submitted to preevaluation committee

thesis/chapters/chap7_results.tex

@@ -43,9 +43,11 @@ recorded (see \cref{fig:cdc_toy_mc_p_spec_500um}).
 \begin{figure}[!htb]
   \centering
     \includegraphics[width=0.75\textwidth]{figs/cdc_toy_mc_p_spec_500um}
-  \caption{Toy MC study of the CDC hit rate due to protons. The absorber
-    thickness was set at \SI{0.5}{\mm} in this plot.}
-  \label{fig:cdc_toy_mc_p_spec_500um}
+    \caption{Proton energy spectra at different stages from birth to the
+      sensitive volume of the CDC. The baseline design of \SI{0.5}{\mm} thick
+      absorber and \SI{0.5}{\mm} thick inner wall was used to produce this
+      plot.} 
+    \label{fig:cdc_toy_mc_p_spec_500um}
 \end{figure}
 
 A muon stopping rate of \SI{1.3E9}{\Hz} is assumed as in the COMET Phase I's
@@ -55,34 +57,44 @@ layer due to these protons with
 different absorber thickness are shown in \cref{tab:proton_cdc_hitrate}.
 \begin{table}[htb]
   \begin{center}
-    \begin{tabular}{S S S S}
+    \begin{tabular}{S S S S S}
       \toprule
       {\textbf{Absorber}} &{\textbf{Inner wall}} & {\textbf{Total CFRP}}&
-      {\textbf{Proton}}\\
+      {\textbf{Proton}} & {\textbf{Momentum}}\\
       {\textbf{thickness}} &{\textbf{thickness}} & {\textbf{thickness}}&
-      {\textbf{hit rate}}\\
-      {(\si{\mm})} & {(\si{\mm})} & {(\si{\mm})} & {(\si{\Hz})}\\
+      {\textbf{hit rate}} &{\textbf{spread $\Delta p$}}\\
+      {(\si{\mm})} & {(\si{\mm})} & {(\si{\mm})} & {(\si{\Hz})}
+      & {(\si{\keV\per\cc)}}\\
       \midrule 
-      1   &0.5&1.5 & 2\\
-      0.5 &0.5&1.0 & 126\\
-      0   &0.5&0.5 & 1436\\
-      0   &0.3&0.3 & 8281\\
-      0   &0.1&0.1 & 15011\\
+      1   &0.5&1.5 & 2    & 195\\
+      0.5 &0.5&1.0 & 126  & 167\\
+      0   &0.5&0.5 & 1436 & 133\\
+      0   &0.3&0.3 & 8281 & {-}\\
+      0   &0.1&0.1 & 15011& {-}\\
       \bottomrule
     \end{tabular}
   \end{center}
-  \caption{CDC proton hit rates}
+  \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}
 
 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}. Therefore a proton
-absorber is not needed for the COMET Phase I's CDC.
+absorber, proton hit rate remains low at \SI{1.4}{\kHz}. 
+%Therefore a proton
+%absorber is not needed for the COMET Phase I's CDC.
 
-Without the proton absorber, the momentum spread of the signal electron
-reduces from \SI{167}{\keV} to \SI{131}{\keV}. If a lower momentum spread is
-desired, it is possible to reduce the thickness of the inner wall. The last
+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.
+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
+prediction of the hit rate caused by protons.