m-thesis-documentation/documents/thesis/chapters/introduction.tex
Eric Teunis de Boone 580521d72c Thesis: Structure change: feedback Harm
Had a short discussion on the structure with Harm.

Introduce new chapter on waveforms and ways to analyse them.

Also, move the single sine period degeneracy to a separate chapter.
2023-05-24 21:17:40 +02:00

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TeX

\documentclass[../thesis.tex]{subfiles}
\graphicspath{
{.}
{../../figures/}
{../../../figures/}
}
\begin{document}
\chapter{Introduction}
\label{sec:introduction}
\section{Cosmic Particles}
\label{sec:crs}
Particles from outer space,
Particle type,
Energy,
magnetic fields -- origin,
\subsection{Air Showers}
\label{sec:airshowers}
Particle cascades,
Xmax?,
Radio emission,
\subsection{Experiments}
\label{sec:detectors}
Standalone devices,
\gls*{PA},
AugerPrime RD,
\gls*{GRAND},
\gls*{LOFAR}?,
\section{Interferometry}
\label{sec:interferometry}
Rough outline of Interferometry?
\\
Requires $\sigma_t \lesssim 1\ns$ \cite{Schoorlemmer:2020low}
\begin{figure}
\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 = \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{equation}
\label{eq:coherence_condition}
\Delta t \leq \frac{1}{f}
\end{equation}
\begin{figure}
\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}
\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.
}
\label{fig:reference-clock}
\todo{
redo figure with less margins,
remove spines,
rotate labels
}
\end{figure}
\end{document}