Thesis: Introduction: WuotD

documents/thesis/chapters/introduction.tex

@@ -11,8 +11,27 @@
 \chapter{Introduction}
 \label{sec:introduction}
 
+% Intro Cosmic Ray
+In the beginning of the 20th century, various types of radiation were discovered.
+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''.
+With many discoveries following, the field of (astro-)particle physics evolved.
+\\
+% Current state, (nudge to radio)
+Large collaborations are now detecting cosmic rays with a variety of methods over a large range of energy\Todo{ref figure}.
+Still, questions on their origin remain.\Todo{list questions or remove}
+\\
+% Radio
+In the last decade, the detection using radio antennas has received significant attention \Todo{ref}, such that collaborations such as \gls{GRAND} are building observatoria that fully rely on radio measurements.
+%
+For such radio arrays, the analyses require an accurate timing of signals within the array.
+Generally, \gls{GNSS} is used to synchronise the detectors.
+However, advanced analyses require an even higher accuracy.
+\\
 
-\section{Cosmic Particles}
+In this thesis, methods (and their limits) to obtain this accuracy for radio arrays are investigated.
+
+
+\section{Cosmic Particles}%<<<<<<
 \label{sec:crs}
 Particles from outer space,
 Particle type,
@@ -21,17 +40,80 @@ magnetic fields -- origin,
 
 \hrule
 
-In the beginning of the 20th century, various types of radiation were discovered.
+% Cosmic Particles = CR + Photon + Neutrino
-Dubbed ``Cosmic Rays'', one type was determined to come from beyond the atmosphere.
+There is a variety of extra terrestrial particles with which the Earth is bombarded.\Todo{rephrase}
+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.
+\\
+The charged nuclei are the bulk of the measured particles.
+They do not point back to their sources because they are deflected by magnetic fields due to being charged.
+\\
+Photons do not suffer from being charged, and thus have the potential to identify their sources.
+However, they can be absorbed and created by multiple mechanisms.\Todo{rephrase}
+\\
+Finally, neutrino's interact weakly, thus pointing back to their sources as well.
+Unfortunately, this weak interaction also troubles the detection of the neutrino's.\Todo{rephrase}
+\\
+Note that cosmic rays are deemed\Todo{rephrase} to be charged nuclei.
+\\
+
+\begin{figure}%<<< cr_flux
+	\centering
+	\includegraphics[width=0.8\textwidth]{astroparticle/The_CR_spectrum_2023.pdf}
+	\caption{
+		From \protect \cite{The_CR_spectrum}.
+		Cosmic Ray flux as a function of energy-per-nucleon.
+	}
+	\label{fig:cr_flux}
+\end{figure}%>>>
 
 
-\subsection{Air Showers}
+% Energy
+Cosmic rays span a large range of energy as illustrated in Figure~\ref{fig:cr_flux}.
+The acceleration of cosmic rays is thought to occur in highly energetic regions
+\\
+
+Using the charged nuclei, an argument can be made to distinguish two types of sources.
+\\
+Being charged, the nuclei will gyrate in magnetic fields.
+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}.
+Still, particles with higher energies have been observed (see Figure~\ref{fig:}).
+These higher energy particles must thus come from beyond our galaxy.
+\\
+Likewise, with an rapidly increasing flux for lower energies, one component can be assorted\Todo{rephrase} as coming from within the galaxy.
+\\
+
+
+
+%>>>
+\subsection{Air Showers}%<<<
 \label{sec:airshowers}
 Particle cascades,
 Xmax?,
 Radio emission,
 
-\begin{figure}
+\hrule
+When a particle with a high enough energy comes into contact with the atmosphere, secondary particles are generated, forming an air shower.
+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.
+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.
+\\
+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 $\Xmax$.
+Part of this is explained by the depth of first interaction.
+Due to the higher charge of heavy nuclei, they interact earlier in the atmosphere.
+\\
+
+The particle content of an air shower is dependent on the initial particle type.
+Protons (and other nuclei) have access to hadronic interaction channels (pions, kaons, etc.)\Todo{ref?} through which most energy is passed.
+In turn, the resulting air showers contain a large hadronic component.\Todo{check wording}
+\\
+In contrast, an initial photon cannot interact hadronicly, meaning its energy is 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.
+This muonic component is a reliable part to measure.\Todo{rephrase}
+\\
+
+
+\begin{figure}%<<< airshower:depth
 	\centering
 	\includegraphics[width=0.3\textwidth]{airshower/shower_development_depth_iron_proton_photon.pdf}
 	\caption{
@@ -39,9 +121,10 @@ Radio emission,
 		Shower development as a function of atmospheric depth for an energy of $10^{19}\eV$.
 	}
 	\label{fig:airshower:depth}
-\end{figure}
+\end{figure}%>>>
 
-\begin{figure}
+
+\begin{figure}%<<< airshower:polarisation
 	\centering
 	\begin{subfigure}{0.47\textwidth}
 		\includegraphics[width=\textwidth]{airshower/airshower_radio_polarisation_geomagnetic.png}%
@@ -55,27 +138,16 @@ Radio emission,
 		\protect \Todo{Krijn?}
 		Radio Emission mechanisms (left: geomagnetic, right: charge-excess)
 	}
-\end{figure}
+	\label{fig:airshower:polarisation}
-
+\end{figure}%>>>>>>
-\subsection{Experiments}
+\subsection{Experiments}%<<<
 \label{sec:detectors}
-
+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}).
-\begin{figure}
-	\centering
-	\includegraphics[width=0.8\textwidth]{astroparticle/The_CR_spectrum_2023.pdf}
-	\caption{
-		From \protect \cite{The_CR_spectrum}.
-		Cosmic Ray flux as a function of energy-per-nucleon.
-	}
-	\label{fig:cr_flux}
-\end{figure}
-
-
-Cosmic particles have been observed over a large range of energies.
-However, for increasing energies, their flux decreases dramatically (see Figure~\ref{fig:cr_flux}).
 To gather decent statistics at these highest energies on a practical timescale, observatories therefore have to span huge areas.
 \\
 
+The earliest 
+
 \hrule
 Standalone devices,
 \gls*{Auger},
@@ -83,11 +155,12 @@ AugerPrime RD,
 \gls*{GRAND},
 \gls*{LOFAR}?,
 
-
+%>>>>>>
 \section{Radio Interferometry}
 \label{sec:interferometry}
-Rough outline of Interferometry?
+The radio signals emitted from the air shower can be recorded by radio antennas.
-\\
+
+Unlike, astronomical interferometry, the source of the signal is closeby, therefore
 
 
 \begin{figure}