390 lines
15 KiB
TeX
390 lines
15 KiB
TeX
\documentclass[11pt]{article}
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\usepackage{mhchem}
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\usepackage{booktabs}
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\usepackage{hyperref}
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\usepackage[
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detect-weight=true,
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separate-uncertainty=true]{siunitx}
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% \usepackage{listings}
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\usepackage[dvipsnames]{xcolor}
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\usepackage{upquote}
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\usepackage{minted}
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% \mdtheorem[style=theoremstyle]{warning}{Warning}
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% frametitlerule=true,
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innertopmargin=\topskip,
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}
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% \mdtheorem[style=listing]{listing}{Listing}
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% \DeclareSIUnit\eVperc{\eV\per\clight}
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% \DeclareSIUnit\clight{\text{\ensuremath{c}}}
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\begin{document}
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\title{Hit rate estimation for STM detectors}
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\author{Nam H. Tran \\ Boston University}
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\date{\today}
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\maketitle
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\begin{abstract}
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This report presents estimated hit rate on STM detectors with the updated
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geometry in Offline version TODO.
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\end{abstract}
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\section{Overview}
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\label{sec:overview}
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In order to measure the eponymous rate of the Mu2e experiment, the number of
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stopped muons needs to be known to about \SI{10}{\percent}. The most promising
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schemes have involved photon detectors far downstream of the Muon Beam Stop
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measuring emissions from the Stopping Target (ST) at different times with
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respect to each pulse of muons stopping in the target. There are three
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categories we explore here for this stopping-target monitor (STM):
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\begin{itemize}
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\item Prompt: X-rays emitted when the muon comes to rest in the ST and is
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captured into atomic orbit (atomic capture, sometimes referred to as “muon
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stop” in this text). These X-rays are emitted essentially O(ps) with the
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atomic capture time.
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\item Semiprompt: $\gamma$-rays emitted upon nuclear capture (sometimes
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referred to simply as ``capture'' in this text) of the muon after stop.
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These exhibit timing characteristics of the muonic lifetime ($\tau
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= \SI{864}{\ns}$).
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\item Delayed: $\gamma$-rays from activated daughters resulting from muon
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nuclear capture in the ST.
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\end{itemize}
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The baseline design of the STM has been described by Miller et
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al~\cite{Miller2016}, the estimated hit rate on STM detector was about
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\SI{1.1}{\kHz} in the time window \SIrange{200}{1695}{\ns} from arrival time of
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a proton bunch. But this design would cause a high hit rate on the Cosmic
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Ray Veto (CRV) system, therefore changes have been made in the Offline version
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v6\textunderscore 0\textunderscore 2 by the CRV team to reduce the CRV hit
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rate. The goal of this study is to re-estimate hit rates on STM detectors in
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this new geometry.
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The actual changes relevant to the STM are:
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\begin{itemize}
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\item \SI{10}{\mm} polyethylene liner added to CRV shielding,
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\item field-of-view (FOV) collimator absorber thickness reduced to
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\SI{10}{\mm} (from \SI{20}{\mm}).
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\end{itemize}
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\section{Simulation details}
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\label{sec:simulation_details}
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The study was done using Mu2e Offline version v6\textunderscore
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0\textunderscore 2 (released on Oct 16,
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2016), hashtag \texttt{3d1e9154d7}. The simulation starts from the entrance of
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TS5 (see \cref{fig:stm_geo_all}), taking \texttt{cd3-beam-g4s2-mubeam.0728a}
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dataset as input. The dataset contains 5098 files, each corresponds to
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\num{1e6} proton-on-target (POT). The dataset were reused 16 times with
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different random seeds, where \SI{97.6}{\percent} of runs succeeded, equivalent
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to \num{7.96e10} POTs.
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\begin{figure}[htbp]
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\centering
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\includegraphics[width=1.0\textwidth]{figs/stm_geo_all}
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\caption{Simulation geometry showing the Detector Solenoid region on the
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left, sweeper magnet, Field-Of-View collimator, Spot-Size collimator, and
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the STM detectors on the right. Particles saved in the input files are
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shoot from the TS5 (orange circle), and transported to the STM region.}
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\label{fig:stm_geo_all}
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\end{figure}
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There were 8 virtual detectors (VD) in STM region enabled in this study, their
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identification numbers (\texttt{vdid}), locations, and abbreviation names
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(appear in the simulation output) are listed in \cref{tab:vds_list}.
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Information recorded by the VDs includes: particle type (\texttt{pdgid}),
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global and local coordinates, time, kinetic energy, and parent particle type.
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Only particles considered important to the STM, namely electrons,
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positrons, negative and positive muons, neutrons and photons, were written to
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the output file.
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\begin{table}[htbp]
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\centering
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\caption{List of virtual detectors read out in this study}
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\label{tab:vds_list}
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\begin{adjustbox}{max width=\textwidth}
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\begin{tabular}{@{}ccll@{}}
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\toprule
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&VDID & Location & Abbreviation \\
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\midrule
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1 & 81 & Exit of neutron shield of the DS & DSNeutronShieldExit \\
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2 & 86 & Upstream of the STM system & STM\textunderscore UpStr \\
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3 & 87 & Downstream of the sweeper magnet & STM\textunderscore MagDnStr \\
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4 & 101 & Upstream of the spot-size collimator & STM\textunderscore SpotSizeCollUpStr \\
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5 & 88 & Downstream of the spot-size collimator& STM\textunderscore CollDnStr \\
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6 & 89 & Upstream of the STM detector 1 & STM\textunderscore Det1UpStr \\
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7 & 90 & Upstream of the STM detector 2 & STM\textunderscore Det2UpStr \\
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8 & 100 & Downstream of the FOV collimator & STM\textunderscore FieldOfViewCollDnStr \\
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\bottomrule
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\end{tabular}
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\end{adjustbox}
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\end{table}
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\section{Simulation and analysis code}
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\label{sec:simulation_and_analysis_code}
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The simulation and analysis code are located at:
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\url{/mu2e/app/users/namtran/STM_study_201611}.
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% \lstinputlisting[language=bash,frame=single]{listings/code_dir_tree.sh}
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\begin{mdframed}[style=listing]
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\inputminted[fontsize=\footnotesize]{bash}{listings/code_dir_tree.sh}
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\end{mdframed}
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\texttt{step00} contains configuration files for this simulation and a script to
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submit all 5098 jobs to the FermiGrid. It took about 14 hours to complete one
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job in average.
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The \texttt{analysis} folder contains a script
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(\texttt{run\textunderscore statistics.sh}) which checks if a job has finished
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successfully, and makes a list of such runs.
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There is a simple analysis code (\texttt{main.cc}) to read the VD records and
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make plots.
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\section{Results}
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\label{sec:results}
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\begin{mdframed}[style=warning]
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Muonic X-rays and probabilities in the simulation are not correct (see
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\cref{sec:muonic_x_rays_in_geant4}).
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\end{mdframed}
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\subsection{STM detector energy spectra}
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\label{sub:stm_detector_spectra}
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Energy spectrum of particles hitting STM detectors in the range
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\SIrange{0.1}{3.1}{\MeV} are presented in \cref{fig:stm_det_ke}. There were not many
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hits, and only the annihilation peak stands out. Most of the particles are
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photons as shown in
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\cref{fig:stm_det_ptype}.
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\begin{figure}[htbp]
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\centering
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\includegraphics[width=0.85\textwidth]{figs/ke_det1UpStr}
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\includegraphics[width=0.85\textwidth]{figs/ke_det2UpStr}
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\caption{Kinetic energy of particles hitting STM detectors 1 (top), and
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2 (bottom).}
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\label{fig:stm_det_ke}
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\end{figure}
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\begin{figure}[htbp]
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\centering
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\includegraphics[width=\textwidth]{figs/ke_pdg_det1UpStr}
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\includegraphics[width=\textwidth]{figs/ke_pdg_det2UpStr}
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\caption{Kinetic energy and type of particles hitting STM detectors 1 (top),
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and 2 (bottom).}
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\label{fig:stm_det_ptype}
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\end{figure}
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\subsection{STM detector hit rate estimation}
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\label{sub:stm_detector_hit_rate_estimation}
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The average number of hits on a STM detector per POT is:
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\begin{equation}
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\frac{672 + 714}{2 \times 7.96 \times 10^{10}} = 8.7 \times 10^{-9}.
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\label{eqn:stm_hit_count}
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\end{equation}
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There would be \num{3.1e7} POTs per proton bunch, so the number of hits each
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bunch is:
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\begin{equation}
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8.7 \times 10^{-9} \times 3.1 \times 10^7 = 0.27.
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\end{equation}
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The instantaneous hit rate, assuming an interval of \SI{1695}{\ns} between
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bunches, is:
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\begin{equation}
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\frac{0.27}{1695\times 10^{-9}} = \SI{158.9e3}{\Hz}
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\end{equation}
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The uncertainty on the hit rate estimation is \SI{2.6}{\percent} if
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only statistical uncertainty of the hit counting in \cref{eqn:stm_hit_count} is
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taken into account. This hit rate is too high for a HPGe detector to function
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well, so an attenuator would be installed upstream of the spot-size collimator
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to lower the hit rate to about \SI{50}{\kHz}.
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\subsection{Hit timing on STM detectors}
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\label{sub:timing_of_hits_on_stm_detectors}
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Timing in the simulation starts from the birth of a primary proton, which means
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all events start at the same $t = 0$ time. In order to mimic the pulse
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structure of the proton beam (\SI{250}{\ns} pulse width, \SI{1695}{\ns} between
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pulses~\cite{Bartoszek2014}), the recorded times on each event are smeared by
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a Gaussian distribution with a $\sigma = 250 / 6 = \SI{41.7}{\ns}$.
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The hit timing as a function of kinetic energy for several virtual detectors
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are shown in \cref{fig:ke_time_4vds}. Most of hits arrive between
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\num{100} and \SI{400}{\ns} from the center of a proton pulse. Only a few of
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particles could hit the STM detectors, especially in the energy region around
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the $2p-1s$ peak, that it is hard to investigate the
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dependence between timing and energy of hits. Therefore I will only analyze the
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timing information of hits STM\_SpotSizeCollUpStr.
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\begin{figure}[htbp]
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\centering
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\includegraphics[width=1.0\textwidth]{figs/ke_time_4vds}
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\caption{Hit timing as a function of kinetic energy at spot size
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collimator upstream (top left) and down stream (top right), and two STM
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detectors (bottom left and right).}
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\label{fig:ke_time_4vds}
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\end{figure}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\subsection{Signal to background ratio: $2p-1s$ peak at spot-size collimator
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upstream}
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\label{sub:signal_to_background_ratio_2p_1s_peak_at_spot_size_collimator_upstream}
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The energy of muonic $2p-1s$ transition in aluminum is given as \SI{335}{\keV}
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by Geant4. Background is taken as the average counts for 10 bins around
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\SI{335}{\keV}, and signal strength is calculated by subtracting the background
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from the count under the peak. Energy spectra at spot-size
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collimator upstream (VD 101: STM\_SpotSizeCollUpStr) in \SI{50}{\ns} windows
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and their signal-to-background ratios are shown in
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\cref{fig:ke_SpotSizeCollUpStr_time_slices}.
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\begin{figure}[htbp]
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\centering
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\includegraphics[width=1.0\textwidth]{figs/ke_SpotSizeCollUpStr_time_slices}
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\caption{Energy spectra at STM\_SpotSizeCollUpStr and signal-to-background
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ratios in 50-ns time windows.}
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\label{fig:ke_SpotSizeCollUpStr_time_slices}
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\end{figure}
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\subsection{Signal to background ratio: \SI{1809}{\keV} at spot-size collimator
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upstream}
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\label{sub:signal_to_background_ratio_1809_kev_at_spot_size_collimator_upstream}
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%%%% Appendices
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\pagebreak
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\appendix
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\section{How to run the simulation and analyze data}
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%%%%%%%%%%%%%%%%%%%
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\label{sec:how_to_run_the_simulation_and_analyze_data}
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\subsection{Simulating beam flash}
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\label{sub:simulating_beam_flash}
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Simulation scripts are in:
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\url{/mu2e/app/users/namtran/STM_study_201611/step00}:
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\begin{itemize}
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\item \url{fcl/step00.fcl}: configuration for this study (primary particles,
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virtual detectors to be read out, particle filtering, ...)
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\item \url{geom/geom.txt}: specify geometry settings (thickness
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of shields, enabled virtual detectors, ...)
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\item \url{submit.sh}: submit all jobs (5098) in the
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\url{cd3-beam-g4s2-mubeam.0728a.list} to the grid
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\end{itemize}
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\noindent Steps to run the simulation:
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\begin{itemize}
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\item preparing user's code: follow Mu2e instruction to create an
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\texttt{Offline} distribution (mine is at
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\url{/mu2e/app/users/namtran/Offline}),
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\item setting up \texttt{mu2e} environment \footnote{I used \texttt{mu2egrid}
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version \texttt{v3\_02\_00} which supports \texttt{mu2eart} command}:
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\begin{mdframed}[style=listing]
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\inputminted[
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fontsize=\scriptsize,
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firstline=1,
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lastline=11,
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breaklines=true,
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breakanywhere=true
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]{bash}{listings/runall.sh}
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\end{mdframed}
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\item submitting all jobs:
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\begin{mdframed}[style=listing]
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\inputminted[
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fontsize=\scriptsize,
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firstline=13,
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breaklines=true,
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breakanywhere=true
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]{bash}{listings/runall.sh}
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\end{mdframed}
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\end{itemize}
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\noindent Analysis code
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\url{/mu2e/app/users/namtran/STM_study_201611/analysis}:
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\begin{itemize}
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\item \texttt{run\_statistics}: skims the log files (\texttt{mu2e.log} in
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each subdirectory`) to make a list of successful runs, and collect CPU
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time, random seeds. This script should be run first.
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\item \texttt{main.cc}: the analysis code, it is rather simple now, only
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exports a few histograms from virtual detector hits. Run \texttt{make}
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to produce the executable \texttt{read\_vd}.
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\item \texttt{read\_vd}: takes a list of simulation outputs as input to
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produce a single ROOT file which contains several histograms.
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\end{itemize}
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%%%%%%%%%%%%%%%%%%%
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\section{Muonic X-rays in Geant4}
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\label{sec:muonic_x_rays_in_geant4}
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The muonic energy levels and transition probabilities were calculated using
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a simple model described by Mukhopadhyay~\cite{Mukhopadhyay.1977}.
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\begin{itemize}
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\item Energy of K-shell electrons are precisely corrected based on
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that of hydrogen atom, taking finite size of the nucleus into account:
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% \lstinputlisting[
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% language=c++, firstline=64, lastline=93,firstnumber=64,
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% breaklines=true, breakatwhitespace=true,
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% frame=single]{listings/G4EmCaptureCascade.cc}
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\begin{mdframed}[style=listing]
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\inputminted[
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breaklines=true,
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stepnumber=5,
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linenos=true,
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firstline=64,
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fontsize=\footnotesize,
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lastline=93]{c++}{listings/G4EmCaptureCascade.cc}
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\end{mdframed}
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\item Energy of K-shell muons are calculated from energy of K-shell
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electrons:
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\begin{mdframed}[style=listing]
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\inputminted[
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breaklines=true,
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stepnumber=5,
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linenos=true,
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fontsize=\footnotesize,
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firstline=118,
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lastline=122]{c++}{listings/G4EmCaptureCascade.cc}
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\end{mdframed}
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\item Energies of muons on other shells are calculated by scaling from that
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of K-shell muons:
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\begin{mdframed}[style=listing]
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\inputminted[
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breaklines=true,
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stepnumber=5,
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linenos=true,
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fontsize=\footnotesize,
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firstline=123,
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lastline=125]{c++}{listings/G4EmCaptureCascade.cc}
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\end{mdframed}
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\end{itemize}
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Above listings are from the Geant4 source file:
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\url{source/processes/hadronic/stopping/src/G4EmCaptureCascade.cc}
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\bibliographystyle{h-physrev}
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\bibliography{stm_study}
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\end{document}
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