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Thesis: Introduction: better typesetting of fig1.2
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@ -35,7 +35,7 @@ For very high energies, above $10^{6}\GeV$, the flux approaches one particle per
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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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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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\\
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% CR: galaxy / extra-galactic
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@ -54,7 +54,6 @@ Unfortunately, aside from both being much less frequent, photons can be absorbed
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% source / targets
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%}
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\\
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\pagebreak[1]
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%>>>
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%\subsection{Air Showers}%<<<
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@ -66,23 +65,26 @@ This happens until the mean energy per particle is sufficiently lowered from whe
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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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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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\pagebreak
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In Figure~\ref{fig:airshower:depth}, $\Xmax$ is different 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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\\
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\begin{figure}%<<< airshower:depth
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\centering
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\vspace*{-10mm}
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\includegraphics[width=0.5\textwidth]{airshower/shower_development_depth_iron_proton_photon.pdf}
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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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For air showers from photons this is even further down the atmosphere.
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They are, however, much more rare than cosmic rays.
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}
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\label{fig:airshower:depth}
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\vspace*{-5mm}
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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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@ -92,6 +94,7 @@ Each component shows particular development and can be related to different obse
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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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@ -141,6 +144,7 @@ It is therefore crucial for radio detection to obtain measurements in this regio
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See text for explanation.
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}
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\label{fig:airshower:polarisation}
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\vspace{-2mm}
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\end{figure}%>>>>>>
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%>>>>>>
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@ -157,7 +161,7 @@ Unfortunately, this timing accuracy is not continuously achieved by \glspl{GNSS}
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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}.
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\\
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\pagebreak
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\pagebreak[1]
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% Structure summary
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This thesis investigates a relatively straightforward method (and its limits) to improve the timing accuracy of air shower radio detectors
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@ -170,11 +174,15 @@ This will be used later on and gives an insight into the timing accuracy require
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\\
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Chapter~\ref{sec:waveform} reviews some typical techniques to analyse waveforms and to obtain timing information from them.
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\\
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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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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 periodicity of a continuous beacon, the synchronisation is impaired.
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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.
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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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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.
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\end{document}
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@ -20,11 +20,13 @@ For suitable frequencies, an array of radio antennas can be used as an interfero
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Therefore, air showers can be analysed using radio interferometry.
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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.
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\\
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In Reference~\cite{Schoorlemmer:2020low}, a technique was developed to obtain properties of an air shower using radio interferometry.%
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\footnote{
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Available as a python package at \url{https://gitlab.com/harmscho/asira}.
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}
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A power mapping of a simulated air shower is shown in Figure~\ref{fig:radio_air_shower}.
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It exploits the coherent emissions in the air shower by mapping the power.
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Such a power mapping (of a simulated air shower) is shown in Figure~\ref{fig:radio_air_shower}.
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It reveals the air shower in one vertical and three horizontal slices.
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Analysing the power mapping, we can then infer properties of the air shower such as the shower axis and $\Xmax$.
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\\
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@ -35,6 +37,7 @@ For detector synchronisations under $2\ns$, the atmospheric depth resolution is
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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.
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However, for worse synchronisations, the $\Xmax$ resolution for interferometry degrades linearly.
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\\
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An advantage of radio antennas with respect to fluorescence detectors is the increased duty-cycle.
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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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\\
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