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Thesis: Introduction: better typesetting of fig1.2

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documents/thesis/chapters/introduction.tex
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@ -35,7 +35,7 @@ For very high energies, above $10^{6}\GeV$, the flux approaches one particle per
At these high energies, the incoming particles are primarily cosmic rays\footnote{These are therefore known as \glspl{UHECR}.}, atomic nuclei typically ranging from protons ($Z=1$) up to iron ($Z=26$). At these high energies, the incoming particles are primarily cosmic rays\footnote{These are therefore known as \glspl{UHECR}.}, atomic nuclei typically ranging from protons ($Z=1$) up to iron ($Z=26$).
Because these are charged, the various magnetic fields they pass through will deflect and randomise their trajectories. Because these are charged, the various magnetic fields they pass through will deflect and randomise their trajectories.
Of course, this effect is dependent on the strength and size of the magnetic field and the speed of the particle. Of course, this effect is dependent on the strength and size of the magnetic field and the speed of the particle.
It is therefore only at the very highest energies that the direction of an initial particle might be used to (conservatively) estimate the direction of its origin.\Todo{Harm rephrase} It is therefore only at the very highest energies that the direction of an initial particle might be used to (conservatively) infer the direction of its origin.
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% CR: galaxy / extra-galactic % CR: galaxy / extra-galactic
@ -54,7 +54,6 @@ Unfortunately, aside from both being much less frequent, photons can be absorbed
% source / targets % source / targets
%} %}
\\ \\
\pagebreak[1]
%>>> %>>>
%\subsection{Air Showers}%<<< %\subsection{Air Showers}%<<<
@ -66,23 +65,26 @@ This happens until the mean energy per particle is sufficiently lowered from whe
Figure~\ref{fig:airshower:depth} shows the number of particles as a function of atmospheric depth where $0\;\mathrm{g/cm^2}$ corresponds with the top of the atmosphere. Figure~\ref{fig:airshower:depth} shows the number of particles as a function of atmospheric depth where $0\;\mathrm{g/cm^2}$ corresponds with the top of the atmosphere.
The atmospheric depth at which this number of particles reaches its maximum is called $\Xmax$. The atmospheric depth at which this number of particles reaches its maximum is called $\Xmax$.
\\ \pagebreak
The $\Xmax$ is different in Figure~\ref{ref:airshower:depth} for the airshowers generated by a photon, a proton or an iron nucleus.
In Figure~\ref{fig:airshower:depth}, $\Xmax$ is different for the airshowers generated by a photon, a proton or an iron nucleus.
Typically, heavy nuclei have their first interaction higher up in the atmosphere than protons, with photons penetrating the atmosphere even further. Typically, heavy nuclei have their first interaction higher up in the atmosphere than protons, with photons penetrating the atmosphere even further.
Therefore, accurate measurements of $\Xmax$ allow to statistically discriminate between photons, protons and iron nuclei. Therefore, accurate measurements of $\Xmax$ allow to statistically discriminate between photons, protons and iron nuclei.
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\begin{figure}%<<< airshower:depth \begin{figure}%<<< airshower:depth
\centering \centering
\vspace*{-10mm}
\includegraphics[width=0.5\textwidth]{airshower/shower_development_depth_iron_proton_photon.pdf} \includegraphics[width=0.5\textwidth]{airshower/shower_development_depth_iron_proton_photon.pdf}
\caption{ \caption{
From H. Schoorlemmer. From H. Schoorlemmer.
Shower development as a function of atmospheric depth for an energy of $10^{19}\eV$. Shower development as a function of atmospheric depth for an energy of $10^{19}\eV$.
Typically, iron- and proton-induced air showers have a difference in $\langle \Xmax \rangle$ of $100\;\mathrm{g/cm^2}$~\cite{Deligny:2023yms}. Typically, iron- and proton-induced air showers have a difference in $\langle \Xmax \rangle$ of $100\;\mathrm{g/cm^2}$~\cite{Deligny:2023yms}.
Air showers from photons are even further down the atmosphere. For air showers from photons this is even further down the atmosphere.
They are, however, much rarer than cosmic rays. They are, however, much more rare than cosmic rays.
} }
\label{fig:airshower:depth} \label{fig:airshower:depth}
\vspace*{-5mm}
\end{figure}%>>> \end{figure}%>>>
The initial particle type also influences the particle content of an air shower. The initial particle type also influences the particle content of an air shower.
@ -92,6 +94,7 @@ Each component shows particular development and can be related to different obse
For example, detecting a large hadronic component means the initial particle has access to hadronic interactions (creating hadrons such as pions, kaons, etc.) which is a typical sign of a cosmic ray. For example, detecting a large hadronic component means the initial particle has access to hadronic interactions (creating hadrons such as pions, kaons, etc.) which is a typical sign of a cosmic ray.
In contrast, for an initial photon, which cannot interact hadronicly, the energy will be dumped into the electromagnetic part of the air shower, mainly producing electrons, positrons and photons. In contrast, for an initial photon, which cannot interact hadronicly, the energy will be dumped into the electromagnetic part of the air shower, mainly producing electrons, positrons and photons.
\\ \\
Finally, any charged pions created in the air shower will decay into muons while still in the atmosphere, thus comprising the muonic component. Finally, any charged pions created in the air shower will decay into muons while still in the atmosphere, thus comprising the muonic component.
The lifetime, and ease of penetration of relativistic muons allow them to propagate to the Earth's surface, even if other particles have decayed or have been absorbed in the atmosphere. The lifetime, and ease of penetration of relativistic muons allow them to propagate to the Earth's surface, even if other particles have decayed or have been absorbed in the atmosphere.
These are therefore prime candidates for air shower detectors on the Earth's surface. These are therefore prime candidates for air shower detectors on the Earth's surface.
@ -141,6 +144,7 @@ It is therefore crucial for radio detection to obtain measurements in this regio
See text for explanation. See text for explanation.
} }
\label{fig:airshower:polarisation} \label{fig:airshower:polarisation}
\vspace{-2mm}
\end{figure}%>>>>>> \end{figure}%>>>>>>
%>>>>>> %>>>>>>
@ -157,7 +161,7 @@ Unfortunately, this timing accuracy is not continuously achieved by \glspl{GNSS}
For example, in the~\gls{AERA}, this was found to range up to multiple tens of nanoseconds over the course of a single day\cite{PierreAuger:2015aqe}. For example, in the~\gls{AERA}, this was found to range up to multiple tens of nanoseconds over the course of a single day\cite{PierreAuger:2015aqe}.
\\ \\
\pagebreak \pagebreak[1]
% Structure summary % Structure summary
This thesis investigates a relatively straightforward method (and its limits) to improve the timing accuracy of air shower radio detectors This thesis investigates a relatively straightforward method (and its limits) to improve the timing accuracy of air shower radio detectors
@ -170,11 +174,15 @@ This will be used later on and gives an insight into the timing accuracy require
\\ \\
Chapter~\ref{sec:waveform} reviews some typical techniques to analyse waveforms and to obtain timing information from them. Chapter~\ref{sec:waveform} reviews some typical techniques to analyse waveforms and to obtain timing information from them.
\\ \\
In Chapter~\ref{sec:disciplining} the concept of a beacon transmitter is introduced to synchronise an array of radio antennas.
In Chapter~\ref{sec:disciplining}, the concept of a beacon transmitter is introduced to synchronise an array of radio antennas.
It demonstrates the achievable timing accuracy for a sine and pulse beacon using the techniques described in the preceding chapter. It demonstrates the achievable timing accuracy for a sine and pulse beacon using the techniques described in the preceding chapter.
\\ \\
When the timing accuracy of the \gls{GNSS} is in the order periodicity of a continuous beacon, the synchronisation is impaired.
A degeneracy in the synchronisation is encountered when the timing accuracy of the \gls{GNSS} is in the order of the periodicity of a continuous beacon.
Chapter~\ref{sec:single_sine_sync} establishes a method using a single sine wave beacon while using the radio interferometric approach to observe an air shower and correct for this effect. Chapter~\ref{sec:single_sine_sync} establishes a method using a single sine wave beacon while using the radio interferometric approach to observe an air shower and correct for this effect.
\\ \\
Finally, Chapter~\ref{sec:gnss_accuracy} investigates limitations of the current hardware of \gls{GRAND} and its ability to record and reconstruct a beacon signal.
Finally, Chapter~\ref{sec:gnss_accuracy} investigates some possible limitations of the current hardware of \gls{GRAND} and its ability to record and reconstruct a beacon signal.
\end{document} \end{document}

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documents/thesis/chapters/radio_interferometry.tex
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@ -20,11 +20,13 @@ For suitable frequencies, an array of radio antennas can be used as an interfero
Therefore, air showers can be analysed using radio interferometry. Therefore, air showers can be analysed using radio interferometry.
Note that since the radio waves are mainly caused by processes involving electrons, any derived properties are tied to the electromagnetic component of the air shower. Note that since the radio waves are mainly caused by processes involving electrons, any derived properties are tied to the electromagnetic component of the air shower.
\\ \\
In Reference~\cite{Schoorlemmer:2020low}, a technique was developed to obtain properties of an air shower using radio interferometry.% In Reference~\cite{Schoorlemmer:2020low}, a technique was developed to obtain properties of an air shower using radio interferometry.%
\footnote{ \footnote{
Available as a python package at \url{https://gitlab.com/harmscho/asira}. Available as a python package at \url{https://gitlab.com/harmscho/asira}.
} }
A power mapping of a simulated air shower is shown in Figure~\ref{fig:radio_air_shower}. It exploits the coherent emissions in the air shower by mapping the power.
Such a power mapping (of a simulated air shower) is shown in Figure~\ref{fig:radio_air_shower}.
It reveals the air shower in one vertical and three horizontal slices. It reveals the air shower in one vertical and three horizontal slices.
Analysing the power mapping, we can then infer properties of the air shower such as the shower axis and $\Xmax$. Analysing the power mapping, we can then infer properties of the air shower such as the shower axis and $\Xmax$.
\\ \\
@ -35,6 +37,7 @@ For detector synchronisations under $2\ns$, the atmospheric depth resolution is
With a difference in $\langle \Xmax \rangle$ of $\sim 100\,\mathrm{g/cm^2}$ between iron and proton initiated air showers, this depth of shower maximum resolution allows to study the mass composition of cosmic rays. With a difference in $\langle \Xmax \rangle$ of $\sim 100\,\mathrm{g/cm^2}$ between iron and proton initiated air showers, this depth of shower maximum resolution allows to study the mass composition of cosmic rays.
However, for worse synchronisations, the $\Xmax$ resolution for interferometry degrades linearly. However, for worse synchronisations, the $\Xmax$ resolution for interferometry degrades linearly.
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An advantage of radio antennas with respect to fluorescence detectors is the increased duty-cycle. An advantage of radio antennas with respect to fluorescence detectors is the increased duty-cycle.
Fluorescence detectors require clear, moonless nights, resulting in a duty-cycle of about $10\%$ whereas radio detectors have a near permanent duty-cycle. Fluorescence detectors require clear, moonless nights, resulting in a duty-cycle of about $10\%$ whereas radio detectors have a near permanent duty-cycle.
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