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Thesis: final introduction
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@ -15,9 +15,9 @@
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\phantomsection
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\label{sec:crs}
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% Energy and flux
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The Earth is bombarded with a variety of 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, 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 flux of these particles decreases exponentially with increasing energy.
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For \gls{UHE}, above $10^{6}\GeV$\Todo{limit}, 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 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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\\
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\begin{figure}%<<< fig:cr_flux
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@ -33,16 +33,16 @@ For \gls{UHE}, above $10^{6}\GeV$\Todo{limit}, it approaches one particle per~sq
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\end{figure}%>>>
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% CR: magnetic field
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At \gls{UHE}, the incoming particles are primarily cosmic rays, atomic nuclei typically ranging from protons ($Z=1$) up to iron ($Z=26$).
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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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\\
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% CR: galaxy / extra-galactic
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The same argument (but in reverse) can be used to distinguish galactic and extra-galactic origins.
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The acceleration of these charged particles equally\Todo{word} requires strong and/or sizable magnetic fields.
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Size constraints on our galaxy lead to a maximum energy for which a cosmic ray can still be contained in the galaxy.
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This mechanism is expected to explain the steeper slope in Figure~\ref{fig:cr_flux} from the ``knee'' ($10^{6}\GeV$) onwards.
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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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Size constraints on the Milky~Way lead to a maximum energy for which a cosmic ray can still be contained in our galaxy.
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It is thus at these energies that we can distinguish between galactic and extra-galactic origins.
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\\
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% Photons and Neutrinos
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@ -57,9 +57,10 @@ Unfortunately, aside from both being much less frequent, photons can be absorbed
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%>>>
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%\subsection{Air Showers}%<<<
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\pagebreak[2]
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\phantomsection
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\label{sec:airshowers}
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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 air shower.
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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}\Todo{EAS at energy?}.
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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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@ -79,7 +80,7 @@ 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.)\Todo{ref?} which is a typical sign for protons and other nuclei.
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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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@ -96,6 +97,7 @@ The lifetime, and ease of penetration of relativistic muons allow them to propag
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\label{fig:airshower:depth}
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\end{figure}%>>>
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\pagebreak[2]
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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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@ -109,12 +111,12 @@ In turn, this generates radiation that is polarised radially towards the shower
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\\
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%% Cherenkov ring
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Due to the (varying) refractive index of the atmosphere, the produced radiation is concentrated on a ring-like structure called the Cherenkov-ring.
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A peculiar time-inversion of the radiation from the whole air shower signals happens at this ring.
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Outside this ring, radiation from the top of the air shower arrives earlier than radiation from the end of the air shower, whereas this is reversed inside thering.
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\\
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Consequently, all radiation from the whole air shower is concentrated in a small time-window at the Cherenkov-ring.
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It is therefore important for radio detection to obtain measurements in this region.
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Due to charged particles moving relativistically through the refractive atmosphere, the produced radiation is concentrated on a cone-like structure.
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On the surface, this creates a ring called the Cherenkov-ring.
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On this ring, a peculiar inversion happens in the time-domain of the air shower signals.
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Outside the ring, radiation from the top of the air shower arrives earlier than radiation from the end of the air shower, whereas this is reversed inside the ring.
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Consequently, the radiation received at the Cherenkov-ring is maximally coherent, being concentrated in a small time-window.
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It is therefore crucial for radio detection to obtain measurements in this region.
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\\
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\begin{figure}%<<< airshower:polarisation
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@ -153,39 +155,28 @@ With distances up to $1.5\;\mathrm{km}$ (\gls{Auger}), the detectors therefore h
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\\
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In the last two decades, with the advent of advanced electronics, the detection using radio antennas has received significant attention.
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A difficulty for radio detectors at these large distances.
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\Todo{write paragraph}
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For the detectors (and its upgrade \acrlong{AugerPrime}\cite{Huege:2023pfb}),
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Previously, for the timing of surface detectors such as water-Cherenkov detectors, this timing accuracy was better than the resolved data.
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Even for the first analyses of radio data, this was sufficient.\Todo{ref or rm}
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However, for advanced analyses such as radio interferometry, the timing accuracy must be improved.
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Analysing air showers using radio interferometry requires a time synchronisation of the detectors to an accuracy in the order of $1\ns$\cite{Schoorlemmer:2020low} (see Chapter~\ref{sec:interferometry} for further details).
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Unfortunately, this timing accuracy is not continuously achieved by \glspl{GNSS}, if at all.
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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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%%<<<
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%% Radio
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%In the last two decades, the detection using radio antennas has received significant attention \Todo{ref}, such that collaborations such as the~\gls{GRAND}\Todo{more?} are building observatoria that fully rely on radio measurements.
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%%
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%For such radio arrays, the analyses require an accurate timing of signals within the array.
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%Generally, \glspl{GNSS} are used to synchronise the detectors.
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%However, advanced analyses require an even higher accuracy than currently achieved with these systems.
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%\\
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%This thesis investigates a relatively straightforward method (and its limits) to obtain this required timing accuracy for radio arrays.
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%\\
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%\Todo{remove - repeated at end of chapter}
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% >>>
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\pagebreak[2]
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% Structure summary
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In this thesis, a solution to enhance the timing accuracy of air shower radio detectors is demonstrated.
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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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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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Chapter~\ref{sec:waveform} reviews typical techniques to analyse waveforms to obtain timing information.
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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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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.
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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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Chapter~\ref{sec:single_sine_sync} establishes a method to synchronise an array using a single sine wave beacon while using the radio interferometric approach to resolve\Todo{word} an airshower.
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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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\\
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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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