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Thesis: Introduction: WuotD
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@ -12,7 +12,7 @@
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\label{sec:introduction}
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% Intro Cosmic Ray
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In the beginning of the 20th century, various types of radiation were discovered.
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In the beginning of the $\mathrm{20^{th}}$~century, various types of radiation were discovered.
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With the balloonflight of Victor Hess \Todo{ref} in \Todo{year}, one type was determined to come from beyond the atmosphere and named ``Cosmic Rays''.
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With many discoveries following, the field of (astro-)particle physics evolved.
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\\
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@ -27,11 +27,11 @@ For such radio arrays, the analyses require an accurate timing of signals within
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Generally, \gls{GNSS} is used to synchronise the detectors.
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However, advanced analyses require an even higher accuracy.
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\\
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In this thesis, methods (and their limits) to obtain this accuracy for radio arrays are investigated.
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\section{Cosmic Particles}%<<<<<<
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%<<<
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\label{sec:crs}
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Particles from outer space,
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Particle type,
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@ -45,10 +45,11 @@ There is a variety of extra terrestrial particles with which the Earth is bombar
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These can be classified into three main types: charged nuclei (typically protons $Z=1$ up to iron $Z=26$), photons and neutrinos, each with different propagation effects.
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\\
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The charged nuclei are the bulk of the measured particles.
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They do not point back to their sources because they are deflected by magnetic fields due to being charged.
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The various magnetic fields that they travel through deflect\Todo{word} them due to their charge.
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They do not point back to their sources because of this.
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\\
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Photons do not suffer from being charged, and thus have the potential to identify their sources.
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However, they can be absorbed and created by multiple mechanisms.\Todo{rephrase}
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However, they can be absorbed and created by multiple mechanisms.\Todo{rephrase/expand}
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\\
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Finally, neutrino's interact weakly, thus pointing back to their sources as well.
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Unfortunately, this weak interaction also troubles the detection of the neutrino's.\Todo{rephrase}
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@ -69,13 +70,13 @@ Note that cosmic rays are deemed\Todo{rephrase} to be charged nuclei.
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% Energy
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Cosmic rays span a large range of energy as illustrated in Figure~\ref{fig:cr_flux}.
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The acceleration of cosmic rays is thought to occur in highly energetic regions
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The acceleration of cosmic rays is thought to occur in highly energetic regions\Todo{expand}
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\\
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Using the charged nuclei, an argument can be made to distinguish two types of sources.
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\\
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Being charged, the nuclei will gyrate in magnetic fields.
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With an approximate size of $ $\Todo{size} and an average magnetic field of $5\mathrm{\;\mu G}$\Todo{}, the Milky Way can only contain particles up to an energy of about $10^{16}\eV$\Todo{fill}.
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With an approximate size of $ $\Todo{size} and an average magnetic field of $5\mathrm{\;\mu G}$\Todo{}, the Milky Way can only contain particles up to an energy of about $10^{17}\eV$\Todo{fill}.
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Still, particles with higher energies have been observed (see Figure~\ref{fig:}).
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These higher energy particles must thus come from beyond our galaxy.
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\\
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@ -92,18 +93,23 @@ Xmax?,
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Radio emission,
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\hrule
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When a particle with a high enough energy comes into contact with the atmosphere, secondary particles are generated, forming an air shower.
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When a particle with an energy above $1\;\TeV$ comes into contact with the atmosphere, secondary particles are generated, forming an air shower.
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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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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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\\
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An important feature that allows to statistically discriminate photons from protons and iron nuclei is the atmospheric depth at which this number of particles reaches its maximum, called $\Xmax$.
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Part of this is explained by the depth of first interaction.
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Due to the higher charge of heavy nuclei, they interact earlier in the atmosphere.
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This happens until the energy is spread out\Todo{word} enough that the number of interactions decreases.
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\\
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The particle content of an air shower is dependent on the initial particle type.
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Protons (and other nuclei) have access to hadronic interaction channels (pions, kaons, etc.)\Todo{ref?} through which most energy is passed.
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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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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, measurements of $\Xmax$ allow to statistically discriminate between photons, protons and iron nuclei.
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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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Protons (and other nuclei) have access to hadronic interaction channels (such as pions, kaons, etc.)\Todo{ref?} through which most energy is passed.
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In turn, the resulting air showers contain a large hadronic component.\Todo{check wording}
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\\
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In contrast, an initial photon cannot interact hadronicly, meaning its energy is dumped into the electromagnetic part of the air shower.
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@ -111,7 +117,9 @@ In contrast, an initial photon cannot interact hadronicly, meaning its energy is
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Finally, any charged pions created in the air shower will decay into muons while still in the atmosphere.
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This muonic component is a reliable part to measure.\Todo{rephrase}
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\\
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These different components have a different width.\Todo{rephrase}
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The hadronic component is greatly collimated, while the electromagnetic component.
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\\
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\begin{figure}%<<< airshower:depth
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\centering
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\label{fig:airshower:depth}
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\end{figure}%>>>
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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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Due to the magnetic field of the Earth, the electrons in the air shower generate radiation.
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Termed geomagnetic emission in Figure~\ref{fig:airshower:polarisation}, this has a polarisation that is dependent on the magnetic field vector $B$ and the air shower velocity $v$.
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\Todo{expand?}
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\\
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%% Askaryan / Charge excess
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An additional mechanism emitting radiation was first theorised by Askaryan\Todo{ref}.
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Due to the large inertia of the positively charged ions with respect to their light, negatively charged electrons, a negative charge excess is created.
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In turn, this generates radiation that is polarised radially towards the shower axis (see Figure~\ref{fig:airshower:polarisation}).
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\\
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%% Cherenkov ring
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The relativistic speeds of the particles cause any radiation that is produced in the air shower to be forward beamed along the shower axis.
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Additionally, the shower travels faster than the speed of light in the atmosphere.
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This generates an
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The detection of the radio signals is limited to an
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This is limited by the so-called Cherenkov angle.
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\begin{figure}%<<< airshower:polarisation
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\centering
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\begin{subfigure}{0.47\textwidth}
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\includegraphics[width=\textwidth]{airshower/airshower_radio_polarisation_geomagnetic.png}%
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\caption{
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Geomagnetic emission
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}
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\label{fig:airshower:polarisation:geomagnetic}
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\end{subfigure}
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\hfill
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\begin{subfigure}{0.47\textwidth}
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\includegraphics[width=\textwidth]{airshower/airshower_radio_polarisation_askaryan.png}%
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\caption{
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Askaryan or charge-excess emission
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}
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\label{fig:airshower:polarisation:askaryan}
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\end{subfigure}
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\caption{
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From \protect \cite{Schoorlemmer:2012xpa} \protect\cite{Huege:2017bqv}
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\protect \Todo{Krijn?}
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Radio Emission mechanisms (left: geomagnetic, right: charge-excess)
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Radio Emission mechanisms: \subref{fig:airshower:polarisation:geomagnetic} geomagnetic and \subref{fig:airshower:polarisation:askaryan} charge-excess)
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}
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\label{fig:airshower:polarisation}
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\end{figure}%>>>>>>
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\subsection{Experiments}%<<<
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\label{sec:detectors}
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%>>>>>>
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%\subsection{Experiments}%<<<
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%\label{sec:detectors}
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\bigskip
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At the very highest energy, the flux is in the order of one particle per square kilometer per century (see Figure~\ref{fig:cr_flux}).
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To gather decent statistics at these highest energies on a practical timescale, observatories therefore have to span huge areas.
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Observatories therefore have to span huge areas to gather decent statistics at these highest energies on a practical timescale.
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In recent and upcoming experiments, such as \gls{Auger}, \gls{GRAND} or \gls{LOFAR}, the approach is typically to instrument an area with a sparse grid of detectors to detect the generated air shower.
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With distances up to $1.5\;\mathrm{km}$ (\gls{Auger}), the detectors therefore have to operate in a self-sufficient manner\Todo{word} with only wireless communication channels.
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\\
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The earliest
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Standalone detectors typically receive their timing from a \gls{GNSS}.
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Previously, for timing of water-Cherenkov detectors, this timing accuracy was better than the resolved data\Todo{rephrase}.
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Even for the first analyses of radio data, this was sufficient.
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However, for advanced analyses such as radio interferometry, the timing accuracy must be improved.
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\\
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\hrule
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Standalone devices,
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\gls*{Auger},
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AugerPrime RD,
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\gls*{GRAND},
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\gls*{LOFAR}?,
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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 worked out\Todo{word}.
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First, introductions to radio interferometry and waveform analysis are given in Chapters~\ref{sec:interferometry}~and~\ref{sec:waveform}.
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%>>>>>>
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\section{Radio Interferometry}
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\cleardoublepage
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\chapter{Air Shower Radio Interferometry}
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\label{sec:interferometry}
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The radio signals emitted from the air shower can be recorded by radio antennas.
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The radio signals emitted by the air shower (see Section~\ref{sec:airshowers}) can be recorded by radio antennas.
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An array of radio antennas can be used as an interferometer.
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Therefore, air showers can be analysed using radio interferometry.
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\\
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%
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Unlike, astronomical interferometry, the source of the signal is closeby.
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Unlike, astronomical interferometry, the source of the signal is closeby, therefore
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\begin{figure}
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\label{fig:trace_overlap}
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\end{figure}
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\begin{figure}
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\centering
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\includegraphics[width=0.7\textwidth]{2006.10348/fig03_b.png}%
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% \label{fig:reference-clock}
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%\end{figure}
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\end{document}
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