diff --git a/documents/thesis/chapters/introduction.tex b/documents/thesis/chapters/introduction.tex index 7f7cb29..b805f4a 100644 --- a/documents/thesis/chapters/introduction.tex +++ b/documents/thesis/chapters/introduction.tex @@ -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} diff --git a/documents/thesis/chapters/radio_interferometry.tex b/documents/thesis/chapters/radio_interferometry.tex new file mode 100644 index 0000000..7a8d237 --- /dev/null +++ b/documents/thesis/chapters/radio_interferometry.tex @@ -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} diff --git a/documents/thesis/thesis.tex b/documents/thesis/thesis.tex index 4c4a11d..20eb6d6 100644 --- a/documents/thesis/thesis.tex +++ b/documents/thesis/thesis.tex @@ -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}