155 lines
7.3 KiB
TeX
155 lines
7.3 KiB
TeX
\chapter{Impact to the COMET Phase-I}
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\label{cha:discussions_on_the_impact_to_the_comet_phase_i}
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The measured proton emission rate of 3.5\% is about 5 times
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smaller than the figure using to make the baseline design of the CDC in COMET
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Phase-I. The spectrum shape is softer than that of silicon,
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peaks around \SI{4}{\MeV} rather than at \SI{2.5}{\MeV}
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(\cref{fig:sobottka_spec}). Therefore CDC hit rate due to proton should be
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smaller than the current estimation.
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The CDC proton hit rate is calculated by a toy MC study. The dimensions of the
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geometry shown in \cref{fig:cdc_toy_mc} are from \cref{ssub:CDC_configuration}.
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The inner wall of the CDC is \SI{0.5}{\mm} thick CFRP.
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A proton absorber made
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of CFRP is placed \SI{5}{\cm} far from the inner wall of the CDC. The
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absorber's thickness is varied from 0 (no absorber) to \SI{1}{\mm}.
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\begin{figure}[htb]
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\centering
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\includegraphics[width=0.55\textwidth]{figs/cdc_toy_mc}
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\caption{Geometry of the toy MC study for hit rate study.}
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\label{fig:cdc_toy_mc}
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\end{figure}
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The protons with the energy spectrum shape as in
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\cref{sub:proton_emission_rate} are generated inside the COMET's muon stopping
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targets which are 17 200-\si{\um}-thick aluminium discs. The spatial
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distribution of protons resembles the stopping distribution of muons inside the
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target discs calculated from the full MC simulation of the COMET detectors
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(\cref{fig:cdc_toy_mc_init_pos}).
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\begin{figure}[htb]
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\centering
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\includegraphics[width=0.65\textwidth]{figs/cdc_toy_mc_init_pos_xy}
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\includegraphics[width=0.60\textwidth]{figs/cdc_toy_mc_init_pos_z}
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\caption{Spatial distribution of the generated protons in X, Y (top) and
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Z (bottom). Z is the axis of the CDC, X, Y are the horizontal and vertical
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axes respectively.}
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\label{fig:cdc_toy_mc_init_pos}
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\end{figure}
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The protons are then tracked in a \SI{1}{\tesla} magnetic field. The protons
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reaching the absorber, inner wall and the sensitive volume of the CDC are
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recorded (see \cref{fig:cdc_toy_mc_p_spec_500um}).
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\begin{figure}[!htb]
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\centering
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\includegraphics[width=0.75\textwidth]{figs/cdc_toy_mc_p_spec_500um}
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\caption{Proton energy spectra at different stages from birth to the
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sensitive volume of the CDC. The baseline design of \SI{0.5}{\mm} thick
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absorber and \SI{0.5}{\mm} thick inner wall was used to produce this
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plot.}
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\label{fig:cdc_toy_mc_p_spec_500um}
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\end{figure}
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A muon stopping rate of \SI{1.3E9}{\Hz} is assumed as in the COMET Phase I's
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TDR. The number of proton emitted is then $\num{1.3E9} \times 0.609 \times
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0.035 = \SI{2.8E7}{\Hz}$. The hit rates on a single cell in the inner most
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layer due to these protons with
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different absorber configurations are listed in
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\cref{tab:proton_cdc_hitrate_comp}.
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\begin{table}[htb]
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\begin{center}
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\begin{tabular}{S S S S S}
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\toprule
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{\textbf{Absorber}} &{\textbf{Inner wall}} & {\textbf{Total CFRP}}&
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{\textbf{Proton hit rate}} & {\textbf{Proton hit rate}}\\
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{\textbf{thickness}} &{\textbf{thickness}} & {\textbf{thickness}}&
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{\textbf{Phase-I TDR}} & {\textbf{New estimation}}\\
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{(\si{\mm})} & {(\si{\mm})} & {(\si{\mm})} & {(\si{\Hz})}& {(\si{\Hz})}\\
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\midrule
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1 &0.5&1.5 & 4E+3 & 2 \\
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0.5 &0.5&1.0 & 11E+3& 126 \\
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0 &0.5&0.5 & 30E+3& 1436 \\
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\bottomrule
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\end{tabular}
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\end{center}
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\caption{CDC proton hit rates in this study in comparison with the expected
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rates in COMET Phase-I's Technical Design Report~\cite{COMET.2014} at
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different configurations of proton absorber and inner wall.}
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\label{tab:proton_cdc_hitrate_comp}
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\end{table}
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%\begin{table}[htb]
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%\begin{center}
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%\begin{tabular}{S S S S S S}
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%\toprule
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%{\textbf{Absorber}} &{\textbf{Inner wall}} & {\textbf{Total CFRP}}& {\textbf{Proton}} & {\textbf{Momentum}} & {\textbf{Integrated charge}}\\
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%{\textbf{thickness}} &{\textbf{thickness}} & {\textbf{thickness}}& {\textbf{hit rate}} &{\textbf{spread $\Delta p$}} &{\textbf{300 days}}\\
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%{(\si{\mm})} & {(\si{\mm})} & {(\si{\mm})} & {(\si{\Hz})} & {(\si{\keV\per\cc)}} &{(mC/cm)}\\
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%\midrule
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%1 &0.5&1.5 & 2 & 195 & 25\\
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%0.5 &0.5&1.0 & 126 & 167 & 60\\
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%0 &0.5&0.5 & 1436 & 133 & 160\\
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%\bottomrule
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%\end{tabular}
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%\end{center}
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%\caption{CDC proton hit rates at different configuration of proton absorber
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%and inner wall. The momentum spreads for \SI{0.5}{\mm} thick inner wall are
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%taken from \cref{tab:comet_absorber_impact}.}
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%\end{table}
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At the baseline design of \SI{0.5}{\mm}, the hit rate is only \SI{126}{\Hz},
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much smaller than the current estimation at \SI{11}{\kHz}. Even without the
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absorber, proton hit rate remains lower than that level at \SI{1.4}{\kHz}.
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Therefore the absorber is not necessary as far as the hit rate is concerned.
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%Therefore a proton
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%absorber is not needed for the COMET Phase I's CDC.
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If the proton absorber is not used, the momentum spread of the signal electron
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reduces from \SI{167}{\keV\per\cc} to \SI{131}{\keV\per\cc} (\cref{tab:proton_cdc_hitrate}).
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This is a small improvement since the momentum resolution is dominated by
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intrinsic spread of \SI{197}{\keV\per\cc} due to multiple scattering in gas
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and wires.
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The last column of \cref{tab:proton_cdc_hitrate} shows the integrated charge
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per unit length of a wire. The TDR deems an integrated charge level of
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\SI{200}{\milli\coulomb\per\cm} safe. So even with the pessimistic estimation using
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silicon rate and spectrum and without the proton absorber, the integrated
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charge level in the CDC is still below the requirement. Therefore removing the
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absorber will not worsen the ageing process of the wires.
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\begin{table}[htb]
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\begin{center}
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\begin{tabular}{S S S S S}
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\toprule
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{\textbf{Absorber}} &{\textbf{Inner wall}} & {\textbf{Total CFRP}}&
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{\textbf{Momentum}} & {\textbf{Integrated charge}}\\
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{\textbf{thickness}} &{\textbf{thickness}} & {\textbf{thickness}}&
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{\textbf{spread $\Delta p$}} &{\textbf{300 days}}\\
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{(\si{\mm})} & {(\si{\mm})} & {(\si{\mm})}
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& {(\si{\keV\per\cc)}} &{(mC/cm)}\\
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\midrule
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1 &0.5&1.5 & 195 & 25\\
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0.5 &0.5&1.0 & 167 & 60\\
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0 &0.5&0.5 & 133 & 160\\
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%0 &0.3&0.3 & 8281 & {-} & {-}\\
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%0 &0.1&0.1 & 15011& {-} & {-}\\
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\bottomrule
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\end{tabular}
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\end{center}
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\caption{Momentum spreads due to the inner wall and absorber, and integrated
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charge per unit length of wire as calculated in the COMET Phase-I's TDR.
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The momentum spreads were calculated for signal electrons at
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\SI{104.96}{\MeV\per\cc}. The integrated charge is estimated assuming 300
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days of operation.}
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\label{tab:proton_cdc_hitrate}
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\end{table}
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%In case a lower momentum spread is desired, it is possible to reduce the
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%thickness of the inner wall. The last
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%two rows of \cref{tab:proton_cdc_hitrate} show that even with thinner walls at
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%\SI{0.3}{\mm} and \SI{0.1}{\mm} the hit rate by protons are still at
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%manageable levels. However, reducing the wall thickness would be governed by
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%other requirements such as mechanical structure and gas-tightness.
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In summary, the toy MC study with the preliminary proton rate and spectrum
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shows that a proton absorber is not needed. It confirms the known fact that the
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estimation used in COMET Phase-I is conservative, and provides a solid
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prediction of the hit rate caused by protons.
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