Thesis: Introduction rewrite (WIP)

documents/thesis/chapters/introduction.tex

@@ -8,118 +8,67 @@
 }
 
 \begin{document}
-\chapter{Cosmic Rays and Extensive Air Showers}
+\chapter{An Introduction to Cosmic Rays and Extensive Air Showers}
 \label{sec:introduction}
-%<<<
-% Intro Cosmic Ray
-In the beginning of the $\mathrm{20^{th}}$~century, various types of radiation were discovered.
-With the balloonflight of Victor Hess in 1912, one type was determined to come from beyond the atmosphere and therefore labelled ``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 (see Figure~\ref{fig:cr_flux}).
-\\
-% Radio
-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.
-%
-For such radio arrays, the analyses require an accurate timing of signals within the array.
-Generally, \glspl{GNSS} are used to synchronise the detectors.
-However, advanced analyses require an even higher accuracy than currently achieved with these systems.
-\\
-This thesis investigates a relatively straightforward method (and its limits) to obtain this required timing accuracy for radio arrays.
-\\
-\Todo{remove - repeated at end of chapter}
-
-% >>>
 %\section{Cosmic Particles}%<<<<<<
 %<<<
 \phantomsection
 \label{sec:crs}
-%Particles from outer space,
-%Particle type,
-%Energy,
-%magnetic fields -- origin,
-%
-%\hrule
+% Energy and flux
+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}.
+The flux of these particles decreases exponentially with increasing energy.
+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.
+\\
 
-% Cosmic Particles = CR + Photon + Neutrino
-The Earth is bombarded with a variety of extra terrestrial particles.
-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.
-\Todo{Energy lowerlimit or electrons}
-\\
-The charged nuclei are the bulk of the measured particles.\Todo{define CR}
-The various magnetic fields that they travel through deflect them due to their charge.
-Because of this, they do not point back to their sources.
-\\
-Photons do not suffer from being charged, and thus have the potential to reveal their sources.
-However, they can be absorbed and created by multiple mechanisms.
-\\
-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}
-\\
-\Todo{
-	$\gamma + \nu$ production by CR,
-	source / targets
-}
-
-
-\begin{figure}%<<< cr_flux
+\begin{figure}%<<< fig:cr_flux
 	\centering
-	\includegraphics[width=\textwidth]{astroparticle/The_CR_spectrum_2023.pdf}
+	\includegraphics[width=0.9\textwidth]{astroparticle/The_CR_spectrum_2023.pdf}
 	\caption{
 		From \protect \cite{The_CR_spectrum}.
 		The diffuse cosmic ray spectrum (upper line) as measured by various experiments.
 		The intensity and fluxes can generally be described by rapidly decreasing power laws.
 		The grey shading indicates the order of magnitude of the particle flux, such that from the ankle onwards ($E>10^9\GeV$) the flux reaches $1$~particle per~square~kilometer per~year.
-		\protect \Todo{Knee - (inter)galactic}
 	}
 	\label{fig:cr_flux}
 \end{figure}%>>>
 
-
-% Energy
-Cosmic rays span a large range of energy and flux as illustrated in Figure~\ref{fig:cr_flux}.
-At lower energies, the flux is high enough for direct detection.
-At energies above $10^{6}\GeV$, however, the flux decrease requires indirect detection to obtain decent statistics.
+% CR: magnetic field
+At \gls{UHE}, the incoming particles are primarily cosmic rays, atomic nuclei typically ranging from protons ($Z=1$) up to iron ($Z=26$).
+Because these are charged, the various magnetic fields they passthrough will deflect and randomise their trajectories.
+Ofcourse, this effect is dependent on the strength and size of the magnetic field and the speed of the particle.
+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.
 \\
-% Acceleration
-The acceleration of high energy cosmic rays is thought to occur in highly energetic regions.
-Being charged, the nuclei can be accelerated in strong magnetic fields with the extent of the magnetic fields limiting the maximum obtainable energy for a cosmic ray.
+% CR: galaxy / extra-galactic
+The same argument (but in reverse) can be used to distinguish galactic and extra-galactic origins. 
+The acceleration of these charged particles equally\Todo{word} requires strong and/or sizable magnetic fields.
+Size constraints on our galaxy lead to a maximum energy for which a cosmic ray can still be contained in the galaxy.
+This mechanism is expected to explain the steeper slope in Figure~\ref{fig:cr_flux} from the ``knee'' ($10^{6}\GeV$) onwards.
 \\
-%\\
-%Likewise, thi
-%
-%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 $10^{17}\eV$\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.
-%\Todo{rewrite paragraph}
-%\\
-%Likewise, with an rapidly increasing flux for lower energies, one component can be assorted\Todo{rephrase} as coming from within the galaxy.
-%\\
-%\Todo{remove/rewrite paragraph}
-
 
+% Photons and Neutrinos
+Other particles at these energies include photons and neutrinos, which are not charged.
+Therefore, these particle types do not suffer from magnetic deflections and have the potential to reveal their source regions.
+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.
+%\Todo{
+%	$\gamma + \nu$ production by CR,
+%	source / targets
+%}
+\\
 
 %>>>
 %\subsection{Air Showers}%<<<
 \phantomsection
 \label{sec:airshowers}
-%Particle cascades,
-%Xmax?,
-%Radio emission,
-%
-%\hrule
-When a particle with an energy above $1\;\TeV$ comes into contact with the atmosphere, secondary particles are generated, forming an air shower.
+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.
 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.
-This happens until the energy is spread out\Todo{word} enough that the number of interactions decreases.
+This happens until the mean energy per particle is sufficiently lowered such that these particles are absorbed by the atmosphere.
 \\
 
 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.
 The atmospheric depth at which this number of particles reaches its maximum is called $\Xmax$.
 \\
-In Figure~\ref{fig:airshower:depth} the \Xmax is different for a photon, a proton and iron.
+In Figure~\ref{fig:airshower:depth} the $\Xmax$ is different for a photon, a proton and iron.
 Typically, heavy nuclei have their first interaction higher up in the atmosphere than protons, with photons penetrating the atmosphere even further.
 Therefore, accurate measurements of $\Xmax$ allow to statistically discriminate between photons, protons and iron nuclei.
 For example, the difference in $\langle\Xmax\rangle$ for iron and protons is roughly $100\;\mathrm{g/cm^2}$~\cite{Deligny:2023yms}.
@@ -131,15 +80,15 @@ Depending on the available interaction channels we distinguish three components
 Each component shows particular development and can be related to different observables of the air shower.
 \\
 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.
-In contrast, for an initial photon which cannot interact hadronicly, its energy will be dumped into the electromagnetic part of the air shower.
+In contrast, for an initial photon, which cannot interact hadronicly, the energy will be 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, thus comprising the muonic component.
-The lifetime, and ease of penetration\Todo{wording} 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.
+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.
 \\
 
 \begin{figure}%<<< airshower:depth
 	\centering
-	\includegraphics[width=0.4\textwidth]{airshower/shower_development_depth_iron_proton_photon.pdf}
+	\includegraphics[width=0.5\textwidth]{airshower/shower_development_depth_iron_proton_photon.pdf}
 	\caption{
 		From H. Schoorlemmer.
 		Shower development as a function of atmospheric depth for an energy of $10^{19}\eV$.
@@ -151,21 +100,22 @@ The lifetime, and ease of penetration\Todo{wording} of relativistic muons allow
 Processes in an air showers also generate radiation that can be picked up as coherent radio signals.
 %% Geo Synchro
 Due to the magnetic field of the Earth, the electrons in the air shower generate radiation.
-Termed geomagnetic emission in Figure~\ref{fig:airshower:polarisation}, this has a polarisation that is dependent on the magnetic field vector $\vec{B}$ and the air shower velocity $\vec{v}$.
+Termed geomagnetic emission in Figure~\ref{fig:airshower:polarisation}, this has a polarisation that is dependent on the magnetic field vector ($\vec{B}$) and the air shower velocity ($\vec{v}$).
 \\
 %% Askaryan / Charge excess
-An additional mechanism emitting radiation was first theorised by Askaryan\Todo{ref}.
+An additional mechanism emitting radiation was theorised by Askaryan\Todo{ref}.
 Due to the large inertia of the positively charged ions with respect to their light, negatively charged electrons, a negative charge excess is created.
 In turn, this generates radiation that is polarised radially towards the shower axis (see Figure~\ref{fig:airshower:polarisation}).
 \\
-%% Cherenkov ring
-The relativistic speeds of the particles cause any radiation that is produced in the air shower to be forward beamed along the shower axis.
-Additionally, the shower travels faster than the speed of light in the atmosphere.
-This generates an
-The detection of the radio signals is limited to an
-This is limited by the so-called Cherenkov angle.
-\Todo{finish paragraph}
 
+%% Cherenkov ring
+Due to the (varying) refractive index of the atmosphere, the produced radiation is concentrated on a ring-like structure called the Cherenkov-ring.
+A peculiar time-inversion of the radiation from the whole air shower signals happens at this ring.
+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.
+\\
+Consequently, all radiation from the whole air shower is concentrated in a small time-window at the Cherenkov-ring.
+It is therefore important for radio detection to obtain measurements in this region.
+\\
 
 \begin{figure}%<<< airshower:polarisation
 	\centering
@@ -193,22 +143,38 @@ This is limited by the so-called Cherenkov angle.
 \end{figure}%>>>>>>
 %>>>>>>
 
-
 %\subsection{Experiments}%<<<
 \phantomsection
 \label{sec:detectors}
-\bigskip
-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}).
+As mentioned, the flux at the very highest energy is in the order of one particle per square kilometer per century (see Figure~\ref{fig:cr_flux}).
 Observatories therefore have to span huge areas to gather decent statistics at these highest energies on a practical timescale.
-In recent and upcoming experiments, such as the~\gls{Auger} (and its upgrade \gls{AugerPrime}), \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.\Todo{cite experiments here}
-With distances up to $1.5\;\mathrm{km}$ (\gls{Auger}), the detectors therefore have to operate in a self-sufficient manner with only wireless communication channels.
+In recent and upcoming experiments, such as the~\gls{Auger}\cite{Deligny:2023yms} and the~\gls{GRAND}\cite{GRAND:2018iaj}, the approach is typically to instrument a large area with a (sparse) grid of detectors to detect the generated air shower.
+With distances up to $1.5\;\mathrm{km}$ (\gls{Auger}), the detectors therefore have to operate in a self-sufficient manner with only wireless communication channels and timing provided by \gls{GNSS}.
 \\
 
-These standalone detectors typically receive their timing from a \gls{GNSS}.
-Previously, for timing of water-Cherenkov detectors, this timing accuracy was better than the resolved data.
+In the last two decades, with the advent of advanced electronics, the detection using radio antennas has received significant attention.
+A difficulty for radio detectors at these large distances.
+\Todo{write paragraph}
+
+For the detectors  (and its upgrade \acrlong{AugerPrime}\cite{Huege:2023pfb}),
+
+Previously, for the timing of surface detectors such as water-Cherenkov detectors, this timing accuracy was better than the resolved data.
 Even for the first analyses of radio data, this was sufficient.\Todo{ref or rm}
 However, for advanced analyses such as radio interferometry, the timing accuracy must be improved.
 \\
+%%<<<
+%% Radio
+%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.
+%%
+%For such radio arrays, the analyses require an accurate timing of signals within the array.
+%Generally, \glspl{GNSS} are used to synchronise the detectors.
+%However, advanced analyses require an even higher accuracy than currently achieved with these systems.
+%\\
+%This thesis investigates a relatively straightforward method (and its limits) to obtain this required timing accuracy for radio arrays.
+%\\
+%\Todo{remove - repeated at end of chapter}
+
+% >>>
 
 % Structure summary
 In this thesis, a solution to enhance the timing accuracy of air shower radio detectors is demonstrated.