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

prog saved

Browse Source
This commit is contained in:
nam
2014-10-29 12:09:24 +09:00
parent 078802df95
commit ac5ab79de3
4 changed files with 81 additions and 16 deletions
Download Patch File Download Diff File Expand all files Collapse all files

2
thesis/chapters/chap1_intro.tex
View File

@@ -83,6 +83,6 @@ sensitivities. Details of the study on proton emission are described in
Chapters~\ref{cha:alcap_phys},~\ref{cha:the_alcap_run_2013},~\ref{cha:data_analysis}:
physics, method, experimental set up, data analysis. The results and impacts of
the study on COMET Phase-I design is discussed in
Chapter~\ref{cha:discussions}.
Chapter~\ref{cha:results_and_discussions}.
% chapter introduction (end)

18
thesis/chapters/chap6_analysis.tex
View File

@@ -343,9 +343,9 @@ calculated as:
where $\Delta E_{\textrm{meas.}}$ is energy deposition measured by the thin
silicon detector by a certain proton at energy $E_i$, $\Delta E_i$ and
$\sigma_{\Delta E}$ are the expected and standard deviation of the energy loss
caused by the proton calculated by MC study. A threshold is set to extract
protons at 0.011 (equivalent to $3\sigma_{\Delta E}$), the band of protons is
shown in (\cref{fig:al100_protons}).
caused by the proton calculated by MC study. A threshold is set at \num{1E-4} to
extract protons, the resulted band of protons is shown in
(\cref{fig:al100_protons}).
\begin{figure}[htb]
\centering
\includegraphics[width=0.47\textwidth]{figs/al100_protons}
@@ -510,9 +510,15 @@ The proton emission rate in the range from \SIrange{4}{8}{\MeV} is therefore:
The total proton emission rate can be estimated by assuming a spectrum shape
with the same parameterisation as in \eqref{eqn:EH_pdf}. The fit parameters
are shown in . With such parameterisation, the integration in
range from \SIrange{4}{8}{\MeV} is 51\% of the total number of protons. The
total proton emission rate is therefore $3.5\times 10^{-2}$.
are shown in \cref{fig:al100_parameterisation}. With such parameterisation, the
integration in range from \SIrange{4}{8}{\MeV} is 51\% of the total number of
protons. The total proton emission rate is therefore $3.5\times 10^{-2}$.
\begin{figure}[htb]
\centering
\includegraphics[width=0.85\textwidth]{figs/al100_parameterisation}
\caption{Fitting of the unfolded spectra.}
\label{fig:al100_parameterisation}
\end{figure}
\subsection{Uncertainties of the emission rate}
\label{sub:uncertainties_of_the_emission_rate}

64
thesis/chapters/chap7_results.tex
View File

@@ -2,13 +2,71 @@
\label{cha:results_and_discussions}
\section{Verification of the experimental method}
\label{sec:verification_of_the_experimental_method}
\subsection{Number of stopped muons normalisation}
\subsection{Number of stopped muons calculation}
\label{sub:number_of_stopped_muons_normalisation}
The number of stopped muons calculated from the muonic X-ray spectrum is shown
to be consistent with that calculated from the active target spectrum. This
proves the validity of normalisation using muon X-ray measurement.
\subsection{Particle identification and unfolding}
\label{sub:particle_identification_and_unfolding}
The particle identification using specific energy loss using cut on
likelihood probability is shown in
\cref{sub:event_selection_for_the_passive_targets}. Since the distribution of
$\Delta E$ at a given $E$ is not Gaussian, the fraction of protons that do not
make the cut is 0.5\%, much larger than the threshold at \num{1E-4}. However,
that missing fraction is small compared to the statistical uncertainty of the
measurement (2.3\%) so the threshold is sufficient.
The observed spectra on the two silicon arms reflect the muon stopping
distribution discussed in \cref{sub:momentum_scan_for_the_100_} where more
muons stopped at the downstream side of the target. The proton yields
calculated from two arms are consistent with each other, and show that the muon
stopping distribution used to generate the response matrices is reasonable.
\section{Emission rate of protons and the COMET Phase I's CDC}
\label{sec:emission_rate_of_protons_and_the_comet_phase_i_s_cdc}
The proton emission rate from the 100-\si{\um} aluminium target is
$(3.5 \pm 0.2)$\%. This rate is significantly larger than the calculation rate
of 0.97\% by Lifshitz and Singer~\cite{LifshitzSinger.1978, LifshitzSinger.1980}.
The $(\mu^-,\nu p):(\mu^-,\nu pn)$ ratio is then roughly 1:1, not 1:6 as in
\eqref{eqn:wyttenbach_ratio}.
The rate smaller that the proton emission rate from silicon of
5.3\%~\cite{Measday.2001} which is expected since an odd-odd nucleus as
$^{28}$Al is less stable than an even-odd one.
For the COMET Phase I experiment, the emission rate of 3.5\% is about 5 times
smaller than the figure using to design the CDC. The measured spectrum shape
peaks around \SI{4}{\MeV} rather than \SI{2.5}{\MeV} in the silicon
spectrum(\cref{fig:sobottka_spec}). Therefore the proton hit rate on the CDC
should be smaller than the current estimation.
The CDC proton hit rate is calculated by a toy MC study. The protons with the
energy spectrum as the parameterisation in \cref{sub:proton_emission_rate} are
generated inside the COMET's muon stopping targets which are 17
200-\si{\um}-thick aluminium discs. A proton absorber made of CFRP is placed
\SI{5}{\cm} far from the inner wall of the CDC.
A muon stopping rate of \SI{1.3E9}{\Hz} is assumed as in the COMET Phase I's
TDR. The number of proton emitted is then $\num{1.3E9} \times 0.609 \times
0.035 = \SI{2.8E7}{\Hz}$. The hit rates on a single cell in the inner most
layer due to these protons with
different absorber thickness are shown in \cref{tab:proton_cdc_hitrate}.
\begin{table}[htb]
\begin{center}
\begin{tabular}{l r}
\toprule
\textbf{Absorber thickness} & \textbf{Hit rate}\\
\midrule
\SI{1}{\mm} & \SI{2}{\Hz}\\
\SI{0.5}{\mm} & \SI{126}{\Hz}\\
\SI{0}{\mm} & \SI{1436}{\Hz}\\
\bottomrule
\end{tabular}
\end{center}
\caption{CDC proton hit rates}
\label{tab:proton_cdc_hitrate}
\end{table}
The proton hit rate even without the absorber is only \SI{1.4}{\kHz}, much
smaller than the current estimation of \SI{11}{\kHz} (using 1-mm-thick
absorber). Therefore a proton absorber is not needed for the COMET Phase I's
CDC.

13
thesis/thesis.tex
View File

@@ -29,13 +29,14 @@ for the COMET experiment}
\end{frontmatter}
\mainmatter
%\input{chapters/chap1_intro}
%\input{chapters/chap2_mu_e_conv}
%\input{chapters/chap3_comet}
%\input{chapters/chap4_alcap_phys}
%\input{chapters/chap5_alcap_setup}
\input{chapters/chap1_intro}
\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/chap7_results}
\input{chapters/chap7_results}
%\input{chapters/chap8_conclusions}
\begin{backmatter}
\input{chapters/backmatter}