Merge branch 'finalise-introduction'

documents/thesis/chapters/introduction.tex

@@ -13,9 +13,9 @@
 %\section{Cosmic Particles}%<<<<<<
 %<<<
 % 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 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}.
 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.
+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.
 \\
 
 \begin{figure}%<<< fig:cr_flux
@@ -31,16 +31,16 @@ For \gls{UHE}, above $10^{6}\GeV$\Todo{limit}, it approaches one particle per~sq
 \end{figure}%>>>
 
 % CR: magnetic field
-At \gls{UHE}, the incoming particles are primarily cosmic rays, atomic nuclei typically ranging from protons ($Z=1$) up to iron ($Z=26$).
+At these high energies, 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.
 \\
 % CR: galaxy / extra-galactic
-The same argument (but in reverse) can be used to distinguish galactic and extra-galactic origins. 
+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}.
-The acceleration of these charged particles equally\Todo{word} requires strong and/or sizable magnetic fields.
+The acceleration of cosmic rays equally requires strong and 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.
+Size constraints on the Milky~Way lead to a maximum energy for which a cosmic ray can still be contained in our galaxy.
-This mechanism is expected to explain the steeper slope in Figure~\ref{fig:cr_flux} from the ``knee'' ($10^{6}\GeV$) onwards.
+It is thus at these energies that we can distinguish between galactic and extra-galactic origins.
 \\
 
 % Photons and Neutrinos
@@ -55,7 +55,8 @@ Unfortunately, aside from both being much less frequent, photons can be absorbed
 
 %>>>
 %\subsection{Air Showers}%<<<
-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.
+\pagebreak[2]
+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?}.
 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 mean energy per particle is sufficiently lowered such that these particles are absorbed by the atmosphere.
@@ -75,7 +76,7 @@ The initial particle type also influences the particle content of an air shower.
 Depending on the available interaction channels we distinguish three components in air showers: the hadronic, electromagnetic and muonic 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.
+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.
 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.
@@ -92,6 +93,7 @@ The lifetime, and ease of penetration of relativistic muons allow them to propag
 	\label{fig:airshower:depth}
 \end{figure}%>>>
 
+\pagebreak[2]
 % Radio measurements
 Processes in an air showers also generate radiation that can be picked up as coherent radio signals.
 %% Geo Synchro
@@ -105,12 +107,12 @@ In turn, this generates radiation that is polarised radially towards the shower
 \\
 
 %% 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.
+Due to charged particles moving relativistically through the refractive atmosphere, the produced radiation is concentrated on a cone-like structure.
-A peculiar time-inversion of the radiation from the whole air shower signals happens at this ring.
+On the surface, this creates a ring called the Cherenkov-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.
+On this ring, a peculiar inversion happens in the time-domain of the air shower signals.
-\\
+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.
-Consequently, all radiation from the whole air shower is concentrated in a small time-window at the Cherenkov-ring.
+Consequently, the radiation received at the Cherenkov-ring is maximally coherent, being concentrated in a small time-window.
-It is therefore important for radio detection to obtain measurements in this region.
+It is therefore crucial for radio detection to obtain measurements in this region.
 \\
 
 \begin{figure}%<<< airshower:polarisation
@@ -147,39 +149,28 @@ With distances up to $1.5\;\mathrm{km}$ (\gls{Auger}), the detectors therefore h
 \\
 
 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.
+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).
-\Todo{write paragraph}
+Unfortunately, this timing accuracy is not continuously achieved by \glspl{GNSS}, if at all.
-
+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}.
-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}
 
-% >>>
+\pagebreak[2]
 
 % Structure summary
-In this thesis, a solution to enhance the timing accuracy of air shower radio detectors is demonstrated.
+This thesis investigates a relatively straightforward method (and its limits) to improve the timing accuracy of air shower radio detectors
+by using an additional radio signal called a beacon.
+It is organised as follows.
+\\
 First, an introduction to radio interferometry is given in Chapter~\ref{sec:interferometry}.
 This will be used later on and gives an insight into the timing accuracy requirements.
 \\
-Chapter~\ref{sec:waveform} reviews typical techniques to analyse waveforms to obtain timing information.
+Chapter~\ref{sec:waveform} reviews some typical techniques to analyse waveforms and to obtain timing information from them.
 \\
-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.
+In Chapter~\ref{sec:disciplining} the concept of a beacon transmitter is introduced to synchronise an array of radio antennas.
+It demonstrates the achievable timing accuracy for a sine and pulse beacon using the techniques described in the preceding chapter.
 \\
-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.
+When the timing accuracy of the \gls{GNSS} is in the order of a continuous beacon's periodicity, the synchronisation is impaired.
+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.
 \\
 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.
 \end{document}