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%%\title{Advanced LIGO}
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\chapter{Advanced LIGO}
\label{Ch.2}
The ambition of this work is to give a contribution to the improvement of one of the interferometric detectors in use at present time, based in the USA: the Advanced Laser Interferometric Gravitational-wave Observatory (aLIGO).\\
The configuration of aLIGO is shown in Fig. \ref{aligo}: it is a Michelson interferometer provided with Fabry-Perot cavities, power and signal recycling cavities and 4 km-long arms. The light source is a solid-state Nd:YAG laser of wavelength $\lambda$= 1064 nm, injected at a power between 5 - 125 W.\\ The instrument design is extremely intricate in its details: this thesis will provide technical information useful for the understanding of the work made on specific sections of LIGO.

\begin{figure}[h!]
\centering
\includegraphics[scale=0.9]{images/aligo.png}
\caption{Advanced LIGO configuration as proposed in \cite{ligo}.}
\label{aligo}
\end{figure}

\noindent
The fused silica mirrors at the end of each arm, called End Test Masses (ETM), are 34 cm $\times$ 20 cm in size and 40 kg in weight. A photodiode (PD) detects the power at the output. The optic able to split the injected beam into two parts along the arms is called Beam Splitter (BS) and it is placed at 45$^{\circ}$ between the arms. There are two LIGOs in the USA, one in Hanford (WA) and one in Livingston (LA): some of the work that will be presented in the next chapters has been physically done in Hanford, in remote collaboration with Livingston team.

\section{LIGO sensitivity and noise sources}
The performance of LIGO in terms of how far in the Universe it can detect gravitational waves and from which sources depends on the sensitivity: this in turn depends on the quality of the technologies involved and on the limitation given by nature.
Fig. \ref{sens} shows the sensitivity of LIGO during the first observation run with the main noises shown.

\begin{figure}[h!]
\centering
\includegraphics[scale=0.7]{images/ligosens.png}
\caption{Advanced LIGO sensitivity during the first observation run (O1) \cite{abb}. The sensitivity curve tells us that we can observe an event emitting gravitational waves of a given amplitude at a given frequency in an average observation time of 1 s. Since every source emits waves at a certain frequency and amplitude, lowering the curve means opening the viewing on currently hidden sources.}
\label{sens}
\end{figure}

\noindent
Advanced LIGO can be tuned to adjust the frequency band of detection: for each operational mode and detection frequency band there is a gravitational wave source candidate, typically mergers of neutron stars (NS-NS) and black holes (BH-BH).\\
Noise sources make LIGO blind in some frequency windows: technological limitations can be in principle overcome thanks to improvements in science, and this is what this present work is aiming to offer. The most important noise sources for LIGO are shown in the noise budget for LIGO Hanford (LHO) in Fig. \ref{lho}.

\begin{figure}[h!]
\centering
\includegraphics[scale=1]{images/LHO.png}
\caption{Noise budget of LIGO Hanford Obsevatory \cite{mar}.}
\label{lho}
\end{figure}

\noindent
Noises can be of fundamental, technical and environmental origin. Fundamental noises come from first principles, and they determine the ultimate design sensitivity of the instrument. They include thermal and quantum noise, and cannot be reduced without a major instrument upgrade. Quantum noises include shot noise of the sensors, causing power fluctuations, and radiation pressure forces, causing a physical displacement of the test masses. Thermal noise arises from the suspensions and the optical coatings and dominates in the 5-100 Hz frequency range.\\
Technical noises arise from electronics, control loops, charging noise and other effects that can be reduced once identified and carefully studied.\\
Environmental noises include seismic motion, acoustic and magnetic noises. This thesis focuses on the improvement of the seismic isolation system, which noises affect the inertial sensors placed on the suspension benches.

\section{LIGO seismic isolation system}
Every optic needs to be stable with respect to seismic motion, because movements in the mirrors will cause unwanted displacement of the laser beam on the optical surface, resulting in noise during the laser journey into the cavities and then at the output. The main mirrors (test masses and beam splitter) are suspended from a stabilized bench and every suspension chain is placed in vacuum chambers called \textit{Basic Symmetric Chamber} (BSC). The auxiliary optics are placed on optical benches enclosed in the \textit{Horizontal Access Module} (HAM) chambers.

\begin{figure}[h!]
\centering
\includegraphics[scale=1]{images/chambers.png}
\caption{Schematic view of the vacuum chambers enclosing the optics \cite{mat}. There are 5 BSCs and 6 HAMs, for a total of 11 vacuum chambers for each LIGO. Each chamber provides a mixture of passive-active isolation from seismic motion, using pendulums, inertial sensors and hydraulic systems.}
\end{figure}

\noindent
The HAMs provide five levels of isolation, among which there is the Internal Seismic Isolation platform (HAM-ISI), where the auxiliary optics are placed, giving both passive and active isolation. A detailed drawing in Fig. \ref{ham} shows the design of a HAM chamber. The control system of the ISI 

\begin{figure}[h!]
\centering
\includegraphics[scale=1]{images/HAM.png}
\caption{Schematic (a) and CAD model (b) of a HAM chamber \cite{mat}. Suspensions of auxiliary optics provide levels of passive isolation above 10 Hz. The ISI platforms where the suspensions live are optical tables actively isolated via low noise inertial sensors at low frequency ($\sim 0.1 Hz$). The hydraulic attenuators of the \textit{Hydraulic External Pre-Isolator} (HEPI) and the geophones gives isolation from ground motion.}
\label{ham}
\end{figure}

\noindent
The BSCs have a similar design as the HAMs, but they have two stages of ISI to support the suspensions isolating the test masses (Fig. \ref{bsc}).

\begin{figure}
\centering
\includegraphics[scale=1]{images/BSC.png}
\caption{Schematic (a) and CAD model (b) of a BSC chamber \cite{mat}. The active isolation is similar to the one exposed for HAM chambers. The two ISIs provide two stages of isolation while and the suspensions  are design to be quadruple pendulums, for a total of seven levels of isolation.}
\label{bsc}
\end{figure}

\paragraph{Stabilizing the ISI}
Part of the work presented in this thesis focussed on the improvement of the performances of the active isolation system of the ISIs of both BSC and HAM chambers.\\
Active isolation implies a sensing system of the noise to reduce and a control system to compensate the disturbance. Each platform includes relative position sensors, inertial sensors and actuators, working in all degrees of freedom.\\
The control loop of a generic ISI stage on the X degree of freedom is  simplified in the block diagram in Fig. \ref{control}. The platform motion is the sum of the input disturbance and the contribution from the control signal and it is measured by relative position and inertial sensors; then this motion is low- and high-passed via filters suitably built to fit the requirements and tuned to obtain the best performances combining the best results of both filters: this technique is called \textit{blending}, and the frequency where the relative and the inertial sensors contribute at their best is called \textit{blend frequency}. The result of this blend is called \textit{super sensor}. The output of the super sensor feeds the feedback loop, where the actuators close the loop \footnote{A general overview of control loops theory is exposed in Appendix B}.\\
The sensor correction loop takes the ground motion signal from an inertial instrument, filtering it before adding it to the relative sensor signal. This filter is needed because the sum of the motions from the ground inertial and the relative sensors can in principle provide a measurement of the absolute motion of the platform. However, the ground sensors are affected by low frequency noise and need to be suitably filtered. 

\begin{figure}[h!]
\centering
\includegraphics[scale=0.7]{images/control.png}
\caption{Control loop of a generic HAM-ISI platform. Similar block diagrams can be applied for BSC-ISI platforms, including relative position sensors between the two stages of ISIs. \textbf{Green:} there is an inertial sensor measuring the ground motion along the x axis (GNDx), a Capacitive Position Sensor (CPS) measuring relative motions between the platform and the ground. Rotational sensors take care of tilt motion and GS13 are seismometers measuring seismic motion. Tilt and GS13 sensors are both placed on the platform. \textbf{Blue:} the Sensor Correction (SC) filter is typically a Finite Impulse Response (FIR) designed to provide required magnitude and phase match at 100 mHz (where isolation is needed). High- and low-pass filters (LP and HP) manipulate the signals from the low and high frequency sensors and are blended to form the super sensor, which output is sent to the control loop in \textbf{pink}. The overall corrected signal is then sent to the plant (\textbf{yellow}), which represents the processing phase for platform motion actuation.}
\label{control}
\end{figure}

\section{Length Sensing and Control}

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