding neutron spectra
%indicate that a general error of 5\% in the folded
%data can be amplified at least an order of magnitude in the
%unfolding process~\cite{suman2014}. Thus in 2015, the intent
%is to hold statistical
%error to better than 5\% per energy bin.
In order to determine a neutron rate in the
detector, a data run using a 50 \textmu m target was analyzed
using timing cuts. The beam rate corresponding to the
collected data was 4.5 kHz and after PSD cuts a neutron detector
observed 1.1 neutrons/s. If the beam intensity is increased to 40 kHz
using an incident momentum of \SI{40}{MeV\per\cc} and a sufficiently thick target
is used to stop the total beam, the rate in a similar neutron detector
would be expected to increase by a factor of 100 to approximately 100
per second.
However, the scintillator in the neutron detectors proposed for R2015
are thinner by approximately a factor of 2. This provides better
resolution but decreases the detection efficiency.
The folded neutron spectrum in an energy bin between 5.5 to 6.0
MeVee is approximately 0.2\% of the total spectrum. Thus not including the
loss in detection efficiency due to the thinner scintillator,
approximately 19\,000 neutrons are expected to be obtained in 24 hours
within the energy bin.
%However, this does not include inefficiencies in data collection.
\subsubsection{Anticipated results}
A two day run provides a 1\% statistical error in a 0.5 MeV
energy bin. Obviously there are
other errors which we hope to control to a level
of 5\%. A data run for Al and perhaps a smaller
statistical run on Ti and H$_{2}$O is foreseen.

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The Mu2e~\cite{mu2e} (FNAL) and COMET~\cite{comet} (J-PARC) experiments seek
to determine the branching
ratio for the charged lepton flavor violating process \muec to better than
10$^{-16}$, which is a factor of 10,000 improvement compared to the current
best limit established by SINDRUM II~\cite{SindrumGold} (PSI).
The AlCap experiment is a
combined effort of the Mu2e and COMET collaborations to study important
background reactions from muon capture in candidate target materials (Al, Ti),
which are required to optimise the new muon-electron conversion experiments.
In 2013 the AlCap collaboration performed its first run (R2013) at PSI,
focusing on
work package WP1 with preliminary work done on WP2 and WP3.
The goal of WP1 is to measure the rate and spectrum of
protons emitted after nuclear muon capture since, in both Mu2e and COMET
Phase-I, the single-hit rate of these in the tracking chamber could be
significant. These protons have never been measured in the relevant low energy
regime of 2.5 to 15 MeV.
This progress report presents the status of the analysis of this run
and our beam request for 2015. In short, the program and plans can be
summarised as follows.
\begin{itemize}
\item
\textbf{WP1: Charged Particle Emission after Muon Capture.}
In spite of the commissioning challenges in R2013, the
preliminary analysis presented in the first AlCap PhD. Thesis~\cite{Nam:2014}
led
to the first physics result. The result was both surprising and of high
impact for
the Mu2e and COMET Phase-I designs.
The preliminary emission fraction of protons after
muon capture in aluminium was found to be 1.7\% in the energy range from
4 MeV to 8 MeV. The total proton emission fraction is estimated to be 3.5\% if
a simple description of the spectral shape holds.
This is much smaller
than the 15\% emission measured in silicon, and the assumed
10-15\% for aluminium which has been the basis
for both designs up-to-now. If this preliminary result holds up, it will
be possible to reduce the thickness of proton absorbers in COMET and Mu2e,
with a corresponding reduction in energy straggling and therefore
improved energy resolution on conversion electron
candidates. Indeed, no proton absorber might be needed at all
for COMET Phase-I~\cite{Nam:2014}.
The goal of the 2015 run is to corroborate these findings in an
upgraded set-up and to extend the measurement to titanium.
\item
\textbf{WP2: Gamma and X-ray Emission after Muon Capture.}
In R2013, the low energy X-ray and gamma ray spectra were measured with a
resolution of about 2 keV using a germanium detector. The measurement
of the number of \atrn{2p}{1s} muonic X-ray transitions provides the number of
stopped muons for the normalisation of the spectra in R2013.
In addition, the full gamma ray spectra can provide a wealth of information
from the peaks associated with muon capture and are being evaluated
for their use as alternative means of monitoring the number of stopped
muons in the full Mu2e and COMET experiments.
%Gamma lines associated with capture on surrounding materials (mainly lead and stainless steel) could interfere with the lines of interest in aluminum. Indeed, we have found one lead gamma line that is close to the Al $2p \to 1s$ muonic X-ray transition and so, in the next run, we will minimize the number of muons stopping in lead.
For the planned AlCap run, we will improve the measurement of the branching
ratio of an 844 keV delayed gamma ray in aluminium, which is of particular
interest to COMET and Mu2e.
In addition, we will explore the muonic X-rays and gamma rays in titanium, as
well as in any material that will be present in Mu2e and COMET such as lead,
stainless steel, and plastic. For these measurements,
a vacuum chamber is not required and a thicker target can be used compared
to the proton measurements. This
will allow data collection with substantially less background and higher data
rates.
The INFN group will bring a stand-alone $5\times5$ LYSO array
calorimeter which will allow them to parasitically measure the high
energy photon spectrum produced by stopped muons. This will provide
information on the spectrum that can be expected in the Mu2e and COMET
calorimeters, and also will allow an evaluation of the use of high
energy photons for normalisation in Mu2e or COMET.
\item
\textbf{WP3: Neutron Emission after Muon Capture.}
Neutron emission after muon capture, ie $\mu^- + A(Z,N)\rightarrow n
+ [A-1](Z-1,N) $
is governed by the weak interaction and is similar to electron
capture on a nucleus with much larger momentum transfer. The
distribution of neutron energies with emission greater than 10 MeV
can explained by a statistical model with effective temperature, $N =
N_{0} e^{-(E/T)^2}$. However, at lower energies the residual nuclear
particle-hole states can excite giant dipole resonances, and these
potentially dominate emission, although present data quality is
insufficient to build an accurate nuclear physics
model \cite{Raphael:1967}. Previous emission spectra were obtained on
selected nuclear targets 30--40 years ago and are of low quality and
low statistics. A FLUKA Monte Carlo (MC) simulation of emission
probabilities predicts the ratio of proton to neutron emission is
approximately 24\%, with non-negligible multi-neutron emission. While
the MC was calibrated at CERN in the NTOF experiment, better emission
data and nuclear models are important. MC codes need more accurate
low energy data to develop the models. Neutron emission from the
stopping target in the Mu2e experiment is an important background to
be understood and controlled. For example, the MC predicted gamma
background from neutron capture in the proton attenuation shield
surrounding the target caused it to be redesigned. Also as the front end
electronic systems are placed within the detector solenoid, neutron
induced single-event-upsets (SEU) in the readout electronics requires
detailed attention. Time-to-failure in memory and logic components
has shown to be significant and this must be evaluated using accurate
neutron flux calculations.
\end{itemize}

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A preliminary analysis has been done on half of the Al100 dataset. The analysis used information from silicon, germanium and
upstream muon detectors. Pulse parameters were extracted from waveforms by the
methods described above. Purposes of the analysis
include:
\begin{itemize}
\item testing the analysis chain;
\item verification of the experimental method, specifically the
normalisation of number of stopped muons, and particle identification
using specific energy loss;
\item extracting a preliminary rate and spectrum of proton emission from
aluminium.
\end{itemize}
\subsubsection{Event selection}
\label{ssub:event_selection}
As described earlier, the hits on all detectors are re-organised into
muon-centred events, each event consists of one central muon and all hits
within \SI{\pm 10}{\us} from the central muon. A pile-up protection mechanism
is used to ensure only one muon appears in each event: if there are muon
hits within \SI{\pm 10}{\us} of each other, both of them will be rejected. The
dataset from runs \numrange{2808}{2873} contains \num{1.17E+9} such muon
events.
Selection of proton (and other heavy charged particles) events start from
searching for a muon event that has at least one hit in the thick silicon. If there
is a thin silicon hit within a coincidence window of $\pm 0.5$~\si{\us}\ around
the thick silicon hit, the two hits are considered to belong to one particle.
The thresholds for energy deposited in all silicon channels, except the thin
silicon on the left arm, are set at \SI{100}{\keV} in this analysis. The
threshold on the left $\Delta E$ counter was higher, at roughly
\SI{400}{\keV}, in order to suppress higher noise in this channel that caused an excessive trigger rate.
\begin{figure}[htb]
\centering
\includegraphics[width=0.85\textwidth]{figs/al100_dedx_overlay}
\caption{Identification of charged particle bands: the dots are measured
points, the histograms are the expected bands of protons (red), deuterons
(green) and tritons (blue). The MC bands are calculated
for a pair of 58-\si{\um}-thick and 1535-\si{\um}-thick silicon
detectors. The error bars on MC bands show the standard deviation of
$\Delta E$ in the respective bins of E.
}
\label{fig:pid_sim}
\end{figure}
\subsubsection{Charged particle identification}
\label{ssub:charged_particle_identification}
Charged particle identification is done using the energy deposition
in the silicon detectors. \Cref{fig:al100_dedx} shows the energy
deposited in the thin silicon detector as a function of the total energy
deposited in both thin and thick detectors.
With the aid of the MC simulation, the band of protons in \cref{fig:al100_dedx}
can be identified as shown in \cref{fig:pid_sim}.
A proton likelihood probability is defined as:
\begin{equation}
P_{i} = \dfrac{1}{\sqrt{2\pi}\sigma_{\Delta E}}
\exp{\left[\dfrac{(\Delta E_\mathrm{meas} - \Delta E_i)^2} {2\sigma^2_{\Delta
E}}\right]}\,,
\end{equation}
where $\Delta E_{\mathrm{meas}}$ is the measured energy deposition in
the thin silicon detector; $\Delta E_i$ and
$\sigma_{\Delta E}$ are the expected value and the standard deviation of the energy
loss in the thin detector, of protons with summed energy $E_i$, calculated by the MC simulation.
With a cut on proton-like probability of $P_{i}>\num{1E-4}$, the proton band
can be extracted as shown in \cref{fig:al100_protons}. The numbers of protons
observed in the
two silicon arms in the energy range from \SIrange{2.2}{8}{\MeV} are:
\begin{align}
N_{\textrm{p right}} &= 2373\,,\\
N_{\textrm{p left}} &= 1822\,.
\end{align}
\begin{figure}[htb]
\centering
\includegraphics[width=0.47\textwidth]{figs/al100_protons}
\includegraphics[width=0.47\textwidth]{figs/al100_protons_px_r}
\caption{Protons (green) selected using the likelihood probability cut of
\num{1.0E-4} (left). The proton spectrum (right) is obtained by projecting
the proton band onto the total energy axis.}
\label{fig:al100_protons}
\end{figure}
\subsubsection{Correction for energy loss in target and geometrical acceptance}
\label{ssub:correction_for_energy_loss_in_target_and_geometrical_acceptance}
The observed proton spectra are modified by the energy loss of protons travelling through the
target, therefore correction (or unfolding) of the observed energy spectrum is needed to find the true spectrum. The iterative Bayesian
unfolding method implemented in RooUnfold package~\cite{Adye.2011} was used.
The unfolding code was trained by a MC-generated proton spectra. The unfolded
results are shown in \cref{fig:al100_unfold}. The proton yields observed in the
range \SIrange{4}{8}{\MeV} by the two silicon arms are:
\begin{align}
N_{\textrm{p unfold left}} &= (165.4 \pm 2.7)\times 10^3\,,\\
N_{\textrm{p unfold right}} &= (173.1 \pm 2.9)\times 10^3\,.
\end{align}
The average proton yield is then:
\begin{equation}
N_{\textrm{p unfold avg}} = (169.3 \pm 1.9) \times 10^3
\end{equation}
\begin{figure}[htb]
\centering
\includegraphics[width=0.80\textwidth]{figs/al100_unfolded_lr}
\caption{Unfolded proton spectra from the 100-\si{\um} aluminium target.}
\label{fig:al100_unfold}
\end{figure}
\subsubsection{Normalisation to the number of nuclear muon captures}
\label{ssub:number_of_stopped_muons}
The number of stopped muons in the target is inferred from the number of
X-rays recorded. The number of \atrn{2p}{1s} transitions and the number of nuclear
captures are calculated to be:
\begin{align}
N_{\mu \textrm{ stopped}} &= (1.57 \pm 0.05)\times 10^7\,,\\
N_{\mu \textrm{ nucl. cap.}} &= (9.57\pm 0.31)\times 10^6\,.
\end{align}
The emission rate of protons in the energy range of \SIrange{4}{8}{\MeV} is
then:
\begin{equation}
R_{\textrm{p}} = \frac{169.3\times 10^3}{9.57\times 10^6} = 1.7\times
10^{-2}\,.
\label{eq:proton_rate_al}
\end{equation}
Uncertainty of the rate in Equation~\eqref{eq:proton_rate_al} is estimated to be 6.1\%,
where the dominant sources are from the unfolding process (5\%), and
from the number of nuclear captures (3.2\%). We are studying the consistency
between the data sets to check for any overlooked systematic uncertainty.
%There are two sources of uncertainties in the emission
%rate~\eqref{eq:proton_rate_al}:
%\begin{itemize}
%\item from the number of nuclear captures, including the statistical
%uncertainty of the peak area determination and
%\item uncertainties in the number of protons:
%\begin{itemize}
%\item statistical uncertainties of the measured spectra which are
%propagated during the unfolding process;
%\item systematic uncertainties due to misidentification: this number is
%small compared to other uncertainties as discussed in
%\cref{sub:event_selection_for_the_passive_targets};
%\item systematic uncertainty from the unfolding
%\end{itemize}
%\end{itemize}
%The last item is studied by MC method using the parameterisation in
%\cref{sub:proton_emission_rate}:
%\begin{itemize}
%\item protons with energy distribution obeying the parameterisation are
%generated inside the target. The spatial distribution is the same as that
%of in \cref{sub:corrections_for_the_number_of_protons}. MC truth including
%initial energies and positions are recorded;
%\item the number of protons reaching the silicon detectors are counted,
%the proton yield is set to be the same as the measured yield to make the
%statistical uncertainties comparable;
%\item the unfolding is applied on the observed proton spectra, and the
%results are compared with the MC truth.
%\end{itemize}
%\begin{figure}[htb]
%\centering
%\includegraphics[width=0.48\textwidth]{figs/al100_MCvsUnfold}
%\includegraphics[width=0.48\textwidth]{figs/al100_unfold_truth_ratio}
%\caption{Comparison between an unfolded spectrum and MC truth. On the left
%hand side, the solid, red line is MC truth, the blue histogram is the
%unfoldede spectrum. The ratio between the two yields is compared in the
%right hand side plot with the upper end of integration is fixed at
%\SI{8}{\MeV}, and a moving lower end of integration. The discrepancy
%is genenerally smaller than 5\% if the lower end energy is smaller than
%\SI{6}{\MeV}.}
%\label{fig:al100_MCvsUnfold}
%\end{figure}
%\Cref{fig:al100_MCvsUnfold} shows that the yield obtained after unfolding is
%in agreement with that from the MC truth. The difference is less than 5\% if
%the integration is taken in the range from \SIrange{4}{8}{\MeV}. Therefore
%a systematic uncertainty of 5\% is assigned for the unfolding routine.
%A summary of uncertainties in the measurement of proton emission rate is
%presented in \cref{tab:al100_uncertainties_all}.
%\begin{table}[htb]
%\begin{center}
%\begin{tabular}{@{}ll@{}}
%\toprule
%\textbf{Item}& \textbf{Value} \\
%\midrule
%Number of muons & 3.2\% \\
%Statistical from measured spectra & 1.1\% \\
%Systematic from unfolding & 5.0\% \\
%Systematic from PID & \textless1.0\% \\
%\midrule
%Total & 6.1\%\\
%\bottomrule
%\end{tabular}
%\end{center}
%\caption{Uncertainties of the proton emission rate.}
%\label{tab:al100_uncertainties_all}
%\end{table}

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\begin{itemize}
\item
\textbf{Active silicon target 1.5~mm and 50~\textmu m, 4 days}. The R2015
charged particle run will begin
with an Si active
target, as this target is ideal for setting up the experiment.
The emission spectrum in a thick Si detector was measured in 2013
and compared to
the only low energy proton spectrum in the literature. However, the
measurement is partially compromised with FADC data losses and an
unoptimised fast signal
chain. The emission spectrum in a new thin silicon detector will be
measured, to verify the overall measurement strategy, as the rate
and spectrum are known from the thick Si measurement. Moreover, the
active detector will allow the reconstruction of the response matrix.
\item
\textbf{Aluminium 50~\textmu m, 3 days}. This measurement should corroborate a key result of the charged particle measurement program
under a well defined condition. The statistics and improved signal to
noise will
completely cover the emission spectrum. In particular, the shaping
times of the fast signals
will be optimised. This will allow the rejection of background events
due to muon stops with proton emission in
the Si detectors.
\item
\textbf{Titanium 100~\textmu m, 50~\textmu m, 3 days}. This measurement
will characterise proton emission in muon capture on titanium, which
is a promising
target option for future muon-electron conversion experiments.
\end{itemize}

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This is the README file for the 'textgreek' package.
textgreek - text symbols for the Greek alphabet
SUMMARY
The LaTeX package textgreek provides NFSS text symbols for Greek
letters. This way an author can use Greek letters in text without
changing to math mode. The usual font selection commands---e.g.
\textbf---apply to these Greek letters as to usual text and the font
is upright in an upright environment. Further, hyperref can use these
symbols in PDF-strings such as PDF-bookmarks.
To produce the textgreek.sty file run
latex textgreek.ins
FEEDBACK
Comments, suggestions, questions etc. are welcome. Send email to
leonard.michlmayr at gmail.com. (Preferably in German, English, or
Japanese)
LICENSE
Copyright 2010,2011 Leonard Michlmayr
This work may be distributed and/or modified under the
conditions of the LaTeX Project Public License, either version 1.3
of this license or (at your option) any later version.
The latest version of this license is in
http://www.latex-project.org/lppl.txt
and version 1.3 or later is part of all distributions of LaTeX
version 2005/12/01 or later.
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%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 their spectrum following muon capture on aluminium.
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 (wire chamber, plastic scintillator) and a downstream muon veto (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.
\begin{figure}[btp]
\centering
\subfigure{
\includegraphics[width=0.55\textwidth]{figs/Chamber_layout}
}
\subfigure{
\includegraphics[width=0.4\textwidth,trim= 0 -20 0 0]{figs/Chamber_dimensions}
}
\caption{Layout of the AlCap experiment for R2013. Left: Photograph final setup. Muons entered from the right of the image and after passing through the muon trigger system and collimator stopped in the target in the centre. Charged particles could then be detected in the Silicon detector packages(top and bottom), X-rays in the germanium (lower-right corner, out of image) and neutrons in the liquid scintillator (lower-left corner, out of image). Right: The dimensions of the R2013 setup. All measurements are in \si{mm}.
%The two silicon packages inside the vacuum vessel (SiL and SiR) measure the charged particles emitted from the target, the upstream muon counters consist of plastic scintillators and a wire chamber for defining the input muon beam ($\mu$PC),
%germanium detector measures the emitted X-rays and gamma rays and the veto plastic scintillator vetos muons that don't stop in target ($\mu$Ve).
}
\label{fig:alcap_setup_detailed}
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsubsection{Muon beam}
\label{ssub:muon_beam}
%\Cref{fig:alcap_setup_detailed} shows the experimental setup. The muon
%beam enters from the right of the image and hits the target, which is
%placed at the center of the vacuum chamber and orientated at 45
%degrees to the beam axis.
%In order to define
%stopped muon events, four muon counters are used: a 500~\rmmu m thick
%scintillator muon trigger counter (\rmmu SC); a muon anti-coincidence
%counter (\rmmu SCA) surrounding the trigger counter with a hole of 35
%mm diameter to define the beam radius; and a multiwire proportional
%chamber (\rmmu PC) that uses 24 X wires and 24 Y wires with at 2 mm
%intervals. This detector system belongs to the MuSun experiment and
%was well tuned in advance. A muon veto counter (\rmmu Ve) is placed
%at the downstream end of the chamber and is used to reject muons that
%pass through the stopping target.
One of the main requirements of the AlCap experiment was a muon beam
with narrow momentum bite in order to achieve a high fraction of
stopping muons in the very thin targets. The actual set up used in the Run
2013 was: muon momentum from \SIrange{28}{45}{\MeV\per c} and momentum spread of
3\% FWHM.
\subsubsection{Silicon detectors}
\label{ssub:silicon_detectors}
The main detectors for charged particles measurement are four large area
silicon detectors. The silicon detectors were grouped into two detector
packages located symmetrically at 90 degrees relative to
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 both silicon detectors.
The area of each of these silicon detectors and the
scintillators is $50\times50 \textrm{mm}^2$.
Due to the large capacitance of the thin detectors, noise and
pickup suppression had to be carefully optimised in the real PSI accelerator
environment. The achievable electronic resolution was between 55 and 76
keV FWHM in the thin silicon detectors, and between 35 and 40 keV for the
thick detectors.
\subsubsection{Germanium detector}
\label{ssub:germanium_detectors}
We used a germanium detector to normalise the number of stopped muons by
measuring characteristic muonic X-rays from the target material. The primary
X-rays of interest are the \atrn{2p}{1s} transitions,
the 346.828~keV line for aluminium targets, and the
400.177~keV line for silicon targets.
The germanium detector is
a model 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-ray
measurements, with an ultra-thin entrance window of 0.5-mm-thick beryllium and
a 0.3-\si{\micro\meter}-thick ion implanted contact. The germanium crystal is
\SI{52.5}{\mm} in diameter and \SI{55.3}{\mm} in length. The axial well has
a diameter of \SI{9.9}{\mm} and is \SI{47.8}{\mm} deep.
The detector was energy and acceptance calibrated with the many lines
from a Eu-152 source of known activity.
Energy resolutions are better than 2 keV for all calibrated peaks. Absolute
efficiencies at the energies of interest are listed in \cref{tab:xray_ref}.
\begin{table}[btp]
\centering
\caption{Reference values of major muonic X-rays from aluminium and silicon. Energy and intensity values are taken from~\cite{MeasdayAl}.}
\begin{tabular}{c l l l l c}
\addlinespace
\toprule
\textbf{Elements} & \textbf{Transition}
& \textbf{Energy (keV)} & \textbf{Intensity (\%)} & \textbf{Calibrated eff.}\\
\midrule
$^{27}\textrm{Al}$ & \atrn{2p}{1s} & $346.828 \pm 0.002$ & $79.8\pm 0.8$ &$4.95\times10^{-4}$\\
& \atrn{3p}{1s} & $412.87 \pm 0.05$ & $7.62\pm 0.15$ & $4.41\times10^{-4}$\\
\addlinespace
$^{28}\textrm{Si}$ & \atrn{2p}{1s} & $400.177 \pm 0.005$ & $80.3\pm 0.8$
&$4.40\times10^{-4}$\\
& \atrn{3p}{1s} & $476.80 \pm 0.05$ & $7.40 \pm 0.20$ &$3.81\times10^{-4}$\\
\bottomrule
\end{tabular}
\label{tab:xray_ref}
\end{table}
\subsubsection{Neutron detectors}
\label{ssub:neutron_detectors}
The main emphasis of R2013 was on the measurement of charged
particle emission after muon capture, however, some neutron
emission data were collected and used to develop analysis
tools, and to study efficiencies and rates. Two BC501 neutron
counters ($5''$ diameter and $5''$ depth) were borrowed from the
MuSun experiment, and placed outside the vacuum chamber on
both sides of the muon beam and centred on the stopping
target. Data collection used a 12-bit, 170-MHz FADC and readout
was by means of the MIDAS framework.
%346.828,4.95E-04,1.216E-05
%412.87,4.41E-04,9.780E-06
%400.177,4.40E-04,9.747E-06
%476.800,3.81E-04,7.680E-06

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During R2013, there were data collected for both silicon and aluminium
targets with the aluminium data being most useful for COMET and Mu2e
and the silicon data being collected so that a cross check with the
existing silicon data~\cite{sobo68} could be performed.
For both materials, two different target thicknesses were used.
For silicon, a thick, active target of 1500 \textmu m thickness was used with
three different beam momenta to investigate muons stopping on the surface of
the target and muons stopping closer to the centre. In addition, a thin,
passive silicon target of 62 \textmu m was used.
For aluminium, there were two different target thicknesses:
100 \textmu m and 50 \textmu m with the muon beam momentum tuned so that the
muon beam stopped towards the centre of the target.
Table~\ref{tab:alcap:datasets} summarises the datasets and gives the
muon beam momentum as a scale factor and the total number of muons
as entering the experiment as counted by the $\mu$Sc beam scintillator counter.
\begin{table}
\centering
\caption{Summary of the data that was collected during Run2013.}
\begin{tabular}{cccl}
\addlinespace
\toprule
\bf Target & \bf Beam Momentum & \bf Number of Muons & \bf Comments \\
& [$\times$\SI{28}{MeV\per \cc}] & & \\
\midrule
%\hline
Si (1500 \textmu m) & 1.32 & $2.78\times10^{7}$ & Active Target\\
& 1.30 & $2.89\times10^{8}$ & Cross check with \\
& 1.10 & $1.37\times10^{8}$ & existing Si data\\
\addlinespace
Si (62 \textmu m) & 1.06 & $1.72\times10^{7}$ & Passive Target\\
\addlinespace
Al (100 \textmu m) & 1.09 & $2.94\times10^{8}$ & \\
& 1.07 & $4.99\times10^{7}$ & \\
\addlinespace
Al (50 \textmu m) & 1.07 & $8.81\times10^{8}$ & \\
\bottomrule
\end{tabular}
\label{tab:alcap:datasets}
\end{table}
For all datasets, the aim was to measure the proton emission spectrum and normalise to the number of stopped muons by analysing the X-ray spectrum. In addition, preliminary investigations were made into the gamma ray and neutron emission spectra in preparation for a future run.

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The X-ray analysis is used to determine the number of stopped muons in the
AlCap target by counting the number of
muonic X-rays produced. In addition to the X-rays, there are gamma rays
that can be observed and are relevant to Mu2e/COMET as well as AlCap.
The entrance beam scintillator
counters can be used to count the muons
as they enter the vacuum chamber, however
collimation and accounting for
those muons that pass through the thin target,
the stopping efficiency in the target is significantly
less than 100\%.
The factor of interest for normalisation is the rate
of muon nuclear capture inside the target. The branching ratio of
capture is known for the targets of interest \cite{MeasdayAl} and is
proportional to the number of muon stops.
With the active silicon target
we have a reliable method of detecting a stop, namely, an energy
deposited in the silicon corresponding to the incoming muon beam energy, and
a time coincidence between signals from the beam counters and the silicon
detector. This is not the case with
the passive silicon and aluminium targets, for which we use instead the muonic
X-rays for normalisation.
When a muon is captured by an atom, it gives off
characteristic X-rays as it falls to the 1s state that can be counted
to determine the stopping rate.
For aluminium and silicon, the energies and intensities of the X-rays
from the $2p\to1s$ transitions
are well known and listed in Table~\ref{tab:xray_ref}.
The stopping rate
can then be inferred from the number of these X-rays measured,
after accounting for
geometric and photo-efficiencies. The rate from this method was cross-checked with that determined directly from stops in the active
silicon target, and the numbers are within each other's uncertainties.
A peak from the natural background ${}^{214}$Pb (351.9 keV) exists near
the ${}^{27}$Al \atrn{2p}{1s} ($K_\alpha$) X-ray.
To suppress this neighbouring peak and the
background, we required an entering muon in time coincidence with the
germanium pulse. However, we noticed that an unexpected
$\gamma$ line prompt with muon nuclear capture on lead appears at a slightly
lower energy than the ${}^{214}$Pb line (Figure \ref{fig:xrayanalysis:tl207}).
This is consistent with an intermediate excited
state of $^{207}$Tl, produced by muon capture on $^{208}$Pb.
Though not spoiling our measurement, the classification of
this peak is important so that it can be confirmed in the next run.
\begin{figure}
\centering
\includegraphics[width=0.5\linewidth]{figs/tl207.png}
\caption{To reduce the nearby pollution of the Al$_{K\alpha}$ by natural $^{214}$Pb,
only germanium signals within 300 ns of an entering muon were examined. When
the background peak persisted, we realised it was a prompt $\gamma$ from
muon capture on lead going via an intermediate excited $^{207}$Tl$^*$ state. This was
confirmed by the time structure of photons in that peak, which matches
the muonic lead lifetime.}
\label{fig:xrayanalysis:tl207}
\end{figure}
Though muonic X-rays are the primary method of normalisation in AlCap,
there are others that can be used and since both Mu2e and COMET are interested
in alternative normalisation schemes, it is important to examine the
viability of other peaks as
indicators of stopped muons. One is the $\gamma$ from the reaction
$^{27}_{13}\mbox{Al}+\mu^-\to\nu_{\mu}+n+\gamma+^{26}_{12}\mbox{Mg}$, with an intensity of
about 50\% per stopped
muon and an energy of 1809 keV \cite{MeasdayAl}.
What is appealing about this peak
is that there are few nearby peaks to worry about, and the signal-to-noise
ratio is
favourable, see the data in Figure \ref{fig:xrayanalysis:mg26_1809}.
The ratio of the number of observed
counts in the 1809 keV gamma ray line relative to
the $2p\to 1s$ muonic X-ray line is in good agreement with the value in the
literature.
\begin{figure}
\centering
\includegraphics[width=0.6\textwidth]{figs/mg26_1809keV}
\caption{The $\gamma$ produced in
$\mu^-+^{27}_{13}\mbox{Al}\to\nu_{\mu}+n+^{26}_{12}\mbox{Mg}^*$
followed by $^{26}_{12}\mbox{Mg}^*\to ^{26}_{12}\mbox{Mg}+\gamma$,
occurs at 1809 keV with an intensity of 0.51 per $\mu$-capture \cite{MeasdayAl}.
Because this line occurs in such a clean region of the photon spectrum and is so intense,
it could possibly be used for monitoring the number of stopped muons
in Mu2e and COMET.}
\label{fig:xrayanalysis:mg26_1809}
\end{figure}
A second gamma line at 844 keV results from the beta decay of
the relatively long-lived (9.5 minutes) $^{27}$Mg isotope
produced in the reaction
$^{27}_{13}\mbox{Al}+\mu^-\to\nu_{\mu}+^{27}_{12}\mbox{Mg}$.
Though counting this peak agreed within error with that expected from published
branching ratios, the uncertainty is large due to poor statistics.
By improving the statistics
under this peak in the proposed run we will
determine a more precise branching ratio, making it useful as a potential
normalisation to the number of muon stops in Mu2e and COMET.
The current data for this peak, as well as nearby peaks,
is illustrated in figure \ref{fig:xrayanalysis:mg27_844kev}.
\begin{figure}
\centering
\includegraphics[width=0.5\textwidth]{figs/mg27_844keV}
\caption{A peak at 844 keV from the decay of $^{27}_{12}$Mg is
correlated with the number of stopped muons in the target.
Unfortunately the yield is low and additionally polluted
by a nearby iron peak. With the statistics from our first run,
we could not determine to a sufficient precision the number
of these $\gamma$s we expect per captured muon, however we
will be able to achieve this in the proposed next run when the statistics will be much improved.}
\label {fig:xrayanalysis:mg27_844kev}
\end{figure}

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%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 their spectrum following muon capture on aluminium.
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=0.55\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}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsubsection{Muon beam and vacuum chamber}
<<<<<<< Setup.tex
The muon beam of low energy at \SIrange{28}{45}{\MeV\per\cc}, and narrow
momentum spread of 3\% were used.
=======
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. Muons with momenta from
\SIrange{28}{45}{\MeV\per c} and 3\% FWHM momentum bite were used.
>>>>>>> 1.3
\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 recorded by
our silicon detector.
\begin{figure}[btp]
\centering
\includegraphics[width=0.65\textwidth]{figs/Rates.png}
\caption{Measured muon rates at low momenta during the Run 2013. Beam rates
at 1 \% FWHM momentum bite were about 3 times smaller than the rates at
3 \% FWHM.}
\label{fig:Rates}
\end{figure}
\begin{figure}[btp]
\centering
\includegraphics[width=1.00\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. The
electron peak are the same in both plots as beam electrons are minimum
ionisation particles and passed though the detector easily. The muon peak
at the 3 \% FWHM momentum bite is notably broader than that at 1 \% FWHM
setting.}
\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 \cref{fig:alcap_setup_detailed} 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
to quickly capture muons that do not stop in the actual target.
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.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsubsection{Silicon detectors}
The main detectors for charged particles measurement are 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}
% subsubsection silicon_detectors (end)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsubsection{Upstream counters}
\label{sub:upstream_counters}
The upstream detector consists of three counters: a \SI{500}{\micro\meter}-thick
scintillator muon trigger counter ($\mu$SC); a muon anti-coincidence counter
($\mu$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 ($\mu$PC) that uses 24 X wires and 24 Y wires at
2~\si{\milli\meter}~intervals.
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.
% subsubsection upstream_counters (end)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsubsection{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. The germanium crystal is
\SI{52.5}{\mm} in diameter, and \SI{55.3}{\mm} in length. The axial well has
a diameter of \SI{9.9}{\mm} and \SI{47.8}{\mm} deep.
%(\cref{fig:ge_det_dimensions}).
%\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, viewing 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.
\subsubsection{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.
% subsubsection plastic_scintillators (end)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsubsection{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 the same dimensions 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 ($\mu$SC, $\mu$SCA
and $\mu$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 the 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 started 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.

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\documentclass[11pt]{article}
\usepackage{geometry}
\geometry{verbose,tmargin=20mm,bmargin=20mm,lmargin=30mm,rmargin=30mm}
\usepackage{graphics}
\usepackage{rotating}
\usepackage{textcomp}
\usepackage{subfigure}
\usepackage{verbatim}
\usepackage{float}
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%\usepackage{wasysym}
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%\linenumbers
%\usepackage[noabbrev]{cleveref}
\usepackage[noabbrev, capitalize]{cleveref}
\usepackage[detect-weight=true, detect-family=true]{siunitx}
\usepackage[]{xspace}
\newcommand{\rmmu}{\ensuremath{\mu}}
%\renewcommand{\rmmu}{\ensuremath{\mathrm{\mu}}}
\renewcommand{\rmmu}{\textmugreek}
%\newcommand{\cc}{$c$\xspace}
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\newcommand{\us}{\micro\second}
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bookmarks=true, % show bookmarks bar?
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pdffitwindow=false, % window fit to page when opened
pdfstartview={FitH}, % fits the width of the page to the window
pdftitle={My title}, % title
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pdfcreator={Creator}, % creator of the document
pdfproducer={Producer}, % producer of the document
pdfkeywords={keyword1} {key2} {key3}, % list of keywords
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% Function for the name of the MU and MTA programs.
% To get the spacing right, always invoke this as "... \MU{} ..."
\newcommand{\MU}{\emph{MU}}
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\newcommand{\muec}{$\mu^{-} N \rightarrow e^{-} N$\xspace}
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\begin{document}
\begin{center}
{\large\bf Progress Report 2014 and Beam Request 2015} \\
\vspace*{7mm}
{\Large\bf Study of Muon Capture for\\
Muon to Electron Conversion Experiments }\\[5mm]
\vspace{0.cm}
{\bf\em\large The AlCap Experiment\\}
\vspace*{5mm}
{\bf PSI Experiment R-13-03, spokespersons P.~Kammel and Y.~Kuno}\\[2mm]
{\bf \large AlCap Collaboration }\\
[2mm]
{\bf
Argonne National Laboratory --
Boston~University --
Brookhaven National Laboratory --
Fermilab National Accelerator Laboratory--
Imperial College London --
INFN Lecce --
INFN Pisa --
Institute of High Energy Physics, China --
Laboratori Nazionali di Frascati, INFN --
Nanjing University --
Osaka University --
University College London --
University of Houston --
University~of~Washington,~Seattle
\vspace{5mm}}
\begin{figure}[h]
\centering
%\includegraphics[width=0.85\textwidth]{figs/al100_EdE_left}
%\includegraphics[width=0.85\textwidth]{figs/al100_EdE_right}
\includegraphics[width=0.85\textwidth]{figs/al100_EdE_right_annotated}
\caption{Particle identification of the capture products determined with the combination of the thin/thick silicon detector
packages. On the $y$-axis is the energy deposited in the thin silicon detector and on the $x$-axis is the energy deposited in both the thin and the thick silicon layers. Each different particle band is annotated.}
\label{fig:al100_dedx}
\end{figure}
\end{center}
\vspace{3mm}
\normalsize
%\clearpage
\newpage
\setcounter{secnumdepth}{3}
\setcounter{tocdepth}{3}
\tableofcontents
%\listoftables
%\listoffigures
\newpage
%-------------------------------------------------------
%\textbf{General Guidelines}\\
%\begin{itemize}
%\item Brief description of the set-up
%\item Run overview
%\begin{itemize}
%\item System description and performance
%\item Chronology, statistics and data sets
%\end{itemize}
%\item Plans and Beam request
%\begin{itemize}
%\item Analysis plans
%\item Hardware plans
%\item Beam Request
%\end{itemize}
%\end{itemize}
%-------------------------------------------------------
\section{Overview}
%Peter 1.5 pages
\label{sec:Overview}
\input{Overview.tex}
\section{AlCap Run R2013}
\label{sec:R2013}
\subsection{Set-up}
%Nam 1.5 p
\input{Setup.tex}
\input{DAQ.tex}
\subsection{Summary of Measurements}
%Andy 1 p
\label{sec:SummaryMeasurements}
\input{SummaryMeasurements.tex}
\section{Analysis}
\subsection{Software Framework}
\subsubsection{Analysis Framework}
%Ben 1 p
\input{AnalysisFramework.tex}
\subsubsection{GEANT Simulation}
%Andy 1 p
\input{GeantSimulation.tex}
\subsection{Muon Beam}
%Andy 1p
\input{MuonBeam.tex}
\subsection{X-ray Analysis}
%John 1p
\label{sec:XRayAnalysis}
\input{XrayAnalysis.tex}
\subsection{Charged Particle Analysis}
%Ben and Nam, 1 p, just intro, different analysis active silicon and
%passive Al
\input{ChargedParticleAnalysis.tex}
\subsection{Neutron Analysis}
%AJI, EVH
\input{NeutronAnalysis.tex}
\subsection{Preliminary Analysis of Partial Data Set}
%Nam 3p
\input{PartialAnalysis.tex}
\section{Improvements, New Capabilities and Plans 2014}
\subsection{Improvements to Current Set-up}
% Peter 1p
\input{Improvements.tex}
\subsection{Charged Particle Measurement Program}
% Ed 1.5 p
\input{Protons.tex}
\subsection{Neutron Measurement Program}
% Ed 1.5 p
\input{Neutrons.tex}
\subsection{Gamma Measurement Program}
\label{sec:gammameas}
% Jim 1p
\input{Gammas.tex}
\section{Beam Request}
% summary table measurement plan and request
% Jim 1 page
\input{BeamRequest.tex}
\section{Acknowledgements}
We want to express our gratitude to the terrific PSI
staff. Without their help, we would not reached production quality in
our first run. This includes, in particular, Stefan Ritt, who
supported us as the PSI contact person, Konrad Deiters and his group, for
providing
his studio and infrastructure for the preparation of the experiment,
Claude Petitjean for beam tuning,
the vacuum group, who taught and helped us in many respects,
the IT department for assisting in
refurbishing and upgrading our frontend computer,
the electronics group,
the survey group and last, not least, the Hallendienst.
\newpage
\bibliography{progress14}
\end{document}

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%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 their spectrum following muon capture on aluminium.
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.
\begin{figure}[btp]
\centering
\includegraphics[width=0.55\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}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsubsection{Muon beam}
\label{ssub:muon_beam}
%\Cref{fig:alcap_setup_detailed} shows the experimental setup. The muon
%beam enters from the right of the image and hits the target, which is
%placed at the center of the vacuum chamber and orientated at 45
%degrees to the beam axis.
%In order to define
%stopped muon events, four muon counters are used: a 500~\rmmu m thick
%scintillator muon trigger counter (\rmmu SC); a muon anti-coincidence
%counter (\rmmu SCA) surrounding the trigger counter with a hole of 35
%mm diameter to define the beam radius; and a multiwire proportional
%chamber (\rmmu PC) that uses 24 X wires and 24 Y wires with at 2 mm
%intervals. This detector system belongs to the MuSun experiment and
%was well tuned in advance. A muon veto counter (\rmmu Ve) is placed
%at the downstream end of the chamber and is used to reject muons that
%pass through the stopping target.
One of the main requirements of the AlCap experiment was a muon beam
with narrow momentum bite in order to achieve a high fraction of
stopping muons in the very thin targets. The actual set up used in the Run
2013 was: muon momentum from \SIrange{28}{45}{\MeV\cc} and momentum spread of
3\% FWHM.