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Thesis: tweak title + use correct name for Katie
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@ -13,9 +13,10 @@
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%\section{Cosmic Particles}%<<<<<<
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%<<<
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% Energy and flux
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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}.
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The Earth is bombarded with a variety of energetic, extra-terrestrial particles.
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The energies of these particles extend over many orders of magnitude (see Figure~\ref{fig:cr_flux}).
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The flux of these particles decreases exponentially with increasing energy.
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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.
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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 $10^{10}\GeV$.
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\\
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\begin{figure}%<<< fig:cr_flux
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@ -31,11 +32,12 @@ For energies above $10^{6}\GeV$, it approaches one particle per~square~meter per
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\end{figure}%>>>
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% CR: magnetic field
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At these high energies, the incoming particles are primarily cosmic rays, atomic nuclei typically ranging from protons ($Z=1$) up to iron ($Z=26$).
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Because these are charged, the various magnetic fields they passthrough will deflect and randomise their trajectories.
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Ofcourse, this effect is dependent on the strength and size of the magnetic field and the speed of the particle.
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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.
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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 ($Z=26$).
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Because these are charged, the various magnetic fields they pass through will deflect and randomise their trajectories.
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Of course, this effect is dependent on the strength and size of the magnetic field and the speed of the particle.
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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}
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\\
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% CR: galaxy / extra-galactic
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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}.
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The acceleration of cosmic rays equally requires strong and sizable magnetic fields.
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@ -46,7 +48,7 @@ It is thus at these energies that we can distinguish between galactic and extra-
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% Photons and Neutrinos
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Other particles at these energies include photons and neutrinos, which are not charged.
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Therefore, these particle types do not suffer from magnetic deflections and have the potential to reveal their source regions.
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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.
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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.
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%\Todo{
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% $\gamma + \nu$ production by CR,
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% source / targets
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@ -59,28 +61,15 @@ Unfortunately, aside from both being much less frequent, photons can be absorbed
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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}.
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This air shower consists of a cascade of interactions producing more particles that subsequently undergo further interactions.
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Thus, the number of particles rapidly increases further down the air shower.
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This happens until the mean energy per particle is sufficiently lowered such that these particles are absorbed by the atmosphere.
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This happens until the mean energy per particle is sufficiently lowered from whereon these particles are absorbed in the atmosphere.
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\\
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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.
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The atmospheric depth at which this number of particles reaches its maximum is called $\Xmax$.
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\\
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In Figure~\ref{fig:airshower:depth} the $\Xmax$ is different for a photon, a proton and iron.
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The $\Xmax$ is different in Figure~\ref{ref:airshower:depth} for the airshowers generated by a photon, a proton or an iron nucleus.
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Typically, heavy nuclei have their first interaction higher up in the atmosphere than protons, with photons penetrating the atmosphere even further.
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Therefore, accurate measurements of $\Xmax$ allow to statistically discriminate between photons, protons and iron nuclei.
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For example, the difference in $\langle\Xmax\rangle$ for iron and protons is roughly $100\;\mathrm{g/cm^2}$~\cite{Deligny:2023yms}.
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\\
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The initial particle type also influences the particle content of an air shower.
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Depending on the available interaction channels we distinguish three components in air showers: the hadronic, electromagnetic and muonic components.
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Each component shows particular development and can be related to different observables of the air shower.
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\\
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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.
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In contrast, for an initial photon, which cannot interact hadronicly, the energy will be dumped into the electromagnetic part of the air shower.
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\\
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Finally, any charged pions created in the air shower will decay into muons while still in the atmosphere, thus comprising the muonic component.
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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.
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\\
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\begin{figure}%<<< airshower:depth
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@ -89,10 +78,25 @@ The lifetime, and ease of penetration of relativistic muons allow them to propag
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\caption{
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From H. Schoorlemmer.
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Shower development as a function of atmospheric depth for an energy of $10^{19}\eV$.
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Typically, iron- and proton-induced air showers have a difference in $\langle \Xmax \rangle$ of $100\;\mathrm{g/cm^2}$~\cite{Deligny:2023yms}.
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Air showers from photons are even further down the atmosphere.
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They are, however, much rarer than cosmic rays.
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}
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\label{fig:airshower:depth}
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\end{figure}%>>>
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The initial particle type also influences the particle content of an air shower.
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Depending on the available interaction channels, we distinguish three components in air showers: the hadronic, electromagnetic and muonic components.
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Each component shows particular development and can be related to different observables of the air shower.
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\\
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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.
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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.
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\\
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Finally, any charged pions created in the air shower will decay into muons while still in the atmosphere, thus comprising the muonic component.
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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.
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These are therefore prime candidates for air shower detectors on the Earth's surface.
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\\
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% Radio measurements
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Processes in an air showers also generate radiation that can be picked up as coherent radio signals.
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%% Geo Synchro
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@ -160,6 +164,7 @@ This thesis investigates a relatively straightforward method (and its limits) to
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by using an additional radio signal called a beacon.
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It is organised as follows.
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\\
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First, an introduction to radio interferometry is given in Chapter~\ref{sec:interferometry}.
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This will be used later on and gives an insight into the timing accuracy requirements.
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\\
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@ -168,8 +173,8 @@ Chapter~\ref{sec:waveform} reviews some typical techniques to analyse waveforms
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In Chapter~\ref{sec:disciplining} the concept of a beacon transmitter is introduced to synchronise an array of radio antennas.
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It demonstrates the achievable timing accuracy for a sine and pulse beacon using the techniques described in the preceding chapter.
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\\
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When the timing accuracy of the \gls{GNSS} is in the order of a continuous beacon's periodicity, the synchronisation is impaired.
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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.
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When the timing accuracy of the \gls{GNSS} is in the order periodicity of a continuous beacon, the synchronisation is impaired.
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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.
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\\
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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.
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\end{document}
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@ -6,7 +6,7 @@
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%% <<<< Thesis titling
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%%
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\def\thesistitle{Synchronisation Methods of\texorpdfstring{\\[0.3cm]}{ }Air Shower Radio Detectors}
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\def\thesistitle{Synchronisation Methods for\texorpdfstring{\\[0.3cm]}{ }Air Shower Radio Detectors}
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\def\thesissubtitle{}
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\def\thesisauthorfirst{Eric Teunis}
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\def\thesisauthorsecond{de Boone}
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\def\thesissupervisorfirst{dr. Harm}
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\def\thesissupervisorsecond{Schoorlemmer}
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\def\thesissupervisoremailraw{}%h.schoorlemmer@science.ru.nl}
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\def\thesissecondreaderfirst{dr. Katherine}
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\def\thesissecondreaderfirst{dr. Katharine}
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\def\thesissecondreadersecond{Mulrey}
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\def\thesissecondreaderemailraw{}%k.mulrey@science.ru.nl}
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\def\thesisdate{November 2023}
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