From 4166acb9f321451125e3c2ecafe6f48e672a9f43 Mon Sep 17 00:00:00 2001 From: nam Date: Sun, 7 Sep 2014 12:18:11 +0900 Subject: [PATCH] in progress of adapting things to siunitx, done chap4 --- thesis2/chapters/chap3_comet.tex | 137 +++++++++++++------------- thesis2/chapters/chap4_alcap_phys.tex | 32 +++--- thesis2/thesis.tex | 6 +- 3 files changed, 92 insertions(+), 83 deletions(-) diff --git a/thesis2/chapters/chap3_comet.tex b/thesis2/chapters/chap3_comet.tex index 0f46ab2..da9979b 100644 --- a/thesis2/chapters/chap3_comet.tex +++ b/thesis2/chapters/chap3_comet.tex @@ -83,11 +83,11 @@ The most recent experiments were the SINDRUM and SINDRUM-II at the Paul Scherrer Institute (PSI), Switzerland. The SINDRUM-II measured the branching ratio of \mueconv on a series of heavy targets: Ti, Pb and Au. The proton beam at PSI is a continuous wave beam, with a time structure of 0.3 ns bursts every -19.75 \nano\second. An 8-\milli\meter-thick CH$_2$ degrader was used to reduce +19.75 \si{\nano\second}. An 8-\si{\milli\meter}-thick CH$_2$ degrader was used to reduce the radiative pion capture and other prompt backgrounds. Cosmic backgrounds are rejected using a combination of passive shielding, veto counters and reconstruction cuts. The momenta of muons -were 52 \mega\electronvolt\per\cc and 53 \mega\electronvolt\per\cc, and the +were 52 \si{\mega\electronvolt\per\cc} and 53 \si{\mega\electronvolt\per\cc}, and the momentum spread was 2\%. \begin{figure}[htbp] \centering \includegraphics[width=0.85\textwidth]{figs/sindrumII_setup} @@ -173,7 +173,7 @@ sensitivity of the COMET experiment. A slow-extracted proton beam from the J-PARC main ring (MR), which is designed to deliver \sn{3.6}{15} protons per cycle at a frequency of 0.45 Hz, will be used for the COMET experiment. The proton beam power of the current design is 8 GeV$\times$7 $\mu$A, or -\sn{4.4}{13} protons/s. The beam energy 8 \giga\electronvolt~ helps to minimise +\sn{4.4}{13} protons/s. The beam energy 8 \si{\giga\electronvolt} helps to minimise the production of antiprotons. The proton pulse width is chosen to be 100 ns, and the pulse period to be @@ -196,8 +196,8 @@ Table~\ref{tab:comet_proton_beam}. \includegraphics[width=0.8\textwidth]{figs/comet_mr_4filled} \caption{The COMET proton bunch structure in the RCS (rapid cycle synchrotron) and MR where 4 buckets - are filled producing 100 \nano\second~bunches separated by 1.2 - \micro\second.} + are filled producing 100 \si{\nano\second} bunches separated by + 1.2~\si{\micro\second}.} \label{fig:comet_mr_4filled} \end{figure} @@ -205,14 +205,14 @@ Table~\ref{tab:comet_proton_beam}. \begin{center} \begin{tabular}{l l} \toprule - Beam power & 56 \kilo\watt\\ - Energy & 8 \giga\electronvolt\\ - Average current & 7 \micro\ampere\\ - Beam emittance & 10 $\pi$\cdot mm\cdot mrad\\ + Beam power & 56 \si{\kilo\watt}\\ + Energy & 8 \si{\giga\electronvolt}\\ + Average current & 7 \si{\micro\ampere}\\ + Beam emittance & 10 $\pi\cdot$ mm$\cdot$ mrad\\ Protons per bunch & $<10^{11}$\\ Extinction & \sn{}{-9}\\ - Bunch separation & $1 \sim 2$ \micro\second\\ - Bunch length & 100 \nano\second\\ + Bunch separation & $1 \sim 2$ \si{\micro\second}\\ + Bunch length & 100 \si{\nano\second}\\ \bottomrule \end{tabular} \end{center} @@ -321,7 +321,7 @@ needed to select 40 MeV/$c$ muons as required by the COMET design. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{Muon stopping target} \label{sub:muon_stopping_target} -Muon stopping target is place at 180\degree~bending after the pion production +Muon stopping target is place at 180\si{\degree}~bending after the pion production target (Figure~\ref{fig:comet_beamline_layout}) in its own solenoid. The target is designed to maximise the muon stopping efficiency and minimise the energy loss of signal electrons. @@ -337,7 +337,7 @@ The first choice for the muon stopping target material in the COMET is aluminium. A titanium target is also considered. Configuration of the target is shown in the Table~\ref{tab:comet_al_target}. Monte Carlo studies with this design showed that net stopping efficiency is 0.29, and average energy loss -of signal electrons is about 400 \kilo\electronvolt. +of signal electrons is about 400 \si{\kilo\electronvolt}. \begin{table}[htb] \begin{center} \begin{tabular}{l l} @@ -346,10 +346,10 @@ of signal electrons is about 400 \kilo\electronvolt. \midrule Material & Aluminium\\ Shape & Flat disks\\ - Disk radius & 100 \milli\meter\\ - Disk thickness & 200 \micro\meter\\ + Disk radius & 100 \si{\milli\meter}\\ + Disk thickness & 200 \si{\micro\meter}\\ Number of disks & 17\\ - Disk spacing & 50 \milli\meter\\ + Disk spacing & 50 \si{\milli\meter}\\ \bottomrule \end{tabular} \end{center} @@ -375,15 +375,15 @@ transport section. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{Electron transportation beam line} \label{sub:electron_transportation_beam_line} -The 180\degree~bending electron transport solenoids help remove line-of-sight +The 180\si{\degree}~bending electron transport solenoids help remove line-of-sight between the target and the detector system. It works similarly to the muon transportation section, but is tuned differently to accept electrons of about -105 \mega\electronvolt\per\cc. A compensation field of 0.17 T along the +105~\si{\mega\electronvolt\per\cc}. A compensation field of 0.17 T along the vertical direction will be applied. Electrons with momentum less than 80 -\mega\electronvolt\per\cc are blocked at the exit of this section by +\si{\mega\electronvolt\per\cc} are blocked at the exit of this section by a collimator to reduce DIO electrons rate. The net acceptance of signals of \mueconv is about 0.32, and the detector hit rate will be in the order of -1 \kilo\hertz~for \sn{}{11} stopped muons\per\second. +1~\si{\kilo\hertz}~for \sn{}{11} stopped muons\si{\per\second}. % subsection electron_transportation_beam_line (end) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{Electron detectors} @@ -396,13 +396,14 @@ particles, and measure their momenta, energy and timings. The whole detector system is in a uniform solenoidal magnetic field under vacuum. Passive and active shielding against cosmic rays is considered. -The tracking detector has to provide a momentum resolution less than 350 -\kilo\electronvolt\per\cc in order to achieve a sensitivity of \sn{3}{-17}. -There are five stations of straw-tube gas chambers, each provides two -dimensional information. Each straw tube is 5 \milli\meter in diameter and has -a 25 \micro\meter-thick wall. According to a GEANT4 Monte Carlo simulation, -a position resolution of 250 \micro\meter can be obtained, which is enough for -350 \kilo\electronvolt\per\cc momentum resolution. The DIO background of 0.15 +The tracking detector has to provide a momentum resolution less than +350~\si{\kilo\electronvolt\per\cc} in order to achieve a sensitivity of +\sn{3}{-17}. There are five stations of straw-tube gas chambers, each provides +two +dimensional information. Each straw tube is 5~\si{\milli\meter} in diameter and has +a 25~\si{\micro\meter}-thick wall. According to a GEANT4 Monte Carlo simulation, +a position resolution of 250~\si{\micro\meter} can be obtained, which is enough for +350~\si{\kilo\electronvolt\per\cc} momentum resolution. The DIO background of 0.15 events is estimated. The electromagnetic calorimeter serves three purposes: a) to measure electrons @@ -418,14 +419,14 @@ hit positions. Two candidate crystals, GSO and LYSO, are under consideration. The requirements for \mueconv signals are: \begin{itemize} - \item from the 350 \kilo\electronvolt\per\cc~momentum resolution, the signal - region is determined to be 103.5 \mega\electronvolt\per\cc~to 105.2 - \mega\electronvolt\per\cc; + \item from the 350~\si{\kilo\electronvolt\per\cc}~momentum resolution, the signal + region is determined to be 103.5~\si{\mega\electronvolt\per\cc}~to + 105.2~\si{\mega\electronvolt\per\cc}; \item transversal momentum of signal electrons is required to be greater than - 52 \mega\electronvolt\per\cc to remove backgrounds from beam electrons and + 52~\si{\mega\electronvolt\per\cc} to remove backgrounds from beam electrons and muons decay in flight; \item timing wise, conversion electrons should arrive in the time window of - detection which is about 700 \nano\second~after each proton pulses + detection which is about 700~\si{\nano\second}~after each proton pulses (Figure~\ref{fig:comet_meas_timing}). The acceptance in this detection window is about 0.39 for aluminium. \end{itemize} @@ -449,7 +450,7 @@ The single event sensitivity (SES) of the \mueconv search is defined as: where $N^{\textrm{stop}}_{\mu}$ is the number of muons stopping in the muon target; $f_{\textrm{cap}}$ is the fraction of captured muons; and $A_e$ is the detector acceptance. The total number of stopped muons is projected as -$N^{\textrm{stop}}_{\mu} = 2\times 10^{18}$ for a \sn{2}{7}\second~run time; +$N^{\textrm{stop}}_{\mu} = 2\times 10^{18}$ for a \sn{2}{7}\si{\second}~run time; $f_{\textrm{cap}} = 0.61$ for aluminium; and the total acceptance for the COMET detector system is $A_e =0.031$. Using these numbers, the SES of the COMET is calculated to be @@ -519,7 +520,7 @@ the ultimate COMET experiment, and initial phase is desirable. Also, the 5-year mid-term plan from 2013 of J-PARC includes the construction of the COMET beam line. For these reasons, the COMET collaboration considers a staged approach with the first stage, so called COMET Phase-I, with a shorter muon -transportation solenoid, up to the first 90\degree. +transportation solenoid, up to the first 90\si{\degree}. %\begin{wrapfigure}{r}{0.5\textwidth} %\centering @@ -531,7 +532,7 @@ transportation solenoid, up to the first 90\degree. \begin{SCfigure} \centering \caption{Lay out of the COMET Phase-I, the target and detector solenoid are - placed after the first 90\degree~bend.} + placed after the first 90\si{\degree}~bend.} \includegraphics[width=0.4\textwidth]{figs/comet_phase1_layout} \label{fig:comet_phase1_layout} \end{SCfigure} @@ -556,11 +557,11 @@ The COMET Phase-I has two major goals: \label{sub:proton_beam_for_the_comet_phase_i} Proton beam for the Phase-I differs only in beam power compares to that of the full COMET. It is estimated that a beam power of -3.2~\kilo\watt~$=$~8~\giga\electronvolt~$\times$~0.4~\micro\ampere~(or -\sn{2.5}{12} protons\per\second) will be enough for beam properties +3.2~\si{\kilo\watt}~$=$~8~\si{\giga\electronvolt}~$\times$~0.4~\si{\micro\ampere}~(or +\sn{2.5}{12} protons\si{\per\second}) will be enough for beam properties study and achieving the physics goal of this stage. Starting from a lower intensity is also suitable for performing accelerator -studies that are needed to realise 8 \giga\electronvolt beam extraction from +studies that are needed to realise 8~\si{\giga\electronvolt} beam extraction from the J-PARC main ring. % subsection proton_beam_for_the_comet_phase_i (end) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% @@ -570,14 +571,14 @@ the J-PARC main ring. Since the beam power will be lower, it is proposed to use a graphite target in the Phase-I. This will minimise the activation of the target station and heat shield which will be easier for necessary upgrading for Phase-II operation. -A target length of 600 \milli\meter~(1.5 radiation length) and target radius of -20 \milli\meter~are chosen. The target is located at the centre of the pion +A target length of 600~\si{\milli\meter}~(1.5 radiation length) and target radius of +20~\si{\milli\meter}~are chosen. The target is located at the centre of the pion capture solenoid where the peak magnetic field of 5 T is achieved. A correction dipole filed of 0.05 T is also applied to improve the pion yield. The pion/muon beam line for COMET Phase-I consists of the pion capture solenoid section (CS), muon transport solenoid section (TS) up to the first -90\degree~bending, and a set of matching solenoids (see +90\si{\degree}~bending, and a set of matching solenoids (see Figure~\ref{fig:comet_phase1_magnets}). At the end of the muon beam line, the detectors and the detector solenoid (DS) are installed. To reduce beam backgrounds, a beam collimator is placed upstream of the detector solenoid. @@ -623,45 +624,47 @@ reduce potential high rates caused by protons emitted after nuclear muon capture in the stopping target. The CDC covers the region -from 500 \milli\meter~to 831 \milli\meter~in the radial direction. The length -of the CDC is 1500 \milli\meter. The inner wall is made of a 100 -\micro\meter~thick aluminised Mylar. The end-plates will be conical in shape -and about 10 \milli\meter~thick to support the feedthroughs. The outer wall is -made of 5 \milli\meter~carbon fibre reinforced plastic (CFRP). +from \SIrange{500}{831}{\milli\meter}~in the radial direction. The length +of the CDC is 1500~\si{\milli\meter}. The inner wall is made of +a 100~\si{\micro\meter}-thick aluminised Mylar. The end-plates will be conical +in shape and about 10~\si{\milli\meter}-thick to support the feedthroughs. The outer +wall is +made of 5~\si{\milli\meter}~carbon fibre reinforced plastic (CFRP). The CDC is arranged in 20 concentric sense layers with alternating positive and -negative stereo angles. The sense wires are made of gold-plated tungsten, 30 -\micro\meter~in diameter, tensioned to 50 \gram. The field wires are uncoated -aluminium wires with a diameter of 80 \micro\meter, at the same tension of 50 -\gram. A high voltage of $1700\sim1900$ \volt~will be applied to the sense -wires with the field wires at ground potential, giving an avalanche gain of +negative stereo angles. The sense wires are made of gold-plated tungsten, +30~\si{\micro\meter} in diameter, tensioned to 50~\si{\gram}. The field wires +are uncoated aluminium wires with a diameter of 80~\si{\micro\meter}, at the same +tension of \SI{50}{\gram}. A high voltage of $1700\sim1900$~\si{\volt} will be +applied to the sense wires with the field wires at ground potential, giving an +avalanche gain of approximately \sn{4}{4}. A gas mixture of helium:isobutane(90:10) is preferred since the CDC momentum resolution is dominated by multiple scattering. With -these configurations, an intrinsic momentum resolution of 197 -\kilo\electronvolt\per\cc~is achievable according to our tracking study. +these configurations, an intrinsic momentum resolution of +197~\si{\kilo\electronvolt\per\cc} is achievable according to our tracking study. \begin{table}[htb] \begin{center} \begin{tabular}{l l l} \toprule - \textbf{Inner wall} & Length & 1500 \milli\meter\\ - & Radius & 500 \milli\meter\\ + \textbf{Inner wall} & Length & 1500 \si{\milli\meter}\\ + & Radius & 500 \si{\milli\meter}\\ \midrule - \textbf{Outer wall} & Length & 1740.9 \milli\meter\\ - & Radius & 831 \milli\meter\\ + \textbf{Outer wall} & Length & 1740.9 \si{\milli\meter}\\ + & Radius & 831 \si{\milli\meter}\\ \midrule \textbf{Sense wire} & Number of layers & 20\\ & Material & Gold-plated tungsten\\ - & Diameter & 30 \micro\meter\\ + & Diameter & 30 \si{\micro\meter}\\ & Number of wires & 4986\\ - & Tension & 50 \gram\\ + & Tension & 50 \si{\gram}\\ %& Radius of the innermost wire at the EP & 530 mm\\ %& Radius of the outermost wire at the EP & 802 mm\\ \midrule \textbf{Field wire} & Material & Aluminium\\ - & Diameter & 80 \micro\meter\\ + & Diameter & 80 \si{\micro\meter}\\ & Number of wires & 14562\\ - & Tension & 50 \gram\\ + & Tension & 50 \si{\gram}\\ \midrule \textbf{Gas} & & Helium:Isobutane (90:10)\\ \bottomrule @@ -673,11 +676,12 @@ these configurations, an intrinsic momentum resolution of 197 The maximum usable muon beam intensity will be limited by the detector hit occupancy. Charge particles with transversal momentum greater than 70 -\mega\electronvolt\per\cc~are expected to reach the CDC. Those particles are: +\si{\mega\electronvolt\per\cc} are expected to reach the CDC. Those particles are: protons emitted from nuclear muon capture, and electrons from muon decay in orbit. It is calculated that the hit rate due to proton emission dominates, -where the highest rate is 11 \kilo\hertz\per cell compares to 5 \kilo\hertz\per -cell contribution from DIO electrons. Another potential issue caused by protons +where the highest rate is 11~\si{\kilo\hertz\per}cell compares to +5~\si{\kilo\hertz\per} +cell contributing from DIO electrons. Another potential issue caused by protons is the ageing effect on the CDC as they leave about a 100 times larger energy deposit than the minimum ionisation particles. @@ -687,8 +691,9 @@ of protons emitted after muon capture in aluminium. In the design of the COMET Phase-I, we use a conservative estimation of the rate of protons from energy spectrum of charged particles emitted from muon capture in $^{28}$Si~\cite{SobottkaWills.1968}. The baseline design for the proton -absorber is 1.0 \milli\meter~thick CFRP, which contributes 195 -\kilo\electronvolt\per\cc~to the momentum resolution of reconstructed track. +absorber is 1.0~\si{\milli\meter}-thick CFRP, which contributes +195~\si{\kilo\electronvolt\per\cc} to the momentum resolution of reconstructed +track. In order to obtain a better understanding of the protons emission, and then further optimisation of the CDC, a dedicated experiment to measure proton diff --git a/thesis2/chapters/chap4_alcap_phys.tex b/thesis2/chapters/chap4_alcap_phys.tex index d9cfa2b..a5bd278 100644 --- a/thesis2/chapters/chap4_alcap_phys.tex +++ b/thesis2/chapters/chap4_alcap_phys.tex @@ -66,17 +66,17 @@ emission of particles with emphasis on proton. Theoretically, the capturing process can be described in the following stages~\cite{FermiTeller.1947, WuWilets.1969}: \begin{enumerate} - \item High to low (a few \kilo\electronvolt) energy: the muon velocity are + \item High to low (a few \si{\kilo\electronvolt}) energy: the muon velocity are greater than the velocity of the valence electrons of the atom. Slowing down process is similar to that of fast heavy charged particles. It takes - about \sn{}{-9} to \sn{}{-10} \second~to slow down from a relativistic - \sn{}{8} \electronvolt~energy to 2000 \electronvolt~in condensed matter, + about \sn{}{-9} to \sn{}{-10} \si{\second}~to slow down from a relativistic + \sn{}{8}~\si{\electronvolt}~energy to 2000~\si{\electronvolt}~in condensed matter, and about 1000 times as long in air. \item Low energy to rest: in this phase, the muon velocity is less than that of the valence electrons, the muon is considered to be moving inside a degenerate electron gas. The muon rapidly comes to a stop either in - condensed matters ($\sim$\sn{}{-13} \second) or in gases ($\sim$\sn{}{-9} - \second). + condensed matters ($\sim$\sn{}{-13}~\si{\second}) or in gases ($\sim$\sn{}{-9} + \si{\second}). \item Atomic capture: the muon has no kinetic energy, it is captured by the host atom into one of high orbital states, forming a muonic atom. The distribution of initial states is not well known. The details depend on @@ -86,9 +86,9 @@ stages~\cite{FermiTeller.1947, WuWilets.1969}: by the emission of Auger electrons or characteristic X-rays, or excitation of the nucleus. The time taken for the muon to enter the lowest possible state, 1S, from the instant of its atomic capture is - $\sim$\sn{}{-14}\second. + $\sim$\sn{}{-14}\si{\second}. \item Muon disappearance: after reaching the 1S state, the muons either - decays with a half-life of \sn{2.2}{-6} \second~or gets captured by the + decays with a half-life of \sn{2.2}{-6}~\si{\second}~or gets captured by the nucleus. In hydrogen, the capture to decay probability ratio is about \sn{4}{-4}. Around $Z=11$, the capture probability is roughly equal to the decay probability. In heavy nuclei ($Z\sim50$), the ratio of capture to @@ -98,7 +98,7 @@ stages~\cite{FermiTeller.1947, WuWilets.1969}: than a K-shell electron. The close proximity of the K-shell muon in the Coulomb field of a nuclear, together with its weak interaction with the nucleus, allows the muon to spend a significant fraction of time (\sn{}{-7} - -- \sn{}{-6} \second) within the nucleus, serving as an ideal probe for the + -- \sn{}{-6} \si{\second}) within the nucleus, serving as an ideal probe for the distribution of nuclear charge and nuclear moments. \end{enumerate} @@ -307,7 +307,7 @@ and of course not perfect, description of the existing data~\cite{Measday.2001}: - X_2\left(\frac{A-Z}{2A}\right)\right] \label{eq:primakoff_capture_rate} \end{equation} -where $X_1 = 170$ \reciprocal\second~is the muon capture rate for hydrogen, but +where $X_1 =$ \SI{170}{\second^{-1}}~is the muon capture rate for hydrogen, but reduced because a smaller phase-space in the nuclear muon capture compares to that of a nucleon; and $X_2 = 3.125$ takes into account the fact that it is harder for protons to transforms into neutrons due to the Pauli exclusion @@ -347,20 +347,20 @@ $n_{avg} = (0.3 \pm 0.02)A^{1/3}$~\cite{Singer.1974}. The neutron emission can be explained by several mechanisms: \begin{enumerate} \item Direct emission follows reaction~\eqref{eq:mucap_proton}: these neutrons - have fairly high energy, from a few \mega\electronvolt~to as high as 40--50 - \mega\electronvolt. + have fairly high energy, from a few \si{\mega\electronvolt}~to as high as 40--50 + \si{\mega\electronvolt}. \item Indirect emission through an intermediate compound nucleus: the energy transferred to the neutron in the process~\eqref{eq:mucap_proton} is 5.2 - \mega\electronvolt~if the initial proton is at rest, in nuclear + \si{\mega\electronvolt} if the initial proton is at rest, in nuclear environment, protons have a finite momentum distribution, therefore the mean excitation energy of the daughter nucleus is around 15 to 20 - \mega\electronvolt~\cite{Mukhopadhyay.1977}. This is above the nucleon + \si{\mega\electronvolt}~\cite{Mukhopadhyay.1977}. This is above the nucleon emission threshold in all complex nuclei, thus the daughter nucleus can de-excite by emitting one or more neutrons. In some actinide nuclei, that excitation energy might trigger fission reactions. The energy of indirect - neutrons are mainly in the lower range $E_n \le 10$ \mega\electronvolt~with - characteristically exponential shape of evaporation process. On top of that - are prominent lines might appear where giant resonances occur. + neutrons are mainly in the lower range $E_n \le 10$ \si{\mega\electronvolt} + with characteristically exponential shape of evaporation process. On top of + that are prominent lines might appear where giant resonances occur. \end{enumerate} Experimental measurement of neutron energy spectrum is technically hard, and it is difficult to interpret the results. Due to these difficulties, only a few diff --git a/thesis2/thesis.tex b/thesis2/thesis.tex index cbf08fc..1203101 100644 --- a/thesis2/thesis.tex +++ b/thesis2/thesis.tex @@ -31,7 +31,11 @@ for the COMET experiment} \mainmatter \input{chapters/chap1_intro} \input{chapters/chap2_mu_e_conv} -\lipsum[1-15] +%\input{chapters/chap3_comet} +%\input{chapters/chap4_alcap_phys} +%\input{chapters/chap5_alcap_setup} +%\input{chapters/chap6_analysis} +%\input{chapters/chap7_results} \begin{backmatter} \input{chapters/backmatter}