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Thesis: Introduction: after feedback from Harm

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documents/thesis/chapters/introduction.tex
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@ -13,16 +13,14 @@
%<<<
% Intro Cosmic Ray
In the beginning of the $\mathrm{20^{th}}$~century, various types of radiation were discovered.
With the balloonflight of Victor Hess \Todo{ref} in 1912, one type was determined to come from beyond the atmosphere and therefore labelled ``Cosmic Rays''.
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}).
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.
In the last decade, 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.
@ -30,10 +28,12 @@ However, advanced analyses require an even higher accuracy than currently achiev
\\
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}%<<<<<<
%\section{Cosmic Particles}%<<<<<<
%<<<
\phantomsection
\label{sec:crs}
%Particles from outer space,
%Particle type,
@ -43,28 +43,34 @@ This thesis investigates a relatively straightforward method (and its limits) to
%\hrule
% Cosmic Particles = CR + Photon + Neutrino
There is a variety of extra terrestrial particles with which the Earth is bombarded.
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.
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 identify their sources.
However, they can be absorbed and created by multiple mechanisms.\Todo{rephrase/expand}
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}
\\
Note that cosmic rays are deemed\Todo{rephrase} to be charged nuclei.
\\
\Todo{
$\gamma + \nu$ production by CR,
source / targets
}
\begin{figure}%<<< cr_flux
\centering
\includegraphics[width=0.8\textwidth]{astroparticle/The_CR_spectrum_2023.pdf}
\includegraphics[width=\textwidth]{astroparticle/The_CR_spectrum_2023.pdf}
\caption{
From \protect \cite{The_CR_spectrum}.
Cosmic Ray flux as a function of energy-per-nucleon.
The diffuse cosmic ray spectrum 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 $1/km^2/yr$.
}
\label{fig:cr_flux}
\end{figure}%>>>
@ -72,24 +78,31 @@ Note that cosmic rays are deemed\Todo{rephrase} to be charged nuclei.
% Energy
Cosmic rays span a large range of energy and flux as illustrated in Figure~\ref{fig:cr_flux}.
The acceleration of cosmic rays is thought to occur in highly energetic regions\Todo{expand}
At lower energies, the flux is high enough for direct detection.
At energies above $10^{6}\GeV$, the flux decrease requires indirect detection methods.
\\
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 $10^{17}\eV$\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.
% 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.
\\
%\\
%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}
%>>>
\subsection{Air Showers}%<<<
%\subsection{Air Showers}%<<<
\phantomsection
\label{sec:airshowers}
%Particle cascades,
%Xmax?,
@ -107,27 +120,25 @@ The atmospheric depth at which this number of particles reaches its maximum is c
\\
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, measurements of $\Xmax$ allow to statistically discriminate between photons, protons and iron nuclei.
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}.
\\
The initial particle type also influences the particle content of an air shower.
Protons (and other nuclei) have access to hadronic interaction channels (such as 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}
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.
\\
In contrast, an initial photon cannot interact hadronicly, meaning its energy is dumped into the electromagnetic part 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.
\\
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}
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.
\\
These different components have a different width.\Todo{rephrase}
The hadronic component is greatly collimated, while the electromagnetic component.
\\
\Todo{rewrite paragraph}
\begin{figure}%<<< airshower:depth
\centering
\includegraphics[width=0.3\textwidth]{airshower/shower_development_depth_iron_proton_photon.pdf}
\includegraphics[width=0.4\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 $10^{19}\eV$.
@ -140,7 +151,6 @@ Processes in an air showers also generate radiation that can be picked up as coh
%% 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 $\vec{v}$.
\Todo{expand?}
\\
%% Askaryan / Charge excess
An additional mechanism emitting radiation was first theorised by Askaryan\Todo{ref}.
@ -158,7 +168,7 @@ This is limited by the so-called Cherenkov angle.
\begin{figure}%<<< airshower:polarisation
\centering
\begin{subfigure}{0.47\textwidth}
\begin{subfigure}{0.48\textwidth}
\includegraphics[width=\textwidth]{airshower/airshower_radio_polarisation_geomagnetic.png}%
\caption{
Geomagnetic emission
@ -166,7 +176,7 @@ This is limited by the so-called Cherenkov angle.
\label{fig:airshower:polarisation:geomagnetic}
\end{subfigure}
\hfill
\begin{subfigure}{0.47\textwidth}
\begin{subfigure}{0.48\textwidth}
\includegraphics[width=\textwidth]{airshower/airshower_radio_polarisation_askaryan.png}%
\caption{
Askaryan or charge-excess emission
@ -175,8 +185,7 @@ This is limited by the so-called Cherenkov angle.
\end{subfigure}
\caption{
From \protect \cite{Schoorlemmer:2012xpa, Huege:2017bqv}
\protect \Todo{Krijn?}
The Radio Emission mechanisms and the resulting polarisations of the radio signal: \subref{fig:airshower:polarisation:geomagnetic} geomagnetic and \subref{fig:airshower:polarisation:askaryan} charge-excess)
The Radio Emission mechanisms and the resulting polarisations of the radio signal: \subref{fig:airshower:polarisation:geomagnetic} geomagnetic and \subref{fig:airshower:polarisation:askaryan} charge-excess.
See text for explanation.
}
\label{fig:airshower:polarisation}
@ -185,17 +194,18 @@ This is limited by the so-called Cherenkov angle.
%\subsection{Experiments}%<<<
%\label{sec:detectors}
\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}).
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 \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\Todo{word} with only wireless communication channels.
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.
\\
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.
Even for the first analyses of radio data, this was sufficient.
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.
\\
@ -210,5 +220,5 @@ Chapter~\ref{sec:disciplining} introduces the concept of a beacon transmitter to
\\
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.
\\
Finally, Chapter~\ref{sec:gnss_accuracy} investigates the limitations of the current hardware of \gls{GRAND} and its ability to record and reconstruct a beacon signal.
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}