diff --git a/documents/thesis/chapters/introduction.tex b/documents/thesis/chapters/introduction.tex index 7e386cd..1cb2391 100644 --- a/documents/thesis/chapters/introduction.tex +++ b/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. -Dubbed ``Cosmic Rays'', one type was determined to come from beyond the atmosphere. +% Cosmic Particles = CR + Photon + Neutrino +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} - -\subsection{Experiments} + \label{fig:airshower:polarisation} +\end{figure}%>>>>>> +\subsection{Experiments}%<<< \label{sec:detectors} - -\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}). +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}). 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}