nam/writeup
1
0
Fork 0
Code Issues Pull Requests Projects Releases Wiki Activity

in progress of adapting things to siunitx, done chap4

Browse Source
This commit is contained in:
nam
2014-09-07 12:18:11 +09:00
parent 3530983370
commit 4166acb9f3
3 changed files with 92 additions and 83 deletions
Download Patch File Download Diff File Expand all files Collapse all files

137
thesis2/chapters/chap3_comet.tex
View File

@@ -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

32
thesis2/chapters/chap4_alcap_phys.tex
View File

@@ -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