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53
documents/thesis/chapters/introduction.tex
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@ -13,9 +13,10 @@
%\section{Cosmic Particles}%<<<<<< %\section{Cosmic Particles}%<<<<<<
%<<< %<<<
% Energy and flux % Energy and flux
The Earth is bombarded with a variety of energetic, extra-terrestrial particles, with the energy of these particles extending over many orders of magnitude as depicted in Figure~\ref{fig:cr_flux}. The Earth is bombarded with a variety of energetic, extra-terrestrial particles.
The energies of these particles extend over many orders of magnitude (see Figure~\ref{fig:cr_flux}).
The flux of these particles decreases exponentially with increasing energy. The flux of these particles decreases exponentially with increasing energy.
For energies above $10^{6}\GeV$, it approaches one particle per~square~meter per~year, whereas for even higher energies the flux decreases to a particle per~square~kilometer per~year. For very high energies, above $10^{6}\GeV$, the flux approaches one particle per~square~meter per~year, further decreasing to a single particle per~square~kilometer per~year for Ultra High Energies (UHE) at $10^{10}\GeV$.
\\ \\
\begin{figure}%<<< fig:cr_flux \begin{figure}%<<< fig:cr_flux
@ -31,11 +32,12 @@ For energies above $10^{6}\GeV$, it approaches one particle per~square~meter per
\end{figure}%>>> \end{figure}%>>>
% CR: magnetic field % CR: magnetic field
At these high energies, the incoming particles are primarily cosmic rays, 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 passthrough will deflect and randomise their trajectories. Because these are charged, the various magnetic fields they pass through will deflect and randomise their trajectories.
Ofcourse, 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 constrain the direction of its origin. 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}
\\ \\
% CR: galaxy / extra-galactic % CR: galaxy / extra-galactic
The same argument (but in reverse) can be used to explain the steeper slope from the ``knee'' ($10^{6}\GeV$) onwards in Figure~\ref{fig:cr_flux}. The same argument (but in reverse) can be used to explain the steeper slope from the ``knee'' ($10^{6}\GeV$) onwards in Figure~\ref{fig:cr_flux}.
The acceleration of cosmic rays equally requires strong and sizable magnetic fields. The acceleration of cosmic rays equally requires strong and sizable magnetic fields.
@ -46,7 +48,7 @@ It is thus at these energies that we can distinguish between galactic and extra-
% Photons and Neutrinos % Photons and Neutrinos
Other particles at these energies include photons and neutrinos, which are not charged. Other particles at these energies include photons and neutrinos, which are not charged.
Therefore, these particle types do not suffer from magnetic deflections and have the potential to reveal their source regions. Therefore, these particle types do not suffer from magnetic deflections and have the potential to reveal their source regions.
Unfortunately, aside from both being much less frequent, photons can be absorbed and created by multiple mechanism, and neutrinos are notoriously hard to detect due to their weak interaction. Unfortunately, aside from both being much less frequent, photons can be absorbed and created by multiple mechanisms, while neutrinos are notoriously hard to detect due to their weak interaction.
%\Todo{ %\Todo{
% $\gamma + \nu$ production by CR, % $\gamma + \nu$ production by CR,
% source / targets % source / targets
@ -59,28 +61,15 @@ Unfortunately, aside from both being much less frequent, photons can be absorbed
When a cosmic ray with an energy above $10^{3}\GeV$ comes into contact with the atmosphere, secondary particles are generated, forming an \gls{EAS}. When a cosmic ray with an energy above $10^{3}\GeV$ comes into contact with the atmosphere, secondary particles are generated, forming an \gls{EAS}.
This air shower consists of a cascade of interactions producing more particles that subsequently undergo further interactions. 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. Thus, the number of particles rapidly increases further down the air shower.
This happens until the mean energy per particle is sufficiently lowered such that these particles are absorbed by the atmosphere. This happens until the mean energy per particle is sufficiently lowered from whereon these particles are absorbed in 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. 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 $\Xmax$.
\\ \\
In Figure~\ref{fig:airshower:depth} the $\Xmax$ is different for a photon, a proton and iron. The $\Xmax$ is different in Figure~\ref{ref:airshower:depth} 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.
For example, the difference in $\langle\Xmax\rangle$ for iron and protons is roughly $100\;\mathrm{g/cm^2}$~\cite{Deligny:2023yms}.
\\
The initial particle type also influences the particle content of an air shower.
Depending on the available interaction channels we distinguish three components in air showers: the hadronic, electromagnetic and muonic components.
Each component shows particular development and can be related to different observables of the air shower.
\\
For example, detecting a large hadronic component means the initial particle has access to hadronic interactions (such as pions, kaons, etc.) which is a typical sign for protons and other nuclei.
In contrast, for an initial photon, which cannot interact hadronicly, the energy will be dumped into the electromagnetic part of the air shower.
\\
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.
\\ \\
\begin{figure}%<<< airshower:depth \begin{figure}%<<< airshower:depth
@ -89,10 +78,25 @@ The lifetime, and ease of penetration of relativistic muons allow them to propag
\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}.
Air showers from photons are even further down the atmosphere.
They are, however, much rarer than cosmic rays.
} }
\label{fig:airshower:depth} \label{fig:airshower:depth}
\end{figure}%>>> \end{figure}%>>>
The initial particle type also influences the particle content of an air shower.
Depending on the available interaction channels, we distinguish three components in air showers: the hadronic, electromagnetic and muonic components.
Each component shows particular development and can be related to different observables of the air shower.
\\
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.
\\
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.
These are therefore prime candidates for air shower detectors on the Earth's surface.
\\
% Radio measurements % Radio measurements
Processes in an air showers also generate radiation that can be picked up as coherent radio signals. Processes in an air showers also generate radiation that can be picked up as coherent radio signals.
%% Geo Synchro %% Geo Synchro
@ -160,6 +164,7 @@ This thesis investigates a relatively straightforward method (and its limits) to
by using an additional radio signal called a beacon. by using an additional radio signal called a beacon.
It is organised as follows. It is organised as follows.
\\ \\
First, an introduction to radio interferometry is given in Chapter~\ref{sec:interferometry}. First, an introduction to radio interferometry is given in Chapter~\ref{sec:interferometry}.
This will be used later on and gives an insight into the timing accuracy requirements. This will be used later on and gives an insight into the timing accuracy requirements.
\\ \\
@ -168,8 +173,8 @@ Chapter~\ref{sec:waveform} reviews some typical techniques to analyse waveforms
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 of a continuous beacon's periodicity, the synchronisation is impaired. When the timing accuracy of the \gls{GNSS} is in the order periodicity of a continuous beacon, the synchronisation is impaired.
Chapter~\ref{sec:single_sine_sync} establishes a method using a single sine wave beacon while using the radio interferometric approach to observe an airshower 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 limitations of the current hardware of \gls{GRAND} and its ability to record and reconstruct a beacon signal.
\end{document} \end{document}

4
documents/thesis/thesis.tex
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@ -6,7 +6,7 @@
%% <<<< Thesis titling %% <<<< Thesis titling
%% %%
\def\thesistitle{Synchronisation Methods of\texorpdfstring{\\[0.3cm]}{ }Air Shower Radio Detectors} \def\thesistitle{Synchronisation Methods for\texorpdfstring{\\[0.3cm]}{ }Air Shower Radio Detectors}
\def\thesissubtitle{} \def\thesissubtitle{}
\def\thesisauthorfirst{Eric Teunis} \def\thesisauthorfirst{Eric Teunis}
\def\thesisauthorsecond{de Boone} \def\thesisauthorsecond{de Boone}
@ -14,7 +14,7 @@
\def\thesissupervisorfirst{dr. Harm} \def\thesissupervisorfirst{dr. Harm}
\def\thesissupervisorsecond{Schoorlemmer} \def\thesissupervisorsecond{Schoorlemmer}
\def\thesissupervisoremailraw{}%h.schoorlemmer@science.ru.nl} \def\thesissupervisoremailraw{}%h.schoorlemmer@science.ru.nl}
\def\thesissecondreaderfirst{dr. Katherine} \def\thesissecondreaderfirst{dr. Katharine}
\def\thesissecondreadersecond{Mulrey} \def\thesissecondreadersecond{Mulrey}
\def\thesissecondreaderemailraw{}%k.mulrey@science.ru.nl} \def\thesissecondreaderemailraw{}%k.mulrey@science.ru.nl}
\def\thesisdate{November 2023} \def\thesisdate{November 2023}