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thesis/chapters/chap5_alcap_setup.tex
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@@ -289,6 +289,7 @@ carried out.
% subsection plastic_scintillators (end)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Front-end electronics and data acquisition system}
The front-end electronics of the AlCap experiment was simple since we employed
a trigger-less read out system with waveform digitisers and flash ADCs
@@ -413,6 +414,254 @@ automatically starts a new run with the same parameters after about 6 seconds.
The short period of each run also allows the detection, and helps to reduce the
influence of effects such as electronics drifting, temperature fluctuation.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Detector calibration}
\label{sec:detector_calibration}
The calibration was done mainly for the silicon and germanium detectors
because they would provide energy information. The plastic scintillators were
only checked by oscilloscopes to make sure that the minimum ionisation
particles (MIPs) could be observed. The upstream plastic scintillation
counters and wire chamber, as mentioned, were well-tuned by the MuSun group.
\subsection{Silicon detector}
\label{sub:silicon_detector}
The energy calibration for the silicon detectors were done routinely during the
run, by:
\begin{itemize}
\item a \SI{79.5}{\becquerel} $^{241}\textrm{Am}$ alpha source. The most
prominent alpha particles have energies of \SI{5.484}{\si{\MeV}} (85.2\%)
and \SI{5.442}{\si{\MeV}} (12.5\%). The alpha particles from the source
would lose about \SI{66}{\kilo\eV} in the \SI{0.5}{\um}-thick dead layer,
and the peak would appear at \SI{5418}{\kilo\eV} (\cref{fig:toyMC_alpha});
\item and a tail pulse generator, A tail pulse with amplitude of
\SI{66}{\milli\volt}~was used to simulate the response of the silicon
detectors' preamplifiers to a particle with \SI{1}{\MeV} energy deposition;
\item During data taking period, electrons in the beam were were also used
for energy calibration of thick silicon detectors where energy deposition
is large enough. The muons at different momenta provided another mean of
calibration in the beam tuning period.
\end{itemize}
\begin{figure}[htb]
\centering
\includegraphics[width=0.6\textwidth]{figs/toyMC_alpha}
\caption{Energy loss of the alpha particles after a dead layer of
\SI{0.5}{\um}.}
\label{fig:toyMC_alpha}
\end{figure}
The calibration coefficients for the silicon channels are listed in
\cref{tab:cal_coeff}.
\begin{table}
\begin{center}
\pgfplotstabletypeset[
% separator
col sep=comma,
% columns displayed
display columns/0/.style={column name = \textbf{Detector}, string type,
column type=l},
display columns/1/.style={column name = \textbf{Slope}, column type=c,
dec sep align},
display columns/2/.style={column name = \textbf{Offset}, column type=r,
dec sep align},
% format the line breaks
every head row/.style={
before row={\toprule},
after row={\midrule},
columns/Detector/.style={column type=c},
columns/Slope/.style={column type=c},
columns/Offset/.style={column type=c}
},
every last row/.style={after row=\bottomrule},
]{raw/si_cal_effs.csv}
\caption{Calibration coefficients of the silicon detector channels}
\label{tab:cal_coeff}
\end{center}
\end{table}
% subsection silicon_detector (end)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Germanium detector}
\label{sub:germanium_detector}
The germanium detector was calibrated using a $^{152}\textrm{Eu}$
source
\footnote{Energies and intensities of gamma rays are taken from the
X-ray and Gamma-ray Decay Data Standards for Detector Calibration and Other
Applications, which is published by IAEA at \\
\url{https://www-nds.iaea.org/xgamma_standards/}},
the recorded pulse height spectrum is shown in \cref{fig:ge_eu152_spec}. The
source was placed at the target position so that the absolute efficiencies can
be calculated. The peak centroids and areas were obtained by fitting a Gaussian
peak on top of a first-order polynomial background. The only exception is the
\SI{1085.84}{\keV} line because of the interference of \SI{1089.74}{\keV},
the two were fitted with two Gaussian peaks on top of a first-order
polynomial background.
The relation between pulse height in ADC value and energy is found to be:
\begin{equation}
\textrm{ E [keV]} = 0.1219 \times \textrm{ADC} + 1.1621
\end{equation}
The energy resolution (full width at half maximum - FWHM) was better than
2.6~\si{\keV}\ for all the $^{152}\textrm{Eu}$ peaks. It was
a little worse at 3.1~\si{\keV}~for the annihilation photons at
511.0~\si{\keV}.
\begin{figure}[htb]
\centering
\includegraphics[width=0.70\textwidth]{figs/ge_eu152_spec}
\caption{Energy spectrum of the $\rm^{152}\textrm{Eu}$ calibration source
recorded by the germanium detector. The most prominent peaks of
$^{152}\textrm{Eu}$ along with their energies are
annotated in red; the 1460.82 \si{\keV}~line is background from
$^{40}\textrm{K}$; and the annihilation 511.0~\si{\keV}~photons
come both from the source and the surrounding environment.}
\label{fig:ge_eu152_spec}
\end{figure}
\begin{figure}[htb]
\centering
\includegraphics[width=0.89\textwidth]{figs/ge_ecal_fwhm}
\caption{Germanium energy calibration and resolution.}
\label{fig:ge_fwhm}
\end{figure}
The absolute efficiencies of the referenced points, and calculated
efficiencies at the X-ray of interest are presented in
\cref{tab:xray_eff}.
%The absolute efficiencies for the $(2p-1s)$ lines of aluminium
%(\SI{346.828}{\keV}) and silicon (\SI{400.177}{\keV})
%are presented in \cref{tab:xray_eff}.
In the process of efficiency calibration,
corrections for true coincidence summing and self-absorption were not applied.
The true coincidence summing probability is estimated to be very
small, about \num{5.4d-6}, thanks to the far geometry of the calibration. The
absorption in the source cover made of \SI{22}{\mg\per\cm^2}
polyethylene is less than \num{4d-4} for a \SI{100}{\keV} photon.
A Monte Carlo (MC) study on the acceptance of the germanium detector with two
purposes:
\begin{enumerate}
\item compare between measured and MC efficiencies: a point source made of
$^152$Eu is placed at the target position
\item estimate the uncertainty due to finite-size geometry: the source is
made of silicon with the same dimensions as those of the thick silicon
detector, namely \SI[product-units=power]{1.5 x 50 x 50}{\mm}; then the
primary vertex of $^152$Eu is generated inside the source.
\end{enumerate}
\begin{table}[htb]
\begin{center}
\pgfplotstabletypeset[
% separator
col sep=comma,
% columns displayed
% column type={S} means leave formatting to siunitx
display columns/0/.style={column name = \textbf{Photons (\si{\keV})},
string type,
column type={S[table-format=4.3, table-alignment=center]}},
display columns/1/.style={column name = \textbf{Efficiency},
string type,
column type={S[parse-numbers = true,
round-precision=3,
round-mode=figures,
fixed-exponent=-4,
scientific-notation=fixed,
table-format=1.2e-1,
%table-omit-exponent,
]}},
display columns/2/.style={column name = \textbf{Uncertainty},
string type,
column type={S[parse-numbers = true,
round-precision=3,
round-mode=figures,
fixed-exponent=-5,
scientific-notation=fixed,
table-format=1.3e-1,
%table-omit-exponent,
]}},
% format the line breaks
every head row/.style={
before row={\toprule},
after row={
%\textbf{\si{\keV}} & \textbf{\num{E-4}} & \textbf{\num{E-4}}\\
\midrule},
columns/0/.style={column type=r},
columns/1/.style={column type=c},
columns/2/.style={column type=c}
},
every last row/.style={after row=\bottomrule},
every nth row={8}{before row={\midrule}},
]{raw/ge_eff.csv}
\end{center}
\caption{Absolute efficiencies of the germanium detector in case of
a point-like source placed at the centre of the target (upper half), and
the calculated efficiencies for the X-rays of interest (lower half).}
\label{tab:xray_eff}
\end{table}
\begin{figure}[htb]
\centering
\includegraphics[width=0.40\textwidth]{figs/ge_eff_cal}
\includegraphics[width=0.40\textwidth]{figs/ge_eff_mc_finitesize_vs_pointlike_root}
\caption{Absolute efficiency of the germanium detector, the fit was done with
7 energy points from 244~keV, the shaded area is
95\% confidence interval of the fit.}
%because it is known that the linearity between
%$ln(\textrm{E})$ and $ln(\textrm{eff})$ holds better.
\label{fig:ge_eff_cal}
\end{figure}
% subsection germanium_detector (end)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\subsection{Beam tuning and muon momentum scanning}
%\label{sub:muon_momentum_scanning}
%Before taking any data, we carried out the muon momentum scanning to understand
%the muon beam, as well as calibrate the detector system. The nominal muon
%momentum used in the Run 2013 had been tuned to 28~MeV\cc\ before the run. By
%changing simultaneously the strength of the key magnet elements in the $\pi$E1
%beam line with the same factor, the muon beam momentum would be scaled with the
%same factor.
%The first study was on the range of muons in an active silicon target. The SiL2
%detector was placed perpendicular to the nominal beam path, after an oval
%collimator. The beam momentum scaling factor was scanned from 1.10 to 1.60,
%muon momenta and energies in the measured points are listed in
%\cref{tab:mu_scales}.
%\begin{table}[htbp]
%\begin{center}
%\begin{tabular}{c c c c}
%\toprule
%\textbf{Scaling} & \textbf{Momentum} & \textbf{Kinetic energy}
%& \textbf{Momentum spread}\\
%\textbf{factor} & \textbf{(MeV\per\cc)} & \textbf{(MeV)}
%& \textbf{(MeV\per\cc, 3\% FWHM)}\\
%\midrule
%1.03 & 28.84 & 3.87& 0.87\\
%1.05 & 29.40 & 4.01& 0.88\\
%1.06 & 29.68 & 4.09& 0.89\\
%1.07 & 29.96 & 4.17& 0.90\\
%1.10 & 30.80 & 4.40& 0.92\\
%1.15 & 32.20 & 4.80& 0.97\\
%1.20 & 33.60 & 5.21& 1.01\\
%1.30 & 36.40 & 6.09& 1.09\\
%1.40 & 39.20 & 7.04& 1.18\\
%1.43 & 40.04 & 7.33& 1.20\\
%1.45 & 40.60 & 7.53& 1.22\\
%1.47 & 41.16 & 7.73& 1.23\\
%1.50 & 42.00 & 8.04& 1.26\\
%\bottomrule
%\end{tabular}
%\end{center}
%\caption{Muon beam scaling factors, energies and momenta.}
%\label{tab:mu_scales}
%\end{table}
% subsection muon_momentum_scanning (end)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% section detector_calibration (end)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Data sets and statistics}
\label{sec:data_sets}