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94 lines
2.6 KiB
TeX
94 lines
2.6 KiB
TeX
% vim: fdm=marker fmr=<<<,>>>
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\documentclass[../thesis.tex]{subfiles}
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\graphicspath{
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{.}
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{../../figures/}
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{../../../figures/}
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}
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\begin{document}
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\chapter{Air Shower Radio Interferometry}
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\label{sec:interferometry}
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The radio signals emitted by the air shower (see Section~\ref{sec:airshowers}) can be recorded by radio antennas.
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An array of radio antennas can be used as an interferometer.
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Therefore, air showers can be analysed using radio interferometry.
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\\
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%
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Unlike, astronomical interferometry, the source of the signal is closeby.
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\begin{figure}
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\centering
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\includegraphics[width=0.5\textwidth]{radio_interferometry/rit_schematic_true.pdf}%
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% \includegraphics[width=0.5\textwidth]{radio_interferometry/Schematic_RIT_extracted.png}
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% \caption{From H. Schoorlemmer}
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\end{figure}
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\begin{equation}\label{eq:propagation_delay}%<<<
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\Delta_i(\vec{x}) = \frac{ \left|{ \vec{x} - \vec{a_i} }\right| }{c} n_{eff}
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\end{equation}%>>>
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\begin{equation}\label{eq:interferometric_sum}%<<<
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S(\vec{x}, t) = \sum_i S_i(t + \Delta_i(\vec{x}))
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\end{equation}%>>>
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\begin{figure}
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\centering
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\begin{subfigure}[t]{0.3\textwidth}
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\includegraphics[width=\textwidth]{radio_interferometry/trace_overlap_bad.png}
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\label{fig:trace_overlap:bad}
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\end{subfigure}
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\hfill
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\begin{subfigure}[t]{0.3\textwidth}
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\includegraphics[width=\textwidth]{radio_interferometry/trace_overlap_medium.png}
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\label{fig:trace_overlap:medium}
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\end{subfigure}
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\hfill
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\begin{subfigure}[t]{0.3\textwidth}
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\includegraphics[width=\textwidth]{radio_interferometry/trace_overlap_best.png}
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\label{fig:trace_overlap:best}
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\end{subfigure}
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\caption{
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Trace overlap due to wrong positions
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}
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\label{fig:trace_overlap}
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\end{figure}
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\begin{figure}
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\centering
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\includegraphics[width=0.7\textwidth]{2006.10348/fig03_b.png}%
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\caption{
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From \protect \cite{Schoorlemmer:2020low}.
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$\Xmax$ resolution as a function of detector-to-detector synchronisation.
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}
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\label{fig:xmax_synchronise}
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\end{figure}
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\section{Time Synchronisation}
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\label{sec:timesynchro}
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The main method of synchronising multiple stations is by employing a \gls{GNSS}.
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This system should deliver timing with an accuracy in the order of $10\ns$ \cite{} (see Section~\ref{sec:grand:gnss}).
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\\
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Need reference system with better accuracy to constrain current mechanism (Figure~\ref{fig:reference-clock}).
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%\begin{figure}
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% \centering
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% \includegraphics[width=0.5\textwidth]{clocks/reference-clock.pdf}
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% \caption{
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% Using a reference clock to compare two other clocks.
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% \protect \todo{
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% redo figure with less margins,
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% remove spines,
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% rotate labels
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% }
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% }
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% \label{fig:reference-clock}
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%\end{figure}
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\end{document}
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