status saved

thesis/chapters/chap7_results.tex

@@ -1,12 +1,11 @@
-\chapter{Discussions on the impact to the COMET Phase-I}
+\chapter{Impact to the COMET Phase-I}
 \label{cha:discussions_on_the_impact_to_the_comet_phase_i}
 The measured proton emission rate of 3.5\% is about 5 times
 smaller than the figure using to make the baseline design of the CDC in COMET
-Phase-I. The spectrum shape
-peaks around \SI{4}{\MeV} rather than at \SI{2.5}{\MeV}, and decays more
-quickly in compared with the silicon spectrum(\cref{fig:sobottka_spec}).
-Therefore CDC hit rate due to proton should be smaller than the current
-estimation.
+Phase-I. The spectrum shape is softer than that of silicon,
+peaks around \SI{4}{\MeV} rather than at \SI{2.5}{\MeV}
+(\cref{fig:sobottka_spec}). Therefore CDC hit rate due to proton should be
+smaller than the current estimation.
 
 The CDC proton hit rate is calculated by a toy MC study. The dimensions of the
 geometry shown in \cref{fig:cdc_toy_mc} are from \cref{ssub:CDC_configuration}. 
@@ -54,54 +53,31 @@ 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}.
+different absorber configurations are listed in
+\cref{tab:proton_cdc_hitrate_comp}.
+
 \begin{table}[htb]
   \begin{center}
-    \begin{tabular}{S S S S S S}
+    \begin{tabular}{S S S S S}
       \toprule
       {\textbf{Absorber}} &{\textbf{Inner wall}} & {\textbf{Total CFRP}}&
-      {\textbf{Proton}} & {\textbf{Momentum}} & {\textbf{Integrated charge}}\\
+      {\textbf{Proton hit rate}} & {\textbf{Proton hit rate}}\\  
       {\textbf{thickness}} &{\textbf{thickness}} & {\textbf{thickness}}&
-      {\textbf{hit rate}} &{\textbf{spread $\Delta p$}} &{\textbf{300 days}}\\
-      {(\si{\mm})} & {(\si{\mm})} & {(\si{\mm})} & {(\si{\Hz})}
-      & {(\si{\keV\per\cc)}} &{(mC/cm)}\\
+      {\textbf{Phase-I TDR}} & {\textbf{New estimation}}\\
+      {(\si{\mm})} & {(\si{\mm})} & {(\si{\mm})} & {(\si{\Hz})}& {(\si{\Hz})}\\
       \midrule 
-      1   &0.5&1.5 & 2    & 195 & 25\\
-      0.5 &0.5&1.0 & 126  & 167 & 60\\
-      0   &0.5&0.5 & 1436 & 133 & 160\\
-      %0   &0.3&0.3 & 8281 & {-} & {-}\\
-      %0   &0.1&0.1 & 15011& {-} & {-}\\
+      1   &0.5&1.5 & 4E+3 & 2     \\
+      0.5 &0.5&1.0 & 11E+3& 126   \\
+      0   &0.5&0.5 & 30E+3& 1436 \\
       \bottomrule
     \end{tabular}
   \end{center}
-  \caption{CDC proton hit rates at different configuration of proton absorber
-    and inner wall. The momentum spreads for \SI{0.5}{\mm} thick inner wall are
-    taken from \cref{tab:comet_absorber_impact}.}
-  \label{tab:proton_cdc_hitrate}
+  \caption{CDC proton hit rates in this study in comparison with the expected
+    rates in COMET Phase-I's Technical Design Report~\cite{COMET.2014} at
+    different configurations of proton absorber and inner wall.}
+  \label{tab:proton_cdc_hitrate_comp}
 \end{table}
 
-%\begin{table}[htb]
-  %\begin{center}
-    %\begin{tabular}{S S S S S}
-      %\toprule
-      %{\textbf{Absorber}} &{\textbf{Inner wall}} & {\textbf{Total CFRP}}&
-      %{\textbf{Proton hit rate}} & {\textbf{Proton hit rate}}\\  
-      %{\textbf{thickness}} &{\textbf{thickness}} & {\textbf{thickness}}&
-      %{\textbf{Phase-I TDR}} & {\textbf{New estimation}}\\
-      %{(\si{\mm})} & {(\si{\mm})} & {(\si{\mm})} & {(\si{\Hz})}& {(\si{\Hz})}\\
-      %\midrule 
-      %1   &0.5&1.5 & 4E+3 & 2     \\
-      %0.5 &0.5&1.0 & 11E+3& 126   \\
-      %0   &0.5&0.5 & 30E+3& 1436 \\
-      %\bottomrule
-    %\end{tabular}
-  %\end{center}
-  %\caption{CDC proton hit rates at different configuration of proton absorber
-    %and inner wall. The momentum spreads for \SI{0.5}{\mm} thick inner wall are
-    %taken from \cref{tab:comet_absorber_impact}.}
-  %\label{tab:proton_cdc_hitrate}
-%\end{table}
-
 %\begin{table}[htb]
   %\begin{center}
     %\begin{tabular}{S S S S S S}
@@ -121,19 +97,57 @@ different absorber thickness are shown in \cref{tab:proton_cdc_hitrate}.
     %taken from \cref{tab:comet_absorber_impact}.}
 %\end{table}
 At the baseline design of \SI{0.5}{\mm}, the hit rate is only \SI{126}{\Hz},
-much smaller than the current estimation at \SI{34}{\kHz}. Even without the
-absorber, proton hit rate remains low at \SI{1.4}{\kHz}. 
+much smaller than the current estimation at \SI{11}{\kHz}. Even without the
+absorber, proton hit rate remains lower than that level at \SI{1.4}{\kHz}.
+Therefore the absorber is not necessary as far as the hit rate is concerned.
 %Therefore a proton
 %absorber is not needed for the COMET Phase I's CDC.
 
 If the proton absorber is not used, the momentum spread of the signal electron
-reduces from \SI{167}{\keV} to \SI{131}{\keV}. In case a lower momentum spread
-is desired, it is possible to reduce the thickness of the inner wall. The last
-two rows of \cref{tab:proton_cdc_hitrate} show that even with thinner walls at
-\SI{0.3}{\mm} and \SI{0.1}{\mm} the hit rate by protons are still at
-manageable levels. However, reducing the wall thickness would be governed by
-other requirements such as mechanical structure and gas-tightness.
+reduces from \SI{167}{\keV\per\cc} to \SI{131}{\keV\per\cc} (\cref{tab:proton_cdc_hitrate}).
+This is a small improvement since the momentum resolution is dominated by
+intrinsic spread of \SI{197}{\keV\per\cc} due to multiple scattering in gas
+and wires.
 
+The last column of \cref{tab:proton_cdc_hitrate} shows the integrated charge
+per unit length of a wire. The TDR deems an integrated charge level of
+\SI{200}{\milli\coulomb\per\cm} safe. So even with the pessimistic estimation using
+silicon rate and spectrum and without the proton absorber, the integrated
+charge level in the CDC is still below the requirement.  Therefore removing the
+absorber will not worsen the ageing process of the wires.  
+\begin{table}[htb]
+  \begin{center}
+    \begin{tabular}{S S S S S}
+      \toprule
+      {\textbf{Absorber}} &{\textbf{Inner wall}} & {\textbf{Total CFRP}}&
+      {\textbf{Momentum}} & {\textbf{Integrated charge}}\\
+      {\textbf{thickness}} &{\textbf{thickness}} & {\textbf{thickness}}&
+      {\textbf{spread $\Delta p$}} &{\textbf{300 days}}\\
+      {(\si{\mm})} & {(\si{\mm})} & {(\si{\mm})} 
+      & {(\si{\keV\per\cc)}} &{(mC/cm)}\\
+      \midrule 
+      1   &0.5&1.5 &  195 & 25\\
+      0.5 &0.5&1.0 &  167 & 60\\
+      0   &0.5&0.5 &  133 & 160\\
+      %0   &0.3&0.3 & 8281 & {-} & {-}\\
+      %0   &0.1&0.1 & 15011& {-} & {-}\\
+      \bottomrule
+    \end{tabular}
+  \end{center}
+  \caption{Momentum spreads due to the inner wall and absorber, and integrated
+    charge per unit length of wire as calculated in the COMET Phase-I's TDR.
+    The momentum spreads were calculated for signal electrons at
+    \SI{104.96}{\MeV\per\cc}. The integrated charge is estimated assuming 300
+    days of operation.}
+  \label{tab:proton_cdc_hitrate}
+\end{table}
+
+%In case a lower momentum spread is desired, it is possible to reduce the
+%thickness of the inner wall. The last
+%two rows of \cref{tab:proton_cdc_hitrate} show that even with thinner walls at
+%\SI{0.3}{\mm} and \SI{0.1}{\mm} the hit rate by protons are still at
+%manageable levels. However, reducing the wall thickness would be governed by
+%other requirements such as mechanical structure and gas-tightness.
 In summary, the toy MC study with the preliminary proton rate and spectrum
 shows that a proton absorber is not needed. It confirms the known fact that the
 estimation used in COMET Phase-I is conservative, and provides a solid