101 lines
4.7 KiB
TeX
101 lines
4.7 KiB
TeX
\chapter{Discussions on the 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
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peaks around \SI{4}{\MeV} rather than at \SI{2.5}{\MeV}, and decays more
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quickly in compared with the silicon spectrum(\cref{fig:sobottka_spec}).
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Therefore CDC hit rate due to proton should be smaller than the current
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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 thickness are shown in \cref{tab:proton_cdc_hitrate}.
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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}} & {\textbf{Momentum}}\\
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{\textbf{thickness}} &{\textbf{thickness}} & {\textbf{thickness}}&
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{\textbf{hit rate}} &{\textbf{spread $\Delta p$}}\\
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{(\si{\mm})} & {(\si{\mm})} & {(\si{\mm})} & {(\si{\Hz})}
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& {(\si{\keV\per\cc)}}\\
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\midrule
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1 &0.5&1.5 & 2 & 195\\
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0.5 &0.5&1.0 & 126 & 167\\
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0 &0.5&0.5 & 1436 & 133\\
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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{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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\label{tab:proton_cdc_hitrate}
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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{34}{\kHz}. Even without the
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absorber, proton hit rate remains low at \SI{1.4}{\kHz}.
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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} to \SI{131}{\keV}. In case a lower momentum spread
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is desired, it is possible to reduce the 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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