% CORRETTO BABBO
High-energy physics studies the kinetic features of particles and their interactions by using detectors which reveal, for example, the product of collisions in accelerators, or detect cosmic rays. Different kinds of detectors are used to reveal different properties of the particles themselves: kinetic energy, momentum, charge, mass and even their internal structure.\\

Gas ionization detectors can reveal high-rate electromagnetic-interacting particles. If the incident photon or charged massive particle has enough energy to ionize one atom of gas inside the detector, the flux of ion-electron pairs will be amplified; this will generate a current pulse for each event. Each signal can be revealed by a copper anode and can then be sent to electronic \textit{data acquisition} (DAQ) systems.\\

Gaseous detectors can produce an avalanche multiplication of the signal by accelerating (through an electric field) the first electrons produced by the incident particle, so that they release more pairs. Gas electron multipliers (\textit{GEMs}) work according to such principle. \textit{GEM foils} consist of two thin copper layers, with a kapton foil between them. Small holes are made in a regular pattern through these foils, via chemical processes such as photolitography and acid etching (\figurename~\vref{gem-holes}).\\

A potential is then applied between the two copper layers (\textit{anode} and \textit{cathode}) in order to put the GEM foil into operation; this will create a high electric field through the holes:
$$ E = \dfrac{V}{d} $$
where $E$ is the electric field, $V$ is the voltage and $d$ is the distance between the anode and the cathode. Since the kapton foil is very thin (around $25 \mu m$), but it can resist high electric fields\footnote{Kapton is a plastic polyimide created by DuPont, whose molecular structure remains stable in a wide range of temperatures. It was dicovered to be very radiation-hard, and is commonly used for its good insulating power \cite{kapton}.}, the potential between GEM electrodes can be as high as $500 \div 600 V$. \\

A GEM-based detector consists of one or more GEM foils laid, as shown in \figurename~\vref{gem-1}, between a copper foil (\textit{cathode}) and a readout plane (\textit{anode}).\\
\begin{figure}%[!htbp]
	\centering%
	\subfigure[t][Draft of a single-GEM detector]%
	{\includegraphics[width=9.1cm]{Images/GEMtextfields2}\label{gem-1}}%
	\hspace{2mm}%
	\subfigure[t][Hole pattern]%
	{\includegraphics[width=4.1cm]{Images/holes_pattern}\label{gem-holes}}%
	\caption{Schematic outline of a single-GEM detector and, on the right, view of the hole pattern in a GEM foil}%
	\label{gem-A}%
\end{figure}

A \textit{drift field} is applied to drive electrons from the cathode drift foil to the GEM. An \textit{amplification voltage} between the copper layers of every GEM foil accelerates the electrons, producing avalanche multiplication. Finally, an \textit{induction field} leads them from the GEM bottom layer to the readout plane. In the case of a multiple GEM detector, \textit{transfer} fields drive electrons from a GEM foil to the next.\\
% ADD TRANSFER FIELD BETWEEN FOILS

More GEM foils can be inserted as a cascade in a single detector. This allows to reduce the discharge probability, as we can set quite a low multiplication potential between the electrodes of each foil. The discharge probability is indeed a function of charge density inside the GEM holes. In this configuration, the typical gains of each GEM are around $G \simeq 15 \div 30$; for a triple-GEM detector this leads to a total gain of the order of magnitude of several thousands (for example, for TOTEM \textbf{T2} telescope chambers $G \simeq 8,000$).\\

\begin{figure}
	\centering
	\includegraphics[width=12cm]{Images/triplegem}
	\caption{Draft cross-section of a triple GEM detector \cite{3gem-fast}}
	\label{3ple-gem}
\end{figure}
\figurename~\vref{3ple-gem} shows the usual cross section of a triple GEM chamber. $E_d$, $E_t$ and $E_i$ stand for the drift, transfer and induction fields, respectively. Gap depths $g_d$, $g_t$ and $g_i$ are customizable. In particular, stretching the drift gap allows to increase the number of primary ionizations, but on the other hand it decreases the time performance. Specific application requirements determine the most fitting chamber geometry.\\

The detector being analyzed in this thesis is a triple GEM chamber, whose gaps were set as in \tablename~\vref{lg-gaps}; \tablename~\vref{ext-gain} shows instead the gain values we reached during the tests conducted on this chamber. \tablename~\vref{lg-gaps} also shows the range of electric fields we applied to each gap during the test-beam.
\begin{table}
\begin{tabular}{|c|c|c|c|}
\hline \rule[-2ex]{0pt}{5.5ex} \textbf{Drift gap} & \textbf{Transfer gap 1} & \textbf{Transfer gap 2} & \textbf{Induction gap} \\ 
\hline \rule[-2ex]{0pt}{5.5ex} $g_d = 3mm$ & $g_{t_1} = 2mm$ & $g_{t_2} = 2mm$ & $g_i = 2mm$ \\ 
\hline \rule[-2ex]{0pt}{5.5ex} $E^{MIN}_d = 2.7 \frac{kV}{cm}$ & $E_{t_1}^{MIN} = 4.0 \frac{kV}{cm} $ & $E_{t_2}^{MIN} = 4.0 \frac{kV}{cm} $ & $E_{i}^{MIN} = 4.0 \frac{kV}{cm} $\\
\hline \rule[-2ex]{0pt}{5.5ex} $E_{d}^{MAX} = 3.0 \frac{kV}{cm}$ & $E_{t_1}^{MAX} = 4.4 \frac{kV}{cm} $ & $E_{t_2}^{MAX} = 4.4 \frac{kV}{cm} $ & $E_{i}^{MAX} = 4.4 \frac{kV}{cm} $ \\
\hline 
\end{tabular} 
\caption{Large GEM gap depths and electric fields}
\label{lg-gaps}
\end{table}
%\hline \rule[-2ex]{0pt}{5.5ex} $E_d = 2.67 \div 3 \frac{kV}{cm}$ & $E_{t_1} = 4.0 \sim 4.4 \frac{kV}{cm} $ & $E_{t_2} = 4.0 \sim 4.4 \frac{kV}{cm} $ & $E_{i} = 4.0 \sim 4.4 \frac{kV}{cm} $\\