From c8e33899af1fe6daf8e657eafe038444b14a7d79 Mon Sep 17 00:00:00 2001 From: nam Date: Thu, 2 Oct 2014 16:12:17 +0900 Subject: [PATCH] prog saved --- thesis/chapters/chap5_alcap_setup.tex | 151 ++++++++++++++++---------- thesis/chapters/chap6_analysis.tex | 6 +- thesis/thesis.bib | 24 +++- thesis/thesis.tex | 4 +- 4 files changed, 116 insertions(+), 69 deletions(-) diff --git a/thesis/chapters/chap5_alcap_setup.tex b/thesis/chapters/chap5_alcap_setup.tex index 481bb34..ba56836 100644 --- a/thesis/chapters/chap5_alcap_setup.tex +++ b/thesis/chapters/chap5_alcap_setup.tex @@ -402,10 +402,11 @@ 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 compares 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). +{\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. @@ -495,8 +496,8 @@ 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 +\SI{1085.84}{\keV} line because of the interference of the \SI{1089.74}{\keV} +gamma, the two were fitted with two Gaussian peaks on top of a first-order polynomial background. The relation between pulse height in ADC value and energy is found to be: @@ -527,30 +528,86 @@ a little worse at 3.1~\si{\keV}~for the annihilation photons at \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: +Following corrections for the peak areas are considered: \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. + \item Correction for counting loss due to finite response time of the + detector system, where two gamma rays arrive at the detector within a time + interval short compared to that response time. This correction is + significant in our germanium system because of the current pulse + information extracting method does not count the second pulse. + \item Correction of counting time loss in the reset periods of the transistor + reset preamplifier. A preamplifier of this type would reset itself after + accumulating a predetermined amount of charge. During a reset, the + preamplifier is insensitive so this can be counted as dead time. + \item True coincidence summing correction: two cascade gamma rays hit the + detector at the same time would cause loss of count under the two + respective peaks and gain under the sum energy peak. + \item Correction for self-absorption of a gamma ray by the source itself. \end{enumerate} +The corrections for the first two mechanisms can be estimated by examining +pulse length and intervals between two consecutive pulses in the germanium +detector (\cref{fig:ge_cal_rate_pulselength}). The average pulse +length is \SI{45.7}{\um}, the average count rate obtained from the decay rate +of the interval spectrum is \SI{240}{\per\s}. + +The correction factor for the finite response time of the detector system is +calculated as: +\begin{align} + k_{\textrm{finite response time}} &= e^{2\times \textrm{(pulse length)} + \times \textrm{(count rate)}}\\ + &= e^{2\times 47.5\times10^{-6} \times 241} \nonumber\\ + &= 1.02 \label{eqn:finite_time_response} +\end{align} + +The resets of the preamplifier show up as a peak around \SI{2}{\ms}, +consistent with specification of the manufacturer. Fitting the peak on top of +an exponential background gives the actual reset pulse length of +\SI{1947.34}{\us} and the number of resets during the calibration runs is +2335.0. The total time loss for resetting is hence: +$1947.34\times 10^{-6} \times 2335.0 = 4.55$ \si{\s}. That is a 0.14\% loss +for a measuring time of \SI{3245.5}{\s}. This percentage loss is insignificant +compared with the loss in \eqref{eqn:finite_time_response} and the statistical +uncertainty of peak areas so correction for amplifier resets is not applied. + +\begin{figure}[htb] + \centering + \includegraphics[width=0.95\textwidth]{figs/ge_cal_rate_pulselength} + \caption{Germanium detector pulse length (left) and intervals between pulses + on that detector (right). The peak around \SI{2}{\ms} corresponds to the + resets of the preamplifier. The peak at \SI{250}{\us} is due to triggering + by the timing channel which is on the same digitiser.} + \label{fig:ge_cal_rate_pulselength} +\end{figure} + +The true coincidence summing probability is estimated to be very small, about +\num{5.4d-6}, thanks to the far geometry of the calibration. The absorption in +the source cover made of \SI{22}{\mg\per\cm^2} polyethylene is less than +\num{4d-4} for a \SI{100}{\keV} photon. Therefore these two corrections are +omitted. + +The absolute efficiencies of the reference gamma rays show agreement with those +obtained from a Monte Carlo (MC) study where a point source made of $^{152}$Eu +is placed at the target position (see \cref{fig:ge_eff_cal}). A comparison +between efficiencies in case of the point-like source and a finite-size +source is also done by MC simulation. As shown in \cref{fig:ge_eff_cal}, the +differences are in line with the uncertainties of the measured efficiencies. +%The dimensions of the latter are set to +%resemble the distribution of muons inside the target: Gaussian spreading +%\SI{11}{\mm} vertically, \SI{13}{\mm} horizontally, and \SI{127}{\um} in +\begin{figure}[htb] + \centering + \includegraphics[width=0.40\textwidth]{figs/ge_eff_cal} + \includegraphics[width=0.40\textwidth]{figs/ge_eff_mc_finitesize_vs_pointlike_root} + \caption{Absolute efficiency of the germanium detector, the fit was done with + 7 energy points from 244~keV, the shaded area is + 95\% confidence interval of the fit.} + %because it is known that the linearity between + %$ln(\textrm{E})$ and $ln(\textrm{eff})$ holds better. + \label{fig:ge_eff_cal} +\end{figure} +The absolute efficiencies of the referenced points, and calculated efficiencies +at X-rays of interest are listed in \cref{tab:xray_eff}. \begin{table}[htb] \begin{center} \pgfplotstabletypeset[ @@ -601,18 +658,6 @@ purposes: \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} @@ -684,12 +729,12 @@ different targets were carried out for silicon targets: As the emitted protons deposit a significant amount of energy in the target material, thin targets and thus excellent momentum resolution of the low energy -muon beam are critical. Aluminium targets of 50-\si{\micro\meter}\ and -100~\si{\micro\meter}\ thick were used. Although a beam with low momentum spread of -1\% is preferable, it was used for only a small portion of the run due to the -low beam rate (see \cref{fig:Rates}). The beam momentum for each target -was chosen to maximise the number of stopped muons. The collected data sets are -shown in \cref{tb:stat}. +muon beam are critical, aluminium targets of 50-\si{\micro\meter}\ and +100-\si{\micro\meter}\ thick were used. Although a beam with low momentum +spread of 1\% is preferable, it was used for only a small portion of the run +due to the low beam rate (see \cref{fig:Rates}). The beam momentum for each +target was chosen to maximise the number of stopped muons. The collected data +sets are shown in \cref{tb:stat}. \begin{table}[btp!] \begin{center} @@ -865,20 +910,8 @@ update the plots to reflect real-time status of the detector system. Some offline analysis modules has been developed during the beam time and could provide quick feedback in confirming and guiding the decisions at the time. For example, the X-ray spectrum analysis was done to confirm that we could observe -the muon capture process (\cref{fig:muX}), and to help in choosing optimal -momenta which maximised the number of stopped muons. -\begin{figure}[btp] - \centering - \includegraphics[width=0.7\textwidth]{figs/muX.png} - \caption{Germanium - detector spectra in the range of 300 - 450 keV with different setups: no - target, 62-\si{\micro\meter}-thick silicon target, and - 100-\si{\micro\meter}-thick aluminium target. The ($2p-1s$) lines from - aluminium (346.828 keV) and silicon (400.177 keV) are clearly visible, - the double peaks at 431 and 438 keV are from the lead shield, the peak at - 351~keV is a background gamma ray from $^{211}$Bi.} - \label{fig:muX} -\end{figure} +the muon capture process and to help in choosing optimal momenta which +maximised the number of stopped muons. Although the offline analyser is still not fully developed yet, several modules are ready. They are described in detailed in the next chapter. diff --git a/thesis/chapters/chap6_analysis.tex b/thesis/chapters/chap6_analysis.tex index 6585976..3568bd8 100644 --- a/thesis/chapters/chap6_analysis.tex +++ b/thesis/chapters/chap6_analysis.tex @@ -59,7 +59,7 @@ pulses on all detector channels, and picks all pulses occur in a time window of \SI{\pm 10}{\si{\us}} around each candidate to build a muon event. A muon candidates is a hit on the upstream plastic scintillator with an amplitude higher than a threshold which was chosen to reject MIPs. The -period of \SI{10}{\si{\us}} is long enough compares to the mean life time of +period of \SI{10}{\si{\us}} is long enough compared to the mean life time of muons in the target materials (\SI{0.758}{\si{\us}} for silicon, and \SI{0.864}{\si{\us}} for aluminium~\cite{SuzukiMeasday.etal.1987}) so practically all of emitted @@ -388,7 +388,7 @@ This number of X-rays needs to be corrected for following effects: &= 1.06 \end{align} The 2-ms-long reset pulses effectively reduce the actual measurement time - compares to other channels, so the correction factor for the effect is: + compared to other channels, so the correction factor for the effect is: \begin{align} k_{\textrm{reset pulse}} &= \frac{\textrm{(measurement time)}} {\textrm{(measurement time)} @@ -830,7 +830,7 @@ The uncertainty of the emission rate could come from several sources: collimator. In the worst case when the muon beam is flatly distributed, that displacement could change the acceptance of the silicon detectors by 12\%. Although no measurement was done to determine the efficiency of the - silicon detectors, it would have small effect compare to other factors. + silicon detectors, it would have small effect compared to other factors. \end{enumerate} The combined uncertainty from known sources above therefore could be as large diff --git a/thesis/thesis.bib b/thesis/thesis.bib index f4f825e..8fb2048 100644 --- a/thesis/thesis.bib +++ b/thesis/thesis.bib @@ -462,6 +462,23 @@ Timestamp = {2014-04-08} } +@Article{Bichsel.2006, + Title = {A method to improve tracking and particle identification in TPCs and silicon detectors}, + Author = {Bichsel, Hans}, + Journal = {Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment}, + Year = {2006}, + Number = {1}, + Pages = {154--197}, + Volume = {562}, + + __markedentry = {[NT:6]}, + Doi = {10.1016/j.nima.2006.03.009}, + File = {Published version:Bichsel.2006.pdf:PDF}, + Owner = {NT}, + Publisher = {Elsevier}, + Timestamp = {2014-09-16} +} + @Article{Bichsel.1988, Title = {{Straggling in Thin Silicon Detectors}}, Author = {Bichsel, H.}, @@ -1048,8 +1065,6 @@ Month = {Aug}, Pages = {741--757}, Volume = {36}, - - __markedentry = {[NT:]}, Doi = {10.1103/PhysRevC.36.741}, File = {Published version:GadioliGadioli.1987.pdf:PDF}, Issue = {2}, @@ -1812,6 +1827,7 @@ Month = {Mar}, Pages = {1106--1110}, Volume = {43}, + Doi = {10.1103/PhysRevC.43.1106}, File = {Published version:MartoffCummings.etal.1991.pdf:PDF}, Issue = {3}, @@ -2283,8 +2299,6 @@ Month = {Jan}, Pages = {135--141}, Volume = {19}, - - __markedentry = {[NT:]}, Doi = {10.1103/PhysRevC.19.135}, File = {Published version:SchlepuetzComiso.etal.1979.pdf:PDF}, Issue = {1}, @@ -2471,7 +2485,7 @@ Pages = {MOLT007}, Volume = {C0303241}, - __markedentry = {[NT:6]}, + __markedentry = {[NT:]}, Archiveprefix = {arXiv}, Eprint = {physics/0306116}, File = {arXiv v1:VerkerkeKirkby.2003-eprintv1.pdf:PDF}, diff --git a/thesis/thesis.tex b/thesis/thesis.tex index ad3439f..9aa2d7b 100644 --- a/thesis/thesis.tex +++ b/thesis/thesis.tex @@ -33,8 +33,8 @@ for the COMET experiment} %\input{chapters/chap2_mu_e_conv} %\input{chapters/chap3_comet} %\input{chapters/chap4_alcap_phys} -\input{chapters/chap5_alcap_setup} -%\input{chapters/chap6_analysis} +%\input{chapters/chap5_alcap_setup} +\input{chapters/chap6_analysis} %\input{chapters/chap7_results} \begin{backmatter}