326 lines
11 KiB
TeX
326 lines
11 KiB
TeX
\documentclass[a4paper,11pt]{article}
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\usepackage[utf8x]{inputenc}
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\usepackage{ucs}
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\usepackage{hyperref}
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\usepackage{amsmath}
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\usepackage{amsfonts}
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\usepackage{amssymb}
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\usepackage{labelfig}
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\usepackage{epsf}
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\usepackage{float}
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\usepackage{url}
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\usepackage{fancyhdr}
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\usepackage{verbatim}
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\usepackage{color,listings}
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\usepackage{booktabs}
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\usepackage{tabularx}
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\usepackage{natbib}
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\usepackage[all]{xy}
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\usepackage{graphicx}
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\usepackage{graphics}
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\usepackage{multirow}
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%\makeatletter
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%\def\@xobeysp{}
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%\makeatother
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%\setlength{\textwidth}{14cm}
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\author{Tran Hoai Nam}
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\title{Short report on Geant4 simulation for proton measurements at PSI}
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\begin{document}
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\maketitle
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%\tableofcontents
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%\listoffigures
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%\listoftables
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\section{Set up}
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The geometry for the simulation is shown in Figure~\ref{fig:geo}, and
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parameters of each component are listed in Table~\ref{tb:para}. Each dE/dx
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package consists of:
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\begin{itemize}
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\item one dE detector: silicon, 65 $\mu$m thick
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\item one E detector: silicon, 1500 $\mu$m thick
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\item charged particles veto counter: plastic scintillator, 1 mm thick
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\end{itemize}
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There is
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a small gap of 1 mm between the detectors in each dE/dx package, and distance
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from the beam counter to beam window is 5 mm. The germanium detector
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I used is just a simple cylinder. Some parameters of the germanium detector are
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in this note of Frederik:
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\url{https://muon.npl.washington.edu/elog/mu2e/Capture2012/79}
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Physics list in use is the LHEP\_EMV because it is the fastest one. (see page
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5 in this presentation:
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\url{http://geant4.slac.stanford.edu/SLACTutorial09/ChoosingPhysicsList.pdf})
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\begin{figure}[htpb]
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\centering
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\includegraphics[width=0.55\textwidth]{figs/geo_cut}\includegraphics[width=0.45\textwidth]{figs/geo_top}
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\caption{Geometry used in the simulation, left: cut view, right: top view}
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\label{fig:geo}
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\end{figure}
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\begin{table}[htb]
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\centering
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\caption{Parameters used in simulation}
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\vskip1ex
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\label{tb:para}
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\begin{tabularx}{0.9\textwidth}{lll}
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\toprule
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Items & Material & Dimensions \\
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\midrule
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Vacuum chamber & Stainless steel & H = 380 mm \\
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& & $\Phi$ = 310 mm \\
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& & 5 mm thick wall \\
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\midrule
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Beam window & Mylar & 200 $\mu$m thick ($2\times 100$ $\mu$m,\\
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& & not shown in fig)\\
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\midrule
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Muon counter & Plastic & 5$\times$5 cm$^2$ \\
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and muon veto & scintillator & 0.5 mm thick \\
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\midrule
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dE counter & Silicon & 5$\times$5 cm$^2$ \\
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& & 65 $\mu$m thick \\
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\midrule
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E counter & Silicon & 5$\times$5 cm$^2$ \\
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& & 1500 $\mu$m thick \\
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\midrule
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Charged particle& Plastic & 5$\times$5 cm$^2$ \\
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veto & scintillator & 1 mm thick \\
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\midrule
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Target & Si/Al & 5$\times$5 cm$^2$ \\
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& & various thickness 50 $-$ 200 $\mu$m \\
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\midrule
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Ge detector & Germanium & H = 30 mm \\
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& & $\Phi$ = 30 mm \\
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\midrule
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Lead shield & Lead & 5$\times$5 cm$^2$ \\
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& & 2 mm thick \\
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\bottomrule
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\end{tabularx}
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\end{table}
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%\begin{figure}[htpb]
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%\centering
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%\includegraphics[width=0.6\textwidth]{figs/geo_top}
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%\caption{Top view of the geometry}
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%\label{fig:topview}
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%\end{figure}
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\section{Choosing initial muon momentum}
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Initial muon momentum is varied to maximize muon stopping ratio in the target,
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the muon momentum at the target, after passing through the beam counter and the
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chamber window is plotted in the Figure~\ref{fig:mu_at_target}.
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Other parameters of the muon beam are:
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\begin{itemize}
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\item muon momentum spread 2 \%
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\item Gaussian spatial spread, $\sigma_x = \sigma_y = 5$ mm
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\end{itemize}
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\begin{figure}[!htpb]
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\centering
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\includegraphics[width=\textwidth]{figs/mu_at_target}
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\caption{Momentum of muons at the target with different initial momentum}
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\label{fig:mu_at_target}
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\end{figure}
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I also set the target area to be 15$\times$15 cm$^2$ to see where the muons are
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scattered after the chamber window. The results are shown in
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Figure~\ref{fig:mu_hit_pos_200um}.
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\begin{figure}[!htpb]
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\centering
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\includegraphics[width=\textwidth]{figs/mu_hit_pos_200um_target}
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\caption{Hit position of muons on target with different initial muon
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momentum, the red box is the actual area of the $5\times5$ cm$^2$ target}
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\label{fig:mu_hit_pos_200um}
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\end{figure}
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Muon stopping ratio for different target thicknesses are listed in the
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Table~\ref{tb:stpratio}.
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\begin{table}[htb]
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\begin{center}
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\caption{Muon stopping ratio (\%) in target when adjusting initial muon
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momentum}
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\label{tb:stpratio}
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\vskip1ex
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%\scalebox{0.75}{
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\begin{tabular}{ccccc}
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\toprule
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& 50 $\mu$m & 100 $\mu$m & 150 $\mu$m & 200 $\mu$m \\
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\midrule
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30 MeV/c & 7.8 & - & - & - \\
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29 MeV/c & 40.2 & 6.7 & - & - \\
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28 MeV/c & 51.7 & 38.7 & 4.2 & - \\
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27 MeV/c & 43.0 & 38.5 & 33.1 & 1.3 \\
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26 MeV/c & 31.4 & 31.4 & 31.3 & 22.5 \\
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25 MeV/c & 8.1 & 8.0 & 8.1 & 8.0 \\
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\bottomrule
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\end{tabular}
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%}
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\end{center}
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\end{table}
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%%%%%%%%%%%%%%%%%%%%
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\section{Rate estimation}
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I have run the simulation with different thickness of the target: 50, 100, 150
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and 200 $\mu m$, initial momentum of muons is chosen from
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Table~\ref{tb:stpratio}.
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4$\times 10^6$ muons were generated in each run.
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The result of rate estimation for 10$^4$ muons/sec is shown in
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Table~\ref{tb:rates}. Some notes:
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\begin{itemize}
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\item triggered event: has hit on beam counter, AND no hit on veto counter
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\item stopped muon event: triggered, AND muon actually stopped inside the
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target. This is obtained by tracking the original muon, and seeing that it
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really stopped inside the target.
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\item hit on dE/dx package: coincidence with dE and E counters, AND no hit on
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charged particle veto.
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\end{itemize}
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%\begin{table}[htb]
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%\centering
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%\caption{Rate for 10$^4$ muons/sec}
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%\vskip1ex
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%\label{tb:rate}
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%\begin{tabular}{ccccccccc}
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%\begin{tabularx}{\textwidth}{ccccccccc}
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%\toprule
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%Target & Triggered & Stopped &\multicolumn{3}{c}{Rate dE/dx
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%1 (s$^{-1}$)}&
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%\multicolumn{3}{c}{Rate dE/dx 2 (s$^{-1}$)}\\
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%\cline{4-9}
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%thickness & \% & \% & All &Proton&$\mu$ & All &Proton&$\mu$ \\
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%\midrule
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%200 $\mu m$ & 98.7 & 41.9 & 19.8&2.9 &0.2 & 126.9& 6.7 &104.7\\
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%150 $\mu m$ & 96.5 & 34.9 & 17.1&2.7 &0.2 & 124.7& 7.5 &105.2\\
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%100 $\mu m$ & 87.3 & 8.6 & 7.9&1.7 &0.2 & 122.8& 5.1 &114.6\\
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%50 $\mu m$ & 77.7 & 0.2 & 4.5&1.0 &0.1 & 100.1& 2.9 &96.7\\
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%\bottomrule
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%\end{tabularx}
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%\end{tabular}
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%\end{table}
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\begin{table}[htb]
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\begin{center}
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\caption{Estimated event rates for various targets of different
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thickness. Incoming $10^{4}$ muons/sec and proton
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emission rate of
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0.15 per muon capture are assumed. The efficiency of
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Si detector of 100 \% is also assumed. }
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\label{tb:rates}
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\vskip1ex
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\scalebox{0.85}{
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\begin{tabular}{ccccc}
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\toprule
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Target & Muon momentum &\% Stopping & Event rate (Hz) & Event rate (Hz) \\
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thickness ($\mu$m)& (MeV/c) &in target & All particles
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& Protons \\
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\midrule
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50 & 26 & 22.2 & 34.8 & 4.6 \\
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100 & 27 & 32.9 & 48.5 & 5.4 \\
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150 & 28 & 38.5 & 54.5 & 4.8 \\
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200 & 28 & 51.2 & 47.7 & 4.5 \\
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%50 & 26 & 22.2 & 14.8 & 2.3 \\
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%100 & 27 & 32.9 & 18.5 & 2.1 \\
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%150 & 28 & 38.5 & 16.6 & 1.7 \\
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%200 & 28 & 51.2 & 19.8 & 2.0 \\
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\bottomrule
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\end{tabular}
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}
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\end{center}
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\end{table}
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%The reasons why stopping ratio is very small compares to trigger ratio are:
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%\begin{itemize}
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%\item some muons stopped inside the beam counter,
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%\item and, some muons that passed the beam counter are scattered off the
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%target (the distance from the beam counter to the target is 210 mm).
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%\end{itemize}
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%To investigate those effects, I fixed the target thickness to 200 $\mu m$, and
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%varied the thickness of beam counter from 0.7 mm to 1.5 mm. Fraction of muons
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%stopped in the beam counter, fraction that goes to the target are shown in
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%Table~\ref{tb:stop}. Some figures on momentum of original muons, and muons that
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%hit the target, and spatial distribution of muons that hit target are presented.
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Note:
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\begin{itemize}
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\item \% get to target = $\frac{\text{number of muons hit the target}}
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{\text{total number of muons generated}}$
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\item \% stop in target = $\frac{\text{number of muons stopped inside target}}
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{\text{number of muons hit target}}$
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\item \% total stopping efficiency = $\frac{\text{number of muons stopped inside
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target}}{\text{total number of muons generated}}$
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\end{itemize}
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%\begin{table}[htb]
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%\centering
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%\caption{Percentage of stopping muon}
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%\vskip1ex
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%\label{tb:stop}
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%\begin{tabular}{ccccc}
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%\toprule
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%Beam counter & \% stop in & \% get to & \% stop in & \% total stopping \\
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%thickness & beam counter& target & target & efficiency\\
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%\midrule
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%0.7 mm & 0.02 & 64 & 34 & 42 \\
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%0.8 mm & 0.04 & 57 & 66 & 40 \\
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%0.9 mm & 0.06 & 51 & 89 & 45 \\
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%1.0 mm & 0.09 & 43 & 98 & 42 \\
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%1.1 mm & 0.2 & 35 & 99.4 & 35 \\
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%1.2 mm & 1.4 & 24 & 99.7 & 24 \\
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%1.3 mm & 12 & 12 & 99.7 & 12 \\
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%1.4 mm & 43 & 3 & 99.8 & 3 \\
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%1.5 mm & 79 & 0.5 & 99.9 & 0.5 \\
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%\bottomrule
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%\end{tabular}
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%\end{table}
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%\begin{figure}[!htpb]
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%\centering
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%\includegraphics[width=\textwidth]{figs/mu_at_target}
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%\caption{Momentum of muons when entered target at different thickness of beam
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%counter}
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%\label{fig:mom}
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%\end{figure}
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%\begin{figure}[!htpb]
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%\centering
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%\includegraphics[width=\textwidth]{figs/mu_at_target_all}
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%\caption{Momentum of muons when entered target at different thickness of beam
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%counter, in comparison with original muon momentum}
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%\label{fig:mom_aio}
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%\end{figure}
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%\begin{figure}[!htpb]
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%\centering
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%\includegraphics[width=\textwidth]{figs/xy_target}
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%\caption{Spatial of muon hits on target when changing beam counter thickness}
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%\label{fig:xy}
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%\end{figure}
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\section{Side notes on structure of the output ROOT file}
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I used ROOT TObject to construct the output of the simulation (this is not
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really convenient for analysing). An event contains following information:
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\begin{itemize}
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\item event id,
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\item deposited energies in all detectors and target,
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\item a flag to show if there is a muon stopped inside the target,
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\item hits on each detectors, each hit has:
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\begin{itemize}
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\item type of the hit: initial muon stopped in the target, a particle
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entered or exited a detector, or a new particle is spawned in
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a detector
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\item a detector id,
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\item particle info: name, energy, hit position, time
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\end{itemize}
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\end{itemize}
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\section{To do}
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\begin{itemize}
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\item optimization of geometry
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\item digitization of output data, feeding to DAQ and analyzer, if possible
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\end{itemize}
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\end{document}
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