Thesis: Radio Interferometry: separate chapter

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Eric Teunis de Boone 2023-10-26 11:15:51 +02:00
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commit 89ddf4cc81
3 changed files with 113 additions and 110 deletions

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@ -10,7 +10,7 @@
\begin{document}
\chapter{Introduction}
\label{sec:introduction}
%<<<
% Intro Cosmic Ray
In the beginning of the $\mathrm{20^{th}}$~century, various types of radiation were discovered.
With the balloonflight of Victor Hess \Todo{ref} in \Todo{year}, one type was determined to come from beyond the atmosphere and named ``Cosmic Rays''.
@ -29,16 +29,16 @@ However, advanced analyses require an even higher accuracy.
\\
In this thesis, methods (and their limits) to obtain this accuracy for radio arrays are investigated.
% >>>
\section{Cosmic Particles}%<<<<<<
%<<<
\label{sec:crs}
Particles from outer space,
Particle type,
Energy,
magnetic fields -- origin,
\hrule
%Particles from outer space,
%Particle type,
%Energy,
%magnetic fields -- origin,
%
%\hrule
% Cosmic Particles = CR + Photon + Neutrino
There is a variety of extra terrestrial particles with which the Earth is bombarded.\Todo{rephrase}
@ -69,7 +69,7 @@ Note that cosmic rays are deemed\Todo{rephrase} to be charged nuclei.
% Energy
Cosmic rays span a large range of energy as illustrated in Figure~\ref{fig:cr_flux}.
Cosmic rays span a large range of energy and flux as illustrated in Figure~\ref{fig:cr_flux}.
The acceleration of cosmic rays is thought to occur in highly energetic regions\Todo{expand}
\\
@ -88,11 +88,11 @@ Likewise, with an rapidly increasing flux for lower energies, one component can
%>>>
\subsection{Air Showers}%<<<
\label{sec:airshowers}
Particle cascades,
Xmax?,
Radio emission,
\hrule
%Particle cascades,
%Xmax?,
%Radio emission,
%
%\hrule
When a particle with an energy above $1\;\TeV$ comes into contact with the atmosphere, secondary particles are generated, forming an air shower.
This air shower consists of a cascade of interactions producing more particles that subsequently undergo further interactions.
Thus, the number of particles rapidly increases further down the air shower.
@ -200,103 +200,9 @@ This will be used later on and gives an insight into the timing accuracy require
\\
Chapter~\ref{sec:waveform} reviews typical techniques to analyse waveforms to obtain timing information.
\\
Chapter~\ref{sec:disciplining} introduces the concept of a beacon transmitter to synchronise an array of radio antennas using techniques from the preceding chapter to constrain the achievable timing accuracy.
Chapter~\ref{sec:disciplining} introduces the concept of a beacon transmitter to synchronise an array of radio antennas and constrains the achievable timing accuracy using the techniques described in the preceding chapter.
\\
Chapter~\ref{sec:single_sine_sync} shows\Todo{word} how a sine wave beacon can synchronise an array while using the radio interferometric approach to resolve\Todo{word} an airshower.
\\
Finally, Chapter~\ref{sec:gnss_accuracy} investigates the limitations of the current hardware in \gls{GRAND} and its ability to record and reconstruct a beacon signal.
\cleardoublepage
\chapter{Air Shower Radio Interferometry}
\label{sec:interferometry}
The radio signals emitted by the air shower (see Section~\ref{sec:airshowers}) can be recorded by radio antennas.
An array of radio antennas can be used as an interferometer.
Therefore, air showers can be analysed using radio interferometry.
\\
%
Unlike, astronomical interferometry, the source of the signal is closeby.
\begin{figure}
\centering
\includegraphics[width=0.5\textwidth]{radio_interferometry/rit_schematic_true.pdf}%
% \includegraphics[width=0.5\textwidth]{radio_interferometry/Schematic_RIT_extracted.png}
% \caption{From H. Schoorlemmer}
\end{figure}
\begin{equation}\label{eq:propagation_delay}%<<<
\Delta_i(\vec{x}) = \frac{ \left|{ \vec{x} - \vec{a_i} }\right| }{c} n_{eff}
\end{equation}%>>>
\begin{equation}\label{eq:interferometric_sum}%<<<
S(\vec{x}, t) = \sum_i S_i(t + \Delta_i(\vec{x}))
\end{equation}%>>>
\begin{figure}
\centering
\begin{subfigure}[t]{0.3\textwidth}
\includegraphics[width=\textwidth]{radio_interferometry/trace_overlap_bad.png}
\label{fig:trace_overlap:bad}
\end{subfigure}
\hfill
\begin{subfigure}[t]{0.3\textwidth}
\includegraphics[width=\textwidth]{radio_interferometry/trace_overlap_medium.png}
\label{fig:trace_overlap:medium}
\end{subfigure}
\hfill
\begin{subfigure}[t]{0.3\textwidth}
\includegraphics[width=\textwidth]{radio_interferometry/trace_overlap_best.png}
\label{fig:trace_overlap:best}
\end{subfigure}
\caption{
Trace overlap due to wrong positions
}
\label{fig:trace_overlap}
\end{figure}
\begin{figure}
\centering
\includegraphics[width=0.7\textwidth]{2006.10348/fig03_b.png}%
\caption{
From \protect \cite{Schoorlemmer:2020low}.
$\Xmax$ resolution as a function of detector-to-detector synchronisation.
}
\label{fig:xmax_synchronise}
\end{figure}
\section{Time Synchronisation}
\label{sec:timesynchro}
The main method of synchronising multiple stations is by employing a \gls{GNSS}.
This system should deliver timing with an accuracy in the order of $10\ns$ \cite{} (see Section~\ref{sec:grand:gnss}).
\\
Need reference system with better accuracy to constrain current mechanism (Figure~\ref{fig:reference-clock}).
%\begin{figure}
% \centering
% \includegraphics[width=0.5\textwidth]{clocks/reference-clock.pdf}
% \caption{
% Using a reference clock to compare two other clocks.
% \protect \todo{
% redo figure with less margins,
% remove spines,
% rotate labels
% }
% }
% \label{fig:reference-clock}
%\end{figure}
Finally, Chapter~\ref{sec:gnss_accuracy} investigates the limitations of the current hardware of \gls{GRAND} and its ability to record and reconstruct a beacon signal.
\end{document}

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@ -0,0 +1,94 @@
% vim: fdm=marker fmr=<<<,>>>
\documentclass[../thesis.tex]{subfiles}
\graphicspath{
{.}
{../../figures/}
{../../../figures/}
}
\begin{document}
\chapter{Air Shower Radio Interferometry}
\label{sec:interferometry}
The radio signals emitted by the air shower (see Section~\ref{sec:airshowers}) can be recorded by radio antennas.
An array of radio antennas can be used as an interferometer.
Therefore, air showers can be analysed using radio interferometry.
\\
%
Unlike, astronomical interferometry, the source of the signal is closeby.
\begin{figure}
\centering
\includegraphics[width=0.5\textwidth]{radio_interferometry/rit_schematic_true.pdf}%
% \includegraphics[width=0.5\textwidth]{radio_interferometry/Schematic_RIT_extracted.png}
% \caption{From H. Schoorlemmer}
\end{figure}
\begin{equation}\label{eq:propagation_delay}%<<<
\Delta_i(\vec{x}) = \frac{ \left|{ \vec{x} - \vec{a_i} }\right| }{c} n_{eff}
\end{equation}%>>>
\begin{equation}\label{eq:interferometric_sum}%<<<
S(\vec{x}, t) = \sum_i S_i(t + \Delta_i(\vec{x}))
\end{equation}%>>>
\begin{figure}
\centering
\begin{subfigure}[t]{0.3\textwidth}
\includegraphics[width=\textwidth]{radio_interferometry/trace_overlap_bad.png}
\label{fig:trace_overlap:bad}
\end{subfigure}
\hfill
\begin{subfigure}[t]{0.3\textwidth}
\includegraphics[width=\textwidth]{radio_interferometry/trace_overlap_medium.png}
\label{fig:trace_overlap:medium}
\end{subfigure}
\hfill
\begin{subfigure}[t]{0.3\textwidth}
\includegraphics[width=\textwidth]{radio_interferometry/trace_overlap_best.png}
\label{fig:trace_overlap:best}
\end{subfigure}
\caption{
Trace overlap due to wrong positions
}
\label{fig:trace_overlap}
\end{figure}
\begin{figure}
\centering
\includegraphics[width=0.7\textwidth]{2006.10348/fig03_b.png}%
\caption{
From \protect \cite{Schoorlemmer:2020low}.
$\Xmax$ resolution as a function of detector-to-detector synchronisation.
}
\label{fig:xmax_synchronise}
\end{figure}
\section{Time Synchronisation}
\label{sec:timesynchro}
The main method of synchronising multiple stations is by employing a \gls{GNSS}.
This system should deliver timing with an accuracy in the order of $10\ns$ \cite{} (see Section~\ref{sec:grand:gnss}).
\\
Need reference system with better accuracy to constrain current mechanism (Figure~\ref{fig:reference-clock}).
%\begin{figure}
% \centering
% \includegraphics[width=0.5\textwidth]{clocks/reference-clock.pdf}
% \caption{
% Using a reference clock to compare two other clocks.
% \protect \todo{
% redo figure with less margins,
% remove spines,
% rotate labels
% }
% }
% \label{fig:reference-clock}
%\end{figure}
\end{document}

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@ -53,6 +53,9 @@
%% Introduction
\subfile{chapters/introduction.tex}
%% Radio Interferometry
\subfile{chapters/radio_interferometry.tex}
%% Electric field from airshower to waveform analysis
\subfile{chapters/radio_measurement.tex}