189 lines
11 KiB
TeX
189 lines
11 KiB
TeX
% vim: fdm=marker fmr=<<<,>>>
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\documentclass[../thesis.tex]{subfiles}
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\graphicspath{
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{.}
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{../../figures/}
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{../../../figures/}
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}
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\begin{document}
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\chapter{An Introduction to Cosmic Rays and Extensive Air Showers}
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\label{sec:introduction}
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%\section{Cosmic Particles}%<<<<<<
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%<<<
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% Energy and flux
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The Earth is bombarded with a variety of energetic, extra-terrestrial particles.
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The energies of these particles extend over many orders of magnitude (see Figure~\ref{fig:cr_flux}).
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The flux of these particles decreases exponentially with increasing energy.
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For very high energies, above $10^{6}\GeV$, the flux approaches one particle per~square~meter per~year, further decreasing to a single particle per~square~kilometer per~year for Ultra High Energies (UHE) at $10^{10}\GeV$.
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\\
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\begin{figure}%<<< fig:cr_flux
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\centering
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\includegraphics[width=0.9\textwidth]{astroparticle/The_CR_spectrum_2023.pdf}
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\caption{
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From \protect \cite{The_CR_spectrum}.
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The diffuse cosmic ray spectrum (upper line) as measured by various experiments.
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The intensity and fluxes can generally be described by rapidly decreasing power laws.
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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.
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}
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\label{fig:cr_flux}
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\end{figure}%>>>
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% CR: magnetic field
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At these high energies, the incoming particles are primarily cosmic rays\footnote{These are therefore known as \glspl{UHECR}.}, atomic nuclei typically ranging from protons ($Z=1$) up to iron ($Z=26$).
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Because these are charged, the various magnetic fields they pass through will deflect and randomise their trajectories.
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Of course, this effect is dependent on the strength and size of the magnetic field and the speed of the particle.
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It is therefore only at the very highest energies that the direction of an initial particle might be used to (conservatively) infer the direction of its origin.
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\\
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% CR: galaxy / extra-galactic
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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}.
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The acceleration of cosmic rays equally requires strong and sizeable magnetic fields.
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Size constraints on the Milky~Way lead to a maximum energy for which a cosmic ray can still be contained in our galaxy.
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It is thus at these energies that we can distinguish between galactic and extra-galactic origins.
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\\
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% Photons and Neutrinos
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Other particles at these energies include photons and neutrinos, which are not charged.
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Therefore, these particle types do not suffer from magnetic deflections and have the potential to reveal their source regions.
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Unfortunately, aside from both being much less frequent, photons can be absorbed and created by multiple mechanisms, while neutrinos are notoriously hard to detect due to their weak interaction.
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%\Todo{
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% $\gamma + \nu$ production by CR,
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% source / targets
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%}
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\\
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%>>>
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%\subsection{Air Showers}%<<<
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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}.
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This air shower consists of a cascade of interactions producing more particles that subsequently undergo further interactions.
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Thus, the number of particles rapidly increases further down the air shower.
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This happens until the mean energy per particle is sufficiently lowered from whereon these particles are absorbed in the atmosphere.
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\\
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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.
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The atmospheric depth at which this number of particles reaches its maximum is called $\Xmax$.
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\pagebreak
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In Figure~\ref{fig:airshower:depth}, $\Xmax$ is different for the air showers generated by a photon, a proton or an iron nucleus.
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Typically, heavy nuclei have their first interaction higher up in the atmosphere than protons, with photons penetrating the atmosphere even further.
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Therefore, accurate measurements of $\Xmax$ allow to statistically discriminate between photons, protons and iron nuclei.
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\\
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\begin{figure}%<<< airshower:depth
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\centering
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\vspace*{-10mm}
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\includegraphics[width=0.5\textwidth]{airshower/shower_development_depth_iron_proton_photon.pdf}
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\caption{
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From H. Schoorlemmer.
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Shower development as a function of atmospheric depth for an energy of $10^{19}\eV$.
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Typically, iron- and proton-induced air showers have a difference in $\langle \Xmax \rangle$ of $100\;\mathrm{g/cm^2}$~\cite{Deligny:2023yms}.
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For air showers from photons this is even further down the atmosphere.
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They are, however, much more rare than cosmic rays.
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}
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\label{fig:airshower:depth}
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\vspace*{-5mm}
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\end{figure}%>>>
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The initial particle type also influences the particle content of an air shower.
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Depending on the available interaction channels, we distinguish three components in air showers: the hadronic, electromagnetic and muonic components.
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Each component shows particular development and can be related to different observables of the air shower.
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\\
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For example, detecting a large hadronic component means the initial particle has access to hadronic interactions (creating hadrons such as pions, kaons, etc.) which is a typical sign of a cosmic ray.
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In contrast, for an initial photon, which cannot interact hadronicly, the energy will be dumped into the electromagnetic part of the air shower, mainly producing electrons, positrons and photons.
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\\
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Finally, any charged pions created in the air shower will decay into muons while still in the atmosphere, thus comprising the muonic component.
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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.
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These are therefore prime candidates for air shower detectors on the Earth's surface.
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\\
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% Radio measurements
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Processes in an air showers also generate radiation that can be picked up as coherent radio signals.
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%% Geo Synchro
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Due to the magnetic field of the Earth, the electrons in the air shower generate radiation.
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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 ($\vec{v}$).
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\\
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%% Askaryan / Charge excess
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An additional mechanism emitting radiation was theorised by Askaryan\cite{Askaryan:1961pfb}.
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Due to the large inertia of the positively charged ions with respect to their light, negatively charged electrons, a negative charge excess is created.
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In turn, this generates radiation that is polarised radially towards the shower axis (see Figure~\ref{fig:airshower:polarisation}).
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\\
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%% Cherenkov ring
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Due to charged particles moving relativistically through the refractive atmosphere, the produced radiation is concentrated on a cone-like structure.
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On the surface, this creates a ring called the Cherenkov-ring.
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On this ring, a peculiar inversion happens in the time-domain of the air shower signals.
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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.
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Consequently, the radiation received at the Cherenkov-ring is maximally coherent, being concentrated in a small time-window.
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It is therefore crucial for radio detection to obtain measurements in this region.
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\\
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\begin{figure}%<<< airshower:polarisation
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\centering
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\begin{subfigure}{0.48\textwidth}
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\includegraphics[width=\textwidth]{airshower/airshower_radio_polarisation_geomagnetic.png}%
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\caption{
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Geomagnetic emission
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}
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\label{fig:airshower:polarisation:geomagnetic}
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\end{subfigure}
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\hfill
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\begin{subfigure}{0.48\textwidth}
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\includegraphics[width=\textwidth]{airshower/airshower_radio_polarisation_askaryan.png}%
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\caption{
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Askaryan or charge-excess emission
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}
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\label{fig:airshower:polarisation:askaryan}
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\end{subfigure}
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\caption{
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From \protect \cite{Schoorlemmer:2012xpa, Huege:2017bqv}
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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.
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See text for explanation.
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}
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\label{fig:airshower:polarisation}
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\vspace{-2mm}
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\end{figure}%>>>>>>
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%>>>>>>
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%\subsection{Experiments}%<<<
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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}).
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Observatories therefore have to span huge areas to gather decent statistics at these highest energies on a practical timescale.
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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.
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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}.
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\\
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In the last two decades, with the advent of advanced electronics, the detection using radio antennas has received significant attention.
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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).
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Unfortunately, this timing accuracy is not continuously achieved by \glspl{GNSS}, if at all.
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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}.
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\\
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\pagebreak[1]
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% Structure summary
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This thesis investigates a relatively straightforward method (and its limits) to improve the timing accuracy of air shower radio detectors
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by using an additional radio signal called a beacon.
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It is organised as follows.
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\\
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First, an introduction to radio interferometry is given in Chapter~\ref{sec:interferometry}.
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This will be used later on and gives an insight into the timing accuracy requirements.
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\\
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Chapter~\ref{sec:waveform} reviews some typical techniques to analyse waveforms and to obtain timing information from them.
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\\
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In Chapter~\ref{sec:disciplining}, the concept of a beacon transmitter is introduced to synchronise an array of radio antennas.
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It demonstrates the achievable timing accuracy for a sine and pulse beacon using the techniques described in the preceding chapter.
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\\
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A degeneracy in the synchronisation is encountered when the timing accuracy of the \gls{GNSS} is in the order of the periodicity of a continuous beacon.
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Chapter~\ref{sec:single_sine_sync} establishes a method using a single sine wave beacon while using the radio interferometric approach to observe an air shower and correct for this effect.
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\\
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Finally, Chapter~\ref{sec:gnss_accuracy} investigates some possible limitations of the current hardware of \gls{GRAND} and its ability to record and reconstruct a beacon signal.
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\end{document}
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